DAO (Demostración asistida por ordenador) - Contribuciones del usuario [es]

Documentación

2022-02-08T17:18:22Z

Jalonso:

En esta página se recogen en enlaces que sirven de documentación al curso de demostración asistida por ordenador (DAO). Los enlaces están actualizados en el [https://www.glc.us.es/~jalonso/RA2019/index.php/Documentaci%C3%B3n curso 2019-20].

== Visiones generales de la DAO ==

# J.A. Alonso. [http://goo.gl/NWk7b Razonamiento formalizado: Del sueño a la realidad de las pruebas]. ''Vestigium'', 26 de diciembre de 2012.
# J. Avigad. [http://www.andrew.cmu.edu/user/avigad/Talks/icerm.pdf Interactive theorem proving, automated reasoning, and mathematical computation]. ICERM, 14 de diciembre de 2012.
# M. Davis. [http://www.cs.nyu.edu/cs/faculty/davism/early.ps The early history of automated deduction].
# J.P. Delahaye [http://interstices.info/jcms/int_63417/du-reve-a-la-realite-des-preuves Du rêve à la réalité des preuves]. ''Interstices'', 8 de julio de 2012.
# J. Germoni [http://images.math.cnrs.fr/Coq-et-caracteres.html Coq et caractères: Preuve formelle du théorème de Feit et Thompson]. ''Images des Mathématiques'', CNRS, 23 de noviembre de 2012.
# H. Geuvers [http://www.ias.ac.in/sadhana/Pdf2009Feb/3.pdf Proof assistants: History, ideas and future]. ''Sadhana'', Vol. 34-1, pp. 3-25, février 2009.
# G. Gonthier [http://www.ams.org/notices/200811/tx081101382p.pdf The four-color theorem]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1382-1393, 2008.
# T. Hales. [http://www.ams.org/notices/200811/tx081101370p.pdf Formal proof]. ''Notices of AMS'', Vol. 55, N. 11 (2008) pp. 1370-1380.
# J. Harrison. [http://www.cl.cam.ac.uk/~jrh13/papers/ab.html A short survey of automated reasoning]. ''Lecture Notes in Computer Science'', Vol. 4545, pp. 334-349, 2007.
# J. Harrison. [http://www.ams.org/notices/200811/tx081101395p.pdf Formal proof: Theory and practice]. ''Notices of the AMS'', Vol. 55, N. 11 (2008) p.1395-1406.
# G. Kolata. [http://www.nytimes.com/library/cyber/week/1210math.html Computer math proof shows reasoning power]. ''The New York Times'', 10 de diciembre de 1996.
# D. MacKenzie [https://backspaces.net/temp/Spring2010Seminar/18%20unconventional%20essays%20on%20the%20nature%20of%20mathematics.pdf#page=147 Computers and the sociology of mathematical proof].
# G. Sutcliffe. [http://tptp.org/OverviewOfATP.html What is automated theorem proving?].
# F. Wiedijk [http://www.cs.ru.nl/~freek/100/ Formalizing the «top 100» of mathematical theorems].
# F. Wiedijk [http://www.ams.org/notices/200811/tx081101408p.pdf Formal proof - Getting started]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1408-1414, 2008.
# F. Wiedijk, [https://www.cs.ru.nl/F.Wiedijk/pubs/qed2.pdf The QED manifesto revisited]. ''Studies in Logic, Grammar and Rhetoric'', Vol. 10(23), pp. 121-133, 2007.

== Referencias sobre Isabelle/HOL ==
# B. Grechuk [https://web.cs.wpi.edu/~dd/resources_isabelle/isabelle_primer_mathematicians.pdf Isabelle primer for mathematicians].
# T. Nipkow [https://isabelle.in.tum.de/doc/prog-prove.pdf Programming and proving in Isabelle/HOL].
# T. Nipkow, M. Wenzel y L.C. Paulson [https://isabelle.in.tum.de/website-Isabelle2009/dist/Isabelle/doc/tutorial.pdf A proof assistant for higher-order logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL/document.pdf Isabelle/HOL — Higher-Order Logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/documentation.html Tutorials and manuals for Isabelle].

== Lecturas complementarias ==
=== Programación funcional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/i1m-12/temas/2012-13-IM-temas-PF.pdf Temas de "Programación funcional"]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# J.A. Alonso y M.J. Hidalgo [http://www.cs.us.es/~jalonso/publicaciones/Piensa_en_Haskell.pdf Piensa en Haskell (Ejercicios de programación funcional con Haskell)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# G. Hutton [http://goo.gl/pKqG Programming in Haskell]. Cambridge University Press, 2007.
# M. Lipovača [http://aprendehaskell.es ¡Aprende Haskell por el bien de todos!].

=== Lógica computacional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/li-12/temas/temas-LI-2012-13.pdf Temas de "Lógica informática" (2012-13)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# R. Bornat [http://bit.ly/oithic Proof and disproof in formal logic: an introduction for programmers]. Oxford University Press, 2005.
# K. Broda, S. Eisenbach, H. Khoshnevisan y S. Vickers [https://www.doc.ic.ac.uk/~susan/firstyearbook.pdf Reasoned programming]. Imperial College, 1994.
# K. Doets y J. van Eijck [https://books.google.es/books?id=YCC6lwEACAAJ&dq=The+Haskell+Road+to+Logic,+Maths+and+Programming&hl=es&sa=X&redir_esc=y The Haskell Road to Logic, Maths and Programming].
# M. Huth y M. Ryan [http://goo.gl/TMqOo Logic in computer science: Modelling and reasoning about systems]. Cambridge University Press, 2004. (Incluye el [http://www.cs.bham.ac.uk/research/lics/tutor/index.html tutor en la Red]).

== Cursos relacionados ==
=== Cursos con Isabelle/HOL ===
# Clemens Ballarin. [http://cl-informatik.uibk.ac.at/teaching/ss08/atp/introduction.php Automatic Deduction]. (Univ de Innsbruck, 2008).
# Clemens Ballarin y Gerwin Klein [http://isabelle.in.tum.de/coursematerial/IJCAR04 Introduction to the Isabelle Proof Assistant]. (en el IJCAR-2004).
# Clemens Ballarin y Tjark Weber. [http://cl-informatik.uibk.ac.at/teaching/ws06/atp/introduction.php Automated Theorem Proving in Isabelle/HOL]. (Univ. de Innsbruck, 2006-07).
# A.D. Brucker, D. Basin, J.G. Smaus y B. Wolff. [http://archiv.infsec.ethz.ch/education/permanent/csmr.html Computer-supported Modeling and Reasoning]. (ETH Zurich, 2011).
# Mads Dam. [http://www.csc.kth.se/utbildning/kth/kurser/DD2453/aform07/ Advanced formal methods]. (KTH Royal Institute of Technology, 2007).
# Jacques Fleuriot y Paul Jackson. [http://www.inf.ed.ac.uk/teaching/courses/ar/slides/ Automated reasoning]. (Univ. de Edimburgo, 2012-13).
# Thomas Genet [http://www.irisa.fr/celtique/genet/ACF Software formal analysis and design]. (Univ. de Rennes)
# Gerwin Klein. [http://www.cse.unsw.edu.au/~kleing/teaching/thprv-04 Theorem Proving - Principles, Techniques, Applications]. (NICTA, 2004).
# Gerwin Klein. [http://www.cse.unsw.edu.au/~cs4161/index.html Advanced Topics in Software Verification]. (NICTA, 2012).
# Joao Marcos. [http://www.dimap.ufrn.br/~jmarcos/courses/LC/Ementa.htm Lógica computacional: Demonstração assistida e semi-automática de teoremas].(UFRN, 2000).
# Tobias Nipkow. [https://www21.in.tum.de/teaching/semantics/WS1920/ Semantics of programming languages]. (Univ. de Munich, 2012-13).
# Tobias Nipkow [http://isabelle.in.tum.de/coursematerial/PSV2009-1 Theorem Proving with Isabelle/HOL An Intensive Course].
# Larry Paulson. [http://www.cl.cam.ac.uk/teaching/0910/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2009-10).
# Jan-Georg Smaus. [http://www.informatik.uni-freiburg.de/~ki/teaching/ws0910/csmr/lecture.html Computer-supported modeling and reasoning]. (Univ. de Feiburgo, 2009).
# Christian Sternagel [http://cl-informatik.uibk.ac.at/teaching/ss11/eve/content.php Experiments in Verification – Introduction to Isabelle/HOL]. (Univ. de Innsbruck, 2011-12).
# Tjark Weber. [http://www.cl.cam.ac.uk/teaching/1011/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2010-11).

=== Otros cursos ===
# José A. Alonso [http://www.cs.us.es/~jalonso/cursos/li-12/ Lógica informática] (Univ. de Sevilla, 2012-13).
# Yves Bertot, Pierre Casteran, Benjamin Gregoire, Pierre Letouzey y Assia Mahboubi [http://www.di.ens.fr/~zappa/teaching/coq/ecole11 Modelling and verifying algorithms in Coq: an introduction]. (INRIA Paris-Rocquencourt, 14-18 noviembre 2011).
# Pierre Castéran [http://www.labri.fr/perso/casteran/FM/Logique/index.html Logic (Master In Verification)] (Univ. de Burdeos, 2011-12).
# Ian Hodkinson [http://www.doc.ic.ac.uk/~imh/teaching/140_logic/logic.html Logic] (Imperial College, Londres, 2010-11).
# Peter Lucas [http://www.cs.ru.nl/~peterl/teaching/KeR/ Knowledge Representation and Reasoning] (Radboud University # egen, 2011-12).
# Larry Paulson [http://www.cl.cam.ac.uk/Teaching/current/LogicProof/ Logic and Proof] (Univ. de Cambridge, 2011-12).
# Riccardo Pucella [http://www.ccs.neu.edu/home/riccardo/courses/csu290-sp09/index.html Logic and Computation] (Northeastern University, 2009). Curso con ACL2.

== Bibliotecas de ejemplos de verificación ==
# [http://afp.sourceforge.net Archive of Formal Proofs].
# [http://www.cs.ru.nl/~freek/100 Formalizing 100 Theorems].
# [http://toccata.lri.fr/gallery Gallery of verified programs].

Documentación

2022-02-08T17:16:52Z

Jalonso:

En esta página se recogen en enlaces que sirven de documentación al curso de demostración asistida por ordenador (DAO).

*Nota:* Ver su actualización en las referencias del [https://www.glc.us.es/~jalonso/RA2019/index.php/Documentaci%C3%B3n curso 2019-20].

== Visiones generales de la DAO ==

# J.A. Alonso. [http://goo.gl/NWk7b Razonamiento formalizado: Del sueño a la realidad de las pruebas]. ''Vestigium'', 26 de diciembre de 2012.
# J. Avigad. [http://www.andrew.cmu.edu/user/avigad/Talks/icerm.pdf Interactive theorem proving, automated reasoning, and mathematical computation]. ICERM, 14 de diciembre de 2012.
# M. Davis. [http://www.cs.nyu.edu/cs/faculty/davism/early.ps The early history of automated deduction].
# J.P. Delahaye [http://interstices.info/jcms/int_63417/du-reve-a-la-realite-des-preuves Du rêve à la réalité des preuves]. ''Interstices'', 8 de julio de 2012.
# J. Germoni [http://images.math.cnrs.fr/Coq-et-caracteres.html Coq et caractères: Preuve formelle du théorème de Feit et Thompson]. ''Images des Mathématiques'', CNRS, 23 de noviembre de 2012.
# H. Geuvers [http://www.ias.ac.in/sadhana/Pdf2009Feb/3.pdf Proof assistants: History, ideas and future]. ''Sadhana'', Vol. 34-1, pp. 3-25, février 2009.
# G. Gonthier [http://www.ams.org/notices/200811/tx081101382p.pdf The four-color theorem]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1382-1393, 2008.
# T. Hales. [http://www.ams.org/notices/200811/tx081101370p.pdf Formal proof]. ''Notices of AMS'', Vol. 55, N. 11 (2008) pp. 1370-1380.
# J. Harrison. [http://www.cl.cam.ac.uk/~jrh13/papers/ab.html A short survey of automated reasoning]. ''Lecture Notes in Computer Science'', Vol. 4545, pp. 334-349, 2007.
# J. Harrison. [http://www.ams.org/notices/200811/tx081101395p.pdf Formal proof: Theory and practice]. ''Notices of the AMS'', Vol. 55, N. 11 (2008) p.1395-1406.
# G. Kolata. [http://www.nytimes.com/library/cyber/week/1210math.html Computer math proof shows reasoning power]. ''The New York Times'', 10 de diciembre de 1996.
# D. MacKenzie [https://backspaces.net/temp/Spring2010Seminar/18%20unconventional%20essays%20on%20the%20nature%20of%20mathematics.pdf#page=147 Computers and the sociology of mathematical proof].
# G. Sutcliffe. [http://tptp.org/OverviewOfATP.html What is automated theorem proving?].
# F. Wiedijk [http://www.cs.ru.nl/~freek/100/ Formalizing the «top 100» of mathematical theorems].
# F. Wiedijk [http://www.ams.org/notices/200811/tx081101408p.pdf Formal proof - Getting started]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1408-1414, 2008.
# F. Wiedijk, [https://www.cs.ru.nl/F.Wiedijk/pubs/qed2.pdf The QED manifesto revisited]. ''Studies in Logic, Grammar and Rhetoric'', Vol. 10(23), pp. 121-133, 2007.

== Referencias sobre Isabelle/HOL ==
# B. Grechuk [https://web.cs.wpi.edu/~dd/resources_isabelle/isabelle_primer_mathematicians.pdf Isabelle primer for mathematicians].
# T. Nipkow [https://isabelle.in.tum.de/doc/prog-prove.pdf Programming and proving in Isabelle/HOL].
# T. Nipkow, M. Wenzel y L.C. Paulson [https://isabelle.in.tum.de/website-Isabelle2009/dist/Isabelle/doc/tutorial.pdf A proof assistant for higher-order logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL/document.pdf Isabelle/HOL — Higher-Order Logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/documentation.html Tutorials and manuals for Isabelle].

== Lecturas complementarias ==
=== Programación funcional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/i1m-12/temas/2012-13-IM-temas-PF.pdf Temas de "Programación funcional"]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# J.A. Alonso y M.J. Hidalgo [http://www.cs.us.es/~jalonso/publicaciones/Piensa_en_Haskell.pdf Piensa en Haskell (Ejercicios de programación funcional con Haskell)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# G. Hutton [http://goo.gl/pKqG Programming in Haskell]. Cambridge University Press, 2007.
# M. Lipovača [http://aprendehaskell.es ¡Aprende Haskell por el bien de todos!].

=== Lógica computacional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/li-12/temas/temas-LI-2012-13.pdf Temas de "Lógica informática" (2012-13)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# R. Bornat [http://bit.ly/oithic Proof and disproof in formal logic: an introduction for programmers]. Oxford University Press, 2005.
# K. Broda, S. Eisenbach, H. Khoshnevisan y S. Vickers [https://www.doc.ic.ac.uk/~susan/firstyearbook.pdf Reasoned programming]. Imperial College, 1994.
# K. Doets y J. van Eijck [https://books.google.es/books?id=YCC6lwEACAAJ&dq=The+Haskell+Road+to+Logic,+Maths+and+Programming&hl=es&sa=X&redir_esc=y The Haskell Road to Logic, Maths and Programming].
# M. Huth y M. Ryan [http://goo.gl/TMqOo Logic in computer science: Modelling and reasoning about systems]. Cambridge University Press, 2004. (Incluye el [http://www.cs.bham.ac.uk/research/lics/tutor/index.html tutor en la Red]).

== Cursos relacionados ==
=== Cursos con Isabelle/HOL ===
# Clemens Ballarin. [http://cl-informatik.uibk.ac.at/teaching/ss08/atp/introduction.php Automatic Deduction]. (Univ de Innsbruck, 2008).
# Clemens Ballarin y Gerwin Klein [http://isabelle.in.tum.de/coursematerial/IJCAR04 Introduction to the Isabelle Proof Assistant]. (en el IJCAR-2004).
# Clemens Ballarin y Tjark Weber. [http://cl-informatik.uibk.ac.at/teaching/ws06/atp/introduction.php Automated Theorem Proving in Isabelle/HOL]. (Univ. de Innsbruck, 2006-07).
# A.D. Brucker, D. Basin, J.G. Smaus y B. Wolff. [http://archiv.infsec.ethz.ch/education/permanent/csmr.html Computer-supported Modeling and Reasoning]. (ETH Zurich, 2011).
# Mads Dam. [http://www.csc.kth.se/utbildning/kth/kurser/DD2453/aform07/ Advanced formal methods]. (KTH Royal Institute of Technology, 2007).
# Jacques Fleuriot y Paul Jackson. [http://www.inf.ed.ac.uk/teaching/courses/ar/slides/ Automated reasoning]. (Univ. de Edimburgo, 2012-13).
# Thomas Genet [http://www.irisa.fr/celtique/genet/ACF Software formal analysis and design]. (Univ. de Rennes)
# Gerwin Klein. [http://www.cse.unsw.edu.au/~kleing/teaching/thprv-04 Theorem Proving - Principles, Techniques, Applications]. (NICTA, 2004).
# Gerwin Klein. [http://www.cse.unsw.edu.au/~cs4161/index.html Advanced Topics in Software Verification]. (NICTA, 2012).
# Joao Marcos. [http://www.dimap.ufrn.br/~jmarcos/courses/LC/Ementa.htm Lógica computacional: Demonstração assistida e semi-automática de teoremas].(UFRN, 2000).
# Tobias Nipkow. [https://www21.in.tum.de/teaching/semantics/WS1920/ Semantics of programming languages]. (Univ. de Munich, 2012-13).
# Tobias Nipkow [http://isabelle.in.tum.de/coursematerial/PSV2009-1 Theorem Proving with Isabelle/HOL An Intensive Course].
# Larry Paulson. [http://www.cl.cam.ac.uk/teaching/0910/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2009-10).
# Jan-Georg Smaus. [http://www.informatik.uni-freiburg.de/~ki/teaching/ws0910/csmr/lecture.html Computer-supported modeling and reasoning]. (Univ. de Feiburgo, 2009).
# Christian Sternagel [http://cl-informatik.uibk.ac.at/teaching/ss11/eve/content.php Experiments in Verification – Introduction to Isabelle/HOL]. (Univ. de Innsbruck, 2011-12).
# Tjark Weber. [http://www.cl.cam.ac.uk/teaching/1011/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2010-11).

=== Otros cursos ===
# José A. Alonso [http://www.cs.us.es/~jalonso/cursos/li-12/ Lógica informática] (Univ. de Sevilla, 2012-13).
# Yves Bertot, Pierre Casteran, Benjamin Gregoire, Pierre Letouzey y Assia Mahboubi [http://www.di.ens.fr/~zappa/teaching/coq/ecole11 Modelling and verifying algorithms in Coq: an introduction]. (INRIA Paris-Rocquencourt, 14-18 noviembre 2011).
# Pierre Castéran [http://www.labri.fr/perso/casteran/FM/Logique/index.html Logic (Master In Verification)] (Univ. de Burdeos, 2011-12).
# Ian Hodkinson [http://www.doc.ic.ac.uk/~imh/teaching/140_logic/logic.html Logic] (Imperial College, Londres, 2010-11).
# Peter Lucas [http://www.cs.ru.nl/~peterl/teaching/KeR/ Knowledge Representation and Reasoning] (Radboud University # egen, 2011-12).
# Larry Paulson [http://www.cl.cam.ac.uk/Teaching/current/LogicProof/ Logic and Proof] (Univ. de Cambridge, 2011-12).
# Riccardo Pucella [http://www.ccs.neu.edu/home/riccardo/courses/csu290-sp09/index.html Logic and Computation] (Northeastern University, 2009). Curso con ACL2.

== Bibliotecas de ejemplos de verificación ==
# [http://afp.sourceforge.net Archive of Formal Proofs].
# [http://www.cs.ru.nl/~freek/100 Formalizing 100 Theorems].
# [http://toccata.lri.fr/gallery Gallery of verified programs].

Documentación

2022-02-08T10:46:25Z

Jalonso:

Documentación

2022-02-08T10:45:13Z

Jalonso: /* Bibliotecas de ejemplos de verificación */

En esta página se recogen en enlaces que sirven de documentación al curso de demostración asistida por ordenador (DAO).

== Visiones generales de la DAO ==

# J.A. Alonso. [http://goo.gl/NWk7b Razonamiento formalizado: Del sueño a la realidad de las pruebas]. ''Vestigium'', 26 de diciembre de 2012.
# J. Avigad. [http://www.andrew.cmu.edu/user/avigad/Talks/icerm.pdf Interactive theorem proving, automated reasoning, and mathematical computation]. ICERM, 14 de diciembre de 2012.
# M. Davis. [http://www.cs.nyu.edu/cs/faculty/davism/early.ps The early history of automated deduction].
# J.P. Delahaye [http://interstices.info/jcms/int_63417/du-reve-a-la-realite-des-preuves Du rêve à la réalité des preuves]. ''Interstices'', 8 de julio de 2012.
# J. Germoni [http://images.math.cnrs.fr/Coq-et-caracteres.html Coq et caractères: Preuve formelle du théorème de Feit et Thompson]. ''Images des Mathématiques'', CNRS, 23 de noviembre de 2012.
# H. Geuvers [http://www.ias.ac.in/sadhana/Pdf2009Feb/3.pdf Proof assistants: History, ideas and future]. ''Sadhana'', Vol. 34-1, pp. 3-25, février 2009.
# G. Gonthier [http://www.ams.org/notices/200811/tx081101382p.pdf The four-color theorem]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1382-1393, 2008.
# T. Hales. [http://www.ams.org/notices/200811/tx081101370p.pdf Formal proof]. ''Notices of AMS'', Vol. 55, N. 11 (2008) pp. 1370-1380.
# J. Harrison. [http://www.cl.cam.ac.uk/~jrh13/papers/ab.html A short survey of automated reasoning]. ''Lecture Notes in Computer Science'', Vol. 4545, pp. 334-349, 2007.
# J. Harrison. [http://www.ams.org/notices/200811/tx081101395p.pdf Formal proof: Theory and practice]. ''Notices of the AMS'', Vol. 55, N. 11 (2008) p.1395-1406.
# G. Kolata. [http://www.nytimes.com/library/cyber/week/1210math.html Computer math proof shows reasoning power]. ''The New York Times'', 10 de diciembre de 1996.
# D. MacKenzie [https://backspaces.net/temp/Spring2010Seminar/18%20unconventional%20essays%20on%20the%20nature%20of%20mathematics.pdf#page=147 Computers and the sociology of mathematical proof].
# G. Sutcliffe. [http://tptp.org/OverviewOfATP.html What is automated theorem proving?].
# F. Wiedijk [http://www.cs.ru.nl/~freek/100/ Formalizing the «top 100» of mathematical theorems].
# F. Wiedijk [http://www.ams.org/notices/200811/tx081101408p.pdf Formal proof - Getting started]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1408-1414, 2008.
# F. Wiedijk, [https://www.cs.ru.nl/F.Wiedijk/pubs/qed2.pdf The QED manifesto revisited]. ''Studies in Logic, Grammar and Rhetoric'', Vol. 10(23), pp. 121-133, 2007.

== Referencias sobre Isabelle/HOL ==
# B. Grechuk [https://web.cs.wpi.edu/~dd/resources_isabelle/isabelle_primer_mathematicians.pdf Isabelle primer for mathematicians].
# T. Nipkow [https://isabelle.in.tum.de/doc/prog-prove.pdf Programming and proving in Isabelle/HOL].
# T. Nipkow, M. Wenzel y L.C. Paulson [https://isabelle.in.tum.de/website-Isabelle2009/dist/Isabelle/doc/tutorial.pdf A proof assistant for higher-order logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL/document.pdf Isabelle/HOL — Higher-Order Logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/documentation.html Tutorials and manuals for Isabelle].

== Lecturas complementarias ==
=== Programación funcional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/i1m-12/temas/2012-13-IM-temas-PF.pdf Temas de "Programación funcional"]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# J.A. Alonso y M.J. Hidalgo [http://www.cs.us.es/~jalonso/publicaciones/Piensa_en_Haskell.pdf Piensa en Haskell (Ejercicios de programación funcional con Haskell)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# G. Hutton [http://goo.gl/pKqG Programming in Haskell]. Cambridge University Press, 2007.
# M. Lipovača [http://aprendehaskell.es ¡Aprende Haskell por el bien de todos!].

=== Lógica computacional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/li-12/temas/temas-LI-2012-13.pdf Temas de "Lógica informática" (2012-13)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# R. Bornat [http://bit.ly/oithic Proof and disproof in formal logic: an introduction for programmers]. Oxford University Press, 2005.
# K. Broda, S. Eisenbach, H. Khoshnevisan y S. Vickers [https://www.doc.ic.ac.uk/~susan/firstyearbook.pdf Reasoned programming]. Imperial College, 1994.
# K. Doets y J. van Eijck [https://books.google.es/books?id=YCC6lwEACAAJ&dq=The+Haskell+Road+to+Logic,+Maths+and+Programming&hl=es&sa=X&redir_esc=y The Haskell Road to Logic, Maths and Programming].
# M. Huth y M. Ryan [http://goo.gl/TMqOo Logic in computer science: Modelling and reasoning about systems]. Cambridge University Press, 2004. (Incluye el [http://www.cs.bham.ac.uk/research/lics/tutor/index.html tutor en la Red]).

== Cursos relacionados ==
=== Cursos con Isabelle/HOL ===
# Clemens Ballarin. [http://cl-informatik.uibk.ac.at/teaching/ss08/atp/introduction.php Automatic Deduction]. (Univ de Innsbruck, 2008).
# Clemens Ballarin y Gerwin Klein [http://isabelle.in.tum.de/coursematerial/IJCAR04 Introduction to the Isabelle Proof Assistant]. (en el IJCAR-2004).
# Clemens Ballarin y Tjark Weber. [http://cl-informatik.uibk.ac.at/teaching/ws06/atp/introduction.php Automated Theorem Proving in Isabelle/HOL]. (Univ. de Innsbruck, 2006-07).
# A.D. Brucker, D. Basin, J.G. Smaus y B. Wolff. [http://archiv.infsec.ethz.ch/education/permanent/csmr.html Computer-supported Modeling and Reasoning]. (ETH Zurich, 2011).
# Mads Dam. [http://www.csc.kth.se/utbildning/kth/kurser/DD2453/aform07/ Advanced formal methods]. (KTH Royal Institute of Technology, 2007).
# Jacques Fleuriot y Paul Jackson. [http://www.inf.ed.ac.uk/teaching/courses/ar/slides/ Automated reasoning]. (Univ. de Edimburgo, 2012-13).
# Thomas Genet [http://www.irisa.fr/celtique/genet/ACF Software formal analysis and design]. (Univ. de Rennes)
# Gerwin Klein. [http://www.cse.unsw.edu.au/~kleing/teaching/thprv-04 Theorem Proving - Principles, Techniques, Applications]. (NICTA, 2004).
# Gerwin Klein. [http://www.cse.unsw.edu.au/~cs4161/index.html Advanced Topics in Software Verification]. (NICTA, 2012).
# Joao Marcos. [http://www.dimap.ufrn.br/~jmarcos/courses/LC/Ementa.htm Lógica computacional: Demonstração assistida e semi-automática de teoremas].(UFRN, 2000).
# Tobias Nipkow. [https://www21.in.tum.de/teaching/semantics/WS1920/ Semantics of programming languages]. (Univ. de Munich, 2012-13).
# Tobias Nipkow [http://isabelle.in.tum.de/coursematerial/PSV2009-1 Theorem Proving with Isabelle/HOL An Intensive Course].
# Larry Paulson. [http://www.cl.cam.ac.uk/teaching/0910/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2009-10).
# Jan-Georg Smaus. [http://www.informatik.uni-freiburg.de/~ki/teaching/ws0910/csmr/lecture.html Computer-supported modeling and reasoning]. (Univ. de Feiburgo, 2009).
# Christian Sternagel [http://cl-informatik.uibk.ac.at/teaching/ss11/eve/content.php Experiments in Verification – Introduction to Isabelle/HOL]. (Univ. de Innsbruck, 2011-12).
# Tjark Weber. [http://www.cl.cam.ac.uk/teaching/1011/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2010-11).

=== Otros cursos ===
# José A. Alonso [http://www.cs.us.es/~jalonso/cursos/li-12/ Lógica informática] (Univ. de Sevilla, 2012-13).
# Yves Bertot, Pierre Casteran, Benjamin Gregoire, Pierre Letouzey y Assia Mahboubi [http://www.di.ens.fr/~zappa/teaching/coq/ecole11 Modelling and verifying algorithms in Coq: an introduction]. (INRIA Paris-Rocquencourt, 14-18 noviembre 2011).
# Pierre Castéran [http://www.labri.fr/perso/casteran/FM/Logique/index.html Logic (Master In Verification)] (Univ. de Burdeos, 2011-12).
# Ian Hodkinson [http://www.doc.ic.ac.uk/~imh/teaching/140_logic/logic.html Logic] (Imperial College, Londres, 2010-11).
# Peter Lucas [http://www.cs.ru.nl/~peterl/teaching/KeR/ Knowledge Representation and Reasoning] (Radboud University # egen, 2011-12).
# Larry Paulson [http://www.cl.cam.ac.uk/Teaching/current/LogicProof/ Logic and Proof] (Univ. de Cambridge, 2011-12).
# Riccardo Pucella [http://www.ccs.neu.edu/home/riccardo/courses/csu290-sp09/index.html Logic and Computation] (Northeastern University, 2009). Curso con ACL2.

== Bibliotecas de ejemplos de verificación ==
# [http://afp.sourceforge.net Archive of Formal Proofs].
# [http://www.cs.ru.nl/~freek/100 Formalizing 100 Theorems].
# [http://toccata.lri.fr/gallery Gallery of verified programs].

== Artículos recientes ==
Están en orden cronológico inverso a la fecha de su reseña en [http://www.glc.us.es/~jalonso/vestigium/tag/resena Vestigium]:
# Joachim Breitner, Brian Huffman, Neil Mitchell y Christian Sternagel [http://bit.ly/19fiWAY Certified HLints with Isabelle/HOLCF-Prelude].
# Peter Lammich [http://bit.ly/ZfSQrQ Automatic data refinement].
# Assia Mahboubi [http://bit.ly/18vyjm7 The rooster and the butterflies (a machine-checked proof of the Jordan-Hölder theorem for finite groups)].
# Nathan Wetzler, Marijn J. H. Heule y Warren A. Hunt Jr. [http://bit.ly/114oyZV Mechanical verification of SAT refutations with extended resolution].
# Johannes Hölzl, Fabian Immler y Brian Huffman [http://bit.ly/13H0REu Type classes and filters for mathematical analysis in Isabelle/HOL]
# M. J. H. Heule, W. A. Hunt, Jr. y N. Wetzler [http://bit.ly/10fv8wO Verifying refutations with extended resolution].
# C. Lüth y M. Ring [http://bit.ly/10EcFWj A Web interface for Isabelle: The next generation].
# L. Liu, O. Hasan y S. Tahar [http://bit.ly/18P9CSv On the formalization of continuous-time Markov chains in HOL].
# A. Asperti y W. Ricciotti [http://bit.ly/17H2mqy Formalizing Turing machines].
# A. Lochbihler [http://bit.ly/YwuCeL Light-weight containers for Isabelle: efficient, extensible, nestable].
# L. Noschinski [http://bit.ly/10XLrRA Graph theory].
# G. Gonthier et als. [http://bit.ly/19kPEP4 A machine-checked proof of the odd order theorem].
# C. Doczkal, J.O. Kaiser y G. Smolka [http://goo.gl/LdihL A constructive theory of regular languages in Coq].
# C. Sternagel [http://goo.gl/gwcwL A formal proof of Kruskal’s tree theorem in Isabelle/HOL].
# C. Sternagel y R. Thiemann [http://goo.gl/CUF3e Formalizing Knuth-Bendix orders and Knuth-Bendix completion].
# C. Lange, C. Rowat, W. Windsteiger y M. Kerber [http://goo.gl/9JAfX Developing an auction theory toolbox].
# M. Spasić y F. Marić [http://goo.gl/6OfmQ Formalization of incremental simplex algorithm by stepwise refinement].
# J.C. Blanchette, A. Popescu y D. Traytel [http://goo.gl/Guxky Coinductive pearl: Modular first-order logic completeness].
# J. Esparza et als. [http://goo.gl/HUOl8 A fully verified executable LTL model checker].
# M. Kerber, C. Lange y C. Rowat. [http://goo.gl/RV54S ForMaRE - formal mathematical reasoning in economics].
# J. Urban. [http://goo.gl/Y7sIq AI over large formal knowledge bases: The first decade].
# S. Boldo, C. Lelay y G. Melquiond. [http://goo.gl/vvqNg Formalization of real analysis: A survey of proof assistants and libraries].
# F. Haftmann, A. Krauss, O. Kunčar y T. Nipkow [http://goo.gl/bEFYa Data refinement in Isabelle/HOL].
# A.C. Rocha y M. Ayala. [http://goo.gl/xTyvE Formalizing the confluence of orthogonal rewriting systems].
# Z. Shi et als. [http://goo.gl/zCYHj Formalization of the complex number theory in HOL4].
# F. Loulergue y V. Niculescu [http://goo.gl/kM0dI Programming and reasonning with PowerLists in Coq].
# J. Heras, F.J. Martín y V. Pascual. [http://goo.gl/KkU6s A hierarchy of mathematical structures in ACL2].
# J. Xu, X. Zhang y C. Urban [http://www.inf.kcl.ac.uk/staff/urbanc/Publications/tm.pdf Mechanising Turing Machines and Computability Theory in Isabelle/HOL]

Documentación

2022-02-08T10:44:29Z

Jalonso: /* Bibliotecas de ejemplos de verificación */

En esta página se recogen en enlaces que sirven de documentación al curso de demostración asistida por ordenador (DAO).

== Visiones generales de la DAO ==

# J.A. Alonso. [http://goo.gl/NWk7b Razonamiento formalizado: Del sueño a la realidad de las pruebas]. ''Vestigium'', 26 de diciembre de 2012.
# J. Avigad. [http://www.andrew.cmu.edu/user/avigad/Talks/icerm.pdf Interactive theorem proving, automated reasoning, and mathematical computation]. ICERM, 14 de diciembre de 2012.
# M. Davis. [http://www.cs.nyu.edu/cs/faculty/davism/early.ps The early history of automated deduction].
# J.P. Delahaye [http://interstices.info/jcms/int_63417/du-reve-a-la-realite-des-preuves Du rêve à la réalité des preuves]. ''Interstices'', 8 de julio de 2012.
# J. Germoni [http://images.math.cnrs.fr/Coq-et-caracteres.html Coq et caractères: Preuve formelle du théorème de Feit et Thompson]. ''Images des Mathématiques'', CNRS, 23 de noviembre de 2012.
# H. Geuvers [http://www.ias.ac.in/sadhana/Pdf2009Feb/3.pdf Proof assistants: History, ideas and future]. ''Sadhana'', Vol. 34-1, pp. 3-25, février 2009.
# G. Gonthier [http://www.ams.org/notices/200811/tx081101382p.pdf The four-color theorem]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1382-1393, 2008.
# T. Hales. [http://www.ams.org/notices/200811/tx081101370p.pdf Formal proof]. ''Notices of AMS'', Vol. 55, N. 11 (2008) pp. 1370-1380.
# J. Harrison. [http://www.cl.cam.ac.uk/~jrh13/papers/ab.html A short survey of automated reasoning]. ''Lecture Notes in Computer Science'', Vol. 4545, pp. 334-349, 2007.
# J. Harrison. [http://www.ams.org/notices/200811/tx081101395p.pdf Formal proof: Theory and practice]. ''Notices of the AMS'', Vol. 55, N. 11 (2008) p.1395-1406.
# G. Kolata. [http://www.nytimes.com/library/cyber/week/1210math.html Computer math proof shows reasoning power]. ''The New York Times'', 10 de diciembre de 1996.
# D. MacKenzie [https://backspaces.net/temp/Spring2010Seminar/18%20unconventional%20essays%20on%20the%20nature%20of%20mathematics.pdf#page=147 Computers and the sociology of mathematical proof].
# G. Sutcliffe. [http://tptp.org/OverviewOfATP.html What is automated theorem proving?].
# F. Wiedijk [http://www.cs.ru.nl/~freek/100/ Formalizing the «top 100» of mathematical theorems].
# F. Wiedijk [http://www.ams.org/notices/200811/tx081101408p.pdf Formal proof - Getting started]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1408-1414, 2008.
# F. Wiedijk, [https://www.cs.ru.nl/F.Wiedijk/pubs/qed2.pdf The QED manifesto revisited]. ''Studies in Logic, Grammar and Rhetoric'', Vol. 10(23), pp. 121-133, 2007.

== Referencias sobre Isabelle/HOL ==
# B. Grechuk [https://web.cs.wpi.edu/~dd/resources_isabelle/isabelle_primer_mathematicians.pdf Isabelle primer for mathematicians].
# T. Nipkow [https://isabelle.in.tum.de/doc/prog-prove.pdf Programming and proving in Isabelle/HOL].
# T. Nipkow, M. Wenzel y L.C. Paulson [https://isabelle.in.tum.de/website-Isabelle2009/dist/Isabelle/doc/tutorial.pdf A proof assistant for higher-order logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL/document.pdf Isabelle/HOL — Higher-Order Logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/documentation.html Tutorials and manuals for Isabelle].

== Lecturas complementarias ==
=== Programación funcional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/i1m-12/temas/2012-13-IM-temas-PF.pdf Temas de "Programación funcional"]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# J.A. Alonso y M.J. Hidalgo [http://www.cs.us.es/~jalonso/publicaciones/Piensa_en_Haskell.pdf Piensa en Haskell (Ejercicios de programación funcional con Haskell)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# G. Hutton [http://goo.gl/pKqG Programming in Haskell]. Cambridge University Press, 2007.
# M. Lipovača [http://aprendehaskell.es ¡Aprende Haskell por el bien de todos!].

=== Lógica computacional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/li-12/temas/temas-LI-2012-13.pdf Temas de "Lógica informática" (2012-13)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# R. Bornat [http://bit.ly/oithic Proof and disproof in formal logic: an introduction for programmers]. Oxford University Press, 2005.
# K. Broda, S. Eisenbach, H. Khoshnevisan y S. Vickers [https://www.doc.ic.ac.uk/~susan/firstyearbook.pdf Reasoned programming]. Imperial College, 1994.
# K. Doets y J. van Eijck [https://books.google.es/books?id=YCC6lwEACAAJ&dq=The+Haskell+Road+to+Logic,+Maths+and+Programming&hl=es&sa=X&redir_esc=y The Haskell Road to Logic, Maths and Programming].
# M. Huth y M. Ryan [http://goo.gl/TMqOo Logic in computer science: Modelling and reasoning about systems]. Cambridge University Press, 2004. (Incluye el [http://www.cs.bham.ac.uk/research/lics/tutor/index.html tutor en la Red]).

== Cursos relacionados ==
=== Cursos con Isabelle/HOL ===
# Clemens Ballarin. [http://cl-informatik.uibk.ac.at/teaching/ss08/atp/introduction.php Automatic Deduction]. (Univ de Innsbruck, 2008).
# Clemens Ballarin y Gerwin Klein [http://isabelle.in.tum.de/coursematerial/IJCAR04 Introduction to the Isabelle Proof Assistant]. (en el IJCAR-2004).
# Clemens Ballarin y Tjark Weber. [http://cl-informatik.uibk.ac.at/teaching/ws06/atp/introduction.php Automated Theorem Proving in Isabelle/HOL]. (Univ. de Innsbruck, 2006-07).
# A.D. Brucker, D. Basin, J.G. Smaus y B. Wolff. [http://archiv.infsec.ethz.ch/education/permanent/csmr.html Computer-supported Modeling and Reasoning]. (ETH Zurich, 2011).
# Mads Dam. [http://www.csc.kth.se/utbildning/kth/kurser/DD2453/aform07/ Advanced formal methods]. (KTH Royal Institute of Technology, 2007).
# Jacques Fleuriot y Paul Jackson. [http://www.inf.ed.ac.uk/teaching/courses/ar/slides/ Automated reasoning]. (Univ. de Edimburgo, 2012-13).
# Thomas Genet [http://www.irisa.fr/celtique/genet/ACF Software formal analysis and design]. (Univ. de Rennes)
# Gerwin Klein. [http://www.cse.unsw.edu.au/~kleing/teaching/thprv-04 Theorem Proving - Principles, Techniques, Applications]. (NICTA, 2004).
# Gerwin Klein. [http://www.cse.unsw.edu.au/~cs4161/index.html Advanced Topics in Software Verification]. (NICTA, 2012).
# Joao Marcos. [http://www.dimap.ufrn.br/~jmarcos/courses/LC/Ementa.htm Lógica computacional: Demonstração assistida e semi-automática de teoremas].(UFRN, 2000).
# Tobias Nipkow. [https://www21.in.tum.de/teaching/semantics/WS1920/ Semantics of programming languages]. (Univ. de Munich, 2012-13).
# Tobias Nipkow [http://isabelle.in.tum.de/coursematerial/PSV2009-1 Theorem Proving with Isabelle/HOL An Intensive Course].
# Larry Paulson. [http://www.cl.cam.ac.uk/teaching/0910/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2009-10).
# Jan-Georg Smaus. [http://www.informatik.uni-freiburg.de/~ki/teaching/ws0910/csmr/lecture.html Computer-supported modeling and reasoning]. (Univ. de Feiburgo, 2009).
# Christian Sternagel [http://cl-informatik.uibk.ac.at/teaching/ss11/eve/content.php Experiments in Verification – Introduction to Isabelle/HOL]. (Univ. de Innsbruck, 2011-12).
# Tjark Weber. [http://www.cl.cam.ac.uk/teaching/1011/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2010-11).

=== Otros cursos ===
# José A. Alonso [http://www.cs.us.es/~jalonso/cursos/li-12/ Lógica informática] (Univ. de Sevilla, 2012-13).
# Yves Bertot, Pierre Casteran, Benjamin Gregoire, Pierre Letouzey y Assia Mahboubi [http://www.di.ens.fr/~zappa/teaching/coq/ecole11 Modelling and verifying algorithms in Coq: an introduction]. (INRIA Paris-Rocquencourt, 14-18 noviembre 2011).
# Pierre Castéran [http://www.labri.fr/perso/casteran/FM/Logique/index.html Logic (Master In Verification)] (Univ. de Burdeos, 2011-12).
# Ian Hodkinson [http://www.doc.ic.ac.uk/~imh/teaching/140_logic/logic.html Logic] (Imperial College, Londres, 2010-11).
# Peter Lucas [http://www.cs.ru.nl/~peterl/teaching/KeR/ Knowledge Representation and Reasoning] (Radboud University # egen, 2011-12).
# Larry Paulson [http://www.cl.cam.ac.uk/Teaching/current/LogicProof/ Logic and Proof] (Univ. de Cambridge, 2011-12).
# Riccardo Pucella [http://www.ccs.neu.edu/home/riccardo/courses/csu290-sp09/index.html Logic and Computation] (Northeastern University, 2009). Curso con ACL2.

== Bibliotecas de ejemplos de verificación ==
# [http://afp.sourceforge.net Archive of Formal Proofs].
# [http://www.cs.ru.nl/~freek/100 Formalizing 100 Theorems].
# [http://toccata.lri.fr/gallery Gallery of verified programs].
# [http://automatedreasoning.net/ Larry Wos' Notebooks].
# [http://www.cs.miami.edu/~tptp/ The TPTP Problem Library for Automated Theorem Proving].
# [http://www.macs.hw.ac.uk/vstte10/Competition.html The 1st Verified Software Competition].
# [https://sites.google.com/site/vstte2012/compet The 2nd Verified Software Competition].
# [http://verifythis.cost-ic0701.org VerifyThis (A collection of verification benchmarks].

== Artículos recientes ==
Están en orden cronológico inverso a la fecha de su reseña en [http://www.glc.us.es/~jalonso/vestigium/tag/resena Vestigium]:
# Joachim Breitner, Brian Huffman, Neil Mitchell y Christian Sternagel [http://bit.ly/19fiWAY Certified HLints with Isabelle/HOLCF-Prelude].
# Peter Lammich [http://bit.ly/ZfSQrQ Automatic data refinement].
# Assia Mahboubi [http://bit.ly/18vyjm7 The rooster and the butterflies (a machine-checked proof of the Jordan-Hölder theorem for finite groups)].
# Nathan Wetzler, Marijn J. H. Heule y Warren A. Hunt Jr. [http://bit.ly/114oyZV Mechanical verification of SAT refutations with extended resolution].
# Johannes Hölzl, Fabian Immler y Brian Huffman [http://bit.ly/13H0REu Type classes and filters for mathematical analysis in Isabelle/HOL]
# M. J. H. Heule, W. A. Hunt, Jr. y N. Wetzler [http://bit.ly/10fv8wO Verifying refutations with extended resolution].
# C. Lüth y M. Ring [http://bit.ly/10EcFWj A Web interface for Isabelle: The next generation].
# L. Liu, O. Hasan y S. Tahar [http://bit.ly/18P9CSv On the formalization of continuous-time Markov chains in HOL].
# A. Asperti y W. Ricciotti [http://bit.ly/17H2mqy Formalizing Turing machines].
# A. Lochbihler [http://bit.ly/YwuCeL Light-weight containers for Isabelle: efficient, extensible, nestable].
# L. Noschinski [http://bit.ly/10XLrRA Graph theory].
# G. Gonthier et als. [http://bit.ly/19kPEP4 A machine-checked proof of the odd order theorem].
# C. Doczkal, J.O. Kaiser y G. Smolka [http://goo.gl/LdihL A constructive theory of regular languages in Coq].
# C. Sternagel [http://goo.gl/gwcwL A formal proof of Kruskal’s tree theorem in Isabelle/HOL].
# C. Sternagel y R. Thiemann [http://goo.gl/CUF3e Formalizing Knuth-Bendix orders and Knuth-Bendix completion].
# C. Lange, C. Rowat, W. Windsteiger y M. Kerber [http://goo.gl/9JAfX Developing an auction theory toolbox].
# M. Spasić y F. Marić [http://goo.gl/6OfmQ Formalization of incremental simplex algorithm by stepwise refinement].
# J.C. Blanchette, A. Popescu y D. Traytel [http://goo.gl/Guxky Coinductive pearl: Modular first-order logic completeness].
# J. Esparza et als. [http://goo.gl/HUOl8 A fully verified executable LTL model checker].
# M. Kerber, C. Lange y C. Rowat. [http://goo.gl/RV54S ForMaRE - formal mathematical reasoning in economics].
# J. Urban. [http://goo.gl/Y7sIq AI over large formal knowledge bases: The first decade].
# S. Boldo, C. Lelay y G. Melquiond. [http://goo.gl/vvqNg Formalization of real analysis: A survey of proof assistants and libraries].
# F. Haftmann, A. Krauss, O. Kunčar y T. Nipkow [http://goo.gl/bEFYa Data refinement in Isabelle/HOL].
# A.C. Rocha y M. Ayala. [http://goo.gl/xTyvE Formalizing the confluence of orthogonal rewriting systems].
# Z. Shi et als. [http://goo.gl/zCYHj Formalization of the complex number theory in HOL4].
# F. Loulergue y V. Niculescu [http://goo.gl/kM0dI Programming and reasonning with PowerLists in Coq].
# J. Heras, F.J. Martín y V. Pascual. [http://goo.gl/KkU6s A hierarchy of mathematical structures in ACL2].
# J. Xu, X. Zhang y C. Urban [http://www.inf.kcl.ac.uk/staff/urbanc/Publications/tm.pdf Mechanising Turing Machines and Computability Theory in Isabelle/HOL]

Documentación

2022-02-08T10:43:18Z

Jalonso: /* Otros cursos */

En esta página se recogen en enlaces que sirven de documentación al curso de demostración asistida por ordenador (DAO).

== Visiones generales de la DAO ==

# J.A. Alonso. [http://goo.gl/NWk7b Razonamiento formalizado: Del sueño a la realidad de las pruebas]. ''Vestigium'', 26 de diciembre de 2012.
# J. Avigad. [http://www.andrew.cmu.edu/user/avigad/Talks/icerm.pdf Interactive theorem proving, automated reasoning, and mathematical computation]. ICERM, 14 de diciembre de 2012.
# M. Davis. [http://www.cs.nyu.edu/cs/faculty/davism/early.ps The early history of automated deduction].
# J.P. Delahaye [http://interstices.info/jcms/int_63417/du-reve-a-la-realite-des-preuves Du rêve à la réalité des preuves]. ''Interstices'', 8 de julio de 2012.
# J. Germoni [http://images.math.cnrs.fr/Coq-et-caracteres.html Coq et caractères: Preuve formelle du théorème de Feit et Thompson]. ''Images des Mathématiques'', CNRS, 23 de noviembre de 2012.
# H. Geuvers [http://www.ias.ac.in/sadhana/Pdf2009Feb/3.pdf Proof assistants: History, ideas and future]. ''Sadhana'', Vol. 34-1, pp. 3-25, février 2009.
# G. Gonthier [http://www.ams.org/notices/200811/tx081101382p.pdf The four-color theorem]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1382-1393, 2008.
# T. Hales. [http://www.ams.org/notices/200811/tx081101370p.pdf Formal proof]. ''Notices of AMS'', Vol. 55, N. 11 (2008) pp. 1370-1380.
# J. Harrison. [http://www.cl.cam.ac.uk/~jrh13/papers/ab.html A short survey of automated reasoning]. ''Lecture Notes in Computer Science'', Vol. 4545, pp. 334-349, 2007.
# J. Harrison. [http://www.ams.org/notices/200811/tx081101395p.pdf Formal proof: Theory and practice]. ''Notices of the AMS'', Vol. 55, N. 11 (2008) p.1395-1406.
# G. Kolata. [http://www.nytimes.com/library/cyber/week/1210math.html Computer math proof shows reasoning power]. ''The New York Times'', 10 de diciembre de 1996.
# D. MacKenzie [https://backspaces.net/temp/Spring2010Seminar/18%20unconventional%20essays%20on%20the%20nature%20of%20mathematics.pdf#page=147 Computers and the sociology of mathematical proof].
# G. Sutcliffe. [http://tptp.org/OverviewOfATP.html What is automated theorem proving?].
# F. Wiedijk [http://www.cs.ru.nl/~freek/100/ Formalizing the «top 100» of mathematical theorems].
# F. Wiedijk [http://www.ams.org/notices/200811/tx081101408p.pdf Formal proof - Getting started]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1408-1414, 2008.
# F. Wiedijk, [https://www.cs.ru.nl/F.Wiedijk/pubs/qed2.pdf The QED manifesto revisited]. ''Studies in Logic, Grammar and Rhetoric'', Vol. 10(23), pp. 121-133, 2007.

== Referencias sobre Isabelle/HOL ==
# B. Grechuk [https://web.cs.wpi.edu/~dd/resources_isabelle/isabelle_primer_mathematicians.pdf Isabelle primer for mathematicians].
# T. Nipkow [https://isabelle.in.tum.de/doc/prog-prove.pdf Programming and proving in Isabelle/HOL].
# T. Nipkow, M. Wenzel y L.C. Paulson [https://isabelle.in.tum.de/website-Isabelle2009/dist/Isabelle/doc/tutorial.pdf A proof assistant for higher-order logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL/document.pdf Isabelle/HOL — Higher-Order Logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/documentation.html Tutorials and manuals for Isabelle].

== Lecturas complementarias ==
=== Programación funcional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/i1m-12/temas/2012-13-IM-temas-PF.pdf Temas de "Programación funcional"]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# J.A. Alonso y M.J. Hidalgo [http://www.cs.us.es/~jalonso/publicaciones/Piensa_en_Haskell.pdf Piensa en Haskell (Ejercicios de programación funcional con Haskell)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# G. Hutton [http://goo.gl/pKqG Programming in Haskell]. Cambridge University Press, 2007.
# M. Lipovača [http://aprendehaskell.es ¡Aprende Haskell por el bien de todos!].

=== Lógica computacional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/li-12/temas/temas-LI-2012-13.pdf Temas de "Lógica informática" (2012-13)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# R. Bornat [http://bit.ly/oithic Proof and disproof in formal logic: an introduction for programmers]. Oxford University Press, 2005.
# K. Broda, S. Eisenbach, H. Khoshnevisan y S. Vickers [https://www.doc.ic.ac.uk/~susan/firstyearbook.pdf Reasoned programming]. Imperial College, 1994.
# K. Doets y J. van Eijck [https://books.google.es/books?id=YCC6lwEACAAJ&dq=The+Haskell+Road+to+Logic,+Maths+and+Programming&hl=es&sa=X&redir_esc=y The Haskell Road to Logic, Maths and Programming].
# M. Huth y M. Ryan [http://goo.gl/TMqOo Logic in computer science: Modelling and reasoning about systems]. Cambridge University Press, 2004. (Incluye el [http://www.cs.bham.ac.uk/research/lics/tutor/index.html tutor en la Red]).

== Cursos relacionados ==
=== Cursos con Isabelle/HOL ===
# Clemens Ballarin. [http://cl-informatik.uibk.ac.at/teaching/ss08/atp/introduction.php Automatic Deduction]. (Univ de Innsbruck, 2008).
# Clemens Ballarin y Gerwin Klein [http://isabelle.in.tum.de/coursematerial/IJCAR04 Introduction to the Isabelle Proof Assistant]. (en el IJCAR-2004).
# Clemens Ballarin y Tjark Weber. [http://cl-informatik.uibk.ac.at/teaching/ws06/atp/introduction.php Automated Theorem Proving in Isabelle/HOL]. (Univ. de Innsbruck, 2006-07).
# A.D. Brucker, D. Basin, J.G. Smaus y B. Wolff. [http://archiv.infsec.ethz.ch/education/permanent/csmr.html Computer-supported Modeling and Reasoning]. (ETH Zurich, 2011).
# Mads Dam. [http://www.csc.kth.se/utbildning/kth/kurser/DD2453/aform07/ Advanced formal methods]. (KTH Royal Institute of Technology, 2007).
# Jacques Fleuriot y Paul Jackson. [http://www.inf.ed.ac.uk/teaching/courses/ar/slides/ Automated reasoning]. (Univ. de Edimburgo, 2012-13).
# Thomas Genet [http://www.irisa.fr/celtique/genet/ACF Software formal analysis and design]. (Univ. de Rennes)
# Gerwin Klein. [http://www.cse.unsw.edu.au/~kleing/teaching/thprv-04 Theorem Proving - Principles, Techniques, Applications]. (NICTA, 2004).
# Gerwin Klein. [http://www.cse.unsw.edu.au/~cs4161/index.html Advanced Topics in Software Verification]. (NICTA, 2012).
# Joao Marcos. [http://www.dimap.ufrn.br/~jmarcos/courses/LC/Ementa.htm Lógica computacional: Demonstração assistida e semi-automática de teoremas].(UFRN, 2000).
# Tobias Nipkow. [https://www21.in.tum.de/teaching/semantics/WS1920/ Semantics of programming languages]. (Univ. de Munich, 2012-13).
# Tobias Nipkow [http://isabelle.in.tum.de/coursematerial/PSV2009-1 Theorem Proving with Isabelle/HOL An Intensive Course].
# Larry Paulson. [http://www.cl.cam.ac.uk/teaching/0910/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2009-10).
# Jan-Georg Smaus. [http://www.informatik.uni-freiburg.de/~ki/teaching/ws0910/csmr/lecture.html Computer-supported modeling and reasoning]. (Univ. de Feiburgo, 2009).
# Christian Sternagel [http://cl-informatik.uibk.ac.at/teaching/ss11/eve/content.php Experiments in Verification – Introduction to Isabelle/HOL]. (Univ. de Innsbruck, 2011-12).
# Tjark Weber. [http://www.cl.cam.ac.uk/teaching/1011/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2010-11).

=== Otros cursos ===
# José A. Alonso [http://www.cs.us.es/~jalonso/cursos/li-12/ Lógica informática] (Univ. de Sevilla, 2012-13).
# Yves Bertot, Pierre Casteran, Benjamin Gregoire, Pierre Letouzey y Assia Mahboubi [http://www.di.ens.fr/~zappa/teaching/coq/ecole11 Modelling and verifying algorithms in Coq: an introduction]. (INRIA Paris-Rocquencourt, 14-18 noviembre 2011).
# Pierre Castéran [http://www.labri.fr/perso/casteran/FM/Logique/index.html Logic (Master In Verification)] (Univ. de Burdeos, 2011-12).
# Ian Hodkinson [http://www.doc.ic.ac.uk/~imh/teaching/140_logic/logic.html Logic] (Imperial College, Londres, 2010-11).
# Peter Lucas [http://www.cs.ru.nl/~peterl/teaching/KeR/ Knowledge Representation and Reasoning] (Radboud University # egen, 2011-12).
# Larry Paulson [http://www.cl.cam.ac.uk/Teaching/current/LogicProof/ Logic and Proof] (Univ. de Cambridge, 2011-12).
# Riccardo Pucella [http://www.ccs.neu.edu/home/riccardo/courses/csu290-sp09/index.html Logic and Computation] (Northeastern University, 2009). Curso con ACL2.

== Bibliotecas de ejemplos de verificación ==
# [http://afp.sourceforge.net Archive of Formal Proofs].
# [http://www.cs.ru.nl/~freek/100 Formalizing 100 Theorems].
# [http://toccata.lri.fr/gallery Gallery of verified programs].
# [http://www.cs.nott.ac.uk/~lad/research/challenges/ Induction Challenge Problems].
# [http://automatedreasoning.net/ Larry Wos' Notebooks].
# [http://www.cs.miami.edu/~tptp/ The TPTP Problem Library for Automated Theorem Proving].
# [http://www.macs.hw.ac.uk/vstte10/Competition.html The 1st Verified Software Competition].
# [https://sites.google.com/site/vstte2012/compet The 2nd Verified Software Competition].
# [http://verifythis.cost-ic0701.org VerifyThis (A collection of verification benchmarks].

== Artículos recientes ==
Están en orden cronológico inverso a la fecha de su reseña en [http://www.glc.us.es/~jalonso/vestigium/tag/resena Vestigium]:
# Joachim Breitner, Brian Huffman, Neil Mitchell y Christian Sternagel [http://bit.ly/19fiWAY Certified HLints with Isabelle/HOLCF-Prelude].
# Peter Lammich [http://bit.ly/ZfSQrQ Automatic data refinement].
# Assia Mahboubi [http://bit.ly/18vyjm7 The rooster and the butterflies (a machine-checked proof of the Jordan-Hölder theorem for finite groups)].
# Nathan Wetzler, Marijn J. H. Heule y Warren A. Hunt Jr. [http://bit.ly/114oyZV Mechanical verification of SAT refutations with extended resolution].
# Johannes Hölzl, Fabian Immler y Brian Huffman [http://bit.ly/13H0REu Type classes and filters for mathematical analysis in Isabelle/HOL]
# M. J. H. Heule, W. A. Hunt, Jr. y N. Wetzler [http://bit.ly/10fv8wO Verifying refutations with extended resolution].
# C. Lüth y M. Ring [http://bit.ly/10EcFWj A Web interface for Isabelle: The next generation].
# L. Liu, O. Hasan y S. Tahar [http://bit.ly/18P9CSv On the formalization of continuous-time Markov chains in HOL].
# A. Asperti y W. Ricciotti [http://bit.ly/17H2mqy Formalizing Turing machines].
# A. Lochbihler [http://bit.ly/YwuCeL Light-weight containers for Isabelle: efficient, extensible, nestable].
# L. Noschinski [http://bit.ly/10XLrRA Graph theory].
# G. Gonthier et als. [http://bit.ly/19kPEP4 A machine-checked proof of the odd order theorem].
# C. Doczkal, J.O. Kaiser y G. Smolka [http://goo.gl/LdihL A constructive theory of regular languages in Coq].
# C. Sternagel [http://goo.gl/gwcwL A formal proof of Kruskal’s tree theorem in Isabelle/HOL].
# C. Sternagel y R. Thiemann [http://goo.gl/CUF3e Formalizing Knuth-Bendix orders and Knuth-Bendix completion].
# C. Lange, C. Rowat, W. Windsteiger y M. Kerber [http://goo.gl/9JAfX Developing an auction theory toolbox].
# M. Spasić y F. Marić [http://goo.gl/6OfmQ Formalization of incremental simplex algorithm by stepwise refinement].
# J.C. Blanchette, A. Popescu y D. Traytel [http://goo.gl/Guxky Coinductive pearl: Modular first-order logic completeness].
# J. Esparza et als. [http://goo.gl/HUOl8 A fully verified executable LTL model checker].
# M. Kerber, C. Lange y C. Rowat. [http://goo.gl/RV54S ForMaRE - formal mathematical reasoning in economics].
# J. Urban. [http://goo.gl/Y7sIq AI over large formal knowledge bases: The first decade].
# S. Boldo, C. Lelay y G. Melquiond. [http://goo.gl/vvqNg Formalization of real analysis: A survey of proof assistants and libraries].
# F. Haftmann, A. Krauss, O. Kunčar y T. Nipkow [http://goo.gl/bEFYa Data refinement in Isabelle/HOL].
# A.C. Rocha y M. Ayala. [http://goo.gl/xTyvE Formalizing the confluence of orthogonal rewriting systems].
# Z. Shi et als. [http://goo.gl/zCYHj Formalization of the complex number theory in HOL4].
# F. Loulergue y V. Niculescu [http://goo.gl/kM0dI Programming and reasonning with PowerLists in Coq].
# J. Heras, F.J. Martín y V. Pascual. [http://goo.gl/KkU6s A hierarchy of mathematical structures in ACL2].
# J. Xu, X. Zhang y C. Urban [http://www.inf.kcl.ac.uk/staff/urbanc/Publications/tm.pdf Mechanising Turing Machines and Computability Theory in Isabelle/HOL]

Documentación

2022-02-08T10:42:34Z

Jalonso: /* Otros cursos */

En esta página se recogen en enlaces que sirven de documentación al curso de demostración asistida por ordenador (DAO).

== Visiones generales de la DAO ==

# J.A. Alonso. [http://goo.gl/NWk7b Razonamiento formalizado: Del sueño a la realidad de las pruebas]. ''Vestigium'', 26 de diciembre de 2012.
# J. Avigad. [http://www.andrew.cmu.edu/user/avigad/Talks/icerm.pdf Interactive theorem proving, automated reasoning, and mathematical computation]. ICERM, 14 de diciembre de 2012.
# M. Davis. [http://www.cs.nyu.edu/cs/faculty/davism/early.ps The early history of automated deduction].
# J.P. Delahaye [http://interstices.info/jcms/int_63417/du-reve-a-la-realite-des-preuves Du rêve à la réalité des preuves]. ''Interstices'', 8 de julio de 2012.
# J. Germoni [http://images.math.cnrs.fr/Coq-et-caracteres.html Coq et caractères: Preuve formelle du théorème de Feit et Thompson]. ''Images des Mathématiques'', CNRS, 23 de noviembre de 2012.
# H. Geuvers [http://www.ias.ac.in/sadhana/Pdf2009Feb/3.pdf Proof assistants: History, ideas and future]. ''Sadhana'', Vol. 34-1, pp. 3-25, février 2009.
# G. Gonthier [http://www.ams.org/notices/200811/tx081101382p.pdf The four-color theorem]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1382-1393, 2008.
# T. Hales. [http://www.ams.org/notices/200811/tx081101370p.pdf Formal proof]. ''Notices of AMS'', Vol. 55, N. 11 (2008) pp. 1370-1380.
# J. Harrison. [http://www.cl.cam.ac.uk/~jrh13/papers/ab.html A short survey of automated reasoning]. ''Lecture Notes in Computer Science'', Vol. 4545, pp. 334-349, 2007.
# J. Harrison. [http://www.ams.org/notices/200811/tx081101395p.pdf Formal proof: Theory and practice]. ''Notices of the AMS'', Vol. 55, N. 11 (2008) p.1395-1406.
# G. Kolata. [http://www.nytimes.com/library/cyber/week/1210math.html Computer math proof shows reasoning power]. ''The New York Times'', 10 de diciembre de 1996.
# D. MacKenzie [https://backspaces.net/temp/Spring2010Seminar/18%20unconventional%20essays%20on%20the%20nature%20of%20mathematics.pdf#page=147 Computers and the sociology of mathematical proof].
# G. Sutcliffe. [http://tptp.org/OverviewOfATP.html What is automated theorem proving?].
# F. Wiedijk [http://www.cs.ru.nl/~freek/100/ Formalizing the «top 100» of mathematical theorems].
# F. Wiedijk [http://www.ams.org/notices/200811/tx081101408p.pdf Formal proof - Getting started]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1408-1414, 2008.
# F. Wiedijk, [https://www.cs.ru.nl/F.Wiedijk/pubs/qed2.pdf The QED manifesto revisited]. ''Studies in Logic, Grammar and Rhetoric'', Vol. 10(23), pp. 121-133, 2007.

== Referencias sobre Isabelle/HOL ==
# B. Grechuk [https://web.cs.wpi.edu/~dd/resources_isabelle/isabelle_primer_mathematicians.pdf Isabelle primer for mathematicians].
# T. Nipkow [https://isabelle.in.tum.de/doc/prog-prove.pdf Programming and proving in Isabelle/HOL].
# T. Nipkow, M. Wenzel y L.C. Paulson [https://isabelle.in.tum.de/website-Isabelle2009/dist/Isabelle/doc/tutorial.pdf A proof assistant for higher-order logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL/document.pdf Isabelle/HOL — Higher-Order Logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/documentation.html Tutorials and manuals for Isabelle].

== Lecturas complementarias ==
=== Programación funcional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/i1m-12/temas/2012-13-IM-temas-PF.pdf Temas de "Programación funcional"]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# J.A. Alonso y M.J. Hidalgo [http://www.cs.us.es/~jalonso/publicaciones/Piensa_en_Haskell.pdf Piensa en Haskell (Ejercicios de programación funcional con Haskell)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# G. Hutton [http://goo.gl/pKqG Programming in Haskell]. Cambridge University Press, 2007.
# M. Lipovača [http://aprendehaskell.es ¡Aprende Haskell por el bien de todos!].

=== Lógica computacional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/li-12/temas/temas-LI-2012-13.pdf Temas de "Lógica informática" (2012-13)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# R. Bornat [http://bit.ly/oithic Proof and disproof in formal logic: an introduction for programmers]. Oxford University Press, 2005.
# K. Broda, S. Eisenbach, H. Khoshnevisan y S. Vickers [https://www.doc.ic.ac.uk/~susan/firstyearbook.pdf Reasoned programming]. Imperial College, 1994.
# K. Doets y J. van Eijck [https://books.google.es/books?id=YCC6lwEACAAJ&dq=The+Haskell+Road+to+Logic,+Maths+and+Programming&hl=es&sa=X&redir_esc=y The Haskell Road to Logic, Maths and Programming].
# M. Huth y M. Ryan [http://goo.gl/TMqOo Logic in computer science: Modelling and reasoning about systems]. Cambridge University Press, 2004. (Incluye el [http://www.cs.bham.ac.uk/research/lics/tutor/index.html tutor en la Red]).

== Cursos relacionados ==
=== Cursos con Isabelle/HOL ===
# Clemens Ballarin. [http://cl-informatik.uibk.ac.at/teaching/ss08/atp/introduction.php Automatic Deduction]. (Univ de Innsbruck, 2008).
# Clemens Ballarin y Gerwin Klein [http://isabelle.in.tum.de/coursematerial/IJCAR04 Introduction to the Isabelle Proof Assistant]. (en el IJCAR-2004).
# Clemens Ballarin y Tjark Weber. [http://cl-informatik.uibk.ac.at/teaching/ws06/atp/introduction.php Automated Theorem Proving in Isabelle/HOL]. (Univ. de Innsbruck, 2006-07).
# A.D. Brucker, D. Basin, J.G. Smaus y B. Wolff. [http://archiv.infsec.ethz.ch/education/permanent/csmr.html Computer-supported Modeling and Reasoning]. (ETH Zurich, 2011).
# Mads Dam. [http://www.csc.kth.se/utbildning/kth/kurser/DD2453/aform07/ Advanced formal methods]. (KTH Royal Institute of Technology, 2007).
# Jacques Fleuriot y Paul Jackson. [http://www.inf.ed.ac.uk/teaching/courses/ar/slides/ Automated reasoning]. (Univ. de Edimburgo, 2012-13).
# Thomas Genet [http://www.irisa.fr/celtique/genet/ACF Software formal analysis and design]. (Univ. de Rennes)
# Gerwin Klein. [http://www.cse.unsw.edu.au/~kleing/teaching/thprv-04 Theorem Proving - Principles, Techniques, Applications]. (NICTA, 2004).
# Gerwin Klein. [http://www.cse.unsw.edu.au/~cs4161/index.html Advanced Topics in Software Verification]. (NICTA, 2012).
# Joao Marcos. [http://www.dimap.ufrn.br/~jmarcos/courses/LC/Ementa.htm Lógica computacional: Demonstração assistida e semi-automática de teoremas].(UFRN, 2000).
# Tobias Nipkow. [https://www21.in.tum.de/teaching/semantics/WS1920/ Semantics of programming languages]. (Univ. de Munich, 2012-13).
# Tobias Nipkow [http://isabelle.in.tum.de/coursematerial/PSV2009-1 Theorem Proving with Isabelle/HOL An Intensive Course].
# Larry Paulson. [http://www.cl.cam.ac.uk/teaching/0910/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2009-10).
# Jan-Georg Smaus. [http://www.informatik.uni-freiburg.de/~ki/teaching/ws0910/csmr/lecture.html Computer-supported modeling and reasoning]. (Univ. de Feiburgo, 2009).
# Christian Sternagel [http://cl-informatik.uibk.ac.at/teaching/ss11/eve/content.php Experiments in Verification – Introduction to Isabelle/HOL]. (Univ. de Innsbruck, 2011-12).
# Tjark Weber. [http://www.cl.cam.ac.uk/teaching/1011/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2010-11).

=== Otros cursos ===
# José A. Alonso [http://www.cs.us.es/~jalonso/cursos/li-12/ Lógica informática] (Univ. de Sevilla, 2012-13).
# Yves Bertot, Pierre Casteran, Benjamin Gregoire, Pierre Letouzey y Assia Mahboubi [http://www.di.ens.fr/~zappa/teaching/coq/ecole11 Modelling and verifying algorithms in Coq: an introduction]. (INRIA Paris-Rocquencourt, 14-18 noviembre 2011).
# Pierre Castéran [http://www.labri.fr/perso/casteran/FM/Logique/index.html Logic (Master In Verification)] (Univ. de Burdeos, 2011-12).
# Nuno Gaspar [http://www-sop.inria.fr/members/Nuno.Gaspar/teaching/coq2012.php Verification with the Coq Proof Assistant] (INRIA Sophia Antipolis, 2012-13).
# Michael Genesereth [http://logic.stanford.edu/classes/cs157/2011/cs157.html Computational Logic] (Univ. de Stanford, 2011-12).
# Ian Hodkinson [http://www.doc.ic.ac.uk/~imh/teaching/140_logic/logic.html Logic] (Imperial College, Londres, 2010-11).
# Peter Lucas [http://www.cs.ru.nl/~peterl/teaching/KeR/ Knowledge Representation and Reasoning] (Radboud University # egen, 2011-12).
# Larry Paulson [http://www.cl.cam.ac.uk/Teaching/current/LogicProof/ Logic and Proof] (Univ. de Cambridge, 2011-12).
# Riccardo Pucella [http://www.ccs.neu.edu/home/riccardo/courses/csu290-sp09/index.html Logic and Computation] (Northeastern University, 2009). Curso con ACL2.

== Bibliotecas de ejemplos de verificación ==
# [http://afp.sourceforge.net Archive of Formal Proofs].
# [http://www.cs.ru.nl/~freek/100 Formalizing 100 Theorems].
# [http://toccata.lri.fr/gallery Gallery of verified programs].
# [http://www.cs.nott.ac.uk/~lad/research/challenges/ Induction Challenge Problems].
# [http://automatedreasoning.net/ Larry Wos' Notebooks].
# [http://www.cs.miami.edu/~tptp/ The TPTP Problem Library for Automated Theorem Proving].
# [http://www.macs.hw.ac.uk/vstte10/Competition.html The 1st Verified Software Competition].
# [https://sites.google.com/site/vstte2012/compet The 2nd Verified Software Competition].
# [http://verifythis.cost-ic0701.org VerifyThis (A collection of verification benchmarks].

== Artículos recientes ==
Están en orden cronológico inverso a la fecha de su reseña en [http://www.glc.us.es/~jalonso/vestigium/tag/resena Vestigium]:
# Joachim Breitner, Brian Huffman, Neil Mitchell y Christian Sternagel [http://bit.ly/19fiWAY Certified HLints with Isabelle/HOLCF-Prelude].
# Peter Lammich [http://bit.ly/ZfSQrQ Automatic data refinement].
# Assia Mahboubi [http://bit.ly/18vyjm7 The rooster and the butterflies (a machine-checked proof of the Jordan-Hölder theorem for finite groups)].
# Nathan Wetzler, Marijn J. H. Heule y Warren A. Hunt Jr. [http://bit.ly/114oyZV Mechanical verification of SAT refutations with extended resolution].
# Johannes Hölzl, Fabian Immler y Brian Huffman [http://bit.ly/13H0REu Type classes and filters for mathematical analysis in Isabelle/HOL]
# M. J. H. Heule, W. A. Hunt, Jr. y N. Wetzler [http://bit.ly/10fv8wO Verifying refutations with extended resolution].
# C. Lüth y M. Ring [http://bit.ly/10EcFWj A Web interface for Isabelle: The next generation].
# L. Liu, O. Hasan y S. Tahar [http://bit.ly/18P9CSv On the formalization of continuous-time Markov chains in HOL].
# A. Asperti y W. Ricciotti [http://bit.ly/17H2mqy Formalizing Turing machines].
# A. Lochbihler [http://bit.ly/YwuCeL Light-weight containers for Isabelle: efficient, extensible, nestable].
# L. Noschinski [http://bit.ly/10XLrRA Graph theory].
# G. Gonthier et als. [http://bit.ly/19kPEP4 A machine-checked proof of the odd order theorem].
# C. Doczkal, J.O. Kaiser y G. Smolka [http://goo.gl/LdihL A constructive theory of regular languages in Coq].
# C. Sternagel [http://goo.gl/gwcwL A formal proof of Kruskal’s tree theorem in Isabelle/HOL].
# C. Sternagel y R. Thiemann [http://goo.gl/CUF3e Formalizing Knuth-Bendix orders and Knuth-Bendix completion].
# C. Lange, C. Rowat, W. Windsteiger y M. Kerber [http://goo.gl/9JAfX Developing an auction theory toolbox].
# M. Spasić y F. Marić [http://goo.gl/6OfmQ Formalization of incremental simplex algorithm by stepwise refinement].
# J.C. Blanchette, A. Popescu y D. Traytel [http://goo.gl/Guxky Coinductive pearl: Modular first-order logic completeness].
# J. Esparza et als. [http://goo.gl/HUOl8 A fully verified executable LTL model checker].
# M. Kerber, C. Lange y C. Rowat. [http://goo.gl/RV54S ForMaRE - formal mathematical reasoning in economics].
# J. Urban. [http://goo.gl/Y7sIq AI over large formal knowledge bases: The first decade].
# S. Boldo, C. Lelay y G. Melquiond. [http://goo.gl/vvqNg Formalization of real analysis: A survey of proof assistants and libraries].
# F. Haftmann, A. Krauss, O. Kunčar y T. Nipkow [http://goo.gl/bEFYa Data refinement in Isabelle/HOL].
# A.C. Rocha y M. Ayala. [http://goo.gl/xTyvE Formalizing the confluence of orthogonal rewriting systems].
# Z. Shi et als. [http://goo.gl/zCYHj Formalization of the complex number theory in HOL4].
# F. Loulergue y V. Niculescu [http://goo.gl/kM0dI Programming and reasonning with PowerLists in Coq].
# J. Heras, F.J. Martín y V. Pascual. [http://goo.gl/KkU6s A hierarchy of mathematical structures in ACL2].
# J. Xu, X. Zhang y C. Urban [http://www.inf.kcl.ac.uk/staff/urbanc/Publications/tm.pdf Mechanising Turing Machines and Computability Theory in Isabelle/HOL]

Documentación

2022-02-08T10:42:02Z

Jalonso: /* Cursos con Isabelle/HOL */

En esta página se recogen en enlaces que sirven de documentación al curso de demostración asistida por ordenador (DAO).

== Visiones generales de la DAO ==

# J.A. Alonso. [http://goo.gl/NWk7b Razonamiento formalizado: Del sueño a la realidad de las pruebas]. ''Vestigium'', 26 de diciembre de 2012.
# J. Avigad. [http://www.andrew.cmu.edu/user/avigad/Talks/icerm.pdf Interactive theorem proving, automated reasoning, and mathematical computation]. ICERM, 14 de diciembre de 2012.
# M. Davis. [http://www.cs.nyu.edu/cs/faculty/davism/early.ps The early history of automated deduction].
# J.P. Delahaye [http://interstices.info/jcms/int_63417/du-reve-a-la-realite-des-preuves Du rêve à la réalité des preuves]. ''Interstices'', 8 de julio de 2012.
# J. Germoni [http://images.math.cnrs.fr/Coq-et-caracteres.html Coq et caractères: Preuve formelle du théorème de Feit et Thompson]. ''Images des Mathématiques'', CNRS, 23 de noviembre de 2012.
# H. Geuvers [http://www.ias.ac.in/sadhana/Pdf2009Feb/3.pdf Proof assistants: History, ideas and future]. ''Sadhana'', Vol. 34-1, pp. 3-25, février 2009.
# G. Gonthier [http://www.ams.org/notices/200811/tx081101382p.pdf The four-color theorem]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1382-1393, 2008.
# T. Hales. [http://www.ams.org/notices/200811/tx081101370p.pdf Formal proof]. ''Notices of AMS'', Vol. 55, N. 11 (2008) pp. 1370-1380.
# J. Harrison. [http://www.cl.cam.ac.uk/~jrh13/papers/ab.html A short survey of automated reasoning]. ''Lecture Notes in Computer Science'', Vol. 4545, pp. 334-349, 2007.
# J. Harrison. [http://www.ams.org/notices/200811/tx081101395p.pdf Formal proof: Theory and practice]. ''Notices of the AMS'', Vol. 55, N. 11 (2008) p.1395-1406.
# G. Kolata. [http://www.nytimes.com/library/cyber/week/1210math.html Computer math proof shows reasoning power]. ''The New York Times'', 10 de diciembre de 1996.
# D. MacKenzie [https://backspaces.net/temp/Spring2010Seminar/18%20unconventional%20essays%20on%20the%20nature%20of%20mathematics.pdf#page=147 Computers and the sociology of mathematical proof].
# G. Sutcliffe. [http://tptp.org/OverviewOfATP.html What is automated theorem proving?].
# F. Wiedijk [http://www.cs.ru.nl/~freek/100/ Formalizing the «top 100» of mathematical theorems].
# F. Wiedijk [http://www.ams.org/notices/200811/tx081101408p.pdf Formal proof - Getting started]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1408-1414, 2008.
# F. Wiedijk, [https://www.cs.ru.nl/F.Wiedijk/pubs/qed2.pdf The QED manifesto revisited]. ''Studies in Logic, Grammar and Rhetoric'', Vol. 10(23), pp. 121-133, 2007.

== Referencias sobre Isabelle/HOL ==
# B. Grechuk [https://web.cs.wpi.edu/~dd/resources_isabelle/isabelle_primer_mathematicians.pdf Isabelle primer for mathematicians].
# T. Nipkow [https://isabelle.in.tum.de/doc/prog-prove.pdf Programming and proving in Isabelle/HOL].
# T. Nipkow, M. Wenzel y L.C. Paulson [https://isabelle.in.tum.de/website-Isabelle2009/dist/Isabelle/doc/tutorial.pdf A proof assistant for higher-order logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL/document.pdf Isabelle/HOL — Higher-Order Logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/documentation.html Tutorials and manuals for Isabelle].

== Lecturas complementarias ==
=== Programación funcional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/i1m-12/temas/2012-13-IM-temas-PF.pdf Temas de "Programación funcional"]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# J.A. Alonso y M.J. Hidalgo [http://www.cs.us.es/~jalonso/publicaciones/Piensa_en_Haskell.pdf Piensa en Haskell (Ejercicios de programación funcional con Haskell)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# G. Hutton [http://goo.gl/pKqG Programming in Haskell]. Cambridge University Press, 2007.
# M. Lipovača [http://aprendehaskell.es ¡Aprende Haskell por el bien de todos!].

=== Lógica computacional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/li-12/temas/temas-LI-2012-13.pdf Temas de "Lógica informática" (2012-13)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# R. Bornat [http://bit.ly/oithic Proof and disproof in formal logic: an introduction for programmers]. Oxford University Press, 2005.
# K. Broda, S. Eisenbach, H. Khoshnevisan y S. Vickers [https://www.doc.ic.ac.uk/~susan/firstyearbook.pdf Reasoned programming]. Imperial College, 1994.
# K. Doets y J. van Eijck [https://books.google.es/books?id=YCC6lwEACAAJ&dq=The+Haskell+Road+to+Logic,+Maths+and+Programming&hl=es&sa=X&redir_esc=y The Haskell Road to Logic, Maths and Programming].
# M. Huth y M. Ryan [http://goo.gl/TMqOo Logic in computer science: Modelling and reasoning about systems]. Cambridge University Press, 2004. (Incluye el [http://www.cs.bham.ac.uk/research/lics/tutor/index.html tutor en la Red]).

== Cursos relacionados ==
=== Cursos con Isabelle/HOL ===
# Clemens Ballarin. [http://cl-informatik.uibk.ac.at/teaching/ss08/atp/introduction.php Automatic Deduction]. (Univ de Innsbruck, 2008).
# Clemens Ballarin y Gerwin Klein [http://isabelle.in.tum.de/coursematerial/IJCAR04 Introduction to the Isabelle Proof Assistant]. (en el IJCAR-2004).
# Clemens Ballarin y Tjark Weber. [http://cl-informatik.uibk.ac.at/teaching/ws06/atp/introduction.php Automated Theorem Proving in Isabelle/HOL]. (Univ. de Innsbruck, 2006-07).
# A.D. Brucker, D. Basin, J.G. Smaus y B. Wolff. [http://archiv.infsec.ethz.ch/education/permanent/csmr.html Computer-supported Modeling and Reasoning]. (ETH Zurich, 2011).
# Mads Dam. [http://www.csc.kth.se/utbildning/kth/kurser/DD2453/aform07/ Advanced formal methods]. (KTH Royal Institute of Technology, 2007).
# Jacques Fleuriot y Paul Jackson. [http://www.inf.ed.ac.uk/teaching/courses/ar/slides/ Automated reasoning]. (Univ. de Edimburgo, 2012-13).
# Thomas Genet [http://www.irisa.fr/celtique/genet/ACF Software formal analysis and design]. (Univ. de Rennes)
# Gerwin Klein. [http://www.cse.unsw.edu.au/~kleing/teaching/thprv-04 Theorem Proving - Principles, Techniques, Applications]. (NICTA, 2004).
# Gerwin Klein. [http://www.cse.unsw.edu.au/~cs4161/index.html Advanced Topics in Software Verification]. (NICTA, 2012).
# Joao Marcos. [http://www.dimap.ufrn.br/~jmarcos/courses/LC/Ementa.htm Lógica computacional: Demonstração assistida e semi-automática de teoremas].(UFRN, 2000).
# Tobias Nipkow. [https://www21.in.tum.de/teaching/semantics/WS1920/ Semantics of programming languages]. (Univ. de Munich, 2012-13).
# Tobias Nipkow [http://isabelle.in.tum.de/coursematerial/PSV2009-1 Theorem Proving with Isabelle/HOL An Intensive Course].
# Larry Paulson. [http://www.cl.cam.ac.uk/teaching/0910/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2009-10).
# Jan-Georg Smaus. [http://www.informatik.uni-freiburg.de/~ki/teaching/ws0910/csmr/lecture.html Computer-supported modeling and reasoning]. (Univ. de Feiburgo, 2009).
# Christian Sternagel [http://cl-informatik.uibk.ac.at/teaching/ss11/eve/content.php Experiments in Verification – Introduction to Isabelle/HOL]. (Univ. de Innsbruck, 2011-12).
# Tjark Weber. [http://www.cl.cam.ac.uk/teaching/1011/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2010-11).

=== Otros cursos ===
# José A. Alonso [http://www.cs.us.es/~jalonso/cursos/li/ Lógica informática] (Univ. de Sevilla, 2012-13).
# Yves Bertot, Pierre Casteran, Benjamin Gregoire, Pierre Letouzey y Assia Mahboubi [http://www.di.ens.fr/~zappa/teaching/coq/ecole11 Modelling and verifying algorithms in Coq: an introduction]. (INRIA Paris-Rocquencourt, 14-18 noviembre 2011).
# Pierre Castéran [http://www.labri.fr/perso/casteran/FM/Logique/index.html Logic (Master In Verification)] (Univ. de Burdeos, 2011-12).
# Nuno Gaspar [http://www-sop.inria.fr/members/Nuno.Gaspar/teaching/coq2012.php Verification with the Coq Proof Assistant] (INRIA Sophia Antipolis, 2012-13).
# Michael Genesereth [http://logic.stanford.edu/classes/cs157/2011/cs157.html Computational Logic] (Univ. de Stanford, 2011-12).
# Ian Hodkinson [http://www.doc.ic.ac.uk/~imh/teaching/140_logic/logic.html Logic] (Imperial College, Londres, 2010-11).
# Peter Lucas [http://www.cs.ru.nl/~peterl/teaching/KeR/ Knowledge Representation and Reasoning] (Radboud University # egen, 2011-12).
# Larry Paulson [http://www.cl.cam.ac.uk/Teaching/current/LogicProof/ Logic and Proof] (Univ. de Cambridge, 2011-12).
# Riccardo Pucella [http://www.ccs.neu.edu/home/riccardo/courses/csu290-sp09/index.html Logic and Computation] (Northeastern University, 2009). Curso con ACL2.

== Bibliotecas de ejemplos de verificación ==
# [http://afp.sourceforge.net Archive of Formal Proofs].
# [http://www.cs.ru.nl/~freek/100 Formalizing 100 Theorems].
# [http://toccata.lri.fr/gallery Gallery of verified programs].
# [http://www.cs.nott.ac.uk/~lad/research/challenges/ Induction Challenge Problems].
# [http://automatedreasoning.net/ Larry Wos' Notebooks].
# [http://www.cs.miami.edu/~tptp/ The TPTP Problem Library for Automated Theorem Proving].
# [http://www.macs.hw.ac.uk/vstte10/Competition.html The 1st Verified Software Competition].
# [https://sites.google.com/site/vstte2012/compet The 2nd Verified Software Competition].
# [http://verifythis.cost-ic0701.org VerifyThis (A collection of verification benchmarks].

== Artículos recientes ==
Están en orden cronológico inverso a la fecha de su reseña en [http://www.glc.us.es/~jalonso/vestigium/tag/resena Vestigium]:
# Joachim Breitner, Brian Huffman, Neil Mitchell y Christian Sternagel [http://bit.ly/19fiWAY Certified HLints with Isabelle/HOLCF-Prelude].
# Peter Lammich [http://bit.ly/ZfSQrQ Automatic data refinement].
# Assia Mahboubi [http://bit.ly/18vyjm7 The rooster and the butterflies (a machine-checked proof of the Jordan-Hölder theorem for finite groups)].
# Nathan Wetzler, Marijn J. H. Heule y Warren A. Hunt Jr. [http://bit.ly/114oyZV Mechanical verification of SAT refutations with extended resolution].
# Johannes Hölzl, Fabian Immler y Brian Huffman [http://bit.ly/13H0REu Type classes and filters for mathematical analysis in Isabelle/HOL]
# M. J. H. Heule, W. A. Hunt, Jr. y N. Wetzler [http://bit.ly/10fv8wO Verifying refutations with extended resolution].
# C. Lüth y M. Ring [http://bit.ly/10EcFWj A Web interface for Isabelle: The next generation].
# L. Liu, O. Hasan y S. Tahar [http://bit.ly/18P9CSv On the formalization of continuous-time Markov chains in HOL].
# A. Asperti y W. Ricciotti [http://bit.ly/17H2mqy Formalizing Turing machines].
# A. Lochbihler [http://bit.ly/YwuCeL Light-weight containers for Isabelle: efficient, extensible, nestable].
# L. Noschinski [http://bit.ly/10XLrRA Graph theory].
# G. Gonthier et als. [http://bit.ly/19kPEP4 A machine-checked proof of the odd order theorem].
# C. Doczkal, J.O. Kaiser y G. Smolka [http://goo.gl/LdihL A constructive theory of regular languages in Coq].
# C. Sternagel [http://goo.gl/gwcwL A formal proof of Kruskal’s tree theorem in Isabelle/HOL].
# C. Sternagel y R. Thiemann [http://goo.gl/CUF3e Formalizing Knuth-Bendix orders and Knuth-Bendix completion].
# C. Lange, C. Rowat, W. Windsteiger y M. Kerber [http://goo.gl/9JAfX Developing an auction theory toolbox].
# M. Spasić y F. Marić [http://goo.gl/6OfmQ Formalization of incremental simplex algorithm by stepwise refinement].
# J.C. Blanchette, A. Popescu y D. Traytel [http://goo.gl/Guxky Coinductive pearl: Modular first-order logic completeness].
# J. Esparza et als. [http://goo.gl/HUOl8 A fully verified executable LTL model checker].
# M. Kerber, C. Lange y C. Rowat. [http://goo.gl/RV54S ForMaRE - formal mathematical reasoning in economics].
# J. Urban. [http://goo.gl/Y7sIq AI over large formal knowledge bases: The first decade].
# S. Boldo, C. Lelay y G. Melquiond. [http://goo.gl/vvqNg Formalization of real analysis: A survey of proof assistants and libraries].
# F. Haftmann, A. Krauss, O. Kunčar y T. Nipkow [http://goo.gl/bEFYa Data refinement in Isabelle/HOL].
# A.C. Rocha y M. Ayala. [http://goo.gl/xTyvE Formalizing the confluence of orthogonal rewriting systems].
# Z. Shi et als. [http://goo.gl/zCYHj Formalization of the complex number theory in HOL4].
# F. Loulergue y V. Niculescu [http://goo.gl/kM0dI Programming and reasonning with PowerLists in Coq].
# J. Heras, F.J. Martín y V. Pascual. [http://goo.gl/KkU6s A hierarchy of mathematical structures in ACL2].
# J. Xu, X. Zhang y C. Urban [http://www.inf.kcl.ac.uk/staff/urbanc/Publications/tm.pdf Mechanising Turing Machines and Computability Theory in Isabelle/HOL]

Documentación

2022-02-08T10:41:08Z

Jalonso: /* Cursos con Isabelle/HOL */

En esta página se recogen en enlaces que sirven de documentación al curso de demostración asistida por ordenador (DAO).

== Visiones generales de la DAO ==

# J.A. Alonso. [http://goo.gl/NWk7b Razonamiento formalizado: Del sueño a la realidad de las pruebas]. ''Vestigium'', 26 de diciembre de 2012.
# J. Avigad. [http://www.andrew.cmu.edu/user/avigad/Talks/icerm.pdf Interactive theorem proving, automated reasoning, and mathematical computation]. ICERM, 14 de diciembre de 2012.
# M. Davis. [http://www.cs.nyu.edu/cs/faculty/davism/early.ps The early history of automated deduction].
# J.P. Delahaye [http://interstices.info/jcms/int_63417/du-reve-a-la-realite-des-preuves Du rêve à la réalité des preuves]. ''Interstices'', 8 de julio de 2012.
# J. Germoni [http://images.math.cnrs.fr/Coq-et-caracteres.html Coq et caractères: Preuve formelle du théorème de Feit et Thompson]. ''Images des Mathématiques'', CNRS, 23 de noviembre de 2012.
# H. Geuvers [http://www.ias.ac.in/sadhana/Pdf2009Feb/3.pdf Proof assistants: History, ideas and future]. ''Sadhana'', Vol. 34-1, pp. 3-25, février 2009.
# G. Gonthier [http://www.ams.org/notices/200811/tx081101382p.pdf The four-color theorem]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1382-1393, 2008.
# T. Hales. [http://www.ams.org/notices/200811/tx081101370p.pdf Formal proof]. ''Notices of AMS'', Vol. 55, N. 11 (2008) pp. 1370-1380.
# J. Harrison. [http://www.cl.cam.ac.uk/~jrh13/papers/ab.html A short survey of automated reasoning]. ''Lecture Notes in Computer Science'', Vol. 4545, pp. 334-349, 2007.
# J. Harrison. [http://www.ams.org/notices/200811/tx081101395p.pdf Formal proof: Theory and practice]. ''Notices of the AMS'', Vol. 55, N. 11 (2008) p.1395-1406.
# G. Kolata. [http://www.nytimes.com/library/cyber/week/1210math.html Computer math proof shows reasoning power]. ''The New York Times'', 10 de diciembre de 1996.
# D. MacKenzie [https://backspaces.net/temp/Spring2010Seminar/18%20unconventional%20essays%20on%20the%20nature%20of%20mathematics.pdf#page=147 Computers and the sociology of mathematical proof].
# G. Sutcliffe. [http://tptp.org/OverviewOfATP.html What is automated theorem proving?].
# F. Wiedijk [http://www.cs.ru.nl/~freek/100/ Formalizing the «top 100» of mathematical theorems].
# F. Wiedijk [http://www.ams.org/notices/200811/tx081101408p.pdf Formal proof - Getting started]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1408-1414, 2008.
# F. Wiedijk, [https://www.cs.ru.nl/F.Wiedijk/pubs/qed2.pdf The QED manifesto revisited]. ''Studies in Logic, Grammar and Rhetoric'', Vol. 10(23), pp. 121-133, 2007.

== Referencias sobre Isabelle/HOL ==
# B. Grechuk [https://web.cs.wpi.edu/~dd/resources_isabelle/isabelle_primer_mathematicians.pdf Isabelle primer for mathematicians].
# T. Nipkow [https://isabelle.in.tum.de/doc/prog-prove.pdf Programming and proving in Isabelle/HOL].
# T. Nipkow, M. Wenzel y L.C. Paulson [https://isabelle.in.tum.de/website-Isabelle2009/dist/Isabelle/doc/tutorial.pdf A proof assistant for higher-order logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL/document.pdf Isabelle/HOL — Higher-Order Logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/documentation.html Tutorials and manuals for Isabelle].

== Lecturas complementarias ==
=== Programación funcional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/i1m-12/temas/2012-13-IM-temas-PF.pdf Temas de "Programación funcional"]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# J.A. Alonso y M.J. Hidalgo [http://www.cs.us.es/~jalonso/publicaciones/Piensa_en_Haskell.pdf Piensa en Haskell (Ejercicios de programación funcional con Haskell)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# G. Hutton [http://goo.gl/pKqG Programming in Haskell]. Cambridge University Press, 2007.
# M. Lipovača [http://aprendehaskell.es ¡Aprende Haskell por el bien de todos!].

=== Lógica computacional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/li-12/temas/temas-LI-2012-13.pdf Temas de "Lógica informática" (2012-13)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# R. Bornat [http://bit.ly/oithic Proof and disproof in formal logic: an introduction for programmers]. Oxford University Press, 2005.
# K. Broda, S. Eisenbach, H. Khoshnevisan y S. Vickers [https://www.doc.ic.ac.uk/~susan/firstyearbook.pdf Reasoned programming]. Imperial College, 1994.
# K. Doets y J. van Eijck [https://books.google.es/books?id=YCC6lwEACAAJ&dq=The+Haskell+Road+to+Logic,+Maths+and+Programming&hl=es&sa=X&redir_esc=y The Haskell Road to Logic, Maths and Programming].
# M. Huth y M. Ryan [http://goo.gl/TMqOo Logic in computer science: Modelling and reasoning about systems]. Cambridge University Press, 2004. (Incluye el [http://www.cs.bham.ac.uk/research/lics/tutor/index.html tutor en la Red]).

== Cursos relacionados ==
=== Cursos con Isabelle/HOL ===
# Clemens Ballarin. [http://cl-informatik.uibk.ac.at/teaching/ss08/atp/introduction.php Automatic Deduction]. (Univ de Innsbruck, 2008).
# Clemens Ballarin y Gerwin Klein [http://isabelle.in.tum.de/coursematerial/IJCAR04 Introduction to the Isabelle Proof Assistant]. (en el IJCAR-2004).
# Clemens Ballarin y Tjark Weber. [http://cl-informatik.uibk.ac.at/teaching/ws06/atp/introduction.php Automated Theorem Proving in Isabelle/HOL]. (Univ. de Innsbruck, 2006-07).
# A.D. Brucker, D. Basin, J.G. Smaus y B. Wolff. [http://archiv.infsec.ethz.ch/education/permanent/csmr.html Computer-supported Modeling and Reasoning]. (ETH Zurich, 2011).
# Mads Dam. [http://www.csc.kth.se/utbildning/kth/kurser/DD2453/aform07/ Advanced formal methods]. (KTH Royal Institute of Technology, 2007).
# Jacques Fleuriot y Paul Jackson. [http://www.inf.ed.ac.uk/teaching/courses/ar/slides/ Automated reasoning]. (Univ. de Edimburgo, 2012-13).
# Thomas Genet [http://www.irisa.fr/celtique/genet/ACF Software formal analysis and design]. (Univ. de Rennes)
# Gerwin Klein. [http://www.cse.unsw.edu.au/~kleing/teaching/thprv-04 Theorem Proving - Principles, Techniques, Applications]. (NICTA, 2004).
# Gerwin Klein. [http://www.cse.unsw.edu.au/~cs4161/index.html Advanced Topics in Software Verification]. (NICTA, 2012).
# Joao Marcos. [http://www.dimap.ufrn.br/~jmarcos/courses/LC/Ementa.htm Lógica computacional: Demonstração assistida e semi-automática de teoremas].(UFRN, 2000).
# Tobias Nipkow. [https://www21.in.tum.de/teaching/semantics/WS1920/ Semantics of programming languages]. (Univ. de Munich, 2012-13).
# Tobias Nipkow [http://isabelle.in.tum.de/coursematerial/PSV2009-1 Theorem Proving with Isabelle/HOL An Intensive Course].
# Larry Paulson. [http://www.cl.cam.ac.uk/teaching/0910/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2009-10).
# Jeremy G. Siek. [http://www.cs.colorado.edu/~siek/7000/spring07/ Practical Theorem Proving with Isabelle/Isar]. (Univ. de Colorado, 2007).
# Jeremy G. Siek. [http://ecee.colorado.edu/~siek/ecen5013/spring11/ Theorem proving in Isabelle]. (Univ. de Colorado, 2011).
# Jan-Georg Smaus. [http://www.informatik.uni-freiburg.de/~ki/teaching/ws0910/csmr/lecture.html Computer-supported modeling and reasoning]. (Univ. de Feiburgo, 2009).
# Christian Sternagel [http://cl-informatik.uibk.ac.at/teaching/ss11/eve/content.php Experiments in Verification – Introduction to Isabelle/HOL]. (Univ. de Innsbruck, 2011-12).
# Tjark Weber. [http://www.cl.cam.ac.uk/teaching/1011/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2010-11).

=== Otros cursos ===
# José A. Alonso [http://www.cs.us.es/~jalonso/cursos/li/ Lógica informática] (Univ. de Sevilla, 2012-13).
# Yves Bertot, Pierre Casteran, Benjamin Gregoire, Pierre Letouzey y Assia Mahboubi [http://www.di.ens.fr/~zappa/teaching/coq/ecole11 Modelling and verifying algorithms in Coq: an introduction]. (INRIA Paris-Rocquencourt, 14-18 noviembre 2011).
# Pierre Castéran [http://www.labri.fr/perso/casteran/FM/Logique/index.html Logic (Master In Verification)] (Univ. de Burdeos, 2011-12).
# Nuno Gaspar [http://www-sop.inria.fr/members/Nuno.Gaspar/teaching/coq2012.php Verification with the Coq Proof Assistant] (INRIA Sophia Antipolis, 2012-13).
# Michael Genesereth [http://logic.stanford.edu/classes/cs157/2011/cs157.html Computational Logic] (Univ. de Stanford, 2011-12).
# Ian Hodkinson [http://www.doc.ic.ac.uk/~imh/teaching/140_logic/logic.html Logic] (Imperial College, Londres, 2010-11).
# Peter Lucas [http://www.cs.ru.nl/~peterl/teaching/KeR/ Knowledge Representation and Reasoning] (Radboud University # egen, 2011-12).
# Larry Paulson [http://www.cl.cam.ac.uk/Teaching/current/LogicProof/ Logic and Proof] (Univ. de Cambridge, 2011-12).
# Riccardo Pucella [http://www.ccs.neu.edu/home/riccardo/courses/csu290-sp09/index.html Logic and Computation] (Northeastern University, 2009). Curso con ACL2.

== Bibliotecas de ejemplos de verificación ==
# [http://afp.sourceforge.net Archive of Formal Proofs].
# [http://www.cs.ru.nl/~freek/100 Formalizing 100 Theorems].
# [http://toccata.lri.fr/gallery Gallery of verified programs].
# [http://www.cs.nott.ac.uk/~lad/research/challenges/ Induction Challenge Problems].
# [http://automatedreasoning.net/ Larry Wos' Notebooks].
# [http://www.cs.miami.edu/~tptp/ The TPTP Problem Library for Automated Theorem Proving].
# [http://www.macs.hw.ac.uk/vstte10/Competition.html The 1st Verified Software Competition].
# [https://sites.google.com/site/vstte2012/compet The 2nd Verified Software Competition].
# [http://verifythis.cost-ic0701.org VerifyThis (A collection of verification benchmarks].

== Artículos recientes ==
Están en orden cronológico inverso a la fecha de su reseña en [http://www.glc.us.es/~jalonso/vestigium/tag/resena Vestigium]:
# Joachim Breitner, Brian Huffman, Neil Mitchell y Christian Sternagel [http://bit.ly/19fiWAY Certified HLints with Isabelle/HOLCF-Prelude].
# Peter Lammich [http://bit.ly/ZfSQrQ Automatic data refinement].
# Assia Mahboubi [http://bit.ly/18vyjm7 The rooster and the butterflies (a machine-checked proof of the Jordan-Hölder theorem for finite groups)].
# Nathan Wetzler, Marijn J. H. Heule y Warren A. Hunt Jr. [http://bit.ly/114oyZV Mechanical verification of SAT refutations with extended resolution].
# Johannes Hölzl, Fabian Immler y Brian Huffman [http://bit.ly/13H0REu Type classes and filters for mathematical analysis in Isabelle/HOL]
# M. J. H. Heule, W. A. Hunt, Jr. y N. Wetzler [http://bit.ly/10fv8wO Verifying refutations with extended resolution].
# C. Lüth y M. Ring [http://bit.ly/10EcFWj A Web interface for Isabelle: The next generation].
# L. Liu, O. Hasan y S. Tahar [http://bit.ly/18P9CSv On the formalization of continuous-time Markov chains in HOL].
# A. Asperti y W. Ricciotti [http://bit.ly/17H2mqy Formalizing Turing machines].
# A. Lochbihler [http://bit.ly/YwuCeL Light-weight containers for Isabelle: efficient, extensible, nestable].
# L. Noschinski [http://bit.ly/10XLrRA Graph theory].
# G. Gonthier et als. [http://bit.ly/19kPEP4 A machine-checked proof of the odd order theorem].
# C. Doczkal, J.O. Kaiser y G. Smolka [http://goo.gl/LdihL A constructive theory of regular languages in Coq].
# C. Sternagel [http://goo.gl/gwcwL A formal proof of Kruskal’s tree theorem in Isabelle/HOL].
# C. Sternagel y R. Thiemann [http://goo.gl/CUF3e Formalizing Knuth-Bendix orders and Knuth-Bendix completion].
# C. Lange, C. Rowat, W. Windsteiger y M. Kerber [http://goo.gl/9JAfX Developing an auction theory toolbox].
# M. Spasić y F. Marić [http://goo.gl/6OfmQ Formalization of incremental simplex algorithm by stepwise refinement].
# J.C. Blanchette, A. Popescu y D. Traytel [http://goo.gl/Guxky Coinductive pearl: Modular first-order logic completeness].
# J. Esparza et als. [http://goo.gl/HUOl8 A fully verified executable LTL model checker].
# M. Kerber, C. Lange y C. Rowat. [http://goo.gl/RV54S ForMaRE - formal mathematical reasoning in economics].
# J. Urban. [http://goo.gl/Y7sIq AI over large formal knowledge bases: The first decade].
# S. Boldo, C. Lelay y G. Melquiond. [http://goo.gl/vvqNg Formalization of real analysis: A survey of proof assistants and libraries].
# F. Haftmann, A. Krauss, O. Kunčar y T. Nipkow [http://goo.gl/bEFYa Data refinement in Isabelle/HOL].
# A.C. Rocha y M. Ayala. [http://goo.gl/xTyvE Formalizing the confluence of orthogonal rewriting systems].
# Z. Shi et als. [http://goo.gl/zCYHj Formalization of the complex number theory in HOL4].
# F. Loulergue y V. Niculescu [http://goo.gl/kM0dI Programming and reasonning with PowerLists in Coq].
# J. Heras, F.J. Martín y V. Pascual. [http://goo.gl/KkU6s A hierarchy of mathematical structures in ACL2].
# J. Xu, X. Zhang y C. Urban [http://www.inf.kcl.ac.uk/staff/urbanc/Publications/tm.pdf Mechanising Turing Machines and Computability Theory in Isabelle/HOL]

Documentación

2022-02-08T10:39:58Z

Jalonso: /* Cursos con Isabelle/HOL */

En esta página se recogen en enlaces que sirven de documentación al curso de demostración asistida por ordenador (DAO).

== Visiones generales de la DAO ==

# J.A. Alonso. [http://goo.gl/NWk7b Razonamiento formalizado: Del sueño a la realidad de las pruebas]. ''Vestigium'', 26 de diciembre de 2012.
# J. Avigad. [http://www.andrew.cmu.edu/user/avigad/Talks/icerm.pdf Interactive theorem proving, automated reasoning, and mathematical computation]. ICERM, 14 de diciembre de 2012.
# M. Davis. [http://www.cs.nyu.edu/cs/faculty/davism/early.ps The early history of automated deduction].
# J.P. Delahaye [http://interstices.info/jcms/int_63417/du-reve-a-la-realite-des-preuves Du rêve à la réalité des preuves]. ''Interstices'', 8 de julio de 2012.
# J. Germoni [http://images.math.cnrs.fr/Coq-et-caracteres.html Coq et caractères: Preuve formelle du théorème de Feit et Thompson]. ''Images des Mathématiques'', CNRS, 23 de noviembre de 2012.
# H. Geuvers [http://www.ias.ac.in/sadhana/Pdf2009Feb/3.pdf Proof assistants: History, ideas and future]. ''Sadhana'', Vol. 34-1, pp. 3-25, février 2009.
# G. Gonthier [http://www.ams.org/notices/200811/tx081101382p.pdf The four-color theorem]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1382-1393, 2008.
# T. Hales. [http://www.ams.org/notices/200811/tx081101370p.pdf Formal proof]. ''Notices of AMS'', Vol. 55, N. 11 (2008) pp. 1370-1380.
# J. Harrison. [http://www.cl.cam.ac.uk/~jrh13/papers/ab.html A short survey of automated reasoning]. ''Lecture Notes in Computer Science'', Vol. 4545, pp. 334-349, 2007.
# J. Harrison. [http://www.ams.org/notices/200811/tx081101395p.pdf Formal proof: Theory and practice]. ''Notices of the AMS'', Vol. 55, N. 11 (2008) p.1395-1406.
# G. Kolata. [http://www.nytimes.com/library/cyber/week/1210math.html Computer math proof shows reasoning power]. ''The New York Times'', 10 de diciembre de 1996.
# D. MacKenzie [https://backspaces.net/temp/Spring2010Seminar/18%20unconventional%20essays%20on%20the%20nature%20of%20mathematics.pdf#page=147 Computers and the sociology of mathematical proof].
# G. Sutcliffe. [http://tptp.org/OverviewOfATP.html What is automated theorem proving?].
# F. Wiedijk [http://www.cs.ru.nl/~freek/100/ Formalizing the «top 100» of mathematical theorems].
# F. Wiedijk [http://www.ams.org/notices/200811/tx081101408p.pdf Formal proof - Getting started]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1408-1414, 2008.
# F. Wiedijk, [https://www.cs.ru.nl/F.Wiedijk/pubs/qed2.pdf The QED manifesto revisited]. ''Studies in Logic, Grammar and Rhetoric'', Vol. 10(23), pp. 121-133, 2007.

== Referencias sobre Isabelle/HOL ==
# B. Grechuk [https://web.cs.wpi.edu/~dd/resources_isabelle/isabelle_primer_mathematicians.pdf Isabelle primer for mathematicians].
# T. Nipkow [https://isabelle.in.tum.de/doc/prog-prove.pdf Programming and proving in Isabelle/HOL].
# T. Nipkow, M. Wenzel y L.C. Paulson [https://isabelle.in.tum.de/website-Isabelle2009/dist/Isabelle/doc/tutorial.pdf A proof assistant for higher-order logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL/document.pdf Isabelle/HOL — Higher-Order Logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/documentation.html Tutorials and manuals for Isabelle].

== Lecturas complementarias ==
=== Programación funcional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/i1m-12/temas/2012-13-IM-temas-PF.pdf Temas de "Programación funcional"]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# J.A. Alonso y M.J. Hidalgo [http://www.cs.us.es/~jalonso/publicaciones/Piensa_en_Haskell.pdf Piensa en Haskell (Ejercicios de programación funcional con Haskell)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# G. Hutton [http://goo.gl/pKqG Programming in Haskell]. Cambridge University Press, 2007.
# M. Lipovača [http://aprendehaskell.es ¡Aprende Haskell por el bien de todos!].

=== Lógica computacional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/li-12/temas/temas-LI-2012-13.pdf Temas de "Lógica informática" (2012-13)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# R. Bornat [http://bit.ly/oithic Proof and disproof in formal logic: an introduction for programmers]. Oxford University Press, 2005.
# K. Broda, S. Eisenbach, H. Khoshnevisan y S. Vickers [https://www.doc.ic.ac.uk/~susan/firstyearbook.pdf Reasoned programming]. Imperial College, 1994.
# K. Doets y J. van Eijck [https://books.google.es/books?id=YCC6lwEACAAJ&dq=The+Haskell+Road+to+Logic,+Maths+and+Programming&hl=es&sa=X&redir_esc=y The Haskell Road to Logic, Maths and Programming].
# M. Huth y M. Ryan [http://goo.gl/TMqOo Logic in computer science: Modelling and reasoning about systems]. Cambridge University Press, 2004. (Incluye el [http://www.cs.bham.ac.uk/research/lics/tutor/index.html tutor en la Red]).

== Cursos relacionados ==
=== Cursos con Isabelle/HOL ===
# Clemens Ballarin. [http://cl-informatik.uibk.ac.at/teaching/ss08/atp/introduction.php Automatic Deduction]. (Univ de Innsbruck, 2008).
# Clemens Ballarin y Gerwin Klein [http://isabelle.in.tum.de/coursematerial/IJCAR04 Introduction to the Isabelle Proof Assistant]. (en el IJCAR-2004).
# Clemens Ballarin y Tjark Weber. [http://cl-informatik.uibk.ac.at/teaching/ws06/atp/introduction.php Automated Theorem Proving in Isabelle/HOL]. (Univ. de Innsbruck, 2006-07).
# A.D. Brucker, D. Basin, J.G. Smaus y B. Wolff. [http://archiv.infsec.ethz.ch/education/permanent/csmr.html Computer-supported Modeling and Reasoning]. (ETH Zurich, 2011).
# Mads Dam. [http://www.csc.kth.se/utbildning/kth/kurser/DD2453/aform07/ Advanced formal methods]. (KTH Royal Institute of Technology, 2007).
# Jacques Fleuriot y Paul Jackson. [http://www.inf.ed.ac.uk/teaching/courses/ar/slides/ Automated reasoning]. (Univ. de Edimburgo, 2012-13).
# Thomas Genet [http://www.irisa.fr/celtique/genet/ACF Software formal analysis and design]. (Univ. de Rennes)
# Gerwin Klein. [http://www.cse.unsw.edu.au/~kleing/teaching/thprv-04 Theorem Proving - Principles, Techniques, Applications]. (NICTA, 2004).
# Gerwin Klein. [http://www.cse.unsw.edu.au/~cs4161/index.html Advanced Topics in Software Verification]. (NICTA, 2012).
# Joao Marcos. [http://www.dimap.ufrn.br/~jmarcos/courses/LC/Ementa.htm Lógica computacional: Demonstração assistida e semi-automática de teoremas].(UFRN, 2000).
# Tobias Nipkow. [https://www21.in.tum.de/teaching/semantics/WS1920/ Semantics of programming languages]. (Univ. de Munich, 2012-13).
# Tobias Nipkow [http://isabelle.in.tum.de/coursematerial/PSV2009-1 Theorem Proving with Isabelle/HOL An Intensive Course].
# Larry Paulson. [http://www.cl.cam.ac.uk/teaching/0910/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2009-10).
# Arnd Poetzsch-Heffter. [https://softech.informatik.uni-kl.de/Homepage/SVHOL10 Specification and Verification with Higher-Order Logic].
# Jeremy G. Siek. [http://www.cs.colorado.edu/~siek/7000/spring07/ Practical Theorem Proving with Isabelle/Isar]. (Univ. de Colorado, 2007).
# Jeremy G. Siek. [http://ecee.colorado.edu/~siek/ecen5013/spring11/ Theorem proving in Isabelle]. (Univ. de Colorado, 2011).
# Jan-Georg Smaus. [http://www.informatik.uni-freiburg.de/~ki/teaching/ws0910/csmr/lecture.html Computer-supported modeling and reasoning]. (Univ. de Feiburgo, 2009).
# Christian Sternagel [http://cl-informatik.uibk.ac.at/teaching/ss11/eve/content.php Experiments in Verification – Introduction to Isabelle/HOL]. (Univ. de Innsbruck, 2011-12).
# Tjark Weber. [http://www.cl.cam.ac.uk/teaching/1011/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2010-11).

=== Otros cursos ===
# José A. Alonso [http://www.cs.us.es/~jalonso/cursos/li/ Lógica informática] (Univ. de Sevilla, 2012-13).
# Yves Bertot, Pierre Casteran, Benjamin Gregoire, Pierre Letouzey y Assia Mahboubi [http://www.di.ens.fr/~zappa/teaching/coq/ecole11 Modelling and verifying algorithms in Coq: an introduction]. (INRIA Paris-Rocquencourt, 14-18 noviembre 2011).
# Pierre Castéran [http://www.labri.fr/perso/casteran/FM/Logique/index.html Logic (Master In Verification)] (Univ. de Burdeos, 2011-12).
# Nuno Gaspar [http://www-sop.inria.fr/members/Nuno.Gaspar/teaching/coq2012.php Verification with the Coq Proof Assistant] (INRIA Sophia Antipolis, 2012-13).
# Michael Genesereth [http://logic.stanford.edu/classes/cs157/2011/cs157.html Computational Logic] (Univ. de Stanford, 2011-12).
# Ian Hodkinson [http://www.doc.ic.ac.uk/~imh/teaching/140_logic/logic.html Logic] (Imperial College, Londres, 2010-11).
# Peter Lucas [http://www.cs.ru.nl/~peterl/teaching/KeR/ Knowledge Representation and Reasoning] (Radboud University # egen, 2011-12).
# Larry Paulson [http://www.cl.cam.ac.uk/Teaching/current/LogicProof/ Logic and Proof] (Univ. de Cambridge, 2011-12).
# Riccardo Pucella [http://www.ccs.neu.edu/home/riccardo/courses/csu290-sp09/index.html Logic and Computation] (Northeastern University, 2009). Curso con ACL2.

== Bibliotecas de ejemplos de verificación ==
# [http://afp.sourceforge.net Archive of Formal Proofs].
# [http://www.cs.ru.nl/~freek/100 Formalizing 100 Theorems].
# [http://toccata.lri.fr/gallery Gallery of verified programs].
# [http://www.cs.nott.ac.uk/~lad/research/challenges/ Induction Challenge Problems].
# [http://automatedreasoning.net/ Larry Wos' Notebooks].
# [http://www.cs.miami.edu/~tptp/ The TPTP Problem Library for Automated Theorem Proving].
# [http://www.macs.hw.ac.uk/vstte10/Competition.html The 1st Verified Software Competition].
# [https://sites.google.com/site/vstte2012/compet The 2nd Verified Software Competition].
# [http://verifythis.cost-ic0701.org VerifyThis (A collection of verification benchmarks].

== Artículos recientes ==
Están en orden cronológico inverso a la fecha de su reseña en [http://www.glc.us.es/~jalonso/vestigium/tag/resena Vestigium]:
# Joachim Breitner, Brian Huffman, Neil Mitchell y Christian Sternagel [http://bit.ly/19fiWAY Certified HLints with Isabelle/HOLCF-Prelude].
# Peter Lammich [http://bit.ly/ZfSQrQ Automatic data refinement].
# Assia Mahboubi [http://bit.ly/18vyjm7 The rooster and the butterflies (a machine-checked proof of the Jordan-Hölder theorem for finite groups)].
# Nathan Wetzler, Marijn J. H. Heule y Warren A. Hunt Jr. [http://bit.ly/114oyZV Mechanical verification of SAT refutations with extended resolution].
# Johannes Hölzl, Fabian Immler y Brian Huffman [http://bit.ly/13H0REu Type classes and filters for mathematical analysis in Isabelle/HOL]
# M. J. H. Heule, W. A. Hunt, Jr. y N. Wetzler [http://bit.ly/10fv8wO Verifying refutations with extended resolution].
# C. Lüth y M. Ring [http://bit.ly/10EcFWj A Web interface for Isabelle: The next generation].
# L. Liu, O. Hasan y S. Tahar [http://bit.ly/18P9CSv On the formalization of continuous-time Markov chains in HOL].
# A. Asperti y W. Ricciotti [http://bit.ly/17H2mqy Formalizing Turing machines].
# A. Lochbihler [http://bit.ly/YwuCeL Light-weight containers for Isabelle: efficient, extensible, nestable].
# L. Noschinski [http://bit.ly/10XLrRA Graph theory].
# G. Gonthier et als. [http://bit.ly/19kPEP4 A machine-checked proof of the odd order theorem].
# C. Doczkal, J.O. Kaiser y G. Smolka [http://goo.gl/LdihL A constructive theory of regular languages in Coq].
# C. Sternagel [http://goo.gl/gwcwL A formal proof of Kruskal’s tree theorem in Isabelle/HOL].
# C. Sternagel y R. Thiemann [http://goo.gl/CUF3e Formalizing Knuth-Bendix orders and Knuth-Bendix completion].
# C. Lange, C. Rowat, W. Windsteiger y M. Kerber [http://goo.gl/9JAfX Developing an auction theory toolbox].
# M. Spasić y F. Marić [http://goo.gl/6OfmQ Formalization of incremental simplex algorithm by stepwise refinement].
# J.C. Blanchette, A. Popescu y D. Traytel [http://goo.gl/Guxky Coinductive pearl: Modular first-order logic completeness].
# J. Esparza et als. [http://goo.gl/HUOl8 A fully verified executable LTL model checker].
# M. Kerber, C. Lange y C. Rowat. [http://goo.gl/RV54S ForMaRE - formal mathematical reasoning in economics].
# J. Urban. [http://goo.gl/Y7sIq AI over large formal knowledge bases: The first decade].
# S. Boldo, C. Lelay y G. Melquiond. [http://goo.gl/vvqNg Formalization of real analysis: A survey of proof assistants and libraries].
# F. Haftmann, A. Krauss, O. Kunčar y T. Nipkow [http://goo.gl/bEFYa Data refinement in Isabelle/HOL].
# A.C. Rocha y M. Ayala. [http://goo.gl/xTyvE Formalizing the confluence of orthogonal rewriting systems].
# Z. Shi et als. [http://goo.gl/zCYHj Formalization of the complex number theory in HOL4].
# F. Loulergue y V. Niculescu [http://goo.gl/kM0dI Programming and reasonning with PowerLists in Coq].
# J. Heras, F.J. Martín y V. Pascual. [http://goo.gl/KkU6s A hierarchy of mathematical structures in ACL2].
# J. Xu, X. Zhang y C. Urban [http://www.inf.kcl.ac.uk/staff/urbanc/Publications/tm.pdf Mechanising Turing Machines and Computability Theory in Isabelle/HOL]

Documentación

2022-02-08T10:39:32Z

Jalonso: /* Cursos con Isabelle/HOL */

En esta página se recogen en enlaces que sirven de documentación al curso de demostración asistida por ordenador (DAO).

== Visiones generales de la DAO ==

# J.A. Alonso. [http://goo.gl/NWk7b Razonamiento formalizado: Del sueño a la realidad de las pruebas]. ''Vestigium'', 26 de diciembre de 2012.
# J. Avigad. [http://www.andrew.cmu.edu/user/avigad/Talks/icerm.pdf Interactive theorem proving, automated reasoning, and mathematical computation]. ICERM, 14 de diciembre de 2012.
# M. Davis. [http://www.cs.nyu.edu/cs/faculty/davism/early.ps The early history of automated deduction].
# J.P. Delahaye [http://interstices.info/jcms/int_63417/du-reve-a-la-realite-des-preuves Du rêve à la réalité des preuves]. ''Interstices'', 8 de julio de 2012.
# J. Germoni [http://images.math.cnrs.fr/Coq-et-caracteres.html Coq et caractères: Preuve formelle du théorème de Feit et Thompson]. ''Images des Mathématiques'', CNRS, 23 de noviembre de 2012.
# H. Geuvers [http://www.ias.ac.in/sadhana/Pdf2009Feb/3.pdf Proof assistants: History, ideas and future]. ''Sadhana'', Vol. 34-1, pp. 3-25, février 2009.
# G. Gonthier [http://www.ams.org/notices/200811/tx081101382p.pdf The four-color theorem]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1382-1393, 2008.
# T. Hales. [http://www.ams.org/notices/200811/tx081101370p.pdf Formal proof]. ''Notices of AMS'', Vol. 55, N. 11 (2008) pp. 1370-1380.
# J. Harrison. [http://www.cl.cam.ac.uk/~jrh13/papers/ab.html A short survey of automated reasoning]. ''Lecture Notes in Computer Science'', Vol. 4545, pp. 334-349, 2007.
# J. Harrison. [http://www.ams.org/notices/200811/tx081101395p.pdf Formal proof: Theory and practice]. ''Notices of the AMS'', Vol. 55, N. 11 (2008) p.1395-1406.
# G. Kolata. [http://www.nytimes.com/library/cyber/week/1210math.html Computer math proof shows reasoning power]. ''The New York Times'', 10 de diciembre de 1996.
# D. MacKenzie [https://backspaces.net/temp/Spring2010Seminar/18%20unconventional%20essays%20on%20the%20nature%20of%20mathematics.pdf#page=147 Computers and the sociology of mathematical proof].
# G. Sutcliffe. [http://tptp.org/OverviewOfATP.html What is automated theorem proving?].
# F. Wiedijk [http://www.cs.ru.nl/~freek/100/ Formalizing the «top 100» of mathematical theorems].
# F. Wiedijk [http://www.ams.org/notices/200811/tx081101408p.pdf Formal proof - Getting started]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1408-1414, 2008.
# F. Wiedijk, [https://www.cs.ru.nl/F.Wiedijk/pubs/qed2.pdf The QED manifesto revisited]. ''Studies in Logic, Grammar and Rhetoric'', Vol. 10(23), pp. 121-133, 2007.

== Referencias sobre Isabelle/HOL ==
# B. Grechuk [https://web.cs.wpi.edu/~dd/resources_isabelle/isabelle_primer_mathematicians.pdf Isabelle primer for mathematicians].
# T. Nipkow [https://isabelle.in.tum.de/doc/prog-prove.pdf Programming and proving in Isabelle/HOL].
# T. Nipkow, M. Wenzel y L.C. Paulson [https://isabelle.in.tum.de/website-Isabelle2009/dist/Isabelle/doc/tutorial.pdf A proof assistant for higher-order logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL/document.pdf Isabelle/HOL — Higher-Order Logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/documentation.html Tutorials and manuals for Isabelle].

== Lecturas complementarias ==
=== Programación funcional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/i1m-12/temas/2012-13-IM-temas-PF.pdf Temas de "Programación funcional"]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# J.A. Alonso y M.J. Hidalgo [http://www.cs.us.es/~jalonso/publicaciones/Piensa_en_Haskell.pdf Piensa en Haskell (Ejercicios de programación funcional con Haskell)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# G. Hutton [http://goo.gl/pKqG Programming in Haskell]. Cambridge University Press, 2007.
# M. Lipovača [http://aprendehaskell.es ¡Aprende Haskell por el bien de todos!].

=== Lógica computacional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/li-12/temas/temas-LI-2012-13.pdf Temas de "Lógica informática" (2012-13)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# R. Bornat [http://bit.ly/oithic Proof and disproof in formal logic: an introduction for programmers]. Oxford University Press, 2005.
# K. Broda, S. Eisenbach, H. Khoshnevisan y S. Vickers [https://www.doc.ic.ac.uk/~susan/firstyearbook.pdf Reasoned programming]. Imperial College, 1994.
# K. Doets y J. van Eijck [https://books.google.es/books?id=YCC6lwEACAAJ&dq=The+Haskell+Road+to+Logic,+Maths+and+Programming&hl=es&sa=X&redir_esc=y The Haskell Road to Logic, Maths and Programming].
# M. Huth y M. Ryan [http://goo.gl/TMqOo Logic in computer science: Modelling and reasoning about systems]. Cambridge University Press, 2004. (Incluye el [http://www.cs.bham.ac.uk/research/lics/tutor/index.html tutor en la Red]).

== Cursos relacionados ==
=== Cursos con Isabelle/HOL ===
# Clemens Ballarin. [http://cl-informatik.uibk.ac.at/teaching/ss08/atp/introduction.php Automatic Deduction]. (Univ de Innsbruck, 2008).
# Clemens Ballarin y Gerwin Klein [http://isabelle.in.tum.de/coursematerial/IJCAR04 Introduction to the Isabelle Proof Assistant]. (en el IJCAR-2004).
# Clemens Ballarin y Tjark Weber. [http://cl-informatik.uibk.ac.at/teaching/ws06/atp/introduction.php Automated Theorem Proving in Isabelle/HOL]. (Univ. de Innsbruck, 2006-07).
# A.D. Brucker, D. Basin, J.G. Smaus y B. Wolff. [http://archiv.infsec.ethz.ch/education/permanent/csmr.html Computer-supported Modeling and Reasoning]. (ETH Zurich, 2011).
# Mads Dam. [http://www.csc.kth.se/utbildning/kth/kurser/DD2453/aform07/ Advanced formal methods]. (KTH Royal Institute of Technology, 2007).
# Jacques Fleuriot y Paul Jackson. [http://www.inf.ed.ac.uk/teaching/courses/ar/slides/ Automated reasoning]. (Univ. de Edimburgo, 2012-13).
# Thomas Genet [http://www.irisa.fr/celtique/genet/ACF Software formal analysis and design]. (Univ. de Rennes)
# Gerwin Klein. [http://www.cse.unsw.edu.au/~kleing/teaching/thprv-04 Theorem Proving - Principles, Techniques, Applications]. (NICTA, 2004).
# Gerwin Klein. [http://www.cse.unsw.edu.au/~cs4161/index.html Advanced Topics in Software Verification]. (NICTA, 2012).
# Joao Marcos. [http://www.dimap.ufrn.br/~jmarcos/courses/LC/Ementa.htm Lógica computacional: Demonstração assistida e semi-automática de teoremas].(UFRN, 2000).
# Tobias Nipkow. [https://www21.in.tum.de/teaching/semantics/WS1920/Semantics of programming languages]. (Univ. de Munich, 2012-13).
# Tobias Nipkow [http://isabelle.in.tum.de/coursematerial/PSV2009-1 Theorem Proving with Isabelle/HOL An Intensive Course].
# Larry Paulson. [http://www.cl.cam.ac.uk/teaching/0910/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2009-10).
# Arnd Poetzsch-Heffter. [https://softech.informatik.uni-kl.de/Homepage/SVHOL10 Specification and Verification with Higher-Order Logic].
# Jeremy G. Siek. [http://www.cs.colorado.edu/~siek/7000/spring07/ Practical Theorem Proving with Isabelle/Isar]. (Univ. de Colorado, 2007).
# Jeremy G. Siek. [http://ecee.colorado.edu/~siek/ecen5013/spring11/ Theorem proving in Isabelle]. (Univ. de Colorado, 2011).
# Jan-Georg Smaus. [http://www.informatik.uni-freiburg.de/~ki/teaching/ws0910/csmr/lecture.html Computer-supported modeling and reasoning]. (Univ. de Feiburgo, 2009).
# Christian Sternagel [http://cl-informatik.uibk.ac.at/teaching/ss11/eve/content.php Experiments in Verification – Introduction to Isabelle/HOL]. (Univ. de Innsbruck, 2011-12).
# Tjark Weber. [http://www.cl.cam.ac.uk/teaching/1011/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2010-11).

=== Otros cursos ===
# José A. Alonso [http://www.cs.us.es/~jalonso/cursos/li/ Lógica informática] (Univ. de Sevilla, 2012-13).
# Yves Bertot, Pierre Casteran, Benjamin Gregoire, Pierre Letouzey y Assia Mahboubi [http://www.di.ens.fr/~zappa/teaching/coq/ecole11 Modelling and verifying algorithms in Coq: an introduction]. (INRIA Paris-Rocquencourt, 14-18 noviembre 2011).
# Pierre Castéran [http://www.labri.fr/perso/casteran/FM/Logique/index.html Logic (Master In Verification)] (Univ. de Burdeos, 2011-12).
# Nuno Gaspar [http://www-sop.inria.fr/members/Nuno.Gaspar/teaching/coq2012.php Verification with the Coq Proof Assistant] (INRIA Sophia Antipolis, 2012-13).
# Michael Genesereth [http://logic.stanford.edu/classes/cs157/2011/cs157.html Computational Logic] (Univ. de Stanford, 2011-12).
# Ian Hodkinson [http://www.doc.ic.ac.uk/~imh/teaching/140_logic/logic.html Logic] (Imperial College, Londres, 2010-11).
# Peter Lucas [http://www.cs.ru.nl/~peterl/teaching/KeR/ Knowledge Representation and Reasoning] (Radboud University # egen, 2011-12).
# Larry Paulson [http://www.cl.cam.ac.uk/Teaching/current/LogicProof/ Logic and Proof] (Univ. de Cambridge, 2011-12).
# Riccardo Pucella [http://www.ccs.neu.edu/home/riccardo/courses/csu290-sp09/index.html Logic and Computation] (Northeastern University, 2009). Curso con ACL2.

== Bibliotecas de ejemplos de verificación ==
# [http://afp.sourceforge.net Archive of Formal Proofs].
# [http://www.cs.ru.nl/~freek/100 Formalizing 100 Theorems].
# [http://toccata.lri.fr/gallery Gallery of verified programs].
# [http://www.cs.nott.ac.uk/~lad/research/challenges/ Induction Challenge Problems].
# [http://automatedreasoning.net/ Larry Wos' Notebooks].
# [http://www.cs.miami.edu/~tptp/ The TPTP Problem Library for Automated Theorem Proving].
# [http://www.macs.hw.ac.uk/vstte10/Competition.html The 1st Verified Software Competition].
# [https://sites.google.com/site/vstte2012/compet The 2nd Verified Software Competition].
# [http://verifythis.cost-ic0701.org VerifyThis (A collection of verification benchmarks].

== Artículos recientes ==
Están en orden cronológico inverso a la fecha de su reseña en [http://www.glc.us.es/~jalonso/vestigium/tag/resena Vestigium]:
# Joachim Breitner, Brian Huffman, Neil Mitchell y Christian Sternagel [http://bit.ly/19fiWAY Certified HLints with Isabelle/HOLCF-Prelude].
# Peter Lammich [http://bit.ly/ZfSQrQ Automatic data refinement].
# Assia Mahboubi [http://bit.ly/18vyjm7 The rooster and the butterflies (a machine-checked proof of the Jordan-Hölder theorem for finite groups)].
# Nathan Wetzler, Marijn J. H. Heule y Warren A. Hunt Jr. [http://bit.ly/114oyZV Mechanical verification of SAT refutations with extended resolution].
# Johannes Hölzl, Fabian Immler y Brian Huffman [http://bit.ly/13H0REu Type classes and filters for mathematical analysis in Isabelle/HOL]
# M. J. H. Heule, W. A. Hunt, Jr. y N. Wetzler [http://bit.ly/10fv8wO Verifying refutations with extended resolution].
# C. Lüth y M. Ring [http://bit.ly/10EcFWj A Web interface for Isabelle: The next generation].
# L. Liu, O. Hasan y S. Tahar [http://bit.ly/18P9CSv On the formalization of continuous-time Markov chains in HOL].
# A. Asperti y W. Ricciotti [http://bit.ly/17H2mqy Formalizing Turing machines].
# A. Lochbihler [http://bit.ly/YwuCeL Light-weight containers for Isabelle: efficient, extensible, nestable].
# L. Noschinski [http://bit.ly/10XLrRA Graph theory].
# G. Gonthier et als. [http://bit.ly/19kPEP4 A machine-checked proof of the odd order theorem].
# C. Doczkal, J.O. Kaiser y G. Smolka [http://goo.gl/LdihL A constructive theory of regular languages in Coq].
# C. Sternagel [http://goo.gl/gwcwL A formal proof of Kruskal’s tree theorem in Isabelle/HOL].
# C. Sternagel y R. Thiemann [http://goo.gl/CUF3e Formalizing Knuth-Bendix orders and Knuth-Bendix completion].
# C. Lange, C. Rowat, W. Windsteiger y M. Kerber [http://goo.gl/9JAfX Developing an auction theory toolbox].
# M. Spasić y F. Marić [http://goo.gl/6OfmQ Formalization of incremental simplex algorithm by stepwise refinement].
# J.C. Blanchette, A. Popescu y D. Traytel [http://goo.gl/Guxky Coinductive pearl: Modular first-order logic completeness].
# J. Esparza et als. [http://goo.gl/HUOl8 A fully verified executable LTL model checker].
# M. Kerber, C. Lange y C. Rowat. [http://goo.gl/RV54S ForMaRE - formal mathematical reasoning in economics].
# J. Urban. [http://goo.gl/Y7sIq AI over large formal knowledge bases: The first decade].
# S. Boldo, C. Lelay y G. Melquiond. [http://goo.gl/vvqNg Formalization of real analysis: A survey of proof assistants and libraries].
# F. Haftmann, A. Krauss, O. Kunčar y T. Nipkow [http://goo.gl/bEFYa Data refinement in Isabelle/HOL].
# A.C. Rocha y M. Ayala. [http://goo.gl/xTyvE Formalizing the confluence of orthogonal rewriting systems].
# Z. Shi et als. [http://goo.gl/zCYHj Formalization of the complex number theory in HOL4].
# F. Loulergue y V. Niculescu [http://goo.gl/kM0dI Programming and reasonning with PowerLists in Coq].
# J. Heras, F.J. Martín y V. Pascual. [http://goo.gl/KkU6s A hierarchy of mathematical structures in ACL2].
# J. Xu, X. Zhang y C. Urban [http://www.inf.kcl.ac.uk/staff/urbanc/Publications/tm.pdf Mechanising Turing Machines and Computability Theory in Isabelle/HOL]

Documentación

2022-02-08T10:37:23Z

Jalonso: /* Cursos con Isabelle/HOL */

En esta página se recogen en enlaces que sirven de documentación al curso de demostración asistida por ordenador (DAO).

== Visiones generales de la DAO ==

# J.A. Alonso. [http://goo.gl/NWk7b Razonamiento formalizado: Del sueño a la realidad de las pruebas]. ''Vestigium'', 26 de diciembre de 2012.
# J. Avigad. [http://www.andrew.cmu.edu/user/avigad/Talks/icerm.pdf Interactive theorem proving, automated reasoning, and mathematical computation]. ICERM, 14 de diciembre de 2012.
# M. Davis. [http://www.cs.nyu.edu/cs/faculty/davism/early.ps The early history of automated deduction].
# J.P. Delahaye [http://interstices.info/jcms/int_63417/du-reve-a-la-realite-des-preuves Du rêve à la réalité des preuves]. ''Interstices'', 8 de julio de 2012.
# J. Germoni [http://images.math.cnrs.fr/Coq-et-caracteres.html Coq et caractères: Preuve formelle du théorème de Feit et Thompson]. ''Images des Mathématiques'', CNRS, 23 de noviembre de 2012.
# H. Geuvers [http://www.ias.ac.in/sadhana/Pdf2009Feb/3.pdf Proof assistants: History, ideas and future]. ''Sadhana'', Vol. 34-1, pp. 3-25, février 2009.
# G. Gonthier [http://www.ams.org/notices/200811/tx081101382p.pdf The four-color theorem]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1382-1393, 2008.
# T. Hales. [http://www.ams.org/notices/200811/tx081101370p.pdf Formal proof]. ''Notices of AMS'', Vol. 55, N. 11 (2008) pp. 1370-1380.
# J. Harrison. [http://www.cl.cam.ac.uk/~jrh13/papers/ab.html A short survey of automated reasoning]. ''Lecture Notes in Computer Science'', Vol. 4545, pp. 334-349, 2007.
# J. Harrison. [http://www.ams.org/notices/200811/tx081101395p.pdf Formal proof: Theory and practice]. ''Notices of the AMS'', Vol. 55, N. 11 (2008) p.1395-1406.
# G. Kolata. [http://www.nytimes.com/library/cyber/week/1210math.html Computer math proof shows reasoning power]. ''The New York Times'', 10 de diciembre de 1996.
# D. MacKenzie [https://backspaces.net/temp/Spring2010Seminar/18%20unconventional%20essays%20on%20the%20nature%20of%20mathematics.pdf#page=147 Computers and the sociology of mathematical proof].
# G. Sutcliffe. [http://tptp.org/OverviewOfATP.html What is automated theorem proving?].
# F. Wiedijk [http://www.cs.ru.nl/~freek/100/ Formalizing the «top 100» of mathematical theorems].
# F. Wiedijk [http://www.ams.org/notices/200811/tx081101408p.pdf Formal proof - Getting started]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1408-1414, 2008.
# F. Wiedijk, [https://www.cs.ru.nl/F.Wiedijk/pubs/qed2.pdf The QED manifesto revisited]. ''Studies in Logic, Grammar and Rhetoric'', Vol. 10(23), pp. 121-133, 2007.

== Referencias sobre Isabelle/HOL ==
# B. Grechuk [https://web.cs.wpi.edu/~dd/resources_isabelle/isabelle_primer_mathematicians.pdf Isabelle primer for mathematicians].
# T. Nipkow [https://isabelle.in.tum.de/doc/prog-prove.pdf Programming and proving in Isabelle/HOL].
# T. Nipkow, M. Wenzel y L.C. Paulson [https://isabelle.in.tum.de/website-Isabelle2009/dist/Isabelle/doc/tutorial.pdf A proof assistant for higher-order logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL/document.pdf Isabelle/HOL — Higher-Order Logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/documentation.html Tutorials and manuals for Isabelle].

== Lecturas complementarias ==
=== Programación funcional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/i1m-12/temas/2012-13-IM-temas-PF.pdf Temas de "Programación funcional"]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# J.A. Alonso y M.J. Hidalgo [http://www.cs.us.es/~jalonso/publicaciones/Piensa_en_Haskell.pdf Piensa en Haskell (Ejercicios de programación funcional con Haskell)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# G. Hutton [http://goo.gl/pKqG Programming in Haskell]. Cambridge University Press, 2007.
# M. Lipovača [http://aprendehaskell.es ¡Aprende Haskell por el bien de todos!].

=== Lógica computacional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/li-12/temas/temas-LI-2012-13.pdf Temas de "Lógica informática" (2012-13)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# R. Bornat [http://bit.ly/oithic Proof and disproof in formal logic: an introduction for programmers]. Oxford University Press, 2005.
# K. Broda, S. Eisenbach, H. Khoshnevisan y S. Vickers [https://www.doc.ic.ac.uk/~susan/firstyearbook.pdf Reasoned programming]. Imperial College, 1994.
# K. Doets y J. van Eijck [https://books.google.es/books?id=YCC6lwEACAAJ&dq=The+Haskell+Road+to+Logic,+Maths+and+Programming&hl=es&sa=X&redir_esc=y The Haskell Road to Logic, Maths and Programming].
# M. Huth y M. Ryan [http://goo.gl/TMqOo Logic in computer science: Modelling and reasoning about systems]. Cambridge University Press, 2004. (Incluye el [http://www.cs.bham.ac.uk/research/lics/tutor/index.html tutor en la Red]).

== Cursos relacionados ==
=== Cursos con Isabelle/HOL ===
# Clemens Ballarin. [http://cl-informatik.uibk.ac.at/teaching/ss08/atp/introduction.php Automatic Deduction]. (Univ de Innsbruck, 2008).
# Clemens Ballarin y Gerwin Klein [http://isabelle.in.tum.de/coursematerial/IJCAR04 Introduction to the Isabelle Proof Assistant]. (en el IJCAR-2004).
# Clemens Ballarin y Tjark Weber. [http://cl-informatik.uibk.ac.at/teaching/ws06/atp/introduction.php Automated Theorem Proving in Isabelle/HOL]. (Univ. de Innsbruck, 2006-07).
# A.D. Brucker, D. Basin, J.G. Smaus y B. Wolff. [http://archiv.infsec.ethz.ch/education/permanent/csmr.html Computer-supported Modeling and Reasoning]. (ETH Zurich, 2011).
# Mads Dam. [http://www.csc.kth.se/utbildning/kth/kurser/DD2453/aform07/ Advanced formal methods]. (KTH Royal Institute of Technology, 2007).
# Jacques Fleuriot y Paul Jackson. [http://www.inf.ed.ac.uk/teaching/courses/ar/slides/ Automated reasoning]. (Univ. de Edimburgo, 2012-13).
# Thomas Genet [http://www.irisa.fr/celtique/genet/ACF Software formal analysis and design]. (Univ. de Rennes)
# Gerwin Klein. [http://www.cse.unsw.edu.au/~kleing/teaching/thprv-04 Theorem Proving - Principles, Techniques, Applications]. (NICTA, 2004).
# Gerwin Klein. [http://www.cse.unsw.edu.au/~cs4161/index.html Advanced Topics in Software Verification]. (NICTA, 2012).
# Joao Marcos. [http://www.dimap.ufrn.br/~jmarcos/courses/LC/Ementa.htm Lógica computacional: Demonstração assistida e semi-automática de teoremas].(UFRN, 2000).
# Tobias Nipkow. [http://www4.informatik.tu-muenchen.de/~nipkow/semantics/ Semantics of programming languages]. (Univ. de Munich, 2012-13).
# Tobias Nipkow [http://isabelle.in.tum.de/coursematerial/PSV2009-1 Theorem Proving with Isabelle/HOL An Intensive Course].
# Larry Paulson. [http://www.cl.cam.ac.uk/teaching/0910/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2009-10).
# Arnd Poetzsch-Heffter. [https://softech.informatik.uni-kl.de/Homepage/SVHOL10 Specification and Verification with Higher-Order Logic].
# Jeremy G. Siek. [http://www.cs.colorado.edu/~siek/7000/spring07/ Practical Theorem Proving with Isabelle/Isar]. (Univ. de Colorado, 2007).
# Jeremy G. Siek. [http://ecee.colorado.edu/~siek/ecen5013/spring11/ Theorem proving in Isabelle]. (Univ. de Colorado, 2011).
# Jan-Georg Smaus. [http://www.informatik.uni-freiburg.de/~ki/teaching/ws0910/csmr/lecture.html Computer-supported modeling and reasoning]. (Univ. de Feiburgo, 2009).
# Christian Sternagel [http://cl-informatik.uibk.ac.at/teaching/ss11/eve/content.php Experiments in Verification – Introduction to Isabelle/HOL]. (Univ. de Innsbruck, 2011-12).
# Tjark Weber. [http://www.cl.cam.ac.uk/teaching/1011/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2010-11).

=== Otros cursos ===
# José A. Alonso [http://www.cs.us.es/~jalonso/cursos/li/ Lógica informática] (Univ. de Sevilla, 2012-13).
# Yves Bertot, Pierre Casteran, Benjamin Gregoire, Pierre Letouzey y Assia Mahboubi [http://www.di.ens.fr/~zappa/teaching/coq/ecole11 Modelling and verifying algorithms in Coq: an introduction]. (INRIA Paris-Rocquencourt, 14-18 noviembre 2011).
# Pierre Castéran [http://www.labri.fr/perso/casteran/FM/Logique/index.html Logic (Master In Verification)] (Univ. de Burdeos, 2011-12).
# Nuno Gaspar [http://www-sop.inria.fr/members/Nuno.Gaspar/teaching/coq2012.php Verification with the Coq Proof Assistant] (INRIA Sophia Antipolis, 2012-13).
# Michael Genesereth [http://logic.stanford.edu/classes/cs157/2011/cs157.html Computational Logic] (Univ. de Stanford, 2011-12).
# Ian Hodkinson [http://www.doc.ic.ac.uk/~imh/teaching/140_logic/logic.html Logic] (Imperial College, Londres, 2010-11).
# Peter Lucas [http://www.cs.ru.nl/~peterl/teaching/KeR/ Knowledge Representation and Reasoning] (Radboud University # egen, 2011-12).
# Larry Paulson [http://www.cl.cam.ac.uk/Teaching/current/LogicProof/ Logic and Proof] (Univ. de Cambridge, 2011-12).
# Riccardo Pucella [http://www.ccs.neu.edu/home/riccardo/courses/csu290-sp09/index.html Logic and Computation] (Northeastern University, 2009). Curso con ACL2.

== Bibliotecas de ejemplos de verificación ==
# [http://afp.sourceforge.net Archive of Formal Proofs].
# [http://www.cs.ru.nl/~freek/100 Formalizing 100 Theorems].
# [http://toccata.lri.fr/gallery Gallery of verified programs].
# [http://www.cs.nott.ac.uk/~lad/research/challenges/ Induction Challenge Problems].
# [http://automatedreasoning.net/ Larry Wos' Notebooks].
# [http://www.cs.miami.edu/~tptp/ The TPTP Problem Library for Automated Theorem Proving].
# [http://www.macs.hw.ac.uk/vstte10/Competition.html The 1st Verified Software Competition].
# [https://sites.google.com/site/vstte2012/compet The 2nd Verified Software Competition].
# [http://verifythis.cost-ic0701.org VerifyThis (A collection of verification benchmarks].

== Artículos recientes ==
Están en orden cronológico inverso a la fecha de su reseña en [http://www.glc.us.es/~jalonso/vestigium/tag/resena Vestigium]:
# Joachim Breitner, Brian Huffman, Neil Mitchell y Christian Sternagel [http://bit.ly/19fiWAY Certified HLints with Isabelle/HOLCF-Prelude].
# Peter Lammich [http://bit.ly/ZfSQrQ Automatic data refinement].
# Assia Mahboubi [http://bit.ly/18vyjm7 The rooster and the butterflies (a machine-checked proof of the Jordan-Hölder theorem for finite groups)].
# Nathan Wetzler, Marijn J. H. Heule y Warren A. Hunt Jr. [http://bit.ly/114oyZV Mechanical verification of SAT refutations with extended resolution].
# Johannes Hölzl, Fabian Immler y Brian Huffman [http://bit.ly/13H0REu Type classes and filters for mathematical analysis in Isabelle/HOL]
# M. J. H. Heule, W. A. Hunt, Jr. y N. Wetzler [http://bit.ly/10fv8wO Verifying refutations with extended resolution].
# C. Lüth y M. Ring [http://bit.ly/10EcFWj A Web interface for Isabelle: The next generation].
# L. Liu, O. Hasan y S. Tahar [http://bit.ly/18P9CSv On the formalization of continuous-time Markov chains in HOL].
# A. Asperti y W. Ricciotti [http://bit.ly/17H2mqy Formalizing Turing machines].
# A. Lochbihler [http://bit.ly/YwuCeL Light-weight containers for Isabelle: efficient, extensible, nestable].
# L. Noschinski [http://bit.ly/10XLrRA Graph theory].
# G. Gonthier et als. [http://bit.ly/19kPEP4 A machine-checked proof of the odd order theorem].
# C. Doczkal, J.O. Kaiser y G. Smolka [http://goo.gl/LdihL A constructive theory of regular languages in Coq].
# C. Sternagel [http://goo.gl/gwcwL A formal proof of Kruskal’s tree theorem in Isabelle/HOL].
# C. Sternagel y R. Thiemann [http://goo.gl/CUF3e Formalizing Knuth-Bendix orders and Knuth-Bendix completion].
# C. Lange, C. Rowat, W. Windsteiger y M. Kerber [http://goo.gl/9JAfX Developing an auction theory toolbox].
# M. Spasić y F. Marić [http://goo.gl/6OfmQ Formalization of incremental simplex algorithm by stepwise refinement].
# J.C. Blanchette, A. Popescu y D. Traytel [http://goo.gl/Guxky Coinductive pearl: Modular first-order logic completeness].
# J. Esparza et als. [http://goo.gl/HUOl8 A fully verified executable LTL model checker].
# M. Kerber, C. Lange y C. Rowat. [http://goo.gl/RV54S ForMaRE - formal mathematical reasoning in economics].
# J. Urban. [http://goo.gl/Y7sIq AI over large formal knowledge bases: The first decade].
# S. Boldo, C. Lelay y G. Melquiond. [http://goo.gl/vvqNg Formalization of real analysis: A survey of proof assistants and libraries].
# F. Haftmann, A. Krauss, O. Kunčar y T. Nipkow [http://goo.gl/bEFYa Data refinement in Isabelle/HOL].
# A.C. Rocha y M. Ayala. [http://goo.gl/xTyvE Formalizing the confluence of orthogonal rewriting systems].
# Z. Shi et als. [http://goo.gl/zCYHj Formalization of the complex number theory in HOL4].
# F. Loulergue y V. Niculescu [http://goo.gl/kM0dI Programming and reasonning with PowerLists in Coq].
# J. Heras, F.J. Martín y V. Pascual. [http://goo.gl/KkU6s A hierarchy of mathematical structures in ACL2].
# J. Xu, X. Zhang y C. Urban [http://www.inf.kcl.ac.uk/staff/urbanc/Publications/tm.pdf Mechanising Turing Machines and Computability Theory in Isabelle/HOL]

Documentación

2022-02-08T10:36:02Z

Jalonso: /* Cursos con Isabelle/HOL */

En esta página se recogen en enlaces que sirven de documentación al curso de demostración asistida por ordenador (DAO).

== Visiones generales de la DAO ==

# J.A. Alonso. [http://goo.gl/NWk7b Razonamiento formalizado: Del sueño a la realidad de las pruebas]. ''Vestigium'', 26 de diciembre de 2012.
# J. Avigad. [http://www.andrew.cmu.edu/user/avigad/Talks/icerm.pdf Interactive theorem proving, automated reasoning, and mathematical computation]. ICERM, 14 de diciembre de 2012.
# M. Davis. [http://www.cs.nyu.edu/cs/faculty/davism/early.ps The early history of automated deduction].
# J.P. Delahaye [http://interstices.info/jcms/int_63417/du-reve-a-la-realite-des-preuves Du rêve à la réalité des preuves]. ''Interstices'', 8 de julio de 2012.
# J. Germoni [http://images.math.cnrs.fr/Coq-et-caracteres.html Coq et caractères: Preuve formelle du théorème de Feit et Thompson]. ''Images des Mathématiques'', CNRS, 23 de noviembre de 2012.
# H. Geuvers [http://www.ias.ac.in/sadhana/Pdf2009Feb/3.pdf Proof assistants: History, ideas and future]. ''Sadhana'', Vol. 34-1, pp. 3-25, février 2009.
# G. Gonthier [http://www.ams.org/notices/200811/tx081101382p.pdf The four-color theorem]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1382-1393, 2008.
# T. Hales. [http://www.ams.org/notices/200811/tx081101370p.pdf Formal proof]. ''Notices of AMS'', Vol. 55, N. 11 (2008) pp. 1370-1380.
# J. Harrison. [http://www.cl.cam.ac.uk/~jrh13/papers/ab.html A short survey of automated reasoning]. ''Lecture Notes in Computer Science'', Vol. 4545, pp. 334-349, 2007.
# J. Harrison. [http://www.ams.org/notices/200811/tx081101395p.pdf Formal proof: Theory and practice]. ''Notices of the AMS'', Vol. 55, N. 11 (2008) p.1395-1406.
# G. Kolata. [http://www.nytimes.com/library/cyber/week/1210math.html Computer math proof shows reasoning power]. ''The New York Times'', 10 de diciembre de 1996.
# D. MacKenzie [https://backspaces.net/temp/Spring2010Seminar/18%20unconventional%20essays%20on%20the%20nature%20of%20mathematics.pdf#page=147 Computers and the sociology of mathematical proof].
# G. Sutcliffe. [http://tptp.org/OverviewOfATP.html What is automated theorem proving?].
# F. Wiedijk [http://www.cs.ru.nl/~freek/100/ Formalizing the «top 100» of mathematical theorems].
# F. Wiedijk [http://www.ams.org/notices/200811/tx081101408p.pdf Formal proof - Getting started]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1408-1414, 2008.
# F. Wiedijk, [https://www.cs.ru.nl/F.Wiedijk/pubs/qed2.pdf The QED manifesto revisited]. ''Studies in Logic, Grammar and Rhetoric'', Vol. 10(23), pp. 121-133, 2007.

== Referencias sobre Isabelle/HOL ==
# B. Grechuk [https://web.cs.wpi.edu/~dd/resources_isabelle/isabelle_primer_mathematicians.pdf Isabelle primer for mathematicians].
# T. Nipkow [https://isabelle.in.tum.de/doc/prog-prove.pdf Programming and proving in Isabelle/HOL].
# T. Nipkow, M. Wenzel y L.C. Paulson [https://isabelle.in.tum.de/website-Isabelle2009/dist/Isabelle/doc/tutorial.pdf A proof assistant for higher-order logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL/document.pdf Isabelle/HOL — Higher-Order Logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/documentation.html Tutorials and manuals for Isabelle].

== Lecturas complementarias ==
=== Programación funcional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/i1m-12/temas/2012-13-IM-temas-PF.pdf Temas de "Programación funcional"]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# J.A. Alonso y M.J. Hidalgo [http://www.cs.us.es/~jalonso/publicaciones/Piensa_en_Haskell.pdf Piensa en Haskell (Ejercicios de programación funcional con Haskell)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# G. Hutton [http://goo.gl/pKqG Programming in Haskell]. Cambridge University Press, 2007.
# M. Lipovača [http://aprendehaskell.es ¡Aprende Haskell por el bien de todos!].

=== Lógica computacional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/li-12/temas/temas-LI-2012-13.pdf Temas de "Lógica informática" (2012-13)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# R. Bornat [http://bit.ly/oithic Proof and disproof in formal logic: an introduction for programmers]. Oxford University Press, 2005.
# K. Broda, S. Eisenbach, H. Khoshnevisan y S. Vickers [https://www.doc.ic.ac.uk/~susan/firstyearbook.pdf Reasoned programming]. Imperial College, 1994.
# K. Doets y J. van Eijck [https://books.google.es/books?id=YCC6lwEACAAJ&dq=The+Haskell+Road+to+Logic,+Maths+and+Programming&hl=es&sa=X&redir_esc=y The Haskell Road to Logic, Maths and Programming].
# M. Huth y M. Ryan [http://goo.gl/TMqOo Logic in computer science: Modelling and reasoning about systems]. Cambridge University Press, 2004. (Incluye el [http://www.cs.bham.ac.uk/research/lics/tutor/index.html tutor en la Red]).

== Cursos relacionados ==
=== Cursos con Isabelle/HOL ===
# Clemens Ballarin. [http://cl-informatik.uibk.ac.at/teaching/ss08/atp/introduction.php Automatic Deduction]. (Univ de Innsbruck, 2008).
# Clemens Ballarin. [http://www4.in.tum.de/~ballarin/belgrade08-tut/ Introduction to the Isabelle Proof Assistant]. (Belgrado, 2008).
# Clemens Ballarin y Gerwin Klein [http://isabelle.in.tum.de/coursematerial/IJCAR04 Introduction to the Isabelle Proof Assistant]. (en el IJCAR-2004).
# Clemens Ballarin y Tjark Weber. [http://cl-informatik.uibk.ac.at/teaching/ws06/atp/introduction.php Automated Theorem Proving in Isabelle/HOL]. (Univ. de Innsbruck, 2006-07).
# A.D. Brucker, D. Basin, J.G. Smaus y B. Wolff. [http://archiv.infsec.ethz.ch/education/permanent/csmr.html Computer-supported Modeling and Reasoning]. (ETH Zurich, 2011).
# Mads Dam. [http://www.csc.kth.se/utbildning/kth/kurser/DD2453/aform07/ Advanced formal methods]. (KTH Royal Institute of Technology, 2007).
# Jacques Fleuriot y Paul Jackson. [http://www.inf.ed.ac.uk/teaching/courses/ar/slides/ Automated reasoning]. (Univ. de Edimburgo, 2012-13).
# Thomas Genet [http://www.irisa.fr/celtique/genet/ACF Software formal analysis and design]. (Univ. de Rennes)
# Gerwin Klein. [http://www.cse.unsw.edu.au/~kleing/teaching/thprv-04 Theorem Proving - Principles, Techniques, Applications]. (NICTA, 2004).
# Gerwin Klein. [http://www.cse.unsw.edu.au/~cs4161/index.html Advanced Topics in Software Verification]. (NICTA, 2012).
# Joao Marcos. [http://www.dimap.ufrn.br/~jmarcos/courses/LC/Ementa.htm Lógica computacional: Demonstração assistida e semi-automática de teoremas].(UFRN, 2000).
# Tobias Nipkow. [http://www4.informatik.tu-muenchen.de/~nipkow/semantics/ Semantics of programming languages]. (Univ. de Munich, 2012-13).
# Tobias Nipkow [http://isabelle.in.tum.de/coursematerial/PSV2009-1 Theorem Proving with Isabelle/HOL An Intensive Course].
# Larry Paulson. [http://www.cl.cam.ac.uk/teaching/0910/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2009-10).
# Arnd Poetzsch-Heffter. [https://softech.informatik.uni-kl.de/Homepage/SVHOL10 Specification and Verification with Higher-Order Logic].
# Jeremy G. Siek. [http://www.cs.colorado.edu/~siek/7000/spring07/ Practical Theorem Proving with Isabelle/Isar]. (Univ. de Colorado, 2007).
# Jeremy G. Siek. [http://ecee.colorado.edu/~siek/ecen5013/spring11/ Theorem proving in Isabelle]. (Univ. de Colorado, 2011).
# Jan-Georg Smaus. [http://www.informatik.uni-freiburg.de/~ki/teaching/ws0910/csmr/lecture.html Computer-supported modeling and reasoning]. (Univ. de Feiburgo, 2009).
# Christian Sternagel [http://cl-informatik.uibk.ac.at/teaching/ss11/eve/content.php Experiments in Verification – Introduction to Isabelle/HOL]. (Univ. de Innsbruck, 2011-12).
# Tjark Weber. [http://www.cl.cam.ac.uk/teaching/1011/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2010-11).

=== Otros cursos ===
# José A. Alonso [http://www.cs.us.es/~jalonso/cursos/li/ Lógica informática] (Univ. de Sevilla, 2012-13).
# Yves Bertot, Pierre Casteran, Benjamin Gregoire, Pierre Letouzey y Assia Mahboubi [http://www.di.ens.fr/~zappa/teaching/coq/ecole11 Modelling and verifying algorithms in Coq: an introduction]. (INRIA Paris-Rocquencourt, 14-18 noviembre 2011).
# Pierre Castéran [http://www.labri.fr/perso/casteran/FM/Logique/index.html Logic (Master In Verification)] (Univ. de Burdeos, 2011-12).
# Nuno Gaspar [http://www-sop.inria.fr/members/Nuno.Gaspar/teaching/coq2012.php Verification with the Coq Proof Assistant] (INRIA Sophia Antipolis, 2012-13).
# Michael Genesereth [http://logic.stanford.edu/classes/cs157/2011/cs157.html Computational Logic] (Univ. de Stanford, 2011-12).
# Ian Hodkinson [http://www.doc.ic.ac.uk/~imh/teaching/140_logic/logic.html Logic] (Imperial College, Londres, 2010-11).
# Peter Lucas [http://www.cs.ru.nl/~peterl/teaching/KeR/ Knowledge Representation and Reasoning] (Radboud University # egen, 2011-12).
# Larry Paulson [http://www.cl.cam.ac.uk/Teaching/current/LogicProof/ Logic and Proof] (Univ. de Cambridge, 2011-12).
# Riccardo Pucella [http://www.ccs.neu.edu/home/riccardo/courses/csu290-sp09/index.html Logic and Computation] (Northeastern University, 2009). Curso con ACL2.

== Bibliotecas de ejemplos de verificación ==
# [http://afp.sourceforge.net Archive of Formal Proofs].
# [http://www.cs.ru.nl/~freek/100 Formalizing 100 Theorems].
# [http://toccata.lri.fr/gallery Gallery of verified programs].
# [http://www.cs.nott.ac.uk/~lad/research/challenges/ Induction Challenge Problems].
# [http://automatedreasoning.net/ Larry Wos' Notebooks].
# [http://www.cs.miami.edu/~tptp/ The TPTP Problem Library for Automated Theorem Proving].
# [http://www.macs.hw.ac.uk/vstte10/Competition.html The 1st Verified Software Competition].
# [https://sites.google.com/site/vstte2012/compet The 2nd Verified Software Competition].
# [http://verifythis.cost-ic0701.org VerifyThis (A collection of verification benchmarks].

== Artículos recientes ==
Están en orden cronológico inverso a la fecha de su reseña en [http://www.glc.us.es/~jalonso/vestigium/tag/resena Vestigium]:
# Joachim Breitner, Brian Huffman, Neil Mitchell y Christian Sternagel [http://bit.ly/19fiWAY Certified HLints with Isabelle/HOLCF-Prelude].
# Peter Lammich [http://bit.ly/ZfSQrQ Automatic data refinement].
# Assia Mahboubi [http://bit.ly/18vyjm7 The rooster and the butterflies (a machine-checked proof of the Jordan-Hölder theorem for finite groups)].
# Nathan Wetzler, Marijn J. H. Heule y Warren A. Hunt Jr. [http://bit.ly/114oyZV Mechanical verification of SAT refutations with extended resolution].
# Johannes Hölzl, Fabian Immler y Brian Huffman [http://bit.ly/13H0REu Type classes and filters for mathematical analysis in Isabelle/HOL]
# M. J. H. Heule, W. A. Hunt, Jr. y N. Wetzler [http://bit.ly/10fv8wO Verifying refutations with extended resolution].
# C. Lüth y M. Ring [http://bit.ly/10EcFWj A Web interface for Isabelle: The next generation].
# L. Liu, O. Hasan y S. Tahar [http://bit.ly/18P9CSv On the formalization of continuous-time Markov chains in HOL].
# A. Asperti y W. Ricciotti [http://bit.ly/17H2mqy Formalizing Turing machines].
# A. Lochbihler [http://bit.ly/YwuCeL Light-weight containers for Isabelle: efficient, extensible, nestable].
# L. Noschinski [http://bit.ly/10XLrRA Graph theory].
# G. Gonthier et als. [http://bit.ly/19kPEP4 A machine-checked proof of the odd order theorem].
# C. Doczkal, J.O. Kaiser y G. Smolka [http://goo.gl/LdihL A constructive theory of regular languages in Coq].
# C. Sternagel [http://goo.gl/gwcwL A formal proof of Kruskal’s tree theorem in Isabelle/HOL].
# C. Sternagel y R. Thiemann [http://goo.gl/CUF3e Formalizing Knuth-Bendix orders and Knuth-Bendix completion].
# C. Lange, C. Rowat, W. Windsteiger y M. Kerber [http://goo.gl/9JAfX Developing an auction theory toolbox].
# M. Spasić y F. Marić [http://goo.gl/6OfmQ Formalization of incremental simplex algorithm by stepwise refinement].
# J.C. Blanchette, A. Popescu y D. Traytel [http://goo.gl/Guxky Coinductive pearl: Modular first-order logic completeness].
# J. Esparza et als. [http://goo.gl/HUOl8 A fully verified executable LTL model checker].
# M. Kerber, C. Lange y C. Rowat. [http://goo.gl/RV54S ForMaRE - formal mathematical reasoning in economics].
# J. Urban. [http://goo.gl/Y7sIq AI over large formal knowledge bases: The first decade].
# S. Boldo, C. Lelay y G. Melquiond. [http://goo.gl/vvqNg Formalization of real analysis: A survey of proof assistants and libraries].
# F. Haftmann, A. Krauss, O. Kunčar y T. Nipkow [http://goo.gl/bEFYa Data refinement in Isabelle/HOL].
# A.C. Rocha y M. Ayala. [http://goo.gl/xTyvE Formalizing the confluence of orthogonal rewriting systems].
# Z. Shi et als. [http://goo.gl/zCYHj Formalization of the complex number theory in HOL4].
# F. Loulergue y V. Niculescu [http://goo.gl/kM0dI Programming and reasonning with PowerLists in Coq].
# J. Heras, F.J. Martín y V. Pascual. [http://goo.gl/KkU6s A hierarchy of mathematical structures in ACL2].
# J. Xu, X. Zhang y C. Urban [http://www.inf.kcl.ac.uk/staff/urbanc/Publications/tm.pdf Mechanising Turing Machines and Computability Theory in Isabelle/HOL]

Documentación

2022-02-08T10:35:19Z

Jalonso: /* Lógica computacional */

En esta página se recogen en enlaces que sirven de documentación al curso de demostración asistida por ordenador (DAO).

== Visiones generales de la DAO ==

# J.A. Alonso. [http://goo.gl/NWk7b Razonamiento formalizado: Del sueño a la realidad de las pruebas]. ''Vestigium'', 26 de diciembre de 2012.
# J. Avigad. [http://www.andrew.cmu.edu/user/avigad/Talks/icerm.pdf Interactive theorem proving, automated reasoning, and mathematical computation]. ICERM, 14 de diciembre de 2012.
# M. Davis. [http://www.cs.nyu.edu/cs/faculty/davism/early.ps The early history of automated deduction].
# J.P. Delahaye [http://interstices.info/jcms/int_63417/du-reve-a-la-realite-des-preuves Du rêve à la réalité des preuves]. ''Interstices'', 8 de julio de 2012.
# J. Germoni [http://images.math.cnrs.fr/Coq-et-caracteres.html Coq et caractères: Preuve formelle du théorème de Feit et Thompson]. ''Images des Mathématiques'', CNRS, 23 de noviembre de 2012.
# H. Geuvers [http://www.ias.ac.in/sadhana/Pdf2009Feb/3.pdf Proof assistants: History, ideas and future]. ''Sadhana'', Vol. 34-1, pp. 3-25, février 2009.
# G. Gonthier [http://www.ams.org/notices/200811/tx081101382p.pdf The four-color theorem]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1382-1393, 2008.
# T. Hales. [http://www.ams.org/notices/200811/tx081101370p.pdf Formal proof]. ''Notices of AMS'', Vol. 55, N. 11 (2008) pp. 1370-1380.
# J. Harrison. [http://www.cl.cam.ac.uk/~jrh13/papers/ab.html A short survey of automated reasoning]. ''Lecture Notes in Computer Science'', Vol. 4545, pp. 334-349, 2007.
# J. Harrison. [http://www.ams.org/notices/200811/tx081101395p.pdf Formal proof: Theory and practice]. ''Notices of the AMS'', Vol. 55, N. 11 (2008) p.1395-1406.
# G. Kolata. [http://www.nytimes.com/library/cyber/week/1210math.html Computer math proof shows reasoning power]. ''The New York Times'', 10 de diciembre de 1996.
# D. MacKenzie [https://backspaces.net/temp/Spring2010Seminar/18%20unconventional%20essays%20on%20the%20nature%20of%20mathematics.pdf#page=147 Computers and the sociology of mathematical proof].
# G. Sutcliffe. [http://tptp.org/OverviewOfATP.html What is automated theorem proving?].
# F. Wiedijk [http://www.cs.ru.nl/~freek/100/ Formalizing the «top 100» of mathematical theorems].
# F. Wiedijk [http://www.ams.org/notices/200811/tx081101408p.pdf Formal proof - Getting started]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1408-1414, 2008.
# F. Wiedijk, [https://www.cs.ru.nl/F.Wiedijk/pubs/qed2.pdf The QED manifesto revisited]. ''Studies in Logic, Grammar and Rhetoric'', Vol. 10(23), pp. 121-133, 2007.

== Referencias sobre Isabelle/HOL ==
# B. Grechuk [https://web.cs.wpi.edu/~dd/resources_isabelle/isabelle_primer_mathematicians.pdf Isabelle primer for mathematicians].
# T. Nipkow [https://isabelle.in.tum.de/doc/prog-prove.pdf Programming and proving in Isabelle/HOL].
# T. Nipkow, M. Wenzel y L.C. Paulson [https://isabelle.in.tum.de/website-Isabelle2009/dist/Isabelle/doc/tutorial.pdf A proof assistant for higher-order logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL/document.pdf Isabelle/HOL — Higher-Order Logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/documentation.html Tutorials and manuals for Isabelle].

== Lecturas complementarias ==
=== Programación funcional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/i1m-12/temas/2012-13-IM-temas-PF.pdf Temas de "Programación funcional"]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# J.A. Alonso y M.J. Hidalgo [http://www.cs.us.es/~jalonso/publicaciones/Piensa_en_Haskell.pdf Piensa en Haskell (Ejercicios de programación funcional con Haskell)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# G. Hutton [http://goo.gl/pKqG Programming in Haskell]. Cambridge University Press, 2007.
# M. Lipovača [http://aprendehaskell.es ¡Aprende Haskell por el bien de todos!].

=== Lógica computacional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/li-12/temas/temas-LI-2012-13.pdf Temas de "Lógica informática" (2012-13)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# R. Bornat [http://bit.ly/oithic Proof and disproof in formal logic: an introduction for programmers]. Oxford University Press, 2005.
# K. Broda, S. Eisenbach, H. Khoshnevisan y S. Vickers [https://www.doc.ic.ac.uk/~susan/firstyearbook.pdf Reasoned programming]. Imperial College, 1994.
# K. Doets y J. van Eijck [https://books.google.es/books?id=YCC6lwEACAAJ&dq=The+Haskell+Road+to+Logic,+Maths+and+Programming&hl=es&sa=X&redir_esc=y The Haskell Road to Logic, Maths and Programming].
# M. Huth y M. Ryan [http://goo.gl/TMqOo Logic in computer science: Modelling and reasoning about systems]. Cambridge University Press, 2004. (Incluye el [http://www.cs.bham.ac.uk/research/lics/tutor/index.html tutor en la Red]).

== Cursos relacionados ==
=== Cursos con Isabelle/HOL ===
# Jeremy Avigad. [http://www.phil.cmu.edu/~avigad/formal/ Logic and Formal Verification]. (Carnegie Mellon, 2009).
# Clemens Ballarin. [http://cl-informatik.uibk.ac.at/teaching/ss08/atp/introduction.php Automatic Deduction]. (Univ de Innsbruck, 2008).
# Clemens Ballarin. [http://www4.in.tum.de/~ballarin/belgrade08-tut/ Introduction to the Isabelle Proof Assistant]. (Belgrado, 2008).
# Clemens Ballarin y Gerwin Klein [http://isabelle.in.tum.de/coursematerial/IJCAR04 Introduction to the Isabelle Proof Assistant]. (en el IJCAR-2004).
# Clemens Ballarin y Tjark Weber. [http://cl-informatik.uibk.ac.at/teaching/ws06/atp/introduction.php Automated Theorem Proving in Isabelle/HOL]. (Univ. de Innsbruck, 2006-07).
# A.D. Brucker, D. Basin, J.G. Smaus y B. Wolff. [http://archiv.infsec.ethz.ch/education/permanent/csmr.html Computer-supported Modeling and Reasoning]. (ETH Zurich, 2011).
# Mads Dam. [http://www.csc.kth.se/utbildning/kth/kurser/DD2453/aform07/ Advanced formal methods]. (KTH Royal Institute of Technology, 2007).
# Jacques Fleuriot y Paul Jackson. [http://www.inf.ed.ac.uk/teaching/courses/ar/slides/ Automated reasoning]. (Univ. de Edimburgo, 2012-13).
# Thomas Genet [http://www.irisa.fr/celtique/genet/ACF Software formal analysis and design]. (Univ. de Rennes)
# Gerwin Klein. [http://www.cse.unsw.edu.au/~kleing/teaching/thprv-04 Theorem Proving - Principles, Techniques, Applications]. (NICTA, 2004).
# Gerwin Klein. [http://www.cse.unsw.edu.au/~cs4161/index.html Advanced Topics in Software Verification]. (NICTA, 2012).
# Joao Marcos. [http://www.dimap.ufrn.br/~jmarcos/courses/LC/Ementa.htm Lógica computacional: Demonstração assistida e semi-automática de teoremas].(UFRN, 2000).
# Tobias Nipkow. [http://www4.informatik.tu-muenchen.de/~nipkow/semantics/ Semantics of programming languages]. (Univ. de Munich, 2012-13).
# Tobias Nipkow [http://isabelle.in.tum.de/coursematerial/PSV2009-1 Theorem Proving with Isabelle/HOL An Intensive Course].
# Larry Paulson. [http://www.cl.cam.ac.uk/teaching/0910/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2009-10).
# Arnd Poetzsch-Heffter. [https://softech.informatik.uni-kl.de/Homepage/SVHOL10 Specification and Verification with Higher-Order Logic].
# Jeremy G. Siek. [http://www.cs.colorado.edu/~siek/7000/spring07/ Practical Theorem Proving with Isabelle/Isar]. (Univ. de Colorado, 2007).
# Jeremy G. Siek. [http://ecee.colorado.edu/~siek/ecen5013/spring11/ Theorem proving in Isabelle]. (Univ. de Colorado, 2011).
# Jan-Georg Smaus. [http://www.informatik.uni-freiburg.de/~ki/teaching/ws0910/csmr/lecture.html Computer-supported modeling and reasoning]. (Univ. de Feiburgo, 2009).
# Christian Sternagel [http://cl-informatik.uibk.ac.at/teaching/ss11/eve/content.php Experiments in Verification – Introduction to Isabelle/HOL]. (Univ. de Innsbruck, 2011-12).
# Tjark Weber. [http://www.cl.cam.ac.uk/teaching/1011/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2010-11).

=== Otros cursos ===
# José A. Alonso [http://www.cs.us.es/~jalonso/cursos/li/ Lógica informática] (Univ. de Sevilla, 2012-13).
# Yves Bertot, Pierre Casteran, Benjamin Gregoire, Pierre Letouzey y Assia Mahboubi [http://www.di.ens.fr/~zappa/teaching/coq/ecole11 Modelling and verifying algorithms in Coq: an introduction]. (INRIA Paris-Rocquencourt, 14-18 noviembre 2011).
# Pierre Castéran [http://www.labri.fr/perso/casteran/FM/Logique/index.html Logic (Master In Verification)] (Univ. de Burdeos, 2011-12).
# Nuno Gaspar [http://www-sop.inria.fr/members/Nuno.Gaspar/teaching/coq2012.php Verification with the Coq Proof Assistant] (INRIA Sophia Antipolis, 2012-13).
# Michael Genesereth [http://logic.stanford.edu/classes/cs157/2011/cs157.html Computational Logic] (Univ. de Stanford, 2011-12).
# Ian Hodkinson [http://www.doc.ic.ac.uk/~imh/teaching/140_logic/logic.html Logic] (Imperial College, Londres, 2010-11).
# Peter Lucas [http://www.cs.ru.nl/~peterl/teaching/KeR/ Knowledge Representation and Reasoning] (Radboud University # egen, 2011-12).
# Larry Paulson [http://www.cl.cam.ac.uk/Teaching/current/LogicProof/ Logic and Proof] (Univ. de Cambridge, 2011-12).
# Riccardo Pucella [http://www.ccs.neu.edu/home/riccardo/courses/csu290-sp09/index.html Logic and Computation] (Northeastern University, 2009). Curso con ACL2.

== Bibliotecas de ejemplos de verificación ==
# [http://afp.sourceforge.net Archive of Formal Proofs].
# [http://www.cs.ru.nl/~freek/100 Formalizing 100 Theorems].
# [http://toccata.lri.fr/gallery Gallery of verified programs].
# [http://www.cs.nott.ac.uk/~lad/research/challenges/ Induction Challenge Problems].
# [http://automatedreasoning.net/ Larry Wos' Notebooks].
# [http://www.cs.miami.edu/~tptp/ The TPTP Problem Library for Automated Theorem Proving].
# [http://www.macs.hw.ac.uk/vstte10/Competition.html The 1st Verified Software Competition].
# [https://sites.google.com/site/vstte2012/compet The 2nd Verified Software Competition].
# [http://verifythis.cost-ic0701.org VerifyThis (A collection of verification benchmarks].

== Artículos recientes ==
Están en orden cronológico inverso a la fecha de su reseña en [http://www.glc.us.es/~jalonso/vestigium/tag/resena Vestigium]:
# Joachim Breitner, Brian Huffman, Neil Mitchell y Christian Sternagel [http://bit.ly/19fiWAY Certified HLints with Isabelle/HOLCF-Prelude].
# Peter Lammich [http://bit.ly/ZfSQrQ Automatic data refinement].
# Assia Mahboubi [http://bit.ly/18vyjm7 The rooster and the butterflies (a machine-checked proof of the Jordan-Hölder theorem for finite groups)].
# Nathan Wetzler, Marijn J. H. Heule y Warren A. Hunt Jr. [http://bit.ly/114oyZV Mechanical verification of SAT refutations with extended resolution].
# Johannes Hölzl, Fabian Immler y Brian Huffman [http://bit.ly/13H0REu Type classes and filters for mathematical analysis in Isabelle/HOL]
# M. J. H. Heule, W. A. Hunt, Jr. y N. Wetzler [http://bit.ly/10fv8wO Verifying refutations with extended resolution].
# C. Lüth y M. Ring [http://bit.ly/10EcFWj A Web interface for Isabelle: The next generation].
# L. Liu, O. Hasan y S. Tahar [http://bit.ly/18P9CSv On the formalization of continuous-time Markov chains in HOL].
# A. Asperti y W. Ricciotti [http://bit.ly/17H2mqy Formalizing Turing machines].
# A. Lochbihler [http://bit.ly/YwuCeL Light-weight containers for Isabelle: efficient, extensible, nestable].
# L. Noschinski [http://bit.ly/10XLrRA Graph theory].
# G. Gonthier et als. [http://bit.ly/19kPEP4 A machine-checked proof of the odd order theorem].
# C. Doczkal, J.O. Kaiser y G. Smolka [http://goo.gl/LdihL A constructive theory of regular languages in Coq].
# C. Sternagel [http://goo.gl/gwcwL A formal proof of Kruskal’s tree theorem in Isabelle/HOL].
# C. Sternagel y R. Thiemann [http://goo.gl/CUF3e Formalizing Knuth-Bendix orders and Knuth-Bendix completion].
# C. Lange, C. Rowat, W. Windsteiger y M. Kerber [http://goo.gl/9JAfX Developing an auction theory toolbox].
# M. Spasić y F. Marić [http://goo.gl/6OfmQ Formalization of incremental simplex algorithm by stepwise refinement].
# J.C. Blanchette, A. Popescu y D. Traytel [http://goo.gl/Guxky Coinductive pearl: Modular first-order logic completeness].
# J. Esparza et als. [http://goo.gl/HUOl8 A fully verified executable LTL model checker].
# M. Kerber, C. Lange y C. Rowat. [http://goo.gl/RV54S ForMaRE - formal mathematical reasoning in economics].
# J. Urban. [http://goo.gl/Y7sIq AI over large formal knowledge bases: The first decade].
# S. Boldo, C. Lelay y G. Melquiond. [http://goo.gl/vvqNg Formalization of real analysis: A survey of proof assistants and libraries].
# F. Haftmann, A. Krauss, O. Kunčar y T. Nipkow [http://goo.gl/bEFYa Data refinement in Isabelle/HOL].
# A.C. Rocha y M. Ayala. [http://goo.gl/xTyvE Formalizing the confluence of orthogonal rewriting systems].
# Z. Shi et als. [http://goo.gl/zCYHj Formalization of the complex number theory in HOL4].
# F. Loulergue y V. Niculescu [http://goo.gl/kM0dI Programming and reasonning with PowerLists in Coq].
# J. Heras, F.J. Martín y V. Pascual. [http://goo.gl/KkU6s A hierarchy of mathematical structures in ACL2].
# J. Xu, X. Zhang y C. Urban [http://www.inf.kcl.ac.uk/staff/urbanc/Publications/tm.pdf Mechanising Turing Machines and Computability Theory in Isabelle/HOL]

Documentación

2022-02-08T10:24:45Z

Jalonso: /* Lógica computacional */

En esta página se recogen en enlaces que sirven de documentación al curso de demostración asistida por ordenador (DAO).

== Visiones generales de la DAO ==

# J.A. Alonso. [http://goo.gl/NWk7b Razonamiento formalizado: Del sueño a la realidad de las pruebas]. ''Vestigium'', 26 de diciembre de 2012.
# J. Avigad. [http://www.andrew.cmu.edu/user/avigad/Talks/icerm.pdf Interactive theorem proving, automated reasoning, and mathematical computation]. ICERM, 14 de diciembre de 2012.
# M. Davis. [http://www.cs.nyu.edu/cs/faculty/davism/early.ps The early history of automated deduction].
# J.P. Delahaye [http://interstices.info/jcms/int_63417/du-reve-a-la-realite-des-preuves Du rêve à la réalité des preuves]. ''Interstices'', 8 de julio de 2012.
# J. Germoni [http://images.math.cnrs.fr/Coq-et-caracteres.html Coq et caractères: Preuve formelle du théorème de Feit et Thompson]. ''Images des Mathématiques'', CNRS, 23 de noviembre de 2012.
# H. Geuvers [http://www.ias.ac.in/sadhana/Pdf2009Feb/3.pdf Proof assistants: History, ideas and future]. ''Sadhana'', Vol. 34-1, pp. 3-25, février 2009.
# G. Gonthier [http://www.ams.org/notices/200811/tx081101382p.pdf The four-color theorem]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1382-1393, 2008.
# T. Hales. [http://www.ams.org/notices/200811/tx081101370p.pdf Formal proof]. ''Notices of AMS'', Vol. 55, N. 11 (2008) pp. 1370-1380.
# J. Harrison. [http://www.cl.cam.ac.uk/~jrh13/papers/ab.html A short survey of automated reasoning]. ''Lecture Notes in Computer Science'', Vol. 4545, pp. 334-349, 2007.
# J. Harrison. [http://www.ams.org/notices/200811/tx081101395p.pdf Formal proof: Theory and practice]. ''Notices of the AMS'', Vol. 55, N. 11 (2008) p.1395-1406.
# G. Kolata. [http://www.nytimes.com/library/cyber/week/1210math.html Computer math proof shows reasoning power]. ''The New York Times'', 10 de diciembre de 1996.
# D. MacKenzie [https://backspaces.net/temp/Spring2010Seminar/18%20unconventional%20essays%20on%20the%20nature%20of%20mathematics.pdf#page=147 Computers and the sociology of mathematical proof].
# G. Sutcliffe. [http://tptp.org/OverviewOfATP.html What is automated theorem proving?].
# F. Wiedijk [http://www.cs.ru.nl/~freek/100/ Formalizing the «top 100» of mathematical theorems].
# F. Wiedijk [http://www.ams.org/notices/200811/tx081101408p.pdf Formal proof - Getting started]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1408-1414, 2008.
# F. Wiedijk, [https://www.cs.ru.nl/F.Wiedijk/pubs/qed2.pdf The QED manifesto revisited]. ''Studies in Logic, Grammar and Rhetoric'', Vol. 10(23), pp. 121-133, 2007.

== Referencias sobre Isabelle/HOL ==
# B. Grechuk [https://web.cs.wpi.edu/~dd/resources_isabelle/isabelle_primer_mathematicians.pdf Isabelle primer for mathematicians].
# T. Nipkow [https://isabelle.in.tum.de/doc/prog-prove.pdf Programming and proving in Isabelle/HOL].
# T. Nipkow, M. Wenzel y L.C. Paulson [https://isabelle.in.tum.de/website-Isabelle2009/dist/Isabelle/doc/tutorial.pdf A proof assistant for higher-order logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL/document.pdf Isabelle/HOL — Higher-Order Logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/documentation.html Tutorials and manuals for Isabelle].

== Lecturas complementarias ==
=== Programación funcional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/i1m-12/temas/2012-13-IM-temas-PF.pdf Temas de "Programación funcional"]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# J.A. Alonso y M.J. Hidalgo [http://www.cs.us.es/~jalonso/publicaciones/Piensa_en_Haskell.pdf Piensa en Haskell (Ejercicios de programación funcional con Haskell)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# G. Hutton [http://goo.gl/pKqG Programming in Haskell]. Cambridge University Press, 2007.
# M. Lipovača [http://aprendehaskell.es ¡Aprende Haskell por el bien de todos!].

=== Lógica computacional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/li-12/temas/temas-LI-2012-13.pdf Temas de "Lógica informática" (2012-13)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# R. Bornat [http://bit.ly/oithic Proof and disproof in formal logic: an introduction for programmers]. Oxford University Press, 2005.
# K. Broda, S. Eisenbach, H. Khoshnevisan y S. Vickers [https://www.doc.ic.ac.uk/~susan/firstyearbook.pdf Reasoned programming]. Imperial College, 1994.
# K. Doets y J. van Eijck [http://www.ldc.usb.ve/~astorga/Haskell.Road.pdf The Haskell Road to Logic, Maths and Programming].
# M. Huth y M. Ryan [http://goo.gl/TMqOo Logic in computer science: Modelling and reasoning about systems]. Cambridge University Press, 2004. (Incluye el [http://www.cs.bham.ac.uk/research/lics/tutor/index.html tutor en la Red]).

== Cursos relacionados ==
=== Cursos con Isabelle/HOL ===
# Jeremy Avigad. [http://www.phil.cmu.edu/~avigad/formal/ Logic and Formal Verification]. (Carnegie Mellon, 2009).
# Clemens Ballarin. [http://cl-informatik.uibk.ac.at/teaching/ss08/atp/introduction.php Automatic Deduction]. (Univ de Innsbruck, 2008).
# Clemens Ballarin. [http://www4.in.tum.de/~ballarin/belgrade08-tut/ Introduction to the Isabelle Proof Assistant]. (Belgrado, 2008).
# Clemens Ballarin y Gerwin Klein [http://isabelle.in.tum.de/coursematerial/IJCAR04 Introduction to the Isabelle Proof Assistant]. (en el IJCAR-2004).
# Clemens Ballarin y Tjark Weber. [http://cl-informatik.uibk.ac.at/teaching/ws06/atp/introduction.php Automated Theorem Proving in Isabelle/HOL]. (Univ. de Innsbruck, 2006-07).
# A.D. Brucker, D. Basin, J.G. Smaus y B. Wolff. [http://archiv.infsec.ethz.ch/education/permanent/csmr.html Computer-supported Modeling and Reasoning]. (ETH Zurich, 2011).
# Mads Dam. [http://www.csc.kth.se/utbildning/kth/kurser/DD2453/aform07/ Advanced formal methods]. (KTH Royal Institute of Technology, 2007).
# Jacques Fleuriot y Paul Jackson. [http://www.inf.ed.ac.uk/teaching/courses/ar/slides/ Automated reasoning]. (Univ. de Edimburgo, 2012-13).
# Thomas Genet [http://www.irisa.fr/celtique/genet/ACF Software formal analysis and design]. (Univ. de Rennes)
# Gerwin Klein. [http://www.cse.unsw.edu.au/~kleing/teaching/thprv-04 Theorem Proving - Principles, Techniques, Applications]. (NICTA, 2004).
# Gerwin Klein. [http://www.cse.unsw.edu.au/~cs4161/index.html Advanced Topics in Software Verification]. (NICTA, 2012).
# Joao Marcos. [http://www.dimap.ufrn.br/~jmarcos/courses/LC/Ementa.htm Lógica computacional: Demonstração assistida e semi-automática de teoremas].(UFRN, 2000).
# Tobias Nipkow. [http://www4.informatik.tu-muenchen.de/~nipkow/semantics/ Semantics of programming languages]. (Univ. de Munich, 2012-13).
# Tobias Nipkow [http://isabelle.in.tum.de/coursematerial/PSV2009-1 Theorem Proving with Isabelle/HOL An Intensive Course].
# Larry Paulson. [http://www.cl.cam.ac.uk/teaching/0910/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2009-10).
# Arnd Poetzsch-Heffter. [https://softech.informatik.uni-kl.de/Homepage/SVHOL10 Specification and Verification with Higher-Order Logic].
# Jeremy G. Siek. [http://www.cs.colorado.edu/~siek/7000/spring07/ Practical Theorem Proving with Isabelle/Isar]. (Univ. de Colorado, 2007).
# Jeremy G. Siek. [http://ecee.colorado.edu/~siek/ecen5013/spring11/ Theorem proving in Isabelle]. (Univ. de Colorado, 2011).
# Jan-Georg Smaus. [http://www.informatik.uni-freiburg.de/~ki/teaching/ws0910/csmr/lecture.html Computer-supported modeling and reasoning]. (Univ. de Feiburgo, 2009).
# Christian Sternagel [http://cl-informatik.uibk.ac.at/teaching/ss11/eve/content.php Experiments in Verification – Introduction to Isabelle/HOL]. (Univ. de Innsbruck, 2011-12).
# Tjark Weber. [http://www.cl.cam.ac.uk/teaching/1011/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2010-11).

=== Otros cursos ===
# José A. Alonso [http://www.cs.us.es/~jalonso/cursos/li/ Lógica informática] (Univ. de Sevilla, 2012-13).
# Yves Bertot, Pierre Casteran, Benjamin Gregoire, Pierre Letouzey y Assia Mahboubi [http://www.di.ens.fr/~zappa/teaching/coq/ecole11 Modelling and verifying algorithms in Coq: an introduction]. (INRIA Paris-Rocquencourt, 14-18 noviembre 2011).
# Pierre Castéran [http://www.labri.fr/perso/casteran/FM/Logique/index.html Logic (Master In Verification)] (Univ. de Burdeos, 2011-12).
# Nuno Gaspar [http://www-sop.inria.fr/members/Nuno.Gaspar/teaching/coq2012.php Verification with the Coq Proof Assistant] (INRIA Sophia Antipolis, 2012-13).
# Michael Genesereth [http://logic.stanford.edu/classes/cs157/2011/cs157.html Computational Logic] (Univ. de Stanford, 2011-12).
# Ian Hodkinson [http://www.doc.ic.ac.uk/~imh/teaching/140_logic/logic.html Logic] (Imperial College, Londres, 2010-11).
# Peter Lucas [http://www.cs.ru.nl/~peterl/teaching/KeR/ Knowledge Representation and Reasoning] (Radboud University # egen, 2011-12).
# Larry Paulson [http://www.cl.cam.ac.uk/Teaching/current/LogicProof/ Logic and Proof] (Univ. de Cambridge, 2011-12).
# Riccardo Pucella [http://www.ccs.neu.edu/home/riccardo/courses/csu290-sp09/index.html Logic and Computation] (Northeastern University, 2009). Curso con ACL2.

== Bibliotecas de ejemplos de verificación ==
# [http://afp.sourceforge.net Archive of Formal Proofs].
# [http://www.cs.ru.nl/~freek/100 Formalizing 100 Theorems].
# [http://toccata.lri.fr/gallery Gallery of verified programs].
# [http://www.cs.nott.ac.uk/~lad/research/challenges/ Induction Challenge Problems].
# [http://automatedreasoning.net/ Larry Wos' Notebooks].
# [http://www.cs.miami.edu/~tptp/ The TPTP Problem Library for Automated Theorem Proving].
# [http://www.macs.hw.ac.uk/vstte10/Competition.html The 1st Verified Software Competition].
# [https://sites.google.com/site/vstte2012/compet The 2nd Verified Software Competition].
# [http://verifythis.cost-ic0701.org VerifyThis (A collection of verification benchmarks].

== Artículos recientes ==
Están en orden cronológico inverso a la fecha de su reseña en [http://www.glc.us.es/~jalonso/vestigium/tag/resena Vestigium]:
# Joachim Breitner, Brian Huffman, Neil Mitchell y Christian Sternagel [http://bit.ly/19fiWAY Certified HLints with Isabelle/HOLCF-Prelude].
# Peter Lammich [http://bit.ly/ZfSQrQ Automatic data refinement].
# Assia Mahboubi [http://bit.ly/18vyjm7 The rooster and the butterflies (a machine-checked proof of the Jordan-Hölder theorem for finite groups)].
# Nathan Wetzler, Marijn J. H. Heule y Warren A. Hunt Jr. [http://bit.ly/114oyZV Mechanical verification of SAT refutations with extended resolution].
# Johannes Hölzl, Fabian Immler y Brian Huffman [http://bit.ly/13H0REu Type classes and filters for mathematical analysis in Isabelle/HOL]
# M. J. H. Heule, W. A. Hunt, Jr. y N. Wetzler [http://bit.ly/10fv8wO Verifying refutations with extended resolution].
# C. Lüth y M. Ring [http://bit.ly/10EcFWj A Web interface for Isabelle: The next generation].
# L. Liu, O. Hasan y S. Tahar [http://bit.ly/18P9CSv On the formalization of continuous-time Markov chains in HOL].
# A. Asperti y W. Ricciotti [http://bit.ly/17H2mqy Formalizing Turing machines].
# A. Lochbihler [http://bit.ly/YwuCeL Light-weight containers for Isabelle: efficient, extensible, nestable].
# L. Noschinski [http://bit.ly/10XLrRA Graph theory].
# G. Gonthier et als. [http://bit.ly/19kPEP4 A machine-checked proof of the odd order theorem].
# C. Doczkal, J.O. Kaiser y G. Smolka [http://goo.gl/LdihL A constructive theory of regular languages in Coq].
# C. Sternagel [http://goo.gl/gwcwL A formal proof of Kruskal’s tree theorem in Isabelle/HOL].
# C. Sternagel y R. Thiemann [http://goo.gl/CUF3e Formalizing Knuth-Bendix orders and Knuth-Bendix completion].
# C. Lange, C. Rowat, W. Windsteiger y M. Kerber [http://goo.gl/9JAfX Developing an auction theory toolbox].
# M. Spasić y F. Marić [http://goo.gl/6OfmQ Formalization of incremental simplex algorithm by stepwise refinement].
# J.C. Blanchette, A. Popescu y D. Traytel [http://goo.gl/Guxky Coinductive pearl: Modular first-order logic completeness].
# J. Esparza et als. [http://goo.gl/HUOl8 A fully verified executable LTL model checker].
# M. Kerber, C. Lange y C. Rowat. [http://goo.gl/RV54S ForMaRE - formal mathematical reasoning in economics].
# J. Urban. [http://goo.gl/Y7sIq AI over large formal knowledge bases: The first decade].
# S. Boldo, C. Lelay y G. Melquiond. [http://goo.gl/vvqNg Formalization of real analysis: A survey of proof assistants and libraries].
# F. Haftmann, A. Krauss, O. Kunčar y T. Nipkow [http://goo.gl/bEFYa Data refinement in Isabelle/HOL].
# A.C. Rocha y M. Ayala. [http://goo.gl/xTyvE Formalizing the confluence of orthogonal rewriting systems].
# Z. Shi et als. [http://goo.gl/zCYHj Formalization of the complex number theory in HOL4].
# F. Loulergue y V. Niculescu [http://goo.gl/kM0dI Programming and reasonning with PowerLists in Coq].
# J. Heras, F.J. Martín y V. Pascual. [http://goo.gl/KkU6s A hierarchy of mathematical structures in ACL2].
# J. Xu, X. Zhang y C. Urban [http://www.inf.kcl.ac.uk/staff/urbanc/Publications/tm.pdf Mechanising Turing Machines and Computability Theory in Isabelle/HOL]

Documentación

2022-02-08T10:23:03Z

Jalonso: /* Lógica computacional */

En esta página se recogen en enlaces que sirven de documentación al curso de demostración asistida por ordenador (DAO).

== Visiones generales de la DAO ==

# J.A. Alonso. [http://goo.gl/NWk7b Razonamiento formalizado: Del sueño a la realidad de las pruebas]. ''Vestigium'', 26 de diciembre de 2012.
# J. Avigad. [http://www.andrew.cmu.edu/user/avigad/Talks/icerm.pdf Interactive theorem proving, automated reasoning, and mathematical computation]. ICERM, 14 de diciembre de 2012.
# M. Davis. [http://www.cs.nyu.edu/cs/faculty/davism/early.ps The early history of automated deduction].
# J.P. Delahaye [http://interstices.info/jcms/int_63417/du-reve-a-la-realite-des-preuves Du rêve à la réalité des preuves]. ''Interstices'', 8 de julio de 2012.
# J. Germoni [http://images.math.cnrs.fr/Coq-et-caracteres.html Coq et caractères: Preuve formelle du théorème de Feit et Thompson]. ''Images des Mathématiques'', CNRS, 23 de noviembre de 2012.
# H. Geuvers [http://www.ias.ac.in/sadhana/Pdf2009Feb/3.pdf Proof assistants: History, ideas and future]. ''Sadhana'', Vol. 34-1, pp. 3-25, février 2009.
# G. Gonthier [http://www.ams.org/notices/200811/tx081101382p.pdf The four-color theorem]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1382-1393, 2008.
# T. Hales. [http://www.ams.org/notices/200811/tx081101370p.pdf Formal proof]. ''Notices of AMS'', Vol. 55, N. 11 (2008) pp. 1370-1380.
# J. Harrison. [http://www.cl.cam.ac.uk/~jrh13/papers/ab.html A short survey of automated reasoning]. ''Lecture Notes in Computer Science'', Vol. 4545, pp. 334-349, 2007.
# J. Harrison. [http://www.ams.org/notices/200811/tx081101395p.pdf Formal proof: Theory and practice]. ''Notices of the AMS'', Vol. 55, N. 11 (2008) p.1395-1406.
# G. Kolata. [http://www.nytimes.com/library/cyber/week/1210math.html Computer math proof shows reasoning power]. ''The New York Times'', 10 de diciembre de 1996.
# D. MacKenzie [https://backspaces.net/temp/Spring2010Seminar/18%20unconventional%20essays%20on%20the%20nature%20of%20mathematics.pdf#page=147 Computers and the sociology of mathematical proof].
# G. Sutcliffe. [http://tptp.org/OverviewOfATP.html What is automated theorem proving?].
# F. Wiedijk [http://www.cs.ru.nl/~freek/100/ Formalizing the «top 100» of mathematical theorems].
# F. Wiedijk [http://www.ams.org/notices/200811/tx081101408p.pdf Formal proof - Getting started]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1408-1414, 2008.
# F. Wiedijk, [https://www.cs.ru.nl/F.Wiedijk/pubs/qed2.pdf The QED manifesto revisited]. ''Studies in Logic, Grammar and Rhetoric'', Vol. 10(23), pp. 121-133, 2007.

== Referencias sobre Isabelle/HOL ==
# B. Grechuk [https://web.cs.wpi.edu/~dd/resources_isabelle/isabelle_primer_mathematicians.pdf Isabelle primer for mathematicians].
# T. Nipkow [https://isabelle.in.tum.de/doc/prog-prove.pdf Programming and proving in Isabelle/HOL].
# T. Nipkow, M. Wenzel y L.C. Paulson [https://isabelle.in.tum.de/website-Isabelle2009/dist/Isabelle/doc/tutorial.pdf A proof assistant for higher-order logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL/document.pdf Isabelle/HOL — Higher-Order Logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/documentation.html Tutorials and manuals for Isabelle].

== Lecturas complementarias ==
=== Programación funcional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/i1m-12/temas/2012-13-IM-temas-PF.pdf Temas de "Programación funcional"]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# J.A. Alonso y M.J. Hidalgo [http://www.cs.us.es/~jalonso/publicaciones/Piensa_en_Haskell.pdf Piensa en Haskell (Ejercicios de programación funcional con Haskell)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# G. Hutton [http://goo.gl/pKqG Programming in Haskell]. Cambridge University Press, 2007.
# M. Lipovača [http://aprendehaskell.es ¡Aprende Haskell por el bien de todos!].

=== Lógica computacional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/li-12/temas/temas-LI-2012-13.pdf Temas de "Lógica informática" (2012-13)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# R. Bornat [http://bit.ly/oithic Proof and disproof in formal logic: an introduction for programmers]. Oxford University Press, 2005.
# K. Broda, S. Eisenbach, H. Khoshnevisan y S. Vickers [http://pubs.doc.ic.ac.uk/reasoned-programming/reasoned-programming.pdf Reasoned programming]. Imperial College, 1994.
# K. Doets y J. van Eijck [http://www.ldc.usb.ve/~astorga/Haskell.Road.pdf The Haskell Road to Logic, Maths and Programming].
# M. Huth y M. Ryan [http://goo.gl/TMqOo Logic in computer science: Modelling and reasoning about systems]. Cambridge University Press, 2004. (Incluye el [http://www.cs.bham.ac.uk/research/lics/tutor/index.html tutor en la Red]).

== Cursos relacionados ==
=== Cursos con Isabelle/HOL ===
# Jeremy Avigad. [http://www.phil.cmu.edu/~avigad/formal/ Logic and Formal Verification]. (Carnegie Mellon, 2009).
# Clemens Ballarin. [http://cl-informatik.uibk.ac.at/teaching/ss08/atp/introduction.php Automatic Deduction]. (Univ de Innsbruck, 2008).
# Clemens Ballarin. [http://www4.in.tum.de/~ballarin/belgrade08-tut/ Introduction to the Isabelle Proof Assistant]. (Belgrado, 2008).
# Clemens Ballarin y Gerwin Klein [http://isabelle.in.tum.de/coursematerial/IJCAR04 Introduction to the Isabelle Proof Assistant]. (en el IJCAR-2004).
# Clemens Ballarin y Tjark Weber. [http://cl-informatik.uibk.ac.at/teaching/ws06/atp/introduction.php Automated Theorem Proving in Isabelle/HOL]. (Univ. de Innsbruck, 2006-07).
# A.D. Brucker, D. Basin, J.G. Smaus y B. Wolff. [http://archiv.infsec.ethz.ch/education/permanent/csmr.html Computer-supported Modeling and Reasoning]. (ETH Zurich, 2011).
# Mads Dam. [http://www.csc.kth.se/utbildning/kth/kurser/DD2453/aform07/ Advanced formal methods]. (KTH Royal Institute of Technology, 2007).
# Jacques Fleuriot y Paul Jackson. [http://www.inf.ed.ac.uk/teaching/courses/ar/slides/ Automated reasoning]. (Univ. de Edimburgo, 2012-13).
# Thomas Genet [http://www.irisa.fr/celtique/genet/ACF Software formal analysis and design]. (Univ. de Rennes)
# Gerwin Klein. [http://www.cse.unsw.edu.au/~kleing/teaching/thprv-04 Theorem Proving - Principles, Techniques, Applications]. (NICTA, 2004).
# Gerwin Klein. [http://www.cse.unsw.edu.au/~cs4161/index.html Advanced Topics in Software Verification]. (NICTA, 2012).
# Joao Marcos. [http://www.dimap.ufrn.br/~jmarcos/courses/LC/Ementa.htm Lógica computacional: Demonstração assistida e semi-automática de teoremas].(UFRN, 2000).
# Tobias Nipkow. [http://www4.informatik.tu-muenchen.de/~nipkow/semantics/ Semantics of programming languages]. (Univ. de Munich, 2012-13).
# Tobias Nipkow [http://isabelle.in.tum.de/coursematerial/PSV2009-1 Theorem Proving with Isabelle/HOL An Intensive Course].
# Larry Paulson. [http://www.cl.cam.ac.uk/teaching/0910/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2009-10).
# Arnd Poetzsch-Heffter. [https://softech.informatik.uni-kl.de/Homepage/SVHOL10 Specification and Verification with Higher-Order Logic].
# Jeremy G. Siek. [http://www.cs.colorado.edu/~siek/7000/spring07/ Practical Theorem Proving with Isabelle/Isar]. (Univ. de Colorado, 2007).
# Jeremy G. Siek. [http://ecee.colorado.edu/~siek/ecen5013/spring11/ Theorem proving in Isabelle]. (Univ. de Colorado, 2011).
# Jan-Georg Smaus. [http://www.informatik.uni-freiburg.de/~ki/teaching/ws0910/csmr/lecture.html Computer-supported modeling and reasoning]. (Univ. de Feiburgo, 2009).
# Christian Sternagel [http://cl-informatik.uibk.ac.at/teaching/ss11/eve/content.php Experiments in Verification – Introduction to Isabelle/HOL]. (Univ. de Innsbruck, 2011-12).
# Tjark Weber. [http://www.cl.cam.ac.uk/teaching/1011/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2010-11).

=== Otros cursos ===
# José A. Alonso [http://www.cs.us.es/~jalonso/cursos/li/ Lógica informática] (Univ. de Sevilla, 2012-13).
# Yves Bertot, Pierre Casteran, Benjamin Gregoire, Pierre Letouzey y Assia Mahboubi [http://www.di.ens.fr/~zappa/teaching/coq/ecole11 Modelling and verifying algorithms in Coq: an introduction]. (INRIA Paris-Rocquencourt, 14-18 noviembre 2011).
# Pierre Castéran [http://www.labri.fr/perso/casteran/FM/Logique/index.html Logic (Master In Verification)] (Univ. de Burdeos, 2011-12).
# Nuno Gaspar [http://www-sop.inria.fr/members/Nuno.Gaspar/teaching/coq2012.php Verification with the Coq Proof Assistant] (INRIA Sophia Antipolis, 2012-13).
# Michael Genesereth [http://logic.stanford.edu/classes/cs157/2011/cs157.html Computational Logic] (Univ. de Stanford, 2011-12).
# Ian Hodkinson [http://www.doc.ic.ac.uk/~imh/teaching/140_logic/logic.html Logic] (Imperial College, Londres, 2010-11).
# Peter Lucas [http://www.cs.ru.nl/~peterl/teaching/KeR/ Knowledge Representation and Reasoning] (Radboud University # egen, 2011-12).
# Larry Paulson [http://www.cl.cam.ac.uk/Teaching/current/LogicProof/ Logic and Proof] (Univ. de Cambridge, 2011-12).
# Riccardo Pucella [http://www.ccs.neu.edu/home/riccardo/courses/csu290-sp09/index.html Logic and Computation] (Northeastern University, 2009). Curso con ACL2.

== Bibliotecas de ejemplos de verificación ==
# [http://afp.sourceforge.net Archive of Formal Proofs].
# [http://www.cs.ru.nl/~freek/100 Formalizing 100 Theorems].
# [http://toccata.lri.fr/gallery Gallery of verified programs].
# [http://www.cs.nott.ac.uk/~lad/research/challenges/ Induction Challenge Problems].
# [http://automatedreasoning.net/ Larry Wos' Notebooks].
# [http://www.cs.miami.edu/~tptp/ The TPTP Problem Library for Automated Theorem Proving].
# [http://www.macs.hw.ac.uk/vstte10/Competition.html The 1st Verified Software Competition].
# [https://sites.google.com/site/vstte2012/compet The 2nd Verified Software Competition].
# [http://verifythis.cost-ic0701.org VerifyThis (A collection of verification benchmarks].

== Artículos recientes ==
Están en orden cronológico inverso a la fecha de su reseña en [http://www.glc.us.es/~jalonso/vestigium/tag/resena Vestigium]:
# Joachim Breitner, Brian Huffman, Neil Mitchell y Christian Sternagel [http://bit.ly/19fiWAY Certified HLints with Isabelle/HOLCF-Prelude].
# Peter Lammich [http://bit.ly/ZfSQrQ Automatic data refinement].
# Assia Mahboubi [http://bit.ly/18vyjm7 The rooster and the butterflies (a machine-checked proof of the Jordan-Hölder theorem for finite groups)].
# Nathan Wetzler, Marijn J. H. Heule y Warren A. Hunt Jr. [http://bit.ly/114oyZV Mechanical verification of SAT refutations with extended resolution].
# Johannes Hölzl, Fabian Immler y Brian Huffman [http://bit.ly/13H0REu Type classes and filters for mathematical analysis in Isabelle/HOL]
# M. J. H. Heule, W. A. Hunt, Jr. y N. Wetzler [http://bit.ly/10fv8wO Verifying refutations with extended resolution].
# C. Lüth y M. Ring [http://bit.ly/10EcFWj A Web interface for Isabelle: The next generation].
# L. Liu, O. Hasan y S. Tahar [http://bit.ly/18P9CSv On the formalization of continuous-time Markov chains in HOL].
# A. Asperti y W. Ricciotti [http://bit.ly/17H2mqy Formalizing Turing machines].
# A. Lochbihler [http://bit.ly/YwuCeL Light-weight containers for Isabelle: efficient, extensible, nestable].
# L. Noschinski [http://bit.ly/10XLrRA Graph theory].
# G. Gonthier et als. [http://bit.ly/19kPEP4 A machine-checked proof of the odd order theorem].
# C. Doczkal, J.O. Kaiser y G. Smolka [http://goo.gl/LdihL A constructive theory of regular languages in Coq].
# C. Sternagel [http://goo.gl/gwcwL A formal proof of Kruskal’s tree theorem in Isabelle/HOL].
# C. Sternagel y R. Thiemann [http://goo.gl/CUF3e Formalizing Knuth-Bendix orders and Knuth-Bendix completion].
# C. Lange, C. Rowat, W. Windsteiger y M. Kerber [http://goo.gl/9JAfX Developing an auction theory toolbox].
# M. Spasić y F. Marić [http://goo.gl/6OfmQ Formalization of incremental simplex algorithm by stepwise refinement].
# J.C. Blanchette, A. Popescu y D. Traytel [http://goo.gl/Guxky Coinductive pearl: Modular first-order logic completeness].
# J. Esparza et als. [http://goo.gl/HUOl8 A fully verified executable LTL model checker].
# M. Kerber, C. Lange y C. Rowat. [http://goo.gl/RV54S ForMaRE - formal mathematical reasoning in economics].
# J. Urban. [http://goo.gl/Y7sIq AI over large formal knowledge bases: The first decade].
# S. Boldo, C. Lelay y G. Melquiond. [http://goo.gl/vvqNg Formalization of real analysis: A survey of proof assistants and libraries].
# F. Haftmann, A. Krauss, O. Kunčar y T. Nipkow [http://goo.gl/bEFYa Data refinement in Isabelle/HOL].
# A.C. Rocha y M. Ayala. [http://goo.gl/xTyvE Formalizing the confluence of orthogonal rewriting systems].
# Z. Shi et als. [http://goo.gl/zCYHj Formalization of the complex number theory in HOL4].
# F. Loulergue y V. Niculescu [http://goo.gl/kM0dI Programming and reasonning with PowerLists in Coq].
# J. Heras, F.J. Martín y V. Pascual. [http://goo.gl/KkU6s A hierarchy of mathematical structures in ACL2].
# J. Xu, X. Zhang y C. Urban [http://www.inf.kcl.ac.uk/staff/urbanc/Publications/tm.pdf Mechanising Turing Machines and Computability Theory in Isabelle/HOL]

Documentación

2022-02-08T10:22:17Z

Jalonso: /* Programación funcional */

En esta página se recogen en enlaces que sirven de documentación al curso de demostración asistida por ordenador (DAO).

== Visiones generales de la DAO ==

# J.A. Alonso. [http://goo.gl/NWk7b Razonamiento formalizado: Del sueño a la realidad de las pruebas]. ''Vestigium'', 26 de diciembre de 2012.
# J. Avigad. [http://www.andrew.cmu.edu/user/avigad/Talks/icerm.pdf Interactive theorem proving, automated reasoning, and mathematical computation]. ICERM, 14 de diciembre de 2012.
# M. Davis. [http://www.cs.nyu.edu/cs/faculty/davism/early.ps The early history of automated deduction].
# J.P. Delahaye [http://interstices.info/jcms/int_63417/du-reve-a-la-realite-des-preuves Du rêve à la réalité des preuves]. ''Interstices'', 8 de julio de 2012.
# J. Germoni [http://images.math.cnrs.fr/Coq-et-caracteres.html Coq et caractères: Preuve formelle du théorème de Feit et Thompson]. ''Images des Mathématiques'', CNRS, 23 de noviembre de 2012.
# H. Geuvers [http://www.ias.ac.in/sadhana/Pdf2009Feb/3.pdf Proof assistants: History, ideas and future]. ''Sadhana'', Vol. 34-1, pp. 3-25, février 2009.
# G. Gonthier [http://www.ams.org/notices/200811/tx081101382p.pdf The four-color theorem]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1382-1393, 2008.
# T. Hales. [http://www.ams.org/notices/200811/tx081101370p.pdf Formal proof]. ''Notices of AMS'', Vol. 55, N. 11 (2008) pp. 1370-1380.
# J. Harrison. [http://www.cl.cam.ac.uk/~jrh13/papers/ab.html A short survey of automated reasoning]. ''Lecture Notes in Computer Science'', Vol. 4545, pp. 334-349, 2007.
# J. Harrison. [http://www.ams.org/notices/200811/tx081101395p.pdf Formal proof: Theory and practice]. ''Notices of the AMS'', Vol. 55, N. 11 (2008) p.1395-1406.
# G. Kolata. [http://www.nytimes.com/library/cyber/week/1210math.html Computer math proof shows reasoning power]. ''The New York Times'', 10 de diciembre de 1996.
# D. MacKenzie [https://backspaces.net/temp/Spring2010Seminar/18%20unconventional%20essays%20on%20the%20nature%20of%20mathematics.pdf#page=147 Computers and the sociology of mathematical proof].
# G. Sutcliffe. [http://tptp.org/OverviewOfATP.html What is automated theorem proving?].
# F. Wiedijk [http://www.cs.ru.nl/~freek/100/ Formalizing the «top 100» of mathematical theorems].
# F. Wiedijk [http://www.ams.org/notices/200811/tx081101408p.pdf Formal proof - Getting started]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1408-1414, 2008.
# F. Wiedijk, [https://www.cs.ru.nl/F.Wiedijk/pubs/qed2.pdf The QED manifesto revisited]. ''Studies in Logic, Grammar and Rhetoric'', Vol. 10(23), pp. 121-133, 2007.

== Referencias sobre Isabelle/HOL ==
# B. Grechuk [https://web.cs.wpi.edu/~dd/resources_isabelle/isabelle_primer_mathematicians.pdf Isabelle primer for mathematicians].
# T. Nipkow [https://isabelle.in.tum.de/doc/prog-prove.pdf Programming and proving in Isabelle/HOL].
# T. Nipkow, M. Wenzel y L.C. Paulson [https://isabelle.in.tum.de/website-Isabelle2009/dist/Isabelle/doc/tutorial.pdf A proof assistant for higher-order logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL/document.pdf Isabelle/HOL — Higher-Order Logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/documentation.html Tutorials and manuals for Isabelle].

== Lecturas complementarias ==
=== Programación funcional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/i1m-12/temas/2012-13-IM-temas-PF.pdf Temas de "Programación funcional"]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# J.A. Alonso y M.J. Hidalgo [http://www.cs.us.es/~jalonso/publicaciones/Piensa_en_Haskell.pdf Piensa en Haskell (Ejercicios de programación funcional con Haskell)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# G. Hutton [http://goo.gl/pKqG Programming in Haskell]. Cambridge University Press, 2007.
# M. Lipovača [http://aprendehaskell.es ¡Aprende Haskell por el bien de todos!].

=== Lógica computacional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/li/temas/temas-LI-2012-13.pdf Temas de "Lógica informática" (2012-13)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# R. Bornat [http://bit.ly/oithic Proof and disproof in formal logic: an introduction for programmers]. Oxford University Press, 2005.
# K. Broda, S. Eisenbach, H. Khoshnevisan y S. Vickers [http://pubs.doc.ic.ac.uk/reasoned-programming/reasoned-programming.pdf Reasoned programming]. Imperial College, 1994.
# K. Doets y J. van Eijck [http://www.ldc.usb.ve/~astorga/Haskell.Road.pdf The Haskell Road to Logic, Maths and Programming].
# M. Huth y M. Ryan [http://goo.gl/TMqOo Logic in computer science: Modelling and reasoning about systems]. Cambridge University Press, 2004. (Incluye el [http://www.cs.bham.ac.uk/research/lics/tutor/index.html tutor en la Red]).

== Cursos relacionados ==
=== Cursos con Isabelle/HOL ===
# Jeremy Avigad. [http://www.phil.cmu.edu/~avigad/formal/ Logic and Formal Verification]. (Carnegie Mellon, 2009).
# Clemens Ballarin. [http://cl-informatik.uibk.ac.at/teaching/ss08/atp/introduction.php Automatic Deduction]. (Univ de Innsbruck, 2008).
# Clemens Ballarin. [http://www4.in.tum.de/~ballarin/belgrade08-tut/ Introduction to the Isabelle Proof Assistant]. (Belgrado, 2008).
# Clemens Ballarin y Gerwin Klein [http://isabelle.in.tum.de/coursematerial/IJCAR04 Introduction to the Isabelle Proof Assistant]. (en el IJCAR-2004).
# Clemens Ballarin y Tjark Weber. [http://cl-informatik.uibk.ac.at/teaching/ws06/atp/introduction.php Automated Theorem Proving in Isabelle/HOL]. (Univ. de Innsbruck, 2006-07).
# A.D. Brucker, D. Basin, J.G. Smaus y B. Wolff. [http://archiv.infsec.ethz.ch/education/permanent/csmr.html Computer-supported Modeling and Reasoning]. (ETH Zurich, 2011).
# Mads Dam. [http://www.csc.kth.se/utbildning/kth/kurser/DD2453/aform07/ Advanced formal methods]. (KTH Royal Institute of Technology, 2007).
# Jacques Fleuriot y Paul Jackson. [http://www.inf.ed.ac.uk/teaching/courses/ar/slides/ Automated reasoning]. (Univ. de Edimburgo, 2012-13).
# Thomas Genet [http://www.irisa.fr/celtique/genet/ACF Software formal analysis and design]. (Univ. de Rennes)
# Gerwin Klein. [http://www.cse.unsw.edu.au/~kleing/teaching/thprv-04 Theorem Proving - Principles, Techniques, Applications]. (NICTA, 2004).
# Gerwin Klein. [http://www.cse.unsw.edu.au/~cs4161/index.html Advanced Topics in Software Verification]. (NICTA, 2012).
# Joao Marcos. [http://www.dimap.ufrn.br/~jmarcos/courses/LC/Ementa.htm Lógica computacional: Demonstração assistida e semi-automática de teoremas].(UFRN, 2000).
# Tobias Nipkow. [http://www4.informatik.tu-muenchen.de/~nipkow/semantics/ Semantics of programming languages]. (Univ. de Munich, 2012-13).
# Tobias Nipkow [http://isabelle.in.tum.de/coursematerial/PSV2009-1 Theorem Proving with Isabelle/HOL An Intensive Course].
# Larry Paulson. [http://www.cl.cam.ac.uk/teaching/0910/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2009-10).
# Arnd Poetzsch-Heffter. [https://softech.informatik.uni-kl.de/Homepage/SVHOL10 Specification and Verification with Higher-Order Logic].
# Jeremy G. Siek. [http://www.cs.colorado.edu/~siek/7000/spring07/ Practical Theorem Proving with Isabelle/Isar]. (Univ. de Colorado, 2007).
# Jeremy G. Siek. [http://ecee.colorado.edu/~siek/ecen5013/spring11/ Theorem proving in Isabelle]. (Univ. de Colorado, 2011).
# Jan-Georg Smaus. [http://www.informatik.uni-freiburg.de/~ki/teaching/ws0910/csmr/lecture.html Computer-supported modeling and reasoning]. (Univ. de Feiburgo, 2009).
# Christian Sternagel [http://cl-informatik.uibk.ac.at/teaching/ss11/eve/content.php Experiments in Verification – Introduction to Isabelle/HOL]. (Univ. de Innsbruck, 2011-12).
# Tjark Weber. [http://www.cl.cam.ac.uk/teaching/1011/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2010-11).

=== Otros cursos ===
# José A. Alonso [http://www.cs.us.es/~jalonso/cursos/li/ Lógica informática] (Univ. de Sevilla, 2012-13).
# Yves Bertot, Pierre Casteran, Benjamin Gregoire, Pierre Letouzey y Assia Mahboubi [http://www.di.ens.fr/~zappa/teaching/coq/ecole11 Modelling and verifying algorithms in Coq: an introduction]. (INRIA Paris-Rocquencourt, 14-18 noviembre 2011).
# Pierre Castéran [http://www.labri.fr/perso/casteran/FM/Logique/index.html Logic (Master In Verification)] (Univ. de Burdeos, 2011-12).
# Nuno Gaspar [http://www-sop.inria.fr/members/Nuno.Gaspar/teaching/coq2012.php Verification with the Coq Proof Assistant] (INRIA Sophia Antipolis, 2012-13).
# Michael Genesereth [http://logic.stanford.edu/classes/cs157/2011/cs157.html Computational Logic] (Univ. de Stanford, 2011-12).
# Ian Hodkinson [http://www.doc.ic.ac.uk/~imh/teaching/140_logic/logic.html Logic] (Imperial College, Londres, 2010-11).
# Peter Lucas [http://www.cs.ru.nl/~peterl/teaching/KeR/ Knowledge Representation and Reasoning] (Radboud University # egen, 2011-12).
# Larry Paulson [http://www.cl.cam.ac.uk/Teaching/current/LogicProof/ Logic and Proof] (Univ. de Cambridge, 2011-12).
# Riccardo Pucella [http://www.ccs.neu.edu/home/riccardo/courses/csu290-sp09/index.html Logic and Computation] (Northeastern University, 2009). Curso con ACL2.

== Bibliotecas de ejemplos de verificación ==
# [http://afp.sourceforge.net Archive of Formal Proofs].
# [http://www.cs.ru.nl/~freek/100 Formalizing 100 Theorems].
# [http://toccata.lri.fr/gallery Gallery of verified programs].
# [http://www.cs.nott.ac.uk/~lad/research/challenges/ Induction Challenge Problems].
# [http://automatedreasoning.net/ Larry Wos' Notebooks].
# [http://www.cs.miami.edu/~tptp/ The TPTP Problem Library for Automated Theorem Proving].
# [http://www.macs.hw.ac.uk/vstte10/Competition.html The 1st Verified Software Competition].
# [https://sites.google.com/site/vstte2012/compet The 2nd Verified Software Competition].
# [http://verifythis.cost-ic0701.org VerifyThis (A collection of verification benchmarks].

== Artículos recientes ==
Están en orden cronológico inverso a la fecha de su reseña en [http://www.glc.us.es/~jalonso/vestigium/tag/resena Vestigium]:
# Joachim Breitner, Brian Huffman, Neil Mitchell y Christian Sternagel [http://bit.ly/19fiWAY Certified HLints with Isabelle/HOLCF-Prelude].
# Peter Lammich [http://bit.ly/ZfSQrQ Automatic data refinement].
# Assia Mahboubi [http://bit.ly/18vyjm7 The rooster and the butterflies (a machine-checked proof of the Jordan-Hölder theorem for finite groups)].
# Nathan Wetzler, Marijn J. H. Heule y Warren A. Hunt Jr. [http://bit.ly/114oyZV Mechanical verification of SAT refutations with extended resolution].
# Johannes Hölzl, Fabian Immler y Brian Huffman [http://bit.ly/13H0REu Type classes and filters for mathematical analysis in Isabelle/HOL]
# M. J. H. Heule, W. A. Hunt, Jr. y N. Wetzler [http://bit.ly/10fv8wO Verifying refutations with extended resolution].
# C. Lüth y M. Ring [http://bit.ly/10EcFWj A Web interface for Isabelle: The next generation].
# L. Liu, O. Hasan y S. Tahar [http://bit.ly/18P9CSv On the formalization of continuous-time Markov chains in HOL].
# A. Asperti y W. Ricciotti [http://bit.ly/17H2mqy Formalizing Turing machines].
# A. Lochbihler [http://bit.ly/YwuCeL Light-weight containers for Isabelle: efficient, extensible, nestable].
# L. Noschinski [http://bit.ly/10XLrRA Graph theory].
# G. Gonthier et als. [http://bit.ly/19kPEP4 A machine-checked proof of the odd order theorem].
# C. Doczkal, J.O. Kaiser y G. Smolka [http://goo.gl/LdihL A constructive theory of regular languages in Coq].
# C. Sternagel [http://goo.gl/gwcwL A formal proof of Kruskal’s tree theorem in Isabelle/HOL].
# C. Sternagel y R. Thiemann [http://goo.gl/CUF3e Formalizing Knuth-Bendix orders and Knuth-Bendix completion].
# C. Lange, C. Rowat, W. Windsteiger y M. Kerber [http://goo.gl/9JAfX Developing an auction theory toolbox].
# M. Spasić y F. Marić [http://goo.gl/6OfmQ Formalization of incremental simplex algorithm by stepwise refinement].
# J.C. Blanchette, A. Popescu y D. Traytel [http://goo.gl/Guxky Coinductive pearl: Modular first-order logic completeness].
# J. Esparza et als. [http://goo.gl/HUOl8 A fully verified executable LTL model checker].
# M. Kerber, C. Lange y C. Rowat. [http://goo.gl/RV54S ForMaRE - formal mathematical reasoning in economics].
# J. Urban. [http://goo.gl/Y7sIq AI over large formal knowledge bases: The first decade].
# S. Boldo, C. Lelay y G. Melquiond. [http://goo.gl/vvqNg Formalization of real analysis: A survey of proof assistants and libraries].
# F. Haftmann, A. Krauss, O. Kunčar y T. Nipkow [http://goo.gl/bEFYa Data refinement in Isabelle/HOL].
# A.C. Rocha y M. Ayala. [http://goo.gl/xTyvE Formalizing the confluence of orthogonal rewriting systems].
# Z. Shi et als. [http://goo.gl/zCYHj Formalization of the complex number theory in HOL4].
# F. Loulergue y V. Niculescu [http://goo.gl/kM0dI Programming and reasonning with PowerLists in Coq].
# J. Heras, F.J. Martín y V. Pascual. [http://goo.gl/KkU6s A hierarchy of mathematical structures in ACL2].
# J. Xu, X. Zhang y C. Urban [http://www.inf.kcl.ac.uk/staff/urbanc/Publications/tm.pdf Mechanising Turing Machines and Computability Theory in Isabelle/HOL]

Documentación

2022-02-08T10:21:30Z

Jalonso: /* Referencias sobre Isabelle/HOL */

En esta página se recogen en enlaces que sirven de documentación al curso de demostración asistida por ordenador (DAO).

== Visiones generales de la DAO ==

# J.A. Alonso. [http://goo.gl/NWk7b Razonamiento formalizado: Del sueño a la realidad de las pruebas]. ''Vestigium'', 26 de diciembre de 2012.
# J. Avigad. [http://www.andrew.cmu.edu/user/avigad/Talks/icerm.pdf Interactive theorem proving, automated reasoning, and mathematical computation]. ICERM, 14 de diciembre de 2012.
# M. Davis. [http://www.cs.nyu.edu/cs/faculty/davism/early.ps The early history of automated deduction].
# J.P. Delahaye [http://interstices.info/jcms/int_63417/du-reve-a-la-realite-des-preuves Du rêve à la réalité des preuves]. ''Interstices'', 8 de julio de 2012.
# J. Germoni [http://images.math.cnrs.fr/Coq-et-caracteres.html Coq et caractères: Preuve formelle du théorème de Feit et Thompson]. ''Images des Mathématiques'', CNRS, 23 de noviembre de 2012.
# H. Geuvers [http://www.ias.ac.in/sadhana/Pdf2009Feb/3.pdf Proof assistants: History, ideas and future]. ''Sadhana'', Vol. 34-1, pp. 3-25, février 2009.
# G. Gonthier [http://www.ams.org/notices/200811/tx081101382p.pdf The four-color theorem]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1382-1393, 2008.
# T. Hales. [http://www.ams.org/notices/200811/tx081101370p.pdf Formal proof]. ''Notices of AMS'', Vol. 55, N. 11 (2008) pp. 1370-1380.
# J. Harrison. [http://www.cl.cam.ac.uk/~jrh13/papers/ab.html A short survey of automated reasoning]. ''Lecture Notes in Computer Science'', Vol. 4545, pp. 334-349, 2007.
# J. Harrison. [http://www.ams.org/notices/200811/tx081101395p.pdf Formal proof: Theory and practice]. ''Notices of the AMS'', Vol. 55, N. 11 (2008) p.1395-1406.
# G. Kolata. [http://www.nytimes.com/library/cyber/week/1210math.html Computer math proof shows reasoning power]. ''The New York Times'', 10 de diciembre de 1996.
# D. MacKenzie [https://backspaces.net/temp/Spring2010Seminar/18%20unconventional%20essays%20on%20the%20nature%20of%20mathematics.pdf#page=147 Computers and the sociology of mathematical proof].
# G. Sutcliffe. [http://tptp.org/OverviewOfATP.html What is automated theorem proving?].
# F. Wiedijk [http://www.cs.ru.nl/~freek/100/ Formalizing the «top 100» of mathematical theorems].
# F. Wiedijk [http://www.ams.org/notices/200811/tx081101408p.pdf Formal proof - Getting started]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1408-1414, 2008.
# F. Wiedijk, [https://www.cs.ru.nl/F.Wiedijk/pubs/qed2.pdf The QED manifesto revisited]. ''Studies in Logic, Grammar and Rhetoric'', Vol. 10(23), pp. 121-133, 2007.

== Referencias sobre Isabelle/HOL ==
# B. Grechuk [https://web.cs.wpi.edu/~dd/resources_isabelle/isabelle_primer_mathematicians.pdf Isabelle primer for mathematicians].
# T. Nipkow [https://isabelle.in.tum.de/doc/prog-prove.pdf Programming and proving in Isabelle/HOL].
# T. Nipkow, M. Wenzel y L.C. Paulson [https://isabelle.in.tum.de/website-Isabelle2009/dist/Isabelle/doc/tutorial.pdf A proof assistant for higher-order logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL/document.pdf Isabelle/HOL — Higher-Order Logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/documentation.html Tutorials and manuals for Isabelle].

== Lecturas complementarias ==
=== Programación funcional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/i1m/temas/2012-13-IM-temas-PF.pdf Temas de "Programación funcional"]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# J.A. Alonso y M.J. Hidalgo [http://www.cs.us.es/~jalonso/publicaciones/Piensa_en_Haskell.pdf Piensa en Haskell (Ejercicios de programación funcional con Haskell)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# G. Hutton [http://goo.gl/pKqG Programming in Haskell]. Cambridge University Press, 2007.
# M. Lipovača [http://aprendehaskell.es ¡Aprende Haskell por el bien de todos!].

=== Lógica computacional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/li/temas/temas-LI-2012-13.pdf Temas de "Lógica informática" (2012-13)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# R. Bornat [http://bit.ly/oithic Proof and disproof in formal logic: an introduction for programmers]. Oxford University Press, 2005.
# K. Broda, S. Eisenbach, H. Khoshnevisan y S. Vickers [http://pubs.doc.ic.ac.uk/reasoned-programming/reasoned-programming.pdf Reasoned programming]. Imperial College, 1994.
# K. Doets y J. van Eijck [http://www.ldc.usb.ve/~astorga/Haskell.Road.pdf The Haskell Road to Logic, Maths and Programming].
# M. Huth y M. Ryan [http://goo.gl/TMqOo Logic in computer science: Modelling and reasoning about systems]. Cambridge University Press, 2004. (Incluye el [http://www.cs.bham.ac.uk/research/lics/tutor/index.html tutor en la Red]).

== Cursos relacionados ==
=== Cursos con Isabelle/HOL ===
# Jeremy Avigad. [http://www.phil.cmu.edu/~avigad/formal/ Logic and Formal Verification]. (Carnegie Mellon, 2009).
# Clemens Ballarin. [http://cl-informatik.uibk.ac.at/teaching/ss08/atp/introduction.php Automatic Deduction]. (Univ de Innsbruck, 2008).
# Clemens Ballarin. [http://www4.in.tum.de/~ballarin/belgrade08-tut/ Introduction to the Isabelle Proof Assistant]. (Belgrado, 2008).
# Clemens Ballarin y Gerwin Klein [http://isabelle.in.tum.de/coursematerial/IJCAR04 Introduction to the Isabelle Proof Assistant]. (en el IJCAR-2004).
# Clemens Ballarin y Tjark Weber. [http://cl-informatik.uibk.ac.at/teaching/ws06/atp/introduction.php Automated Theorem Proving in Isabelle/HOL]. (Univ. de Innsbruck, 2006-07).
# A.D. Brucker, D. Basin, J.G. Smaus y B. Wolff. [http://archiv.infsec.ethz.ch/education/permanent/csmr.html Computer-supported Modeling and Reasoning]. (ETH Zurich, 2011).
# Mads Dam. [http://www.csc.kth.se/utbildning/kth/kurser/DD2453/aform07/ Advanced formal methods]. (KTH Royal Institute of Technology, 2007).
# Jacques Fleuriot y Paul Jackson. [http://www.inf.ed.ac.uk/teaching/courses/ar/slides/ Automated reasoning]. (Univ. de Edimburgo, 2012-13).
# Thomas Genet [http://www.irisa.fr/celtique/genet/ACF Software formal analysis and design]. (Univ. de Rennes)
# Gerwin Klein. [http://www.cse.unsw.edu.au/~kleing/teaching/thprv-04 Theorem Proving - Principles, Techniques, Applications]. (NICTA, 2004).
# Gerwin Klein. [http://www.cse.unsw.edu.au/~cs4161/index.html Advanced Topics in Software Verification]. (NICTA, 2012).
# Joao Marcos. [http://www.dimap.ufrn.br/~jmarcos/courses/LC/Ementa.htm Lógica computacional: Demonstração assistida e semi-automática de teoremas].(UFRN, 2000).
# Tobias Nipkow. [http://www4.informatik.tu-muenchen.de/~nipkow/semantics/ Semantics of programming languages]. (Univ. de Munich, 2012-13).
# Tobias Nipkow [http://isabelle.in.tum.de/coursematerial/PSV2009-1 Theorem Proving with Isabelle/HOL An Intensive Course].
# Larry Paulson. [http://www.cl.cam.ac.uk/teaching/0910/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2009-10).
# Arnd Poetzsch-Heffter. [https://softech.informatik.uni-kl.de/Homepage/SVHOL10 Specification and Verification with Higher-Order Logic].
# Jeremy G. Siek. [http://www.cs.colorado.edu/~siek/7000/spring07/ Practical Theorem Proving with Isabelle/Isar]. (Univ. de Colorado, 2007).
# Jeremy G. Siek. [http://ecee.colorado.edu/~siek/ecen5013/spring11/ Theorem proving in Isabelle]. (Univ. de Colorado, 2011).
# Jan-Georg Smaus. [http://www.informatik.uni-freiburg.de/~ki/teaching/ws0910/csmr/lecture.html Computer-supported modeling and reasoning]. (Univ. de Feiburgo, 2009).
# Christian Sternagel [http://cl-informatik.uibk.ac.at/teaching/ss11/eve/content.php Experiments in Verification – Introduction to Isabelle/HOL]. (Univ. de Innsbruck, 2011-12).
# Tjark Weber. [http://www.cl.cam.ac.uk/teaching/1011/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2010-11).

=== Otros cursos ===
# José A. Alonso [http://www.cs.us.es/~jalonso/cursos/li/ Lógica informática] (Univ. de Sevilla, 2012-13).
# Yves Bertot, Pierre Casteran, Benjamin Gregoire, Pierre Letouzey y Assia Mahboubi [http://www.di.ens.fr/~zappa/teaching/coq/ecole11 Modelling and verifying algorithms in Coq: an introduction]. (INRIA Paris-Rocquencourt, 14-18 noviembre 2011).
# Pierre Castéran [http://www.labri.fr/perso/casteran/FM/Logique/index.html Logic (Master In Verification)] (Univ. de Burdeos, 2011-12).
# Nuno Gaspar [http://www-sop.inria.fr/members/Nuno.Gaspar/teaching/coq2012.php Verification with the Coq Proof Assistant] (INRIA Sophia Antipolis, 2012-13).
# Michael Genesereth [http://logic.stanford.edu/classes/cs157/2011/cs157.html Computational Logic] (Univ. de Stanford, 2011-12).
# Ian Hodkinson [http://www.doc.ic.ac.uk/~imh/teaching/140_logic/logic.html Logic] (Imperial College, Londres, 2010-11).
# Peter Lucas [http://www.cs.ru.nl/~peterl/teaching/KeR/ Knowledge Representation and Reasoning] (Radboud University # egen, 2011-12).
# Larry Paulson [http://www.cl.cam.ac.uk/Teaching/current/LogicProof/ Logic and Proof] (Univ. de Cambridge, 2011-12).
# Riccardo Pucella [http://www.ccs.neu.edu/home/riccardo/courses/csu290-sp09/index.html Logic and Computation] (Northeastern University, 2009). Curso con ACL2.

== Bibliotecas de ejemplos de verificación ==
# [http://afp.sourceforge.net Archive of Formal Proofs].
# [http://www.cs.ru.nl/~freek/100 Formalizing 100 Theorems].
# [http://toccata.lri.fr/gallery Gallery of verified programs].
# [http://www.cs.nott.ac.uk/~lad/research/challenges/ Induction Challenge Problems].
# [http://automatedreasoning.net/ Larry Wos' Notebooks].
# [http://www.cs.miami.edu/~tptp/ The TPTP Problem Library for Automated Theorem Proving].
# [http://www.macs.hw.ac.uk/vstte10/Competition.html The 1st Verified Software Competition].
# [https://sites.google.com/site/vstte2012/compet The 2nd Verified Software Competition].
# [http://verifythis.cost-ic0701.org VerifyThis (A collection of verification benchmarks].

== Artículos recientes ==
Están en orden cronológico inverso a la fecha de su reseña en [http://www.glc.us.es/~jalonso/vestigium/tag/resena Vestigium]:
# Joachim Breitner, Brian Huffman, Neil Mitchell y Christian Sternagel [http://bit.ly/19fiWAY Certified HLints with Isabelle/HOLCF-Prelude].
# Peter Lammich [http://bit.ly/ZfSQrQ Automatic data refinement].
# Assia Mahboubi [http://bit.ly/18vyjm7 The rooster and the butterflies (a machine-checked proof of the Jordan-Hölder theorem for finite groups)].
# Nathan Wetzler, Marijn J. H. Heule y Warren A. Hunt Jr. [http://bit.ly/114oyZV Mechanical verification of SAT refutations with extended resolution].
# Johannes Hölzl, Fabian Immler y Brian Huffman [http://bit.ly/13H0REu Type classes and filters for mathematical analysis in Isabelle/HOL]
# M. J. H. Heule, W. A. Hunt, Jr. y N. Wetzler [http://bit.ly/10fv8wO Verifying refutations with extended resolution].
# C. Lüth y M. Ring [http://bit.ly/10EcFWj A Web interface for Isabelle: The next generation].
# L. Liu, O. Hasan y S. Tahar [http://bit.ly/18P9CSv On the formalization of continuous-time Markov chains in HOL].
# A. Asperti y W. Ricciotti [http://bit.ly/17H2mqy Formalizing Turing machines].
# A. Lochbihler [http://bit.ly/YwuCeL Light-weight containers for Isabelle: efficient, extensible, nestable].
# L. Noschinski [http://bit.ly/10XLrRA Graph theory].
# G. Gonthier et als. [http://bit.ly/19kPEP4 A machine-checked proof of the odd order theorem].
# C. Doczkal, J.O. Kaiser y G. Smolka [http://goo.gl/LdihL A constructive theory of regular languages in Coq].
# C. Sternagel [http://goo.gl/gwcwL A formal proof of Kruskal’s tree theorem in Isabelle/HOL].
# C. Sternagel y R. Thiemann [http://goo.gl/CUF3e Formalizing Knuth-Bendix orders and Knuth-Bendix completion].
# C. Lange, C. Rowat, W. Windsteiger y M. Kerber [http://goo.gl/9JAfX Developing an auction theory toolbox].
# M. Spasić y F. Marić [http://goo.gl/6OfmQ Formalization of incremental simplex algorithm by stepwise refinement].
# J.C. Blanchette, A. Popescu y D. Traytel [http://goo.gl/Guxky Coinductive pearl: Modular first-order logic completeness].
# J. Esparza et als. [http://goo.gl/HUOl8 A fully verified executable LTL model checker].
# M. Kerber, C. Lange y C. Rowat. [http://goo.gl/RV54S ForMaRE - formal mathematical reasoning in economics].
# J. Urban. [http://goo.gl/Y7sIq AI over large formal knowledge bases: The first decade].
# S. Boldo, C. Lelay y G. Melquiond. [http://goo.gl/vvqNg Formalization of real analysis: A survey of proof assistants and libraries].
# F. Haftmann, A. Krauss, O. Kunčar y T. Nipkow [http://goo.gl/bEFYa Data refinement in Isabelle/HOL].
# A.C. Rocha y M. Ayala. [http://goo.gl/xTyvE Formalizing the confluence of orthogonal rewriting systems].
# Z. Shi et als. [http://goo.gl/zCYHj Formalization of the complex number theory in HOL4].
# F. Loulergue y V. Niculescu [http://goo.gl/kM0dI Programming and reasonning with PowerLists in Coq].
# J. Heras, F.J. Martín y V. Pascual. [http://goo.gl/KkU6s A hierarchy of mathematical structures in ACL2].
# J. Xu, X. Zhang y C. Urban [http://www.inf.kcl.ac.uk/staff/urbanc/Publications/tm.pdf Mechanising Turing Machines and Computability Theory in Isabelle/HOL]

Documentación

2022-02-08T10:20:53Z

Jalonso: /* Referencias sobre Isabelle/HOL */

En esta página se recogen en enlaces que sirven de documentación al curso de demostración asistida por ordenador (DAO).

== Visiones generales de la DAO ==

# J.A. Alonso. [http://goo.gl/NWk7b Razonamiento formalizado: Del sueño a la realidad de las pruebas]. ''Vestigium'', 26 de diciembre de 2012.
# J. Avigad. [http://www.andrew.cmu.edu/user/avigad/Talks/icerm.pdf Interactive theorem proving, automated reasoning, and mathematical computation]. ICERM, 14 de diciembre de 2012.
# M. Davis. [http://www.cs.nyu.edu/cs/faculty/davism/early.ps The early history of automated deduction].
# J.P. Delahaye [http://interstices.info/jcms/int_63417/du-reve-a-la-realite-des-preuves Du rêve à la réalité des preuves]. ''Interstices'', 8 de julio de 2012.
# J. Germoni [http://images.math.cnrs.fr/Coq-et-caracteres.html Coq et caractères: Preuve formelle du théorème de Feit et Thompson]. ''Images des Mathématiques'', CNRS, 23 de noviembre de 2012.
# H. Geuvers [http://www.ias.ac.in/sadhana/Pdf2009Feb/3.pdf Proof assistants: History, ideas and future]. ''Sadhana'', Vol. 34-1, pp. 3-25, février 2009.
# G. Gonthier [http://www.ams.org/notices/200811/tx081101382p.pdf The four-color theorem]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1382-1393, 2008.
# T. Hales. [http://www.ams.org/notices/200811/tx081101370p.pdf Formal proof]. ''Notices of AMS'', Vol. 55, N. 11 (2008) pp. 1370-1380.
# J. Harrison. [http://www.cl.cam.ac.uk/~jrh13/papers/ab.html A short survey of automated reasoning]. ''Lecture Notes in Computer Science'', Vol. 4545, pp. 334-349, 2007.
# J. Harrison. [http://www.ams.org/notices/200811/tx081101395p.pdf Formal proof: Theory and practice]. ''Notices of the AMS'', Vol. 55, N. 11 (2008) p.1395-1406.
# G. Kolata. [http://www.nytimes.com/library/cyber/week/1210math.html Computer math proof shows reasoning power]. ''The New York Times'', 10 de diciembre de 1996.
# D. MacKenzie [https://backspaces.net/temp/Spring2010Seminar/18%20unconventional%20essays%20on%20the%20nature%20of%20mathematics.pdf#page=147 Computers and the sociology of mathematical proof].
# G. Sutcliffe. [http://tptp.org/OverviewOfATP.html What is automated theorem proving?].
# F. Wiedijk [http://www.cs.ru.nl/~freek/100/ Formalizing the «top 100» of mathematical theorems].
# F. Wiedijk [http://www.ams.org/notices/200811/tx081101408p.pdf Formal proof - Getting started]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1408-1414, 2008.
# F. Wiedijk, [https://www.cs.ru.nl/F.Wiedijk/pubs/qed2.pdf The QED manifesto revisited]. ''Studies in Logic, Grammar and Rhetoric'', Vol. 10(23), pp. 121-133, 2007.

== Referencias sobre Isabelle/HOL ==
# B. Grechuk [https://web.cs.wpi.edu/~dd/resources_isabelle/isabelle_primer_mathematicians.pdf Isabelle primer for mathematicians].
# T. Nipkow [https://isabelle.in.tum.de/doc/prog-prove.pdf Programming and proving in Isabelle/HOL].
# T. Nipkow, M. Wenzel y L.C. Paulson [https://isabelle.in.tum.de/website-Isabelle2009/dist/Isabelle/doc/tutorial.pdf A proof assistant for higher-order logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL/document.pdf Isabelle/HOL — Higher-Order Logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/documentation.html Tutorials and manuals for Isabelle2013].

== Lecturas complementarias ==
=== Programación funcional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/i1m/temas/2012-13-IM-temas-PF.pdf Temas de "Programación funcional"]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# J.A. Alonso y M.J. Hidalgo [http://www.cs.us.es/~jalonso/publicaciones/Piensa_en_Haskell.pdf Piensa en Haskell (Ejercicios de programación funcional con Haskell)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# G. Hutton [http://goo.gl/pKqG Programming in Haskell]. Cambridge University Press, 2007.
# M. Lipovača [http://aprendehaskell.es ¡Aprende Haskell por el bien de todos!].

=== Lógica computacional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/li/temas/temas-LI-2012-13.pdf Temas de "Lógica informática" (2012-13)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# R. Bornat [http://bit.ly/oithic Proof and disproof in formal logic: an introduction for programmers]. Oxford University Press, 2005.
# K. Broda, S. Eisenbach, H. Khoshnevisan y S. Vickers [http://pubs.doc.ic.ac.uk/reasoned-programming/reasoned-programming.pdf Reasoned programming]. Imperial College, 1994.
# K. Doets y J. van Eijck [http://www.ldc.usb.ve/~astorga/Haskell.Road.pdf The Haskell Road to Logic, Maths and Programming].
# M. Huth y M. Ryan [http://goo.gl/TMqOo Logic in computer science: Modelling and reasoning about systems]. Cambridge University Press, 2004. (Incluye el [http://www.cs.bham.ac.uk/research/lics/tutor/index.html tutor en la Red]).

== Cursos relacionados ==
=== Cursos con Isabelle/HOL ===
# Jeremy Avigad. [http://www.phil.cmu.edu/~avigad/formal/ Logic and Formal Verification]. (Carnegie Mellon, 2009).
# Clemens Ballarin. [http://cl-informatik.uibk.ac.at/teaching/ss08/atp/introduction.php Automatic Deduction]. (Univ de Innsbruck, 2008).
# Clemens Ballarin. [http://www4.in.tum.de/~ballarin/belgrade08-tut/ Introduction to the Isabelle Proof Assistant]. (Belgrado, 2008).
# Clemens Ballarin y Gerwin Klein [http://isabelle.in.tum.de/coursematerial/IJCAR04 Introduction to the Isabelle Proof Assistant]. (en el IJCAR-2004).
# Clemens Ballarin y Tjark Weber. [http://cl-informatik.uibk.ac.at/teaching/ws06/atp/introduction.php Automated Theorem Proving in Isabelle/HOL]. (Univ. de Innsbruck, 2006-07).
# A.D. Brucker, D. Basin, J.G. Smaus y B. Wolff. [http://archiv.infsec.ethz.ch/education/permanent/csmr.html Computer-supported Modeling and Reasoning]. (ETH Zurich, 2011).
# Mads Dam. [http://www.csc.kth.se/utbildning/kth/kurser/DD2453/aform07/ Advanced formal methods]. (KTH Royal Institute of Technology, 2007).
# Jacques Fleuriot y Paul Jackson. [http://www.inf.ed.ac.uk/teaching/courses/ar/slides/ Automated reasoning]. (Univ. de Edimburgo, 2012-13).
# Thomas Genet [http://www.irisa.fr/celtique/genet/ACF Software formal analysis and design]. (Univ. de Rennes)
# Gerwin Klein. [http://www.cse.unsw.edu.au/~kleing/teaching/thprv-04 Theorem Proving - Principles, Techniques, Applications]. (NICTA, 2004).
# Gerwin Klein. [http://www.cse.unsw.edu.au/~cs4161/index.html Advanced Topics in Software Verification]. (NICTA, 2012).
# Joao Marcos. [http://www.dimap.ufrn.br/~jmarcos/courses/LC/Ementa.htm Lógica computacional: Demonstração assistida e semi-automática de teoremas].(UFRN, 2000).
# Tobias Nipkow. [http://www4.informatik.tu-muenchen.de/~nipkow/semantics/ Semantics of programming languages]. (Univ. de Munich, 2012-13).
# Tobias Nipkow [http://isabelle.in.tum.de/coursematerial/PSV2009-1 Theorem Proving with Isabelle/HOL An Intensive Course].
# Larry Paulson. [http://www.cl.cam.ac.uk/teaching/0910/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2009-10).
# Arnd Poetzsch-Heffter. [https://softech.informatik.uni-kl.de/Homepage/SVHOL10 Specification and Verification with Higher-Order Logic].
# Jeremy G. Siek. [http://www.cs.colorado.edu/~siek/7000/spring07/ Practical Theorem Proving with Isabelle/Isar]. (Univ. de Colorado, 2007).
# Jeremy G. Siek. [http://ecee.colorado.edu/~siek/ecen5013/spring11/ Theorem proving in Isabelle]. (Univ. de Colorado, 2011).
# Jan-Georg Smaus. [http://www.informatik.uni-freiburg.de/~ki/teaching/ws0910/csmr/lecture.html Computer-supported modeling and reasoning]. (Univ. de Feiburgo, 2009).
# Christian Sternagel [http://cl-informatik.uibk.ac.at/teaching/ss11/eve/content.php Experiments in Verification – Introduction to Isabelle/HOL]. (Univ. de Innsbruck, 2011-12).
# Tjark Weber. [http://www.cl.cam.ac.uk/teaching/1011/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2010-11).

=== Otros cursos ===
# José A. Alonso [http://www.cs.us.es/~jalonso/cursos/li/ Lógica informática] (Univ. de Sevilla, 2012-13).
# Yves Bertot, Pierre Casteran, Benjamin Gregoire, Pierre Letouzey y Assia Mahboubi [http://www.di.ens.fr/~zappa/teaching/coq/ecole11 Modelling and verifying algorithms in Coq: an introduction]. (INRIA Paris-Rocquencourt, 14-18 noviembre 2011).
# Pierre Castéran [http://www.labri.fr/perso/casteran/FM/Logique/index.html Logic (Master In Verification)] (Univ. de Burdeos, 2011-12).
# Nuno Gaspar [http://www-sop.inria.fr/members/Nuno.Gaspar/teaching/coq2012.php Verification with the Coq Proof Assistant] (INRIA Sophia Antipolis, 2012-13).
# Michael Genesereth [http://logic.stanford.edu/classes/cs157/2011/cs157.html Computational Logic] (Univ. de Stanford, 2011-12).
# Ian Hodkinson [http://www.doc.ic.ac.uk/~imh/teaching/140_logic/logic.html Logic] (Imperial College, Londres, 2010-11).
# Peter Lucas [http://www.cs.ru.nl/~peterl/teaching/KeR/ Knowledge Representation and Reasoning] (Radboud University # egen, 2011-12).
# Larry Paulson [http://www.cl.cam.ac.uk/Teaching/current/LogicProof/ Logic and Proof] (Univ. de Cambridge, 2011-12).
# Riccardo Pucella [http://www.ccs.neu.edu/home/riccardo/courses/csu290-sp09/index.html Logic and Computation] (Northeastern University, 2009). Curso con ACL2.

== Bibliotecas de ejemplos de verificación ==
# [http://afp.sourceforge.net Archive of Formal Proofs].
# [http://www.cs.ru.nl/~freek/100 Formalizing 100 Theorems].
# [http://toccata.lri.fr/gallery Gallery of verified programs].
# [http://www.cs.nott.ac.uk/~lad/research/challenges/ Induction Challenge Problems].
# [http://automatedreasoning.net/ Larry Wos' Notebooks].
# [http://www.cs.miami.edu/~tptp/ The TPTP Problem Library for Automated Theorem Proving].
# [http://www.macs.hw.ac.uk/vstte10/Competition.html The 1st Verified Software Competition].
# [https://sites.google.com/site/vstte2012/compet The 2nd Verified Software Competition].
# [http://verifythis.cost-ic0701.org VerifyThis (A collection of verification benchmarks].

== Artículos recientes ==
Están en orden cronológico inverso a la fecha de su reseña en [http://www.glc.us.es/~jalonso/vestigium/tag/resena Vestigium]:
# Joachim Breitner, Brian Huffman, Neil Mitchell y Christian Sternagel [http://bit.ly/19fiWAY Certified HLints with Isabelle/HOLCF-Prelude].
# Peter Lammich [http://bit.ly/ZfSQrQ Automatic data refinement].
# Assia Mahboubi [http://bit.ly/18vyjm7 The rooster and the butterflies (a machine-checked proof of the Jordan-Hölder theorem for finite groups)].
# Nathan Wetzler, Marijn J. H. Heule y Warren A. Hunt Jr. [http://bit.ly/114oyZV Mechanical verification of SAT refutations with extended resolution].
# Johannes Hölzl, Fabian Immler y Brian Huffman [http://bit.ly/13H0REu Type classes and filters for mathematical analysis in Isabelle/HOL]
# M. J. H. Heule, W. A. Hunt, Jr. y N. Wetzler [http://bit.ly/10fv8wO Verifying refutations with extended resolution].
# C. Lüth y M. Ring [http://bit.ly/10EcFWj A Web interface for Isabelle: The next generation].
# L. Liu, O. Hasan y S. Tahar [http://bit.ly/18P9CSv On the formalization of continuous-time Markov chains in HOL].
# A. Asperti y W. Ricciotti [http://bit.ly/17H2mqy Formalizing Turing machines].
# A. Lochbihler [http://bit.ly/YwuCeL Light-weight containers for Isabelle: efficient, extensible, nestable].
# L. Noschinski [http://bit.ly/10XLrRA Graph theory].
# G. Gonthier et als. [http://bit.ly/19kPEP4 A machine-checked proof of the odd order theorem].
# C. Doczkal, J.O. Kaiser y G. Smolka [http://goo.gl/LdihL A constructive theory of regular languages in Coq].
# C. Sternagel [http://goo.gl/gwcwL A formal proof of Kruskal’s tree theorem in Isabelle/HOL].
# C. Sternagel y R. Thiemann [http://goo.gl/CUF3e Formalizing Knuth-Bendix orders and Knuth-Bendix completion].
# C. Lange, C. Rowat, W. Windsteiger y M. Kerber [http://goo.gl/9JAfX Developing an auction theory toolbox].
# M. Spasić y F. Marić [http://goo.gl/6OfmQ Formalization of incremental simplex algorithm by stepwise refinement].
# J.C. Blanchette, A. Popescu y D. Traytel [http://goo.gl/Guxky Coinductive pearl: Modular first-order logic completeness].
# J. Esparza et als. [http://goo.gl/HUOl8 A fully verified executable LTL model checker].
# M. Kerber, C. Lange y C. Rowat. [http://goo.gl/RV54S ForMaRE - formal mathematical reasoning in economics].
# J. Urban. [http://goo.gl/Y7sIq AI over large formal knowledge bases: The first decade].
# S. Boldo, C. Lelay y G. Melquiond. [http://goo.gl/vvqNg Formalization of real analysis: A survey of proof assistants and libraries].
# F. Haftmann, A. Krauss, O. Kunčar y T. Nipkow [http://goo.gl/bEFYa Data refinement in Isabelle/HOL].
# A.C. Rocha y M. Ayala. [http://goo.gl/xTyvE Formalizing the confluence of orthogonal rewriting systems].
# Z. Shi et als. [http://goo.gl/zCYHj Formalization of the complex number theory in HOL4].
# F. Loulergue y V. Niculescu [http://goo.gl/kM0dI Programming and reasonning with PowerLists in Coq].
# J. Heras, F.J. Martín y V. Pascual. [http://goo.gl/KkU6s A hierarchy of mathematical structures in ACL2].
# J. Xu, X. Zhang y C. Urban [http://www.inf.kcl.ac.uk/staff/urbanc/Publications/tm.pdf Mechanising Turing Machines and Computability Theory in Isabelle/HOL]

Documentación

2022-02-08T10:19:07Z

Jalonso: /* Referencias sobre Isabelle/HOL */

En esta página se recogen en enlaces que sirven de documentación al curso de demostración asistida por ordenador (DAO).

== Visiones generales de la DAO ==

# J.A. Alonso. [http://goo.gl/NWk7b Razonamiento formalizado: Del sueño a la realidad de las pruebas]. ''Vestigium'', 26 de diciembre de 2012.
# J. Avigad. [http://www.andrew.cmu.edu/user/avigad/Talks/icerm.pdf Interactive theorem proving, automated reasoning, and mathematical computation]. ICERM, 14 de diciembre de 2012.
# M. Davis. [http://www.cs.nyu.edu/cs/faculty/davism/early.ps The early history of automated deduction].
# J.P. Delahaye [http://interstices.info/jcms/int_63417/du-reve-a-la-realite-des-preuves Du rêve à la réalité des preuves]. ''Interstices'', 8 de julio de 2012.
# J. Germoni [http://images.math.cnrs.fr/Coq-et-caracteres.html Coq et caractères: Preuve formelle du théorème de Feit et Thompson]. ''Images des Mathématiques'', CNRS, 23 de noviembre de 2012.
# H. Geuvers [http://www.ias.ac.in/sadhana/Pdf2009Feb/3.pdf Proof assistants: History, ideas and future]. ''Sadhana'', Vol. 34-1, pp. 3-25, février 2009.
# G. Gonthier [http://www.ams.org/notices/200811/tx081101382p.pdf The four-color theorem]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1382-1393, 2008.
# T. Hales. [http://www.ams.org/notices/200811/tx081101370p.pdf Formal proof]. ''Notices of AMS'', Vol. 55, N. 11 (2008) pp. 1370-1380.
# J. Harrison. [http://www.cl.cam.ac.uk/~jrh13/papers/ab.html A short survey of automated reasoning]. ''Lecture Notes in Computer Science'', Vol. 4545, pp. 334-349, 2007.
# J. Harrison. [http://www.ams.org/notices/200811/tx081101395p.pdf Formal proof: Theory and practice]. ''Notices of the AMS'', Vol. 55, N. 11 (2008) p.1395-1406.
# G. Kolata. [http://www.nytimes.com/library/cyber/week/1210math.html Computer math proof shows reasoning power]. ''The New York Times'', 10 de diciembre de 1996.
# D. MacKenzie [https://backspaces.net/temp/Spring2010Seminar/18%20unconventional%20essays%20on%20the%20nature%20of%20mathematics.pdf#page=147 Computers and the sociology of mathematical proof].
# G. Sutcliffe. [http://tptp.org/OverviewOfATP.html What is automated theorem proving?].
# F. Wiedijk [http://www.cs.ru.nl/~freek/100/ Formalizing the «top 100» of mathematical theorems].
# F. Wiedijk [http://www.ams.org/notices/200811/tx081101408p.pdf Formal proof - Getting started]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1408-1414, 2008.
# F. Wiedijk, [https://www.cs.ru.nl/F.Wiedijk/pubs/qed2.pdf The QED manifesto revisited]. ''Studies in Logic, Grammar and Rhetoric'', Vol. 10(23), pp. 121-133, 2007.

== Referencias sobre Isabelle/HOL ==
# B. Grechuk [https://web.cs.wpi.edu/~dd/resources_isabelle/isabelle_primer_mathematicians.pdf Isabelle primer for mathematicians].
# T. Nipkow [https://isabelle.in.tum.de/doc/prog-prove.pdf Programming and proving in Isabelle/HOL].
# T. Nipkow, M. Wenzel y L.C. Paulson [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/Isabelle2013-2/doc/tutorial.pdf A proof assistant for higher-order logic]. Springer-Verlag.
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL/document.pdf Isabelle/HOL — Higher-Order Logic].
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/documentation.html Tutorials and manuals for Isabelle2013].

== Lecturas complementarias ==
=== Programación funcional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/i1m/temas/2012-13-IM-temas-PF.pdf Temas de "Programación funcional"]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# J.A. Alonso y M.J. Hidalgo [http://www.cs.us.es/~jalonso/publicaciones/Piensa_en_Haskell.pdf Piensa en Haskell (Ejercicios de programación funcional con Haskell)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# G. Hutton [http://goo.gl/pKqG Programming in Haskell]. Cambridge University Press, 2007.
# M. Lipovača [http://aprendehaskell.es ¡Aprende Haskell por el bien de todos!].

=== Lógica computacional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/li/temas/temas-LI-2012-13.pdf Temas de "Lógica informática" (2012-13)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# R. Bornat [http://bit.ly/oithic Proof and disproof in formal logic: an introduction for programmers]. Oxford University Press, 2005.
# K. Broda, S. Eisenbach, H. Khoshnevisan y S. Vickers [http://pubs.doc.ic.ac.uk/reasoned-programming/reasoned-programming.pdf Reasoned programming]. Imperial College, 1994.
# K. Doets y J. van Eijck [http://www.ldc.usb.ve/~astorga/Haskell.Road.pdf The Haskell Road to Logic, Maths and Programming].
# M. Huth y M. Ryan [http://goo.gl/TMqOo Logic in computer science: Modelling and reasoning about systems]. Cambridge University Press, 2004. (Incluye el [http://www.cs.bham.ac.uk/research/lics/tutor/index.html tutor en la Red]).

== Cursos relacionados ==
=== Cursos con Isabelle/HOL ===
# Jeremy Avigad. [http://www.phil.cmu.edu/~avigad/formal/ Logic and Formal Verification]. (Carnegie Mellon, 2009).
# Clemens Ballarin. [http://cl-informatik.uibk.ac.at/teaching/ss08/atp/introduction.php Automatic Deduction]. (Univ de Innsbruck, 2008).
# Clemens Ballarin. [http://www4.in.tum.de/~ballarin/belgrade08-tut/ Introduction to the Isabelle Proof Assistant]. (Belgrado, 2008).
# Clemens Ballarin y Gerwin Klein [http://isabelle.in.tum.de/coursematerial/IJCAR04 Introduction to the Isabelle Proof Assistant]. (en el IJCAR-2004).
# Clemens Ballarin y Tjark Weber. [http://cl-informatik.uibk.ac.at/teaching/ws06/atp/introduction.php Automated Theorem Proving in Isabelle/HOL]. (Univ. de Innsbruck, 2006-07).
# A.D. Brucker, D. Basin, J.G. Smaus y B. Wolff. [http://archiv.infsec.ethz.ch/education/permanent/csmr.html Computer-supported Modeling and Reasoning]. (ETH Zurich, 2011).
# Mads Dam. [http://www.csc.kth.se/utbildning/kth/kurser/DD2453/aform07/ Advanced formal methods]. (KTH Royal Institute of Technology, 2007).
# Jacques Fleuriot y Paul Jackson. [http://www.inf.ed.ac.uk/teaching/courses/ar/slides/ Automated reasoning]. (Univ. de Edimburgo, 2012-13).
# Thomas Genet [http://www.irisa.fr/celtique/genet/ACF Software formal analysis and design]. (Univ. de Rennes)
# Gerwin Klein. [http://www.cse.unsw.edu.au/~kleing/teaching/thprv-04 Theorem Proving - Principles, Techniques, Applications]. (NICTA, 2004).
# Gerwin Klein. [http://www.cse.unsw.edu.au/~cs4161/index.html Advanced Topics in Software Verification]. (NICTA, 2012).
# Joao Marcos. [http://www.dimap.ufrn.br/~jmarcos/courses/LC/Ementa.htm Lógica computacional: Demonstração assistida e semi-automática de teoremas].(UFRN, 2000).
# Tobias Nipkow. [http://www4.informatik.tu-muenchen.de/~nipkow/semantics/ Semantics of programming languages]. (Univ. de Munich, 2012-13).
# Tobias Nipkow [http://isabelle.in.tum.de/coursematerial/PSV2009-1 Theorem Proving with Isabelle/HOL An Intensive Course].
# Larry Paulson. [http://www.cl.cam.ac.uk/teaching/0910/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2009-10).
# Arnd Poetzsch-Heffter. [https://softech.informatik.uni-kl.de/Homepage/SVHOL10 Specification and Verification with Higher-Order Logic].
# Jeremy G. Siek. [http://www.cs.colorado.edu/~siek/7000/spring07/ Practical Theorem Proving with Isabelle/Isar]. (Univ. de Colorado, 2007).
# Jeremy G. Siek. [http://ecee.colorado.edu/~siek/ecen5013/spring11/ Theorem proving in Isabelle]. (Univ. de Colorado, 2011).
# Jan-Georg Smaus. [http://www.informatik.uni-freiburg.de/~ki/teaching/ws0910/csmr/lecture.html Computer-supported modeling and reasoning]. (Univ. de Feiburgo, 2009).
# Christian Sternagel [http://cl-informatik.uibk.ac.at/teaching/ss11/eve/content.php Experiments in Verification – Introduction to Isabelle/HOL]. (Univ. de Innsbruck, 2011-12).
# Tjark Weber. [http://www.cl.cam.ac.uk/teaching/1011/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2010-11).

=== Otros cursos ===
# José A. Alonso [http://www.cs.us.es/~jalonso/cursos/li/ Lógica informática] (Univ. de Sevilla, 2012-13).
# Yves Bertot, Pierre Casteran, Benjamin Gregoire, Pierre Letouzey y Assia Mahboubi [http://www.di.ens.fr/~zappa/teaching/coq/ecole11 Modelling and verifying algorithms in Coq: an introduction]. (INRIA Paris-Rocquencourt, 14-18 noviembre 2011).
# Pierre Castéran [http://www.labri.fr/perso/casteran/FM/Logique/index.html Logic (Master In Verification)] (Univ. de Burdeos, 2011-12).
# Nuno Gaspar [http://www-sop.inria.fr/members/Nuno.Gaspar/teaching/coq2012.php Verification with the Coq Proof Assistant] (INRIA Sophia Antipolis, 2012-13).
# Michael Genesereth [http://logic.stanford.edu/classes/cs157/2011/cs157.html Computational Logic] (Univ. de Stanford, 2011-12).
# Ian Hodkinson [http://www.doc.ic.ac.uk/~imh/teaching/140_logic/logic.html Logic] (Imperial College, Londres, 2010-11).
# Peter Lucas [http://www.cs.ru.nl/~peterl/teaching/KeR/ Knowledge Representation and Reasoning] (Radboud University # egen, 2011-12).
# Larry Paulson [http://www.cl.cam.ac.uk/Teaching/current/LogicProof/ Logic and Proof] (Univ. de Cambridge, 2011-12).
# Riccardo Pucella [http://www.ccs.neu.edu/home/riccardo/courses/csu290-sp09/index.html Logic and Computation] (Northeastern University, 2009). Curso con ACL2.

== Bibliotecas de ejemplos de verificación ==
# [http://afp.sourceforge.net Archive of Formal Proofs].
# [http://www.cs.ru.nl/~freek/100 Formalizing 100 Theorems].
# [http://toccata.lri.fr/gallery Gallery of verified programs].
# [http://www.cs.nott.ac.uk/~lad/research/challenges/ Induction Challenge Problems].
# [http://automatedreasoning.net/ Larry Wos' Notebooks].
# [http://www.cs.miami.edu/~tptp/ The TPTP Problem Library for Automated Theorem Proving].
# [http://www.macs.hw.ac.uk/vstte10/Competition.html The 1st Verified Software Competition].
# [https://sites.google.com/site/vstte2012/compet The 2nd Verified Software Competition].
# [http://verifythis.cost-ic0701.org VerifyThis (A collection of verification benchmarks].

== Artículos recientes ==
Están en orden cronológico inverso a la fecha de su reseña en [http://www.glc.us.es/~jalonso/vestigium/tag/resena Vestigium]:
# Joachim Breitner, Brian Huffman, Neil Mitchell y Christian Sternagel [http://bit.ly/19fiWAY Certified HLints with Isabelle/HOLCF-Prelude].
# Peter Lammich [http://bit.ly/ZfSQrQ Automatic data refinement].
# Assia Mahboubi [http://bit.ly/18vyjm7 The rooster and the butterflies (a machine-checked proof of the Jordan-Hölder theorem for finite groups)].
# Nathan Wetzler, Marijn J. H. Heule y Warren A. Hunt Jr. [http://bit.ly/114oyZV Mechanical verification of SAT refutations with extended resolution].
# Johannes Hölzl, Fabian Immler y Brian Huffman [http://bit.ly/13H0REu Type classes and filters for mathematical analysis in Isabelle/HOL]
# M. J. H. Heule, W. A. Hunt, Jr. y N. Wetzler [http://bit.ly/10fv8wO Verifying refutations with extended resolution].
# C. Lüth y M. Ring [http://bit.ly/10EcFWj A Web interface for Isabelle: The next generation].
# L. Liu, O. Hasan y S. Tahar [http://bit.ly/18P9CSv On the formalization of continuous-time Markov chains in HOL].
# A. Asperti y W. Ricciotti [http://bit.ly/17H2mqy Formalizing Turing machines].
# A. Lochbihler [http://bit.ly/YwuCeL Light-weight containers for Isabelle: efficient, extensible, nestable].
# L. Noschinski [http://bit.ly/10XLrRA Graph theory].
# G. Gonthier et als. [http://bit.ly/19kPEP4 A machine-checked proof of the odd order theorem].
# C. Doczkal, J.O. Kaiser y G. Smolka [http://goo.gl/LdihL A constructive theory of regular languages in Coq].
# C. Sternagel [http://goo.gl/gwcwL A formal proof of Kruskal’s tree theorem in Isabelle/HOL].
# C. Sternagel y R. Thiemann [http://goo.gl/CUF3e Formalizing Knuth-Bendix orders and Knuth-Bendix completion].
# C. Lange, C. Rowat, W. Windsteiger y M. Kerber [http://goo.gl/9JAfX Developing an auction theory toolbox].
# M. Spasić y F. Marić [http://goo.gl/6OfmQ Formalization of incremental simplex algorithm by stepwise refinement].
# J.C. Blanchette, A. Popescu y D. Traytel [http://goo.gl/Guxky Coinductive pearl: Modular first-order logic completeness].
# J. Esparza et als. [http://goo.gl/HUOl8 A fully verified executable LTL model checker].
# M. Kerber, C. Lange y C. Rowat. [http://goo.gl/RV54S ForMaRE - formal mathematical reasoning in economics].
# J. Urban. [http://goo.gl/Y7sIq AI over large formal knowledge bases: The first decade].
# S. Boldo, C. Lelay y G. Melquiond. [http://goo.gl/vvqNg Formalization of real analysis: A survey of proof assistants and libraries].
# F. Haftmann, A. Krauss, O. Kunčar y T. Nipkow [http://goo.gl/bEFYa Data refinement in Isabelle/HOL].
# A.C. Rocha y M. Ayala. [http://goo.gl/xTyvE Formalizing the confluence of orthogonal rewriting systems].
# Z. Shi et als. [http://goo.gl/zCYHj Formalization of the complex number theory in HOL4].
# F. Loulergue y V. Niculescu [http://goo.gl/kM0dI Programming and reasonning with PowerLists in Coq].
# J. Heras, F.J. Martín y V. Pascual. [http://goo.gl/KkU6s A hierarchy of mathematical structures in ACL2].
# J. Xu, X. Zhang y C. Urban [http://www.inf.kcl.ac.uk/staff/urbanc/Publications/tm.pdf Mechanising Turing Machines and Computability Theory in Isabelle/HOL]

Documentación

2022-02-08T10:17:28Z

Jalonso: /* Referencias sobre Isabelle/HOL */

En esta página se recogen en enlaces que sirven de documentación al curso de demostración asistida por ordenador (DAO).

== Visiones generales de la DAO ==

# J.A. Alonso. [http://goo.gl/NWk7b Razonamiento formalizado: Del sueño a la realidad de las pruebas]. ''Vestigium'', 26 de diciembre de 2012.
# J. Avigad. [http://www.andrew.cmu.edu/user/avigad/Talks/icerm.pdf Interactive theorem proving, automated reasoning, and mathematical computation]. ICERM, 14 de diciembre de 2012.
# M. Davis. [http://www.cs.nyu.edu/cs/faculty/davism/early.ps The early history of automated deduction].
# J.P. Delahaye [http://interstices.info/jcms/int_63417/du-reve-a-la-realite-des-preuves Du rêve à la réalité des preuves]. ''Interstices'', 8 de julio de 2012.
# J. Germoni [http://images.math.cnrs.fr/Coq-et-caracteres.html Coq et caractères: Preuve formelle du théorème de Feit et Thompson]. ''Images des Mathématiques'', CNRS, 23 de noviembre de 2012.
# H. Geuvers [http://www.ias.ac.in/sadhana/Pdf2009Feb/3.pdf Proof assistants: History, ideas and future]. ''Sadhana'', Vol. 34-1, pp. 3-25, février 2009.
# G. Gonthier [http://www.ams.org/notices/200811/tx081101382p.pdf The four-color theorem]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1382-1393, 2008.
# T. Hales. [http://www.ams.org/notices/200811/tx081101370p.pdf Formal proof]. ''Notices of AMS'', Vol. 55, N. 11 (2008) pp. 1370-1380.
# J. Harrison. [http://www.cl.cam.ac.uk/~jrh13/papers/ab.html A short survey of automated reasoning]. ''Lecture Notes in Computer Science'', Vol. 4545, pp. 334-349, 2007.
# J. Harrison. [http://www.ams.org/notices/200811/tx081101395p.pdf Formal proof: Theory and practice]. ''Notices of the AMS'', Vol. 55, N. 11 (2008) p.1395-1406.
# G. Kolata. [http://www.nytimes.com/library/cyber/week/1210math.html Computer math proof shows reasoning power]. ''The New York Times'', 10 de diciembre de 1996.
# D. MacKenzie [https://backspaces.net/temp/Spring2010Seminar/18%20unconventional%20essays%20on%20the%20nature%20of%20mathematics.pdf#page=147 Computers and the sociology of mathematical proof].
# G. Sutcliffe. [http://tptp.org/OverviewOfATP.html What is automated theorem proving?].
# F. Wiedijk [http://www.cs.ru.nl/~freek/100/ Formalizing the «top 100» of mathematical theorems].
# F. Wiedijk [http://www.ams.org/notices/200811/tx081101408p.pdf Formal proof - Getting started]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1408-1414, 2008.
# F. Wiedijk, [https://www.cs.ru.nl/F.Wiedijk/pubs/qed2.pdf The QED manifesto revisited]. ''Studies in Logic, Grammar and Rhetoric'', Vol. 10(23), pp. 121-133, 2007.

== Referencias sobre Isabelle/HOL ==
# B. Grechuk [https://web.cs.wpi.edu/~dd/resources_isabelle/isabelle_primer_mathematicians.pdf Isabelle primer for mathematicians].
# T. Nipkow [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/Isabelle2013-2/doc/prog-prove.pdf Programming and proving in Isabelle/HOL]. 5 de diciembre de 2013.
# T. Nipkow, M. Wenzel y L.C. Paulson [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/Isabelle2013-2/doc/tutorial.pdf A proof assistant for higher-order logic]. Springer-Verlag. 5 de diciembre de 2013.
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL/document.pdf Isabelle/HOL — Higher-Order Logic]. 12 de febrero de 2013.
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/documentation.html Tutorials and manuals for Isabelle2013].

== Lecturas complementarias ==
=== Programación funcional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/i1m/temas/2012-13-IM-temas-PF.pdf Temas de "Programación funcional"]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# J.A. Alonso y M.J. Hidalgo [http://www.cs.us.es/~jalonso/publicaciones/Piensa_en_Haskell.pdf Piensa en Haskell (Ejercicios de programación funcional con Haskell)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# G. Hutton [http://goo.gl/pKqG Programming in Haskell]. Cambridge University Press, 2007.
# M. Lipovača [http://aprendehaskell.es ¡Aprende Haskell por el bien de todos!].

=== Lógica computacional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/li/temas/temas-LI-2012-13.pdf Temas de "Lógica informática" (2012-13)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# R. Bornat [http://bit.ly/oithic Proof and disproof in formal logic: an introduction for programmers]. Oxford University Press, 2005.
# K. Broda, S. Eisenbach, H. Khoshnevisan y S. Vickers [http://pubs.doc.ic.ac.uk/reasoned-programming/reasoned-programming.pdf Reasoned programming]. Imperial College, 1994.
# K. Doets y J. van Eijck [http://www.ldc.usb.ve/~astorga/Haskell.Road.pdf The Haskell Road to Logic, Maths and Programming].
# M. Huth y M. Ryan [http://goo.gl/TMqOo Logic in computer science: Modelling and reasoning about systems]. Cambridge University Press, 2004. (Incluye el [http://www.cs.bham.ac.uk/research/lics/tutor/index.html tutor en la Red]).

== Cursos relacionados ==
=== Cursos con Isabelle/HOL ===
# Jeremy Avigad. [http://www.phil.cmu.edu/~avigad/formal/ Logic and Formal Verification]. (Carnegie Mellon, 2009).
# Clemens Ballarin. [http://cl-informatik.uibk.ac.at/teaching/ss08/atp/introduction.php Automatic Deduction]. (Univ de Innsbruck, 2008).
# Clemens Ballarin. [http://www4.in.tum.de/~ballarin/belgrade08-tut/ Introduction to the Isabelle Proof Assistant]. (Belgrado, 2008).
# Clemens Ballarin y Gerwin Klein [http://isabelle.in.tum.de/coursematerial/IJCAR04 Introduction to the Isabelle Proof Assistant]. (en el IJCAR-2004).
# Clemens Ballarin y Tjark Weber. [http://cl-informatik.uibk.ac.at/teaching/ws06/atp/introduction.php Automated Theorem Proving in Isabelle/HOL]. (Univ. de Innsbruck, 2006-07).
# A.D. Brucker, D. Basin, J.G. Smaus y B. Wolff. [http://archiv.infsec.ethz.ch/education/permanent/csmr.html Computer-supported Modeling and Reasoning]. (ETH Zurich, 2011).
# Mads Dam. [http://www.csc.kth.se/utbildning/kth/kurser/DD2453/aform07/ Advanced formal methods]. (KTH Royal Institute of Technology, 2007).
# Jacques Fleuriot y Paul Jackson. [http://www.inf.ed.ac.uk/teaching/courses/ar/slides/ Automated reasoning]. (Univ. de Edimburgo, 2012-13).
# Thomas Genet [http://www.irisa.fr/celtique/genet/ACF Software formal analysis and design]. (Univ. de Rennes)
# Gerwin Klein. [http://www.cse.unsw.edu.au/~kleing/teaching/thprv-04 Theorem Proving - Principles, Techniques, Applications]. (NICTA, 2004).
# Gerwin Klein. [http://www.cse.unsw.edu.au/~cs4161/index.html Advanced Topics in Software Verification]. (NICTA, 2012).
# Joao Marcos. [http://www.dimap.ufrn.br/~jmarcos/courses/LC/Ementa.htm Lógica computacional: Demonstração assistida e semi-automática de teoremas].(UFRN, 2000).
# Tobias Nipkow. [http://www4.informatik.tu-muenchen.de/~nipkow/semantics/ Semantics of programming languages]. (Univ. de Munich, 2012-13).
# Tobias Nipkow [http://isabelle.in.tum.de/coursematerial/PSV2009-1 Theorem Proving with Isabelle/HOL An Intensive Course].
# Larry Paulson. [http://www.cl.cam.ac.uk/teaching/0910/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2009-10).
# Arnd Poetzsch-Heffter. [https://softech.informatik.uni-kl.de/Homepage/SVHOL10 Specification and Verification with Higher-Order Logic].
# Jeremy G. Siek. [http://www.cs.colorado.edu/~siek/7000/spring07/ Practical Theorem Proving with Isabelle/Isar]. (Univ. de Colorado, 2007).
# Jeremy G. Siek. [http://ecee.colorado.edu/~siek/ecen5013/spring11/ Theorem proving in Isabelle]. (Univ. de Colorado, 2011).
# Jan-Georg Smaus. [http://www.informatik.uni-freiburg.de/~ki/teaching/ws0910/csmr/lecture.html Computer-supported modeling and reasoning]. (Univ. de Feiburgo, 2009).
# Christian Sternagel [http://cl-informatik.uibk.ac.at/teaching/ss11/eve/content.php Experiments in Verification – Introduction to Isabelle/HOL]. (Univ. de Innsbruck, 2011-12).
# Tjark Weber. [http://www.cl.cam.ac.uk/teaching/1011/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2010-11).

=== Otros cursos ===
# José A. Alonso [http://www.cs.us.es/~jalonso/cursos/li/ Lógica informática] (Univ. de Sevilla, 2012-13).
# Yves Bertot, Pierre Casteran, Benjamin Gregoire, Pierre Letouzey y Assia Mahboubi [http://www.di.ens.fr/~zappa/teaching/coq/ecole11 Modelling and verifying algorithms in Coq: an introduction]. (INRIA Paris-Rocquencourt, 14-18 noviembre 2011).
# Pierre Castéran [http://www.labri.fr/perso/casteran/FM/Logique/index.html Logic (Master In Verification)] (Univ. de Burdeos, 2011-12).
# Nuno Gaspar [http://www-sop.inria.fr/members/Nuno.Gaspar/teaching/coq2012.php Verification with the Coq Proof Assistant] (INRIA Sophia Antipolis, 2012-13).
# Michael Genesereth [http://logic.stanford.edu/classes/cs157/2011/cs157.html Computational Logic] (Univ. de Stanford, 2011-12).
# Ian Hodkinson [http://www.doc.ic.ac.uk/~imh/teaching/140_logic/logic.html Logic] (Imperial College, Londres, 2010-11).
# Peter Lucas [http://www.cs.ru.nl/~peterl/teaching/KeR/ Knowledge Representation and Reasoning] (Radboud University # egen, 2011-12).
# Larry Paulson [http://www.cl.cam.ac.uk/Teaching/current/LogicProof/ Logic and Proof] (Univ. de Cambridge, 2011-12).
# Riccardo Pucella [http://www.ccs.neu.edu/home/riccardo/courses/csu290-sp09/index.html Logic and Computation] (Northeastern University, 2009). Curso con ACL2.

== Bibliotecas de ejemplos de verificación ==
# [http://afp.sourceforge.net Archive of Formal Proofs].
# [http://www.cs.ru.nl/~freek/100 Formalizing 100 Theorems].
# [http://toccata.lri.fr/gallery Gallery of verified programs].
# [http://www.cs.nott.ac.uk/~lad/research/challenges/ Induction Challenge Problems].
# [http://automatedreasoning.net/ Larry Wos' Notebooks].
# [http://www.cs.miami.edu/~tptp/ The TPTP Problem Library for Automated Theorem Proving].
# [http://www.macs.hw.ac.uk/vstte10/Competition.html The 1st Verified Software Competition].
# [https://sites.google.com/site/vstte2012/compet The 2nd Verified Software Competition].
# [http://verifythis.cost-ic0701.org VerifyThis (A collection of verification benchmarks].

== Artículos recientes ==
Están en orden cronológico inverso a la fecha de su reseña en [http://www.glc.us.es/~jalonso/vestigium/tag/resena Vestigium]:
# Joachim Breitner, Brian Huffman, Neil Mitchell y Christian Sternagel [http://bit.ly/19fiWAY Certified HLints with Isabelle/HOLCF-Prelude].
# Peter Lammich [http://bit.ly/ZfSQrQ Automatic data refinement].
# Assia Mahboubi [http://bit.ly/18vyjm7 The rooster and the butterflies (a machine-checked proof of the Jordan-Hölder theorem for finite groups)].
# Nathan Wetzler, Marijn J. H. Heule y Warren A. Hunt Jr. [http://bit.ly/114oyZV Mechanical verification of SAT refutations with extended resolution].
# Johannes Hölzl, Fabian Immler y Brian Huffman [http://bit.ly/13H0REu Type classes and filters for mathematical analysis in Isabelle/HOL]
# M. J. H. Heule, W. A. Hunt, Jr. y N. Wetzler [http://bit.ly/10fv8wO Verifying refutations with extended resolution].
# C. Lüth y M. Ring [http://bit.ly/10EcFWj A Web interface for Isabelle: The next generation].
# L. Liu, O. Hasan y S. Tahar [http://bit.ly/18P9CSv On the formalization of continuous-time Markov chains in HOL].
# A. Asperti y W. Ricciotti [http://bit.ly/17H2mqy Formalizing Turing machines].
# A. Lochbihler [http://bit.ly/YwuCeL Light-weight containers for Isabelle: efficient, extensible, nestable].
# L. Noschinski [http://bit.ly/10XLrRA Graph theory].
# G. Gonthier et als. [http://bit.ly/19kPEP4 A machine-checked proof of the odd order theorem].
# C. Doczkal, J.O. Kaiser y G. Smolka [http://goo.gl/LdihL A constructive theory of regular languages in Coq].
# C. Sternagel [http://goo.gl/gwcwL A formal proof of Kruskal’s tree theorem in Isabelle/HOL].
# C. Sternagel y R. Thiemann [http://goo.gl/CUF3e Formalizing Knuth-Bendix orders and Knuth-Bendix completion].
# C. Lange, C. Rowat, W. Windsteiger y M. Kerber [http://goo.gl/9JAfX Developing an auction theory toolbox].
# M. Spasić y F. Marić [http://goo.gl/6OfmQ Formalization of incremental simplex algorithm by stepwise refinement].
# J.C. Blanchette, A. Popescu y D. Traytel [http://goo.gl/Guxky Coinductive pearl: Modular first-order logic completeness].
# J. Esparza et als. [http://goo.gl/HUOl8 A fully verified executable LTL model checker].
# M. Kerber, C. Lange y C. Rowat. [http://goo.gl/RV54S ForMaRE - formal mathematical reasoning in economics].
# J. Urban. [http://goo.gl/Y7sIq AI over large formal knowledge bases: The first decade].
# S. Boldo, C. Lelay y G. Melquiond. [http://goo.gl/vvqNg Formalization of real analysis: A survey of proof assistants and libraries].
# F. Haftmann, A. Krauss, O. Kunčar y T. Nipkow [http://goo.gl/bEFYa Data refinement in Isabelle/HOL].
# A.C. Rocha y M. Ayala. [http://goo.gl/xTyvE Formalizing the confluence of orthogonal rewriting systems].
# Z. Shi et als. [http://goo.gl/zCYHj Formalization of the complex number theory in HOL4].
# F. Loulergue y V. Niculescu [http://goo.gl/kM0dI Programming and reasonning with PowerLists in Coq].
# J. Heras, F.J. Martín y V. Pascual. [http://goo.gl/KkU6s A hierarchy of mathematical structures in ACL2].
# J. Xu, X. Zhang y C. Urban [http://www.inf.kcl.ac.uk/staff/urbanc/Publications/tm.pdf Mechanising Turing Machines and Computability Theory in Isabelle/HOL]

Documentación

2022-02-08T10:16:31Z

Jalonso: /* Visiones generales de la DAO */

En esta página se recogen en enlaces que sirven de documentación al curso de demostración asistida por ordenador (DAO).

== Visiones generales de la DAO ==

# J.A. Alonso. [http://goo.gl/NWk7b Razonamiento formalizado: Del sueño a la realidad de las pruebas]. ''Vestigium'', 26 de diciembre de 2012.
# J. Avigad. [http://www.andrew.cmu.edu/user/avigad/Talks/icerm.pdf Interactive theorem proving, automated reasoning, and mathematical computation]. ICERM, 14 de diciembre de 2012.
# M. Davis. [http://www.cs.nyu.edu/cs/faculty/davism/early.ps The early history of automated deduction].
# J.P. Delahaye [http://interstices.info/jcms/int_63417/du-reve-a-la-realite-des-preuves Du rêve à la réalité des preuves]. ''Interstices'', 8 de julio de 2012.
# J. Germoni [http://images.math.cnrs.fr/Coq-et-caracteres.html Coq et caractères: Preuve formelle du théorème de Feit et Thompson]. ''Images des Mathématiques'', CNRS, 23 de noviembre de 2012.
# H. Geuvers [http://www.ias.ac.in/sadhana/Pdf2009Feb/3.pdf Proof assistants: History, ideas and future]. ''Sadhana'', Vol. 34-1, pp. 3-25, février 2009.
# G. Gonthier [http://www.ams.org/notices/200811/tx081101382p.pdf The four-color theorem]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1382-1393, 2008.
# T. Hales. [http://www.ams.org/notices/200811/tx081101370p.pdf Formal proof]. ''Notices of AMS'', Vol. 55, N. 11 (2008) pp. 1370-1380.
# J. Harrison. [http://www.cl.cam.ac.uk/~jrh13/papers/ab.html A short survey of automated reasoning]. ''Lecture Notes in Computer Science'', Vol. 4545, pp. 334-349, 2007.
# J. Harrison. [http://www.ams.org/notices/200811/tx081101395p.pdf Formal proof: Theory and practice]. ''Notices of the AMS'', Vol. 55, N. 11 (2008) p.1395-1406.
# G. Kolata. [http://www.nytimes.com/library/cyber/week/1210math.html Computer math proof shows reasoning power]. ''The New York Times'', 10 de diciembre de 1996.
# D. MacKenzie [https://backspaces.net/temp/Spring2010Seminar/18%20unconventional%20essays%20on%20the%20nature%20of%20mathematics.pdf#page=147 Computers and the sociology of mathematical proof].
# G. Sutcliffe. [http://tptp.org/OverviewOfATP.html What is automated theorem proving?].
# F. Wiedijk [http://www.cs.ru.nl/~freek/100/ Formalizing the «top 100» of mathematical theorems].
# F. Wiedijk [http://www.ams.org/notices/200811/tx081101408p.pdf Formal proof - Getting started]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1408-1414, 2008.
# F. Wiedijk, [https://www.cs.ru.nl/F.Wiedijk/pubs/qed2.pdf The QED manifesto revisited]. ''Studies in Logic, Grammar and Rhetoric'', Vol. 10(23), pp. 121-133, 2007.

== Referencias sobre Isabelle/HOL ==
# B. Grechuk [http://dream.inf.ed.ac.uk/projects/isabelle/Isabelle_Primer.pdf Isabelle primer for mathematicians].
# T. Nipkow [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/Isabelle2013-2/doc/prog-prove.pdf Programming and proving in Isabelle/HOL]. 5 de diciembre de 2013.
# T. Nipkow, M. Wenzel y L.C. Paulson [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/Isabelle2013-2/doc/tutorial.pdf A proof assistant for higher-order logic]. Springer-Verlag. 5 de diciembre de 2013.
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL/document.pdf Isabelle/HOL — Higher-Order Logic]. 12 de febrero de 2013.
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/documentation.html Tutorials and manuals for Isabelle2013].

== Lecturas complementarias ==
=== Programación funcional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/i1m/temas/2012-13-IM-temas-PF.pdf Temas de "Programación funcional"]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# J.A. Alonso y M.J. Hidalgo [http://www.cs.us.es/~jalonso/publicaciones/Piensa_en_Haskell.pdf Piensa en Haskell (Ejercicios de programación funcional con Haskell)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# G. Hutton [http://goo.gl/pKqG Programming in Haskell]. Cambridge University Press, 2007.
# M. Lipovača [http://aprendehaskell.es ¡Aprende Haskell por el bien de todos!].

=== Lógica computacional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/li/temas/temas-LI-2012-13.pdf Temas de "Lógica informática" (2012-13)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# R. Bornat [http://bit.ly/oithic Proof and disproof in formal logic: an introduction for programmers]. Oxford University Press, 2005.
# K. Broda, S. Eisenbach, H. Khoshnevisan y S. Vickers [http://pubs.doc.ic.ac.uk/reasoned-programming/reasoned-programming.pdf Reasoned programming]. Imperial College, 1994.
# K. Doets y J. van Eijck [http://www.ldc.usb.ve/~astorga/Haskell.Road.pdf The Haskell Road to Logic, Maths and Programming].
# M. Huth y M. Ryan [http://goo.gl/TMqOo Logic in computer science: Modelling and reasoning about systems]. Cambridge University Press, 2004. (Incluye el [http://www.cs.bham.ac.uk/research/lics/tutor/index.html tutor en la Red]).

== Cursos relacionados ==
=== Cursos con Isabelle/HOL ===
# Jeremy Avigad. [http://www.phil.cmu.edu/~avigad/formal/ Logic and Formal Verification]. (Carnegie Mellon, 2009).
# Clemens Ballarin. [http://cl-informatik.uibk.ac.at/teaching/ss08/atp/introduction.php Automatic Deduction]. (Univ de Innsbruck, 2008).
# Clemens Ballarin. [http://www4.in.tum.de/~ballarin/belgrade08-tut/ Introduction to the Isabelle Proof Assistant]. (Belgrado, 2008).
# Clemens Ballarin y Gerwin Klein [http://isabelle.in.tum.de/coursematerial/IJCAR04 Introduction to the Isabelle Proof Assistant]. (en el IJCAR-2004).
# Clemens Ballarin y Tjark Weber. [http://cl-informatik.uibk.ac.at/teaching/ws06/atp/introduction.php Automated Theorem Proving in Isabelle/HOL]. (Univ. de Innsbruck, 2006-07).
# A.D. Brucker, D. Basin, J.G. Smaus y B. Wolff. [http://archiv.infsec.ethz.ch/education/permanent/csmr.html Computer-supported Modeling and Reasoning]. (ETH Zurich, 2011).
# Mads Dam. [http://www.csc.kth.se/utbildning/kth/kurser/DD2453/aform07/ Advanced formal methods]. (KTH Royal Institute of Technology, 2007).
# Jacques Fleuriot y Paul Jackson. [http://www.inf.ed.ac.uk/teaching/courses/ar/slides/ Automated reasoning]. (Univ. de Edimburgo, 2012-13).
# Thomas Genet [http://www.irisa.fr/celtique/genet/ACF Software formal analysis and design]. (Univ. de Rennes)
# Gerwin Klein. [http://www.cse.unsw.edu.au/~kleing/teaching/thprv-04 Theorem Proving - Principles, Techniques, Applications]. (NICTA, 2004).
# Gerwin Klein. [http://www.cse.unsw.edu.au/~cs4161/index.html Advanced Topics in Software Verification]. (NICTA, 2012).
# Joao Marcos. [http://www.dimap.ufrn.br/~jmarcos/courses/LC/Ementa.htm Lógica computacional: Demonstração assistida e semi-automática de teoremas].(UFRN, 2000).
# Tobias Nipkow. [http://www4.informatik.tu-muenchen.de/~nipkow/semantics/ Semantics of programming languages]. (Univ. de Munich, 2012-13).
# Tobias Nipkow [http://isabelle.in.tum.de/coursematerial/PSV2009-1 Theorem Proving with Isabelle/HOL An Intensive Course].
# Larry Paulson. [http://www.cl.cam.ac.uk/teaching/0910/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2009-10).
# Arnd Poetzsch-Heffter. [https://softech.informatik.uni-kl.de/Homepage/SVHOL10 Specification and Verification with Higher-Order Logic].
# Jeremy G. Siek. [http://www.cs.colorado.edu/~siek/7000/spring07/ Practical Theorem Proving with Isabelle/Isar]. (Univ. de Colorado, 2007).
# Jeremy G. Siek. [http://ecee.colorado.edu/~siek/ecen5013/spring11/ Theorem proving in Isabelle]. (Univ. de Colorado, 2011).
# Jan-Georg Smaus. [http://www.informatik.uni-freiburg.de/~ki/teaching/ws0910/csmr/lecture.html Computer-supported modeling and reasoning]. (Univ. de Feiburgo, 2009).
# Christian Sternagel [http://cl-informatik.uibk.ac.at/teaching/ss11/eve/content.php Experiments in Verification – Introduction to Isabelle/HOL]. (Univ. de Innsbruck, 2011-12).
# Tjark Weber. [http://www.cl.cam.ac.uk/teaching/1011/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2010-11).

=== Otros cursos ===
# José A. Alonso [http://www.cs.us.es/~jalonso/cursos/li/ Lógica informática] (Univ. de Sevilla, 2012-13).
# Yves Bertot, Pierre Casteran, Benjamin Gregoire, Pierre Letouzey y Assia Mahboubi [http://www.di.ens.fr/~zappa/teaching/coq/ecole11 Modelling and verifying algorithms in Coq: an introduction]. (INRIA Paris-Rocquencourt, 14-18 noviembre 2011).
# Pierre Castéran [http://www.labri.fr/perso/casteran/FM/Logique/index.html Logic (Master In Verification)] (Univ. de Burdeos, 2011-12).
# Nuno Gaspar [http://www-sop.inria.fr/members/Nuno.Gaspar/teaching/coq2012.php Verification with the Coq Proof Assistant] (INRIA Sophia Antipolis, 2012-13).
# Michael Genesereth [http://logic.stanford.edu/classes/cs157/2011/cs157.html Computational Logic] (Univ. de Stanford, 2011-12).
# Ian Hodkinson [http://www.doc.ic.ac.uk/~imh/teaching/140_logic/logic.html Logic] (Imperial College, Londres, 2010-11).
# Peter Lucas [http://www.cs.ru.nl/~peterl/teaching/KeR/ Knowledge Representation and Reasoning] (Radboud University # egen, 2011-12).
# Larry Paulson [http://www.cl.cam.ac.uk/Teaching/current/LogicProof/ Logic and Proof] (Univ. de Cambridge, 2011-12).
# Riccardo Pucella [http://www.ccs.neu.edu/home/riccardo/courses/csu290-sp09/index.html Logic and Computation] (Northeastern University, 2009). Curso con ACL2.

== Bibliotecas de ejemplos de verificación ==
# [http://afp.sourceforge.net Archive of Formal Proofs].
# [http://www.cs.ru.nl/~freek/100 Formalizing 100 Theorems].
# [http://toccata.lri.fr/gallery Gallery of verified programs].
# [http://www.cs.nott.ac.uk/~lad/research/challenges/ Induction Challenge Problems].
# [http://automatedreasoning.net/ Larry Wos' Notebooks].
# [http://www.cs.miami.edu/~tptp/ The TPTP Problem Library for Automated Theorem Proving].
# [http://www.macs.hw.ac.uk/vstte10/Competition.html The 1st Verified Software Competition].
# [https://sites.google.com/site/vstte2012/compet The 2nd Verified Software Competition].
# [http://verifythis.cost-ic0701.org VerifyThis (A collection of verification benchmarks].

== Artículos recientes ==
Están en orden cronológico inverso a la fecha de su reseña en [http://www.glc.us.es/~jalonso/vestigium/tag/resena Vestigium]:
# Joachim Breitner, Brian Huffman, Neil Mitchell y Christian Sternagel [http://bit.ly/19fiWAY Certified HLints with Isabelle/HOLCF-Prelude].
# Peter Lammich [http://bit.ly/ZfSQrQ Automatic data refinement].
# Assia Mahboubi [http://bit.ly/18vyjm7 The rooster and the butterflies (a machine-checked proof of the Jordan-Hölder theorem for finite groups)].
# Nathan Wetzler, Marijn J. H. Heule y Warren A. Hunt Jr. [http://bit.ly/114oyZV Mechanical verification of SAT refutations with extended resolution].
# Johannes Hölzl, Fabian Immler y Brian Huffman [http://bit.ly/13H0REu Type classes and filters for mathematical analysis in Isabelle/HOL]
# M. J. H. Heule, W. A. Hunt, Jr. y N. Wetzler [http://bit.ly/10fv8wO Verifying refutations with extended resolution].
# C. Lüth y M. Ring [http://bit.ly/10EcFWj A Web interface for Isabelle: The next generation].
# L. Liu, O. Hasan y S. Tahar [http://bit.ly/18P9CSv On the formalization of continuous-time Markov chains in HOL].
# A. Asperti y W. Ricciotti [http://bit.ly/17H2mqy Formalizing Turing machines].
# A. Lochbihler [http://bit.ly/YwuCeL Light-weight containers for Isabelle: efficient, extensible, nestable].
# L. Noschinski [http://bit.ly/10XLrRA Graph theory].
# G. Gonthier et als. [http://bit.ly/19kPEP4 A machine-checked proof of the odd order theorem].
# C. Doczkal, J.O. Kaiser y G. Smolka [http://goo.gl/LdihL A constructive theory of regular languages in Coq].
# C. Sternagel [http://goo.gl/gwcwL A formal proof of Kruskal’s tree theorem in Isabelle/HOL].
# C. Sternagel y R. Thiemann [http://goo.gl/CUF3e Formalizing Knuth-Bendix orders and Knuth-Bendix completion].
# C. Lange, C. Rowat, W. Windsteiger y M. Kerber [http://goo.gl/9JAfX Developing an auction theory toolbox].
# M. Spasić y F. Marić [http://goo.gl/6OfmQ Formalization of incremental simplex algorithm by stepwise refinement].
# J.C. Blanchette, A. Popescu y D. Traytel [http://goo.gl/Guxky Coinductive pearl: Modular first-order logic completeness].
# J. Esparza et als. [http://goo.gl/HUOl8 A fully verified executable LTL model checker].
# M. Kerber, C. Lange y C. Rowat. [http://goo.gl/RV54S ForMaRE - formal mathematical reasoning in economics].
# J. Urban. [http://goo.gl/Y7sIq AI over large formal knowledge bases: The first decade].
# S. Boldo, C. Lelay y G. Melquiond. [http://goo.gl/vvqNg Formalization of real analysis: A survey of proof assistants and libraries].
# F. Haftmann, A. Krauss, O. Kunčar y T. Nipkow [http://goo.gl/bEFYa Data refinement in Isabelle/HOL].
# A.C. Rocha y M. Ayala. [http://goo.gl/xTyvE Formalizing the confluence of orthogonal rewriting systems].
# Z. Shi et als. [http://goo.gl/zCYHj Formalization of the complex number theory in HOL4].
# F. Loulergue y V. Niculescu [http://goo.gl/kM0dI Programming and reasonning with PowerLists in Coq].
# J. Heras, F.J. Martín y V. Pascual. [http://goo.gl/KkU6s A hierarchy of mathematical structures in ACL2].
# J. Xu, X. Zhang y C. Urban [http://www.inf.kcl.ac.uk/staff/urbanc/Publications/tm.pdf Mechanising Turing Machines and Computability Theory in Isabelle/HOL]

Documentación

2022-02-08T10:14:51Z

Jalonso: /* Visiones generales de la DAO */

En esta página se recogen en enlaces que sirven de documentación al curso de demostración asistida por ordenador (DAO).

== Visiones generales de la DAO ==

# J.A. Alonso. [http://goo.gl/NWk7b Razonamiento formalizado: Del sueño a la realidad de las pruebas]. ''Vestigium'', 26 de diciembre de 2012.
# J. Avigad. [http://www.andrew.cmu.edu/user/avigad/Talks/icerm.pdf Interactive theorem proving, automated reasoning, and mathematical computation]. ICERM, 14 de diciembre de 2012.
# M. Davis. [http://www.cs.nyu.edu/cs/faculty/davism/early.ps The early history of automated deduction].
# J.P. Delahaye [http://interstices.info/jcms/int_63417/du-reve-a-la-realite-des-preuves Du rêve à la réalité des preuves]. ''Interstices'', 8 de julio de 2012.
# J. Germoni [http://images.math.cnrs.fr/Coq-et-caracteres.html Coq et caractères: Preuve formelle du théorème de Feit et Thompson]. ''Images des Mathématiques'', CNRS, 23 de noviembre de 2012.
# H. Geuvers [http://www.ias.ac.in/sadhana/Pdf2009Feb/3.pdf Proof assistants: History, ideas and future]. ''Sadhana'', Vol. 34-1, pp. 3-25, février 2009.
# G. Gonthier [http://www.ams.org/notices/200811/tx081101382p.pdf The four-color theorem]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1382-1393, 2008.
# T. Hales. [http://www.ams.org/notices/200811/tx081101370p.pdf Formal proof]. ''Notices of AMS'', Vol. 55, N. 11 (2008) pp. 1370-1380.
# J. Harrison. [http://www.cl.cam.ac.uk/~jrh13/papers/ab.html A short survey of automated reasoning]. ''Lecture Notes in Computer Science'', Vol. 4545, pp. 334-349, 2007.
# J. Harrison. [http://www.ams.org/notices/200811/tx081101395p.pdf Formal proof: Theory and practice]. ''Notices of the AMS'', Vol. 55, N. 11 (2008) p.1395-1406.
# G. Kolata. [http://www.nytimes.com/library/cyber/week/1210math.html Computer math proof shows reasoning power]. ''The New York Times'', 10 de diciembre de 1996.
# D. MacKenzie [https://backspaces.net/temp/Spring2010Seminar/18%20unconventional%20essays%20on%20the%20nature%20of%20mathematics.pdf#page=147 Computers and the sociology of mathematical proof].
# G. Sutcliffe. [http://tptp.org/OverviewOfATP.html What is automated theorem proving?].
# F. Wiedijk [http://www.cs.ru.nl/~freek/100/ Formalizing the «top 100» of mathematical theorems].
# F. Wiedijk [http://www.ams.org/notices/200811/tx081101408p.pdf Formal proof - Getting started]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1408-1414, 2008.
# F. Wiedijk, [http://www.cs.ru.nl/~freek/pubs/qed2.ps.gz The QED manifesto revisited]. ''Studies in Logic, Grammar and Rhetoric'', Vol. 10(23), pp. 121-133, 2007.

== Referencias sobre Isabelle/HOL ==
# B. Grechuk [http://dream.inf.ed.ac.uk/projects/isabelle/Isabelle_Primer.pdf Isabelle primer for mathematicians].
# T. Nipkow [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/Isabelle2013-2/doc/prog-prove.pdf Programming and proving in Isabelle/HOL]. 5 de diciembre de 2013.
# T. Nipkow, M. Wenzel y L.C. Paulson [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/Isabelle2013-2/doc/tutorial.pdf A proof assistant for higher-order logic]. Springer-Verlag. 5 de diciembre de 2013.
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL/document.pdf Isabelle/HOL — Higher-Order Logic]. 12 de febrero de 2013.
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/documentation.html Tutorials and manuals for Isabelle2013].

== Lecturas complementarias ==
=== Programación funcional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/i1m/temas/2012-13-IM-temas-PF.pdf Temas de "Programación funcional"]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# J.A. Alonso y M.J. Hidalgo [http://www.cs.us.es/~jalonso/publicaciones/Piensa_en_Haskell.pdf Piensa en Haskell (Ejercicios de programación funcional con Haskell)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# G. Hutton [http://goo.gl/pKqG Programming in Haskell]. Cambridge University Press, 2007.
# M. Lipovača [http://aprendehaskell.es ¡Aprende Haskell por el bien de todos!].

=== Lógica computacional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/li/temas/temas-LI-2012-13.pdf Temas de "Lógica informática" (2012-13)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# R. Bornat [http://bit.ly/oithic Proof and disproof in formal logic: an introduction for programmers]. Oxford University Press, 2005.
# K. Broda, S. Eisenbach, H. Khoshnevisan y S. Vickers [http://pubs.doc.ic.ac.uk/reasoned-programming/reasoned-programming.pdf Reasoned programming]. Imperial College, 1994.
# K. Doets y J. van Eijck [http://www.ldc.usb.ve/~astorga/Haskell.Road.pdf The Haskell Road to Logic, Maths and Programming].
# M. Huth y M. Ryan [http://goo.gl/TMqOo Logic in computer science: Modelling and reasoning about systems]. Cambridge University Press, 2004. (Incluye el [http://www.cs.bham.ac.uk/research/lics/tutor/index.html tutor en la Red]).

== Cursos relacionados ==
=== Cursos con Isabelle/HOL ===
# Jeremy Avigad. [http://www.phil.cmu.edu/~avigad/formal/ Logic and Formal Verification]. (Carnegie Mellon, 2009).
# Clemens Ballarin. [http://cl-informatik.uibk.ac.at/teaching/ss08/atp/introduction.php Automatic Deduction]. (Univ de Innsbruck, 2008).
# Clemens Ballarin. [http://www4.in.tum.de/~ballarin/belgrade08-tut/ Introduction to the Isabelle Proof Assistant]. (Belgrado, 2008).
# Clemens Ballarin y Gerwin Klein [http://isabelle.in.tum.de/coursematerial/IJCAR04 Introduction to the Isabelle Proof Assistant]. (en el IJCAR-2004).
# Clemens Ballarin y Tjark Weber. [http://cl-informatik.uibk.ac.at/teaching/ws06/atp/introduction.php Automated Theorem Proving in Isabelle/HOL]. (Univ. de Innsbruck, 2006-07).
# A.D. Brucker, D. Basin, J.G. Smaus y B. Wolff. [http://archiv.infsec.ethz.ch/education/permanent/csmr.html Computer-supported Modeling and Reasoning]. (ETH Zurich, 2011).
# Mads Dam. [http://www.csc.kth.se/utbildning/kth/kurser/DD2453/aform07/ Advanced formal methods]. (KTH Royal Institute of Technology, 2007).
# Jacques Fleuriot y Paul Jackson. [http://www.inf.ed.ac.uk/teaching/courses/ar/slides/ Automated reasoning]. (Univ. de Edimburgo, 2012-13).
# Thomas Genet [http://www.irisa.fr/celtique/genet/ACF Software formal analysis and design]. (Univ. de Rennes)
# Gerwin Klein. [http://www.cse.unsw.edu.au/~kleing/teaching/thprv-04 Theorem Proving - Principles, Techniques, Applications]. (NICTA, 2004).
# Gerwin Klein. [http://www.cse.unsw.edu.au/~cs4161/index.html Advanced Topics in Software Verification]. (NICTA, 2012).
# Joao Marcos. [http://www.dimap.ufrn.br/~jmarcos/courses/LC/Ementa.htm Lógica computacional: Demonstração assistida e semi-automática de teoremas].(UFRN, 2000).
# Tobias Nipkow. [http://www4.informatik.tu-muenchen.de/~nipkow/semantics/ Semantics of programming languages]. (Univ. de Munich, 2012-13).
# Tobias Nipkow [http://isabelle.in.tum.de/coursematerial/PSV2009-1 Theorem Proving with Isabelle/HOL An Intensive Course].
# Larry Paulson. [http://www.cl.cam.ac.uk/teaching/0910/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2009-10).
# Arnd Poetzsch-Heffter. [https://softech.informatik.uni-kl.de/Homepage/SVHOL10 Specification and Verification with Higher-Order Logic].
# Jeremy G. Siek. [http://www.cs.colorado.edu/~siek/7000/spring07/ Practical Theorem Proving with Isabelle/Isar]. (Univ. de Colorado, 2007).
# Jeremy G. Siek. [http://ecee.colorado.edu/~siek/ecen5013/spring11/ Theorem proving in Isabelle]. (Univ. de Colorado, 2011).
# Jan-Georg Smaus. [http://www.informatik.uni-freiburg.de/~ki/teaching/ws0910/csmr/lecture.html Computer-supported modeling and reasoning]. (Univ. de Feiburgo, 2009).
# Christian Sternagel [http://cl-informatik.uibk.ac.at/teaching/ss11/eve/content.php Experiments in Verification – Introduction to Isabelle/HOL]. (Univ. de Innsbruck, 2011-12).
# Tjark Weber. [http://www.cl.cam.ac.uk/teaching/1011/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2010-11).

=== Otros cursos ===
# José A. Alonso [http://www.cs.us.es/~jalonso/cursos/li/ Lógica informática] (Univ. de Sevilla, 2012-13).
# Yves Bertot, Pierre Casteran, Benjamin Gregoire, Pierre Letouzey y Assia Mahboubi [http://www.di.ens.fr/~zappa/teaching/coq/ecole11 Modelling and verifying algorithms in Coq: an introduction]. (INRIA Paris-Rocquencourt, 14-18 noviembre 2011).
# Pierre Castéran [http://www.labri.fr/perso/casteran/FM/Logique/index.html Logic (Master In Verification)] (Univ. de Burdeos, 2011-12).
# Nuno Gaspar [http://www-sop.inria.fr/members/Nuno.Gaspar/teaching/coq2012.php Verification with the Coq Proof Assistant] (INRIA Sophia Antipolis, 2012-13).
# Michael Genesereth [http://logic.stanford.edu/classes/cs157/2011/cs157.html Computational Logic] (Univ. de Stanford, 2011-12).
# Ian Hodkinson [http://www.doc.ic.ac.uk/~imh/teaching/140_logic/logic.html Logic] (Imperial College, Londres, 2010-11).
# Peter Lucas [http://www.cs.ru.nl/~peterl/teaching/KeR/ Knowledge Representation and Reasoning] (Radboud University # egen, 2011-12).
# Larry Paulson [http://www.cl.cam.ac.uk/Teaching/current/LogicProof/ Logic and Proof] (Univ. de Cambridge, 2011-12).
# Riccardo Pucella [http://www.ccs.neu.edu/home/riccardo/courses/csu290-sp09/index.html Logic and Computation] (Northeastern University, 2009). Curso con ACL2.

== Bibliotecas de ejemplos de verificación ==
# [http://afp.sourceforge.net Archive of Formal Proofs].
# [http://www.cs.ru.nl/~freek/100 Formalizing 100 Theorems].
# [http://toccata.lri.fr/gallery Gallery of verified programs].
# [http://www.cs.nott.ac.uk/~lad/research/challenges/ Induction Challenge Problems].
# [http://automatedreasoning.net/ Larry Wos' Notebooks].
# [http://www.cs.miami.edu/~tptp/ The TPTP Problem Library for Automated Theorem Proving].
# [http://www.macs.hw.ac.uk/vstte10/Competition.html The 1st Verified Software Competition].
# [https://sites.google.com/site/vstte2012/compet The 2nd Verified Software Competition].
# [http://verifythis.cost-ic0701.org VerifyThis (A collection of verification benchmarks].

== Artículos recientes ==
Están en orden cronológico inverso a la fecha de su reseña en [http://www.glc.us.es/~jalonso/vestigium/tag/resena Vestigium]:
# Joachim Breitner, Brian Huffman, Neil Mitchell y Christian Sternagel [http://bit.ly/19fiWAY Certified HLints with Isabelle/HOLCF-Prelude].
# Peter Lammich [http://bit.ly/ZfSQrQ Automatic data refinement].
# Assia Mahboubi [http://bit.ly/18vyjm7 The rooster and the butterflies (a machine-checked proof of the Jordan-Hölder theorem for finite groups)].
# Nathan Wetzler, Marijn J. H. Heule y Warren A. Hunt Jr. [http://bit.ly/114oyZV Mechanical verification of SAT refutations with extended resolution].
# Johannes Hölzl, Fabian Immler y Brian Huffman [http://bit.ly/13H0REu Type classes and filters for mathematical analysis in Isabelle/HOL]
# M. J. H. Heule, W. A. Hunt, Jr. y N. Wetzler [http://bit.ly/10fv8wO Verifying refutations with extended resolution].
# C. Lüth y M. Ring [http://bit.ly/10EcFWj A Web interface for Isabelle: The next generation].
# L. Liu, O. Hasan y S. Tahar [http://bit.ly/18P9CSv On the formalization of continuous-time Markov chains in HOL].
# A. Asperti y W. Ricciotti [http://bit.ly/17H2mqy Formalizing Turing machines].
# A. Lochbihler [http://bit.ly/YwuCeL Light-weight containers for Isabelle: efficient, extensible, nestable].
# L. Noschinski [http://bit.ly/10XLrRA Graph theory].
# G. Gonthier et als. [http://bit.ly/19kPEP4 A machine-checked proof of the odd order theorem].
# C. Doczkal, J.O. Kaiser y G. Smolka [http://goo.gl/LdihL A constructive theory of regular languages in Coq].
# C. Sternagel [http://goo.gl/gwcwL A formal proof of Kruskal’s tree theorem in Isabelle/HOL].
# C. Sternagel y R. Thiemann [http://goo.gl/CUF3e Formalizing Knuth-Bendix orders and Knuth-Bendix completion].
# C. Lange, C. Rowat, W. Windsteiger y M. Kerber [http://goo.gl/9JAfX Developing an auction theory toolbox].
# M. Spasić y F. Marić [http://goo.gl/6OfmQ Formalization of incremental simplex algorithm by stepwise refinement].
# J.C. Blanchette, A. Popescu y D. Traytel [http://goo.gl/Guxky Coinductive pearl: Modular first-order logic completeness].
# J. Esparza et als. [http://goo.gl/HUOl8 A fully verified executable LTL model checker].
# M. Kerber, C. Lange y C. Rowat. [http://goo.gl/RV54S ForMaRE - formal mathematical reasoning in economics].
# J. Urban. [http://goo.gl/Y7sIq AI over large formal knowledge bases: The first decade].
# S. Boldo, C. Lelay y G. Melquiond. [http://goo.gl/vvqNg Formalization of real analysis: A survey of proof assistants and libraries].
# F. Haftmann, A. Krauss, O. Kunčar y T. Nipkow [http://goo.gl/bEFYa Data refinement in Isabelle/HOL].
# A.C. Rocha y M. Ayala. [http://goo.gl/xTyvE Formalizing the confluence of orthogonal rewriting systems].
# Z. Shi et als. [http://goo.gl/zCYHj Formalization of the complex number theory in HOL4].
# F. Loulergue y V. Niculescu [http://goo.gl/kM0dI Programming and reasonning with PowerLists in Coq].
# J. Heras, F.J. Martín y V. Pascual. [http://goo.gl/KkU6s A hierarchy of mathematical structures in ACL2].
# J. Xu, X. Zhang y C. Urban [http://www.inf.kcl.ac.uk/staff/urbanc/Publications/tm.pdf Mechanising Turing Machines and Computability Theory in Isabelle/HOL]

Documentación

2022-02-08T10:14:02Z

Jalonso: /* Visiones generales de la DAO */

En esta página se recogen en enlaces que sirven de documentación al curso de demostración asistida por ordenador (DAO).

== Visiones generales de la DAO ==

# J.A. Alonso. [http://goo.gl/NWk7b Razonamiento formalizado: Del sueño a la realidad de las pruebas]. ''Vestigium'', 26 de diciembre de 2012.
# J. Avigad. [http://www.andrew.cmu.edu/user/avigad/Talks/icerm.pdf Interactive theorem proving, automated reasoning, and mathematical computation]. ICERM, 14 de diciembre de 2012.
# M. Davis. [http://www.cs.nyu.edu/cs/faculty/davism/early.ps The early history of automated deduction].
# J.P. Delahaye [http://interstices.info/jcms/int_63417/du-reve-a-la-realite-des-preuves Du rêve à la réalité des preuves]. ''Interstices'', 8 de julio de 2012.
# J. Germoni [http://images.math.cnrs.fr/Coq-et-caracteres.html Coq et caractères: Preuve formelle du théorème de Feit et Thompson]. ''Images des Mathématiques'', CNRS, 23 de noviembre de 2012.
# H. Geuvers [http://www.ias.ac.in/sadhana/Pdf2009Feb/3.pdf Proof assistants: History, ideas and future]. ''Sadhana'', Vol. 34-1, pp. 3-25, février 2009.
# G. Gonthier [http://www.ams.org/notices/200811/tx081101382p.pdf The four-color theorem]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1382-1393, 2008.
# T. Hales. [http://www.ams.org/notices/200811/tx081101370p.pdf Formal proof]. ''Notices of AMS'', Vol. 55, N. 11 (2008) pp. 1370-1380.
# J. Harrison. [http://www.cl.cam.ac.uk/~jrh13/papers/ab.html A short survey of automated reasoning]. ''Lecture Notes in Computer Science'', Vol. 4545, pp. 334-349, 2007.
# J. Harrison. [http://www.ams.org/notices/200811/tx081101395p.pdf Formal proof: Theory and practice]. ''Notices of the AMS'', Vol. 55, N. 11 (2008) p.1395-1406.
# G. Kolata. [http://www.nytimes.com/library/cyber/week/1210math.html Computer math proof shows reasoning power]. ''The New York Times'', 10 de diciembre de 1996.
# D. MacKenzie [https://backspaces.net/temp/Spring2010Seminar/18%20unconventional%20essays%20on%20the%20nature%20of%20mathematics.pdf#page=147 Computers and the sociology of mathematical proof].
# G. Sutcliffe. [http://www.cs.miami.edu/~tptp/OverviewOfATP.html What is automated theorem proving?].
# F. Wiedijk [http://www.cs.ru.nl/~freek/100/ Formalizing the «top 100» of mathematical theorems].
# F. Wiedijk [http://www.ams.org/notices/200811/tx081101408p.pdf Formal proof - Getting started]. ''Notices of the AMS'', Vol. 55, n° 11, pp. 1408-1414, 2008.
# F. Wiedijk, [http://www.cs.ru.nl/~freek/pubs/qed2.ps.gz The QED manifesto revisited]. ''Studies in Logic, Grammar and Rhetoric'', Vol. 10(23), pp. 121-133, 2007.

== Referencias sobre Isabelle/HOL ==
# B. Grechuk [http://dream.inf.ed.ac.uk/projects/isabelle/Isabelle_Primer.pdf Isabelle primer for mathematicians].
# T. Nipkow [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/Isabelle2013-2/doc/prog-prove.pdf Programming and proving in Isabelle/HOL]. 5 de diciembre de 2013.
# T. Nipkow, M. Wenzel y L.C. Paulson [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/Isabelle2013-2/doc/tutorial.pdf A proof assistant for higher-order logic]. Springer-Verlag. 5 de diciembre de 2013.
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL/document.pdf Isabelle/HOL — Higher-Order Logic]. 12 de febrero de 2013.
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/documentation.html Tutorials and manuals for Isabelle2013].

== Lecturas complementarias ==
=== Programación funcional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/i1m/temas/2012-13-IM-temas-PF.pdf Temas de "Programación funcional"]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# J.A. Alonso y M.J. Hidalgo [http://www.cs.us.es/~jalonso/publicaciones/Piensa_en_Haskell.pdf Piensa en Haskell (Ejercicios de programación funcional con Haskell)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# G. Hutton [http://goo.gl/pKqG Programming in Haskell]. Cambridge University Press, 2007.
# M. Lipovača [http://aprendehaskell.es ¡Aprende Haskell por el bien de todos!].

=== Lógica computacional ===
# J.A. Alonso [http://www.cs.us.es/~jalonso/cursos/li/temas/temas-LI-2012-13.pdf Temas de "Lógica informática" (2012-13)]. Publicaciones del Grupo de Lógica Computacional. Universidad de Sevilla, 2012.
# R. Bornat [http://bit.ly/oithic Proof and disproof in formal logic: an introduction for programmers]. Oxford University Press, 2005.
# K. Broda, S. Eisenbach, H. Khoshnevisan y S. Vickers [http://pubs.doc.ic.ac.uk/reasoned-programming/reasoned-programming.pdf Reasoned programming]. Imperial College, 1994.
# K. Doets y J. van Eijck [http://www.ldc.usb.ve/~astorga/Haskell.Road.pdf The Haskell Road to Logic, Maths and Programming].
# M. Huth y M. Ryan [http://goo.gl/TMqOo Logic in computer science: Modelling and reasoning about systems]. Cambridge University Press, 2004. (Incluye el [http://www.cs.bham.ac.uk/research/lics/tutor/index.html tutor en la Red]).

== Cursos relacionados ==
=== Cursos con Isabelle/HOL ===
# Jeremy Avigad. [http://www.phil.cmu.edu/~avigad/formal/ Logic and Formal Verification]. (Carnegie Mellon, 2009).
# Clemens Ballarin. [http://cl-informatik.uibk.ac.at/teaching/ss08/atp/introduction.php Automatic Deduction]. (Univ de Innsbruck, 2008).
# Clemens Ballarin. [http://www4.in.tum.de/~ballarin/belgrade08-tut/ Introduction to the Isabelle Proof Assistant]. (Belgrado, 2008).
# Clemens Ballarin y Gerwin Klein [http://isabelle.in.tum.de/coursematerial/IJCAR04 Introduction to the Isabelle Proof Assistant]. (en el IJCAR-2004).
# Clemens Ballarin y Tjark Weber. [http://cl-informatik.uibk.ac.at/teaching/ws06/atp/introduction.php Automated Theorem Proving in Isabelle/HOL]. (Univ. de Innsbruck, 2006-07).
# A.D. Brucker, D. Basin, J.G. Smaus y B. Wolff. [http://archiv.infsec.ethz.ch/education/permanent/csmr.html Computer-supported Modeling and Reasoning]. (ETH Zurich, 2011).
# Mads Dam. [http://www.csc.kth.se/utbildning/kth/kurser/DD2453/aform07/ Advanced formal methods]. (KTH Royal Institute of Technology, 2007).
# Jacques Fleuriot y Paul Jackson. [http://www.inf.ed.ac.uk/teaching/courses/ar/slides/ Automated reasoning]. (Univ. de Edimburgo, 2012-13).
# Thomas Genet [http://www.irisa.fr/celtique/genet/ACF Software formal analysis and design]. (Univ. de Rennes)
# Gerwin Klein. [http://www.cse.unsw.edu.au/~kleing/teaching/thprv-04 Theorem Proving - Principles, Techniques, Applications]. (NICTA, 2004).
# Gerwin Klein. [http://www.cse.unsw.edu.au/~cs4161/index.html Advanced Topics in Software Verification]. (NICTA, 2012).
# Joao Marcos. [http://www.dimap.ufrn.br/~jmarcos/courses/LC/Ementa.htm Lógica computacional: Demonstração assistida e semi-automática de teoremas].(UFRN, 2000).
# Tobias Nipkow. [http://www4.informatik.tu-muenchen.de/~nipkow/semantics/ Semantics of programming languages]. (Univ. de Munich, 2012-13).
# Tobias Nipkow [http://isabelle.in.tum.de/coursematerial/PSV2009-1 Theorem Proving with Isabelle/HOL An Intensive Course].
# Larry Paulson. [http://www.cl.cam.ac.uk/teaching/0910/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2009-10).
# Arnd Poetzsch-Heffter. [https://softech.informatik.uni-kl.de/Homepage/SVHOL10 Specification and Verification with Higher-Order Logic].
# Jeremy G. Siek. [http://www.cs.colorado.edu/~siek/7000/spring07/ Practical Theorem Proving with Isabelle/Isar]. (Univ. de Colorado, 2007).
# Jeremy G. Siek. [http://ecee.colorado.edu/~siek/ecen5013/spring11/ Theorem proving in Isabelle]. (Univ. de Colorado, 2011).
# Jan-Georg Smaus. [http://www.informatik.uni-freiburg.de/~ki/teaching/ws0910/csmr/lecture.html Computer-supported modeling and reasoning]. (Univ. de Feiburgo, 2009).
# Christian Sternagel [http://cl-informatik.uibk.ac.at/teaching/ss11/eve/content.php Experiments in Verification – Introduction to Isabelle/HOL]. (Univ. de Innsbruck, 2011-12).
# Tjark Weber. [http://www.cl.cam.ac.uk/teaching/1011/L21/ Interactive Formal Verification]. (Univ. de Cambridge, 2010-11).

=== Otros cursos ===
# José A. Alonso [http://www.cs.us.es/~jalonso/cursos/li/ Lógica informática] (Univ. de Sevilla, 2012-13).
# Yves Bertot, Pierre Casteran, Benjamin Gregoire, Pierre Letouzey y Assia Mahboubi [http://www.di.ens.fr/~zappa/teaching/coq/ecole11 Modelling and verifying algorithms in Coq: an introduction]. (INRIA Paris-Rocquencourt, 14-18 noviembre 2011).
# Pierre Castéran [http://www.labri.fr/perso/casteran/FM/Logique/index.html Logic (Master In Verification)] (Univ. de Burdeos, 2011-12).
# Nuno Gaspar [http://www-sop.inria.fr/members/Nuno.Gaspar/teaching/coq2012.php Verification with the Coq Proof Assistant] (INRIA Sophia Antipolis, 2012-13).
# Michael Genesereth [http://logic.stanford.edu/classes/cs157/2011/cs157.html Computational Logic] (Univ. de Stanford, 2011-12).
# Ian Hodkinson [http://www.doc.ic.ac.uk/~imh/teaching/140_logic/logic.html Logic] (Imperial College, Londres, 2010-11).
# Peter Lucas [http://www.cs.ru.nl/~peterl/teaching/KeR/ Knowledge Representation and Reasoning] (Radboud University # egen, 2011-12).
# Larry Paulson [http://www.cl.cam.ac.uk/Teaching/current/LogicProof/ Logic and Proof] (Univ. de Cambridge, 2011-12).
# Riccardo Pucella [http://www.ccs.neu.edu/home/riccardo/courses/csu290-sp09/index.html Logic and Computation] (Northeastern University, 2009). Curso con ACL2.

== Bibliotecas de ejemplos de verificación ==
# [http://afp.sourceforge.net Archive of Formal Proofs].
# [http://www.cs.ru.nl/~freek/100 Formalizing 100 Theorems].
# [http://toccata.lri.fr/gallery Gallery of verified programs].
# [http://www.cs.nott.ac.uk/~lad/research/challenges/ Induction Challenge Problems].
# [http://automatedreasoning.net/ Larry Wos' Notebooks].
# [http://www.cs.miami.edu/~tptp/ The TPTP Problem Library for Automated Theorem Proving].
# [http://www.macs.hw.ac.uk/vstte10/Competition.html The 1st Verified Software Competition].
# [https://sites.google.com/site/vstte2012/compet The 2nd Verified Software Competition].
# [http://verifythis.cost-ic0701.org VerifyThis (A collection of verification benchmarks].

== Artículos recientes ==
Están en orden cronológico inverso a la fecha de su reseña en [http://www.glc.us.es/~jalonso/vestigium/tag/resena Vestigium]:
# Joachim Breitner, Brian Huffman, Neil Mitchell y Christian Sternagel [http://bit.ly/19fiWAY Certified HLints with Isabelle/HOLCF-Prelude].
# Peter Lammich [http://bit.ly/ZfSQrQ Automatic data refinement].
# Assia Mahboubi [http://bit.ly/18vyjm7 The rooster and the butterflies (a machine-checked proof of the Jordan-Hölder theorem for finite groups)].
# Nathan Wetzler, Marijn J. H. Heule y Warren A. Hunt Jr. [http://bit.ly/114oyZV Mechanical verification of SAT refutations with extended resolution].
# Johannes Hölzl, Fabian Immler y Brian Huffman [http://bit.ly/13H0REu Type classes and filters for mathematical analysis in Isabelle/HOL]
# M. J. H. Heule, W. A. Hunt, Jr. y N. Wetzler [http://bit.ly/10fv8wO Verifying refutations with extended resolution].
# C. Lüth y M. Ring [http://bit.ly/10EcFWj A Web interface for Isabelle: The next generation].
# L. Liu, O. Hasan y S. Tahar [http://bit.ly/18P9CSv On the formalization of continuous-time Markov chains in HOL].
# A. Asperti y W. Ricciotti [http://bit.ly/17H2mqy Formalizing Turing machines].
# A. Lochbihler [http://bit.ly/YwuCeL Light-weight containers for Isabelle: efficient, extensible, nestable].
# L. Noschinski [http://bit.ly/10XLrRA Graph theory].
# G. Gonthier et als. [http://bit.ly/19kPEP4 A machine-checked proof of the odd order theorem].
# C. Doczkal, J.O. Kaiser y G. Smolka [http://goo.gl/LdihL A constructive theory of regular languages in Coq].
# C. Sternagel [http://goo.gl/gwcwL A formal proof of Kruskal’s tree theorem in Isabelle/HOL].
# C. Sternagel y R. Thiemann [http://goo.gl/CUF3e Formalizing Knuth-Bendix orders and Knuth-Bendix completion].
# C. Lange, C. Rowat, W. Windsteiger y M. Kerber [http://goo.gl/9JAfX Developing an auction theory toolbox].
# M. Spasić y F. Marić [http://goo.gl/6OfmQ Formalization of incremental simplex algorithm by stepwise refinement].
# J.C. Blanchette, A. Popescu y D. Traytel [http://goo.gl/Guxky Coinductive pearl: Modular first-order logic completeness].
# J. Esparza et als. [http://goo.gl/HUOl8 A fully verified executable LTL model checker].
# M. Kerber, C. Lange y C. Rowat. [http://goo.gl/RV54S ForMaRE - formal mathematical reasoning in economics].
# J. Urban. [http://goo.gl/Y7sIq AI over large formal knowledge bases: The first decade].
# S. Boldo, C. Lelay y G. Melquiond. [http://goo.gl/vvqNg Formalization of real analysis: A survey of proof assistants and libraries].
# F. Haftmann, A. Krauss, O. Kunčar y T. Nipkow [http://goo.gl/bEFYa Data refinement in Isabelle/HOL].
# A.C. Rocha y M. Ayala. [http://goo.gl/xTyvE Formalizing the confluence of orthogonal rewriting systems].
# Z. Shi et als. [http://goo.gl/zCYHj Formalization of the complex number theory in HOL4].
# F. Loulergue y V. Niculescu [http://goo.gl/kM0dI Programming and reasonning with PowerLists in Coq].
# J. Heras, F.J. Martín y V. Pascual. [http://goo.gl/KkU6s A hierarchy of mathematical structures in ACL2].
# J. Xu, X. Zhang y C. Urban [http://www.inf.kcl.ac.uk/staff/urbanc/Publications/tm.pdf Mechanising Turing Machines and Computability Theory in Isabelle/HOL]

MediaWiki:Sidebar

2018-07-15T15:43:51Z

Jalonso:

MediaWiki:Sidebar

2018-07-15T15:39:28Z

Jalonso:

MediaWiki:Sidebar

2018-07-15T15:30:10Z

Jalonso:

Ejercicios RA2013

2018-07-15T12:14:22Z

Jalonso: /* Ejercicios de Demostración asistida por ordenador */

== Ejercicios de ''Demostración asistida por ordenador'' ==
En esta sección se publicarán las relaciones de ejercicios. Las soluciones se escriben de forma colaborativa por los alumnos del curso y no deben tomarse como definitivas.
* '''Relación 1''': Deducción natural en lógica proposicional con Isabelle/HOL. ([[RA12_Relación_1 |Enunciado]]).
* '''Relación 2''': Argumentación proposicional con Isabelle/HOL. ([[RA12_Relación_2 |Enunciado]]).
* '''Relación 3''': Eliminación de conectivas. ([[RA12_Relación_3 |Enunciado]]).
* '''Relación 4''': Deducción natural en lógica de primer con Isabelle/HOL. ([[RA12_Relación_4 |Enunciado]]).
* '''Relación 5''': Argumentación en lógica de primer con Isabelle/HOL. ([[RA12_Relación_5 |Enunciado]]).
* '''Relación 6''': Argumentación en lógica de primer orden e igualdad con Isabelle/HOL. ([[RA12_Relación_6 |Enunciado]]).
* '''Relación 7''': Programación funcional en Isabelle/HOL. ([[RA12_Relación_7 |Enunciado]]).
* '''Relación 8''': Razonamiento sobre programas en Isabelle/HOL. ([[RA12_Relación_8 |Enunciado]]).
* '''Relación 9''': Cons inverso. ([[RA12_Relación_9 |Enunciado]]).
* '''Relación 10''': Cuantificadores sobre listas. ([[RA12_Relación_10 |Enunciado]]).
* '''Relación 11''': Sustitución, inversión y eliminación. ([[RA12_Relación_11 |Enunciado]]).
* '''Relación 12''': Menor posición válida. ([[RA12_Relación_12 |Enunciado]]).
* '''Relación 13''': Número de elementos válidos. ([[RA12_Relación_13 |Enunciado]]).
* '''Relación 14''': Contador de occurrencias. ([[RA12_Relación_14 |Enunciado]]).
* '''Relación 15''': Suma y aplanamiento de listas. ([[RA12_Relación_15 |Enunciado]]).
* '''Relación 16''': Conjuntos mediante listas. ([[RA12_Relación_16 |Enunciado]]).
* '''Relación 17''': Ordenación de listas por inserción. ([[RA12_Relación_17 |Enunciado]]).
* '''Relación 18''': Ordenación de listas por mezcla. ([[RA12_Relación_18 |Enunciado]]).
* '''Relación 19''': Recorridos de árboles. ([[RA12_Relación_19 |Enunciado]]).
* '''Relación 20''': Plegados de listas y de árboles. ([[RA12_Relación_20 |Enunciado]]).
* '''Relación 21''': Árboles binarios completos. ([[RA12_Relación_21 |Enunciado]]).
* '''Relación 22''': Diagramas de decisión binarios. ([[RA12_Relación_22 |Enunciado]]).
* '''Relación 23''': Representación de fórmulas proposicionales mediante polinomios. ([[RA12_Relación_23 |Enunciado]]).

RA12 Relación 17

2018-07-15T12:04:10Z

Jalonso:

<source lang="isabelle">
header {* R17: Ordenación de listas por inserción *}

theory R17
imports Main
begin

text {*
En esta relación de ejercicios se define el algoritmo de ordenación de
listas por inserción y se demuestra que es correcto.
*}

text {*
---------------------------------------------------------------------
Ejercicio 1. Definir la función
inserta :: nat ⇒ nat list ⇒ nat list
tal que (inserta a xs) es la lista obtenida insertando a delante del
primer elemento de xs que es mayor o igual que a. Por ejemplo,
inserta 3 [2,5,1,7] = [2,3,5,1,7]
------------------------------------------------------------------ *}

fun inserta :: "nat ⇒ nat list ⇒ nat list" where
"inserta a xs = undefined"

value "inserta 3 [2,5,1,7]" -- "= [2,3,5,1,7]"

text {*
---------------------------------------------------------------------
Ejercicio 2. Definir la función
ordena :: nat list ⇒ nat list
tal que (ordena xs) es la lista obtenida ordenando xs por inserción.
Por ejemplo,
ordena [3,2,5,3] = [2,3,3,5]
------------------------------------------------------------------ *}

fun ordena :: "nat list ⇒ nat list" where
"ordena xs = undefined"

value "ordena [3,2,5,3]" -- "[2,3,3,5]"

text {*
---------------------------------------------------------------------
Ejercicio 3. Definir la función
menor :: nat ⇒ nat list ⇒ bool
tal que (menor a xs) se verifica si a es menor o igual que todos los
elementos de xs.Por ejemplo,
menor 2 [3,2,5] = True
menor 2 [3,0,5] = False
------------------------------------------------------------------ *}

fun menor :: "nat ⇒ nat list ⇒ bool" where
"menor a xs = undefined"

value "menor 2 [3,2,5]" -- "= True"
value "menor 2 [3,0,5]" -- "= False"

text {*
---------------------------------------------------------------------
Ejercicio 4. Definir la función
ordenada :: nat list ⇒ bool
tal que (ordenada xs) se verifica si xs es una lista ordenada de
manera creciente. Por ejemplo,
ordenada [2,3,3,5] = True
ordenada [2,4,3,5] = False
------------------------------------------------------------------ *}

fun ordenada :: "nat list ⇒ bool" where
"ordenada xs = undefined"

value "ordenada [2,3,3,5]" -- "= True"
value "ordenada [2,4,3,5]" -- "= False"

text {*
---------------------------------------------------------------------
Ejercicio 5. Demostrar que si y es una cota inferior de xs y x ≤ y,
entonces x es una cota inferior de xs.
------------------------------------------------------------------ *}

lemma menor_menor:
assumes "x ≤ y"
shows "menor y xs ⟶ menor x xs"
oops

text {*
---------------------------------------------------------------------
Ejercicio 6. Demostrar el siguiente teorema de corrección: x es una
cota inferior de la lista obtenida insertando y en zs syss x ≤ y y x
es una cota inferior de zs.
------------------------------------------------------------------ *}

lemma menor_inserta:
"menor x (inserta y zs) = (x ≤ y ∧ menor x zs)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 6. Demostrar que al insertar un elemento la lista obtenida
está ordenada syss lo estaba la original.
------------------------------------------------------------------ *}

lemma ordenada_inserta:
"ordenada (inserta a xs) = ordenada xs"
oops

text {*
---------------------------------------------------------------------
Ejercicio 7. Demostrar que, para toda lista xs, (ordena xs) está
ordenada.
------------------------------------------------------------------ *}

theorem ordenada_ordena:
"ordenada (ordena xs)"
oops

text {*
---------------------------------------------------------------------
Nota. El teorema anterior no garantiza que ordena sea correcta, ya que
puede que (ordena xs) no tenga los mismos elementos que xs. Por
ejemplo, si se define (ordena xs) como [] se tiene que (ordena xs)
está ordenada pero no es una ordenación de xs. Para ello, definimos la
función cuenta.
------------------------------------------------------------------ *}

text {*
---------------------------------------------------------------------
Ejercicio 8. Definir la función
cuenta :: nat list => nat => nat
tal que (cuenta xs y) es el número de veces que aparece el elemento y
en la lista xs. Por ejemplo,
cuenta [1,3,4,3,5] 3 = 2
------------------------------------------------------------------ *}

fun cuenta :: "nat list => nat => nat" where
"cuenta xs y = undefined"

value "cuenta [1,3,4,3,5] 3" -- "= 2"

text {*
---------------------------------------------------------------------
Ejercicio 9. Demostrar que el número de veces que aparece y en
(inserta x xs) es
* uno más el número de veces que aparece en xs, si y = x;
* el número de veces que aparece en xs, si y ≠ x;
------------------------------------------------------------------ *}

lemma cuenta_inserta:
"cuenta (inserta x xs) y =
(if x=y then Suc (cuenta xs y) else cuenta xs y)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 10. Demostrar que el número de veces que aparece y en
(ordena xs) es el número de veces que aparece en xs.
------------------------------------------------------------------ *}

theorem cuenta_ordena:
"cuenta (ordena xs) y = cuenta xs y"
oops

end
</source>

RA12 Relación 22

2018-07-15T12:04:10Z

Jalonso: Texto reemplazado: «"isar"» por «"isabelle"»

<source lang="isabelle">
header {* R22: Diagramas de decisión binarios *}

theory R22
imports Main
begin

text {*
Las funciones booleanas se pueden representar mediante diagramas de
decisión binarios (DDB). Por ejemplo, la función f definida por la
tabla de la izquierda se representa por el DDB de la derecha
+---+---+---+----------+ p
| p | q | r | f(p,q,r) | / \
+---+---+---+----------+ / \
| F | F | * | V | q q
| F | V | * | F | / \ / \
| V | F | * | F | V F F r
| V | V | F | F | / \
| V | V | V | V | F V
+---+---+---+----------+
Para cada variable, si su valor es falso se evalúa su hijo izquierdo y
si es verdadero se evalúa su hijo derecho.
*}

text {*
---------------------------------------------------------------------
Ejercicio 1. Definir el tipo de datos ddb para representar los
diagramas de decisión binarios. Por ejemplo, el DDB anterior se
representa por
N (N (H True) (H False)) (N (H False) (N (H False) (H True)))
---------------------------------------------------------------------
*}

datatype ddb = H bool | N ddb ddb

value "N (N (H True) (H False)) (N (H False) (N (H False) (H True)))"

text {*
---------------------------------------------------------------------
Ejercicio 2. Definir ddb1 para representar el DDB del ejercicio 1.
---------------------------------------------------------------------
*}

abbreviation ddb1 :: ddb where
"ddb1 ≡ N (N (H True) (H False)) (N (H False) (N (H False) (H True)))"

text {*
---------------------------------------------------------------------
Ejercicio 3. Definir int1,..., int8 para representar las
interpretaciones del ejercicio 1.
---------------------------------------------------------------------
*}

abbreviation int1 :: "nat ⇒ bool" where
"int1 x ≡ False"
abbreviation int2 :: "nat ⇒ bool" where
"int2 ≡ int1 (2 := True)"
abbreviation int3 :: "nat ⇒ bool" where
"int3 ≡ int1 (1 := True)"
abbreviation int4 :: "nat ⇒ bool" where
"int4 ≡ int1 (1 := True, 2 := True)"
abbreviation int5 :: "nat ⇒ bool" where
"int5 ≡ int1 (0 := True)"
abbreviation int6 :: "nat ⇒ bool" where
"int6 ≡ int1 (0 := True, 2 := True)"
abbreviation int7 :: "nat ⇒ bool" where
"int7 ≡ int1 (0 := True, 1 := True)"
abbreviation int8 :: "nat ⇒ bool" where
"int8 ≡ int1 (0 := True, 1 := True, 2 := True)"

text {*
---------------------------------------------------------------------
Ejercicio 4. Definir la función
valor :: "(nat ⇒ bool) ⇒ nat ⇒ ddb ⇒ bool"
tal que (valor i n d) es el valor del DDB d en la interpretación i a
partir de la variable de índice n. Por ejemplo,
valor int1 0 ddb1 = True
valor int2 0 ddb1 = True
valor int3 0 ddb1 = False
valor int4 0 ddb1 = False
valor int5 0 ddb1 = False
valor int6 0 ddb1 = False
valor int7 0 ddb1 = False
valor int8 0 ddb1 = True
---------------------------------------------------------------------
*}

fun valor :: "(nat ⇒ bool) ⇒ nat ⇒ ddb ⇒ bool" where
"valor i n a = undefined"

text {*
---------------------------------------------------------------------
Ejercicio 5. Definir la función
ddb_op_un :: "(bool ⇒ bool) ⇒ ddb ⇒ ddb
tal que (ddb_op_un f d) es el diagrama obtenido aplicando el operador
unitario f a cada hoja de DDB d de forma que se conserve el valor; es
decir,
valor i n (ddb_op_un f d) = f (valor i n d)"
Por ejemplo,
value "ddb_op_un (λx. ¬x) ddb1"
= N (N (H False) (H True)) (N (H True) (N (H True) (H False)))
---------------------------------------------------------------------
*}

fun ddb_op_un :: "(bool ⇒ bool) ⇒ ddb ⇒ ddb" where
"ddb_op_un f a = undefined"

text {*
---------------------------------------------------------------------
Ejercicio 6. Demostrar que la definición de ddb_op_un es correcta; es
decir,
valor i n (ddb_op_un f d) = f (valor i n d)"
---------------------------------------------------------------------
*}

theorem ddb_op_un_correcto:
"valor i n (ddb_op_un f d) = f (valor i n d)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 7. Definir la función
ddb_op_bin :: "(bool ⇒ bool ⇒ bool) ⇒ ddb ⇒ ddb ⇒ ddb"
tal que (ddb_op_bin f d1 d2) es el diagrama obtenido aplicando el
operador binario f a los DDB d1 y d2 de forma que se conserve el
valor; es decir,
valor i n (ddb_op_bin f d1 d2) = f (valor i n d1) (valor i n d2)
Por ejemplo,
ddb_op_bin (op ∧) ddb1 (N (H True) (H False))
= N (N (H True) (H False)) (N (H False) (N (H False) (H False)))
ddb_op_bin (op ∧) ddb1 (N (H False) (H True))
= N (N (H False) (H False)) (N (H False) (N (H False) (H True)))
ddb_op_bin (op ∨) ddb1 (N (H True) (H False))
= N (N (H True) (H True)) (N (H False) (N (H False) (H True)))
ddb_op_bin (op ∨) ddb1 (N (H False) (H True))
= N (N (H True) (H False)) (N (H True) (N (H True) (H True)))
---------------------------------------------------------------------
*}

fun ddb_op_bin :: "(bool ⇒ bool ⇒ bool) ⇒ ddb ⇒ ddb ⇒ ddb" where
"ddb_op_bin f d1 d2 = undefined"

text {*
---------------------------------------------------------------------
Ejercicio 8. Demostrar que la definición de ddb_op_bin es correcta;
es decir,
valor i n (ddb_op_bin f d1 d2) = f (valor i n d1) (valor i n d2)
---------------------------------------------------------------------
*}

theorem ddb_op_bin_correcto:
"valor i n (ddb_op_bin f d1 d2) = f (valor i n d1) (valor i n d2)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 9. Definir la función
ddb_and :: "ddb ⇒ ddb ⇒ ddb"
tal que (ddb_and d1 d2) es el diagrama correspondiente a la conjunción
de los DDB d1 y d2 de forma que se conserva el valor; es decir,
valor i n (ddb_and d1 d2) = (valor i n d1 ∧ valor i n d2)
Por ejemplo,
ddb_and ddb1 (N (H True) (H False))
= N (N (H True) (H False)) (N (H False) (N (H False) (H False)))
ddb_and ddb1 (N (H False) (H True))
= N (N (H False) (H False)) (N (H False) (N (H False) (H True)))
---------------------------------------------------------------------
*}

definition ddb_and :: "ddb ⇒ ddb ⇒ ddb" where
"ddb_and ≡ undefined"

text {*
---------------------------------------------------------------------
Ejercicio 10. Demostrar que la definición de ddb_and es correcta;
es decir,
valor i n (ddb_and d1 d2) = (valor i n d1 ∧ valor i n d2)
---------------------------------------------------------------------
*}

theorem ddb_and_correcta:
"valor i n (ddb_and d1 d2) = (valor i n d1 ∧ valor i n d2)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 11. Definir la función
ddb_or :: "ddb ⇒ ddb ⇒ ddb"
tal que (ddb_or d1 d2) es el diagrama correspondiente a la disyunción
de los DDB d1 y d2 de forma que se conserva el valor; es decir,
valor i n (ddb_or d1 d2) = (valor i n d1 ∨ valor i n d2)
Por ejemplo,
ddb_or ddb1 (N (H True) (H False))
= N (N (H True) (H True)) (N (H False) (N (H False) (H True)))
ddb_or ddb1 (N (H False) (H True))
= N (N (H True) (H False)) (N (H True) (N (H True) (H True)))
---------------------------------------------------------------------
*}

definition ddb_or :: "ddb ⇒ ddb ⇒ ddb" where
"ddb_or ≡ undefined"

text {*
---------------------------------------------------------------------
Ejercicio 12. Demostrar que la definición de ddb_or es correcta;
es decir,
valor i n (ddb_or d1 d2) = (valor i n d1 ∨ valor i n d2)
---------------------------------------------------------------------
*}

theorem ddb_or_correcta:
"valor i n (ddb_or d1 d2) = (valor i n d1 ∨ valor i n d2)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 13. Definir la función
ddb_not :: "ddb ⇒ ddb"
tal que (ddb_not d) es el diagrama correspondiente a la negación
del DDB d de forma que se conserva el valor; es decir,
valor i n (ddb_or d1 d2) = (valor i n d1 ∨ valor i n d2)
Por ejemplo,
ddb_not ddb1
= N (N (H False) (H True)) (N (H True) (N (H True) (H False)))
---------------------------------------------------------------------
*}

definition ddb_not :: "ddb ⇒ ddb" where
"ddb_not ≡ undefined"

text {*
---------------------------------------------------------------------
Ejercicio 14. Demostrar que la definición de ddb_not es correcta;
es decir,
valor i n (ddb_not d) = (¬ valor i n d)
---------------------------------------------------------------------
*}

theorem ddb_not_correcta:
"valor i n (ddb_not d) = (¬ valor i n d)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 15. Definir la función
xor :: "bool ⇒ bool ⇒ bool"
tal que (xor x y) es la disyunción excluyente de x e y. Por ejemplo,
xor True False = True
xor True True = False
---------------------------------------------------------------------
*}

definition xor :: "bool ⇒ bool ⇒ bool" where
"xor x y ≡ undefined"

text {*
---------------------------------------------------------------------
Ejercicio 16. Definir la función
ddb_xor :: "ddb ⇒ ddb ⇒ ddb"
tal que (ddb_xor d1 d2) es el diagrama correspondiente a la disyunción
excluyente de los DDB d1 y d2. Por ejemplo,
ddb_xor ddb1 (N (H True) (H False))
= N (N (H True) (H True)) (N (H False) (N (H False) (H True)))
ddb_xor ddb1 (N (H False) (H True))
= N (N (H True) (H False)) (N (H True) (N (H True) (H True)))
---------------------------------------------------------------------
*}

definition ddb_xor :: "ddb ⇒ ddb ⇒ ddb" where
"ddb_xor ≡ undefined"

text {*
---------------------------------------------------------------------
Ejercicio 17. Demostrar que la definición de ddb_xor es correcta;
es decir,
valor i n (ddb_xor d1 d2) = xor (valor i n d1) (valor i n d2)
---------------------------------------------------------------------
*}

theorem ddb_xor_correcta:
"valor i n (ddb_xor d1 d2) = xor (valor i n d1) (valor i n d2)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 18. Definir la función
ddb_var :: "nat ⇒ ddb" where
tal que (ddb_var n) es el diagrama equivalente a la variable p(n). Por
ejemplo,
ddb_var 0
= N (H False) (H True)
ddb_var 1
= N (N (H False) (H True)) (N (H False) (H True))
---------------------------------------------------------------------
*}

fun ddb_var :: "nat ⇒ ddb" where
"ddb_var n = undefined"

text {*
---------------------------------------------------------------------
Ejercicio 19. Demostrar que la definición de ddb_var es correcta;
es decir,
"valor i 0 (ddb_var n) = i n
---------------------------------------------------------------------
*}

lemma ddb_var_correcta:
"valor i 0 (ddb_var n) = i n"
oops

text {*
---------------------------------------------------------------------
Ejercicio 20. Definir el tipo de las fórmulas proposicionales
contruidas con la constante T, las variables (Var n) y las conectivas
Not, And, Or y Xor.
---------------------------------------------------------------------
*}

datatype form = T
| Var nat
| Not form
| And form form
| Or form form
| Xor form form

text {*
---------------------------------------------------------------------
Ejercicio 21. Definir la función
valor_fla :: "(nat ⇒ bool) ⇒ form ⇒ bool"
tal que (valor_fla i f) es el valor de la fórmula f en la
interpretación i. Por ejemplo,
valor_fla (λn. True) (Xor T T) = False
valor_fla (λn. False) (Xor T (Var 1)) = True
---------------------------------------------------------------------
*}

fun valor_fla :: "(nat ⇒ bool) ⇒ form ⇒ bool" where
"valor_fla i f = undefined"

text {*
---------------------------------------------------------------------
Ejercicio 22. Definir la función
ddb_fla :: "form ⇒ ddb"
tal que (ddb_fla f) es el DDB equivalente a la fórmula f; es decir,
valor i 0 (ddb_fla f) = valor_fla i f
---------------------------------------------------------------------
*}

fun ddb_fla :: "form ⇒ ddb" where
"ddb_fla f = undefined"

text {*
---------------------------------------------------------------------
Ejercicio 23. Demostrar que la definición de ddb_fla es correcta; es
decir,
valor i 0 (ddb_fla f) = valor_fla i f
---------------------------------------------------------------------
*}

theorem ddb_fla_correcta:
"valor e 0 (ddb_fla f) = valor_fla e f"
oops

text {*
Referencias:
· J.A. Alonso, F.J. Martín y J.L. Ruiz "Diagramas de decisión
binarios". En
http://www.cs.us.es/cursos/lp-2005/temas/tema-07.pdf
· Wikipedia "Binary decision diagram". En
http://en.wikipedia.org/wiki/Binary_decision_diagram
*}

end
</source>

RA12 Relación 2

2018-07-15T12:04:03Z

Jalonso: Texto reemplazado: «"isar"» por «"isabelle"»

<source lang="isabelle">
header {* R2: Argumentación proposicional *}

theory R2
imports Main
begin

text {*
---------------------------------------------------------------------
El objetivo de esta relación formalizar y demostrar la corrección de
los argumentos usando sólo las reglas básicas de deducción natural de
la lógica proposicional (sin usar el método auto).

Las reglas básicas de la deducción natural son las siguientes:
· conjI: ⟦P; Q⟧ ⟹ P ∧ Q
· conjunct1: P ∧ Q ⟹ P
· conjunct2: P ∧ Q ⟹ Q
· notnotD: ¬¬ P ⟹ P
· notnotI: P ⟹ ¬¬ P
· mp: ⟦P ⟶ Q; P⟧ ⟹ Q
· mt: ⟦F ⟶ G; ¬G⟧ ⟹ ¬F
· impI: (P ⟹ Q) ⟹ P ⟶ Q
· disjI1: P ⟹ P ∨ Q
· disjI2: Q ⟹ P ∨ Q
· disjE: ⟦P ∨ Q; P ⟹ R; Q ⟹ R⟧ ⟹ R
· FalseE: False ⟹ P
· notE: ⟦¬P; P⟧ ⟹ R
· notI: (P ⟹ False) ⟹ ¬P
· iffI: ⟦P ⟹ Q; Q ⟹ P⟧ ⟹ P = Q
· iffD1: ⟦Q = P; Q⟧ ⟹ P
· iffD2: ⟦P = Q; Q⟧ ⟹ P
· ccontr: (¬P ⟹ False) ⟹ P
---------------------------------------------------------------------
*}

text {*
Se usarán las reglas notnotI y mt que demostramos a continuación.
*}

lemma notnotI: "P ⟹ ¬¬ P"
by auto

lemma mt: "⟦F ⟶ G; ¬G⟧ ⟹ ¬F"
by auto

text {* ---------------------------------------------------------------
Ejercicio 1. Formalizar, y demostrar la corrección, del siguiente
argumento
Cuando tanto la temperatura como la presión atmosférica permanecen
contantes, no llueve. La temperatura permanece constante. Por lo
tanto, en caso de que llueva, la presión atmosférica no permanece
constante.
Usar T para "La temperatura permanece constante",
P para "La presión atmosférica permanece constante" y
L para "Llueve".
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 2. Formalizar, y demostrar la corrección, del siguiente
argumento
Siempre que un número x es divisible por 10, acaba en 0. El número
x no acaba en 0. Por lo tanto, x no es divisible por 10.
Usar D para "el número es divisible por 10" y
C para "el número acaba en cero".
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 3. Formalizar, y demostrar la corrección, del siguiente
argumento
En cierto experimento, cuando hemos empleado un fármaco A, el
paciente ha mejorado considerablemente en el caso, y sólo en el
caso, en que no se haya empleado también un fármaco B. Además, o se
ha empleado el fármaco A o se ha empleado el fármaco B. En
consecuencia, podemos afirmar que si no hemos empleado el fármaco
B, el paciente ha mejorado considerablemente.
Usar A: Hemos empleado el fármaco A.
B: Hemos empleado el fármaco B.
M: El paciente ha mejorado notablemente.
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 4. Formalizar, y demostrar la corrección, del siguiente
argumento
Si no está el mañana ni el ayer escrito, entonces no está el mañana
escrito.
Usar M: El mañana está escrito.
A: El ayer está escrito.
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 5. Formalizar, y demostrar la corrección, del siguiente
argumento
Me matan si no trabajo y si trabajo me matan. Me matan siempre me
matan.
Usar M: Me matan.
T: Trabajo.
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 6. Formalizar, y demostrar la corrección, del siguiente
argumento
Si te llamé por teléfono, entonces recibiste mi llamada y no es
cierto que no te avisé del peligro que corrías. Por consiguiente,
como te llamé, es cierto que te avisé del peligro que corrías.
Usar T: Te llamé por teléfono.
R: Recibiste mi llamada.
P: Te avisé del peligro que corrías.
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 7. Formalizar, y demostrar la corrección, del siguiente
argumento
Si no hay control de nacimientos, entonces la población crece
ilimitadamente; pero si la población crece ilimitadamente,
aumentará el índice de pobreza. Por consiguiente, si no hay control
de nacimientos, aumentará el índice de pobreza.
Usar N: Hay control de nacimientos.
P: La población crece ilimitadamente,
I: Aumentará el índice de pobreza.
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 8. Formalizar, y demostrar la corrección, del siguiente
argumento
Si el general era leal, hubiera obedecido las órdenes, y si era
inteligente las hubiera comprendido. O el general desobedeció las
órdenes o no las comprendió. Luego, el general era desleal o no era
inteligente.
Usar L: El general es leal.
O: El general obedece las órdenes.
I: El general es inteligente.
C: El general comprende las órdenes.
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 9. Formalizar, y demostrar la corrección, del siguiente
argumento
Si Dios fuera capaz de evitar el mal y quisiera hacerlo, lo
haría. Si Dios fuera incapaz de evitar el mal, no sería
omnipotente; si no quisiera evitar el mal sería malévolo. Dios no
evita el mal. Si Dios existe, es omnipotente y no es
malévolo. Luego, Dios no existe.
Usar C: Dios es capaz de evitar el mal.
Q: Dios quiere evitar el mal.
O: Dios es omnipotente.
M: Dios es malévolo.
P: Dios evita el mal.
E: Dios existe.
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 10. Formalizar, y demostrar la corrección, del siguiente
argumento
Nadie más que Pedro, Quintín y Raúl están bajo sospecha y al menos
uno es traidor. Pedro nunca trabaja sin llevar al menos un cómplice
(que puede ser Quintín o Raúl). Raúl es leal. Por lo tanto,
Pedro es traidor.
Usar p: Pedro es traidor.
q : Quintín es traidor.
r : Raúl es traidor.
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 11. Formalizar, y demostrar la corrección, del siguiente
argumento
Si la válvula está abierta o la monitorización está preparada,
entonces se envía una señal de reconocimiento y un mensaje de
funcionamiento al controlador del ordenador. Si se envía un mensaje
de funcionamiento al controlador del ordenador o el sistema está en
estado normal, entonces se aceptan las órdenes del operador. Por lo
tanto, si la válvula está abierta, entonces se aceptan las órdenes
del operador.
Usar A: La válvula está abierta.
P : La monitorización está preparada.
R : Envía una señal de reconocimiento.
F : Envía un mensaje de funcionamiento.
N : El sistema está en estado normal.
O : Se aceptan órdenes del operador.
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 12. Formalizar, y demostrar la corrección, del siguiente
argumento
Si trabajo gano dinero, pero si no trabajo gozo de la vida. Sin
embargo, si trabajo no gozo de la vida, mientras que si no trabajo
no gano dinero. Por lo tanto, gozo de la vida si y sólo si no gano
dinero.
Usar p: Trabajo
q: Gano dinero.
r: Gozo de la vida.
------------------------------------------------------------------ *}

end
</source>

GLC T2R1

2018-07-15T12:03:30Z

Jalonso: Texto reemplazado: «lang="isar"» por «lang="isabelle"»

<source lang="isabelle">
header {* T4R1: Deducción natural de primer orden *}

theory T4R1
imports Main
begin

text {*
Demostrar o refutar los siguientes lemas usando sólo las reglas
básicas de deducción natural de la lógica proposicional, de los
cuantificadores y de la igualdad:
· conjI: ⟦P; Q⟧ ⟹ P ∧ Q
· conjunct1: P ∧ Q ⟹ P
· conjunct2: P ∧ Q ⟹ Q
· notnotD: ¬¬ P ⟹ P
· mp: ⟦P ⟶ Q; P⟧ ⟹ Q
· impI: (P ⟹ Q) ⟹ P ⟶ Q
· disjI1: P ⟹ P ∨ Q
· disjI2: Q ⟹ P ∨ Q
· disjE: ⟦P ∨ Q; P ⟹ R; Q ⟹ R⟧ ⟹ R
· FalseE: False ⟹ P
· notE: ⟦¬P; P⟧ ⟹ R
· notI: (P ⟹ False) ⟹ ¬P
· iffI: ⟦P ⟹ Q; Q ⟹ P⟧ ⟹ P = Q
· iffD1: ⟦Q = P; Q⟧ ⟹ P
· iffD2: ⟦P = Q; Q⟧ ⟹ P
· ccontr: (¬P ⟹ False) ⟹ P

· allI: ⟦∀x. P x; P x ⟹ R⟧ ⟹ R
· allE: (⋀x. P x) ⟹ ∀x. P x
· exI: P x ⟹ ∃x. P x
· exE: ⟦∃x. P x; ⋀x. P x ⟹ Q⟧ ⟹ Q

· refl: t = t
· subst: ⟦s = t; P s⟧ ⟹ P t
· trans: ⟦r = s; s = t⟧ ⟹ r = t
· sym: s = t ⟹ t = s
· not_sym: t ≠ s ⟹ s ≠ t
· ssubst: ⟦t = s; P s⟧ ⟹ P t
· box_equals: ⟦a = b; a = c; b = d⟧ ⟹ a: = d
· arg_cong: x = y ⟹ f x = f y
· fun_cong: f = g ⟹ f x = g x
· cong: ⟦f = g; x = y⟧ ⟹ f x = g y
*}

text {*
Se usarán las reglas notnotI y mt que demostramos a continuación.
*}

lemma notnotI: "P ⟹ ¬¬ P"
by auto

lemma mt: "⟦F ⟶ G; ¬G⟧ ⟹ ¬F"
by auto

text {* ---------------------------------------------------------------
Ejercicio 1. Demostrar
∀x. P x ⟶ Q x ⊢ (∀x. P x) ⟶ (∀x. Q x)
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_1a:
"∀x. P x ⟶ Q x ⟹ (∀x. P x) ⟶ (∀x. Q x)"
by auto

-- "La demostración estructurada es"
lemma ejercicio_1b:
assumes "∀x. P x ⟶ Q x"
shows "(∀x. P x) ⟶ (∀x. Q x)"
proof
assume "∀x. P x"
show "∀x. Q x"
proof
fix a
have "P a" using `∀x. P x` ..
have "P a ⟶ Q a" using assms(1) ..
thus "Q a" using `P a` ..
qed
qed

-- "La demostración detallada es"
lemma ejercicio_1c:
assumes "∀x. P x ⟶ Q x"
shows "(∀x. P x) ⟶ (∀x. Q x)"
proof (rule impI)
assume "∀x. P x"
show "∀x. Q x"
proof (rule allI)
fix a
have "P a" using `∀x. P x` by (rule allE)
have "P a ⟶ Q a" using assms(1) by (rule allE)
thus "Q a" using `P a` by (rule mp)
qed
qed

text {* ---------------------------------------------------------------
Ejercicio 2. Demostrar
∃x. ¬(P x) ⊢ ¬(∀x. P x)
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_2a: "∃x. ¬(P x) ⟹ ¬(∀x. P x)"
by auto

-- "La demostración estructurada es"
lemma ejercicio_2b:
assumes "∃x. ¬(P x)"
shows "¬(∀x. P x)"
proof
assume "∀x. P x"
obtain a where "¬(P a)" using assms(1) ..
have "P a" using `∀x. P x` ..
with `¬(P a)` show False ..
qed

-- "La demostración detallada es"
lemma ejercicio_2c:
assumes "∃x. ¬(P x)"
shows "¬(∀x. P x)"
proof (rule notI)
assume "∀x. P x"
obtain a where "¬(P a)" using assms(1) by (rule exE)
have "P a" using `∀x. P x` by (rule allE)
with `¬(P a)` show False by (rule notE)
qed

text {* ---------------------------------------------------------------
Ejercicio 3. Demostrar
∀x. P x ⊢ ∀y. P y
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_3a: "∀x. P x ⟹ ∀y. P y"
by auto

-- "La demostración estructurada es"
lemma ejercicio_3b:
assumes "∀x. P x"
shows "∀y. P y"
proof
fix a
show "P a" using assms ..
qed

-- "La demostración estructurada es"
lemma ejercicio_3c:
assumes "∀x. P x"
shows "∀y. P y"
proof (rule allI)
fix a
show "P a" using assms by (rule allE)
qed

text {* ---------------------------------------------------------------
Ejercicio 4. Demostrar
∀x. P x ⟶ Q x ⊢ (∀x. ¬(Q x)) ⟶ (∀x. ¬ (P x))
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_4a:
"∀x. P x ⟶ Q x ⟹ (∀x. ¬(Q x)) ⟶ (∀x. ¬ (P x))"
by auto

-- "La demostración estructurada es"
lemma ejercicio_4b:
assumes "∀x. P x ⟶ Q x"
shows "(∀x. ¬(Q x)) ⟶ (∀x. ¬ (P x))"
proof
assume "∀x. ¬(Q x)"
show "∀x. ¬(P x)"
proof
fix a
show "¬(P a)"
proof
assume "P a"
have "P a ⟶ Q a" using assms ..
hence "Q a" using `P a` ..
have "¬(Q a)" using `∀x. ¬(Q x)` ..
thus False using `Q a` ..
qed
qed
qed

-- "La demostración detallada es"
lemma ejercicio_4c:
assumes "∀x. P x ⟶ Q x"
shows "(∀x. ¬(Q x)) ⟶ (∀x. ¬ (P x))"
proof (rule impI)
assume "∀x. ¬(Q x)"
show "∀x. ¬(P x)"
proof (rule allI)
fix a
show "¬(P a)"
proof
assume "P a"
have "P a ⟶ Q a" using assms by (rule allE)
hence "Q a" using `P a` by (rule mp)
have "¬(Q a)" using `∀x. ¬(Q x)` by (rule allE)
thus False using `Q a` by (rule notE)
qed
qed
qed

text {* ---------------------------------------------------------------
Ejercicio 5. Demostrar
∀x. P x ⟶ ¬(Q x) ⊢ ¬(∃x. P x ∧ Q x)
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_5a:
"∀x. P x ⟶ ¬(Q x) ⟹ ¬(∃x. P x ∧ Q x)"
by auto

-- "La demostración estructurada es"
lemma ejercicio_5b:
assumes "∀x. P x ⟶ ¬(Q x)"
shows "¬(∃x. P x ∧ Q x)"
proof
assume "∃x. P x ∧ Q x"
then obtain a where "P a ∧ Q a" ..
hence "P a" ..
have "P a ⟶ ¬(Q a)" using assms ..
hence "¬(Q a)" using `P a` ..
have "Q a" using `P a ∧ Q a` ..
with `¬(Q a)` show False ..
qed

-- "La demostración estructurada es"
lemma ejercicio_5c:
assumes "∀x. P x ⟶ ¬(Q x)"
shows "¬(∃x. P x ∧ Q x)"
proof (rule notI)
assume "∃x. P x ∧ Q x"
then obtain a where "P a ∧ Q a" by (rule exE)
hence "P a" by (rule conjunct1)
have "P a ⟶ ¬(Q a)" using assms by (rule allE)
hence "¬(Q a)" using `P a` by (rule mp)
have "Q a" using `P a ∧ Q a` by (rule conjunct2)
with `¬(Q a)` show False by (rule notE)
qed

text {* ---------------------------------------------------------------
Ejercicio 6. Demostrar
∀x y. P x y ⊢ ∀u v. P u v
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_6a:
"∀x y. P x y ⟹ ∀u v. P u v"
by auto

-- "La demostración estructurada es"
lemma ejercicio_6b:
assumes "∀x y. P x y"
shows "∀u v. P u v"
proof
fix a
show "∀v. P a v"
proof
fix b
have "∀y. P a y" using assms ..
thus "P a b" ..
qed
qed

-- "La demostración estructurada simplificada es"
lemma ejercicio_6b2:
assumes "∀x y. P x y"
shows "∀u v. P u v"
proof (rule allI)+
fix a b
have "∀y. P a y" using assms ..
thus "P a b" ..
qed

-- "La demostración detallada es"
lemma ejercicio_6c:
assumes "∀x y. P x y"
shows "∀u v. P u v"
proof (rule allI)+
fix a b
have "∀y. P a y" using assms by (rule allE)
thus "P a b" by (rule allE)
qed

text {* ---------------------------------------------------------------
Ejercicio 7. Demostrar
∃x y. P x y ⟹ ∃u v. P u v
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_7a:
"∃x y. P x y ⟹ ∃u v. P u v"
by auto

-- "La demostración estructurada es"
lemma ejercicio_7b:
assumes "∃x y. P x y"
shows "∃u v. P u v"
proof -
obtain a where "∃y. P a y" using assms ..
then obtain b where "P a b" ..
hence "∃v. P a v" ..
thus "∃u v. P u v" ..
qed

text {* ---------------------------------------------------------------
Ejercicio 8. Demostrar
∃x. ∀y. P x y ⊢ ∀y. ∃x. P x y
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_8a:
"∃x. ∀y. P x y ⟹ ∀y. ∃x. P x y"
by auto

-- "La demostración estructurada es"
lemma ejercicio_8b:
assumes "∃x. ∀y. P x y"
shows "∀y. ∃x. P x y"
proof
fix b
obtain a where "∀y. P a y" using assms ..
hence "P a b" ..
thus "∃x. P x b" ..
qed

-- "La demostración detallada es"
lemma ejercicio_8c:
assumes "∃x. ∀y. P x y"
shows "∀y. ∃x. P x y"
proof (rule allI)
fix b
obtain a where "∀y. P a y" using assms by (rule exE)
hence "P a b" by (rule allE)
thus "∃x. P x b" by (rule exI)
qed

text {* ---------------------------------------------------------------
Ejercicio 9. Demostrar
∃x. P a ⟶ Q x ⊢ P a ⟶ (∃x. Q x)
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_9a:
"∃x. P a ⟶ Q x ⟹ P a ⟶ (∃x. Q x)"
by auto

-- "La demostración estructurada es"
lemma ejercicio_9b:
assumes "∃x. P a ⟶ Q x"
shows "P a ⟶ (∃x. Q x)"
proof
assume "P a"
obtain b where "P a ⟶ Q b" using assms ..
hence "Q b" using `P a` ..
thus "∃x. Q x" ..
qed

-- "La demostración detallada es"
lemma ejercicio_9c:
assumes "∃x. P a ⟶ Q x"
shows "P a ⟶ (∃x. Q x)"
proof (rule impI)
assume "P a"
obtain b where "P a ⟶ Q b" using assms by (rule exE)
hence "Q b" using `P a` by (rule mp)
thus "∃x. Q x" by (rule exI)
qed

text {* ---------------------------------------------------------------
Ejercicio 10. Demostrar
P a ⟶ (∃x. Q x) ⊢ ∃x. P a ⟶ Q x
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_10a:
"P a ⟶ (∃x. Q x) ⟹ ∃x. P a ⟶ Q x"
by auto

-- "La demostración estructurada es"
lemma ejercicio_10b:
fixes P Q :: "'b ⇒ bool"
assumes "P a ⟶ (∃x. Q x)"
shows "∃x. P a ⟶ Q x"
proof -
have "¬(P a) ∨ P a" ..
thus "∃x. P a ⟶ Q x"
proof
assume "¬(P a)"
have "P a ⟶ Q a"
proof
assume "P a"
with `¬(P a)` show "Q a" ..
qed
thus "∃x. P a ⟶ Q x" ..
next
assume "P a"
with assms have "∃x. Q x" by (rule mp)
then obtain b where "Q b" ..
have "P a ⟶ Q b"
proof
assume "P a"
note `Q b`
thus "Q b" .
qed
thus "∃x. P a ⟶ Q x" ..
qed
qed

-- "La demostración detallada es"
lemma ejercicio_10c:
fixes P Q :: "'b ⇒ bool"
assumes "P a ⟶ (∃x. Q x)"
shows "∃x. P a ⟶ Q x"
proof -
have "¬(P a) ∨ P a" by (rule excluded_middle)
thus "∃x. P a ⟶ Q x"
proof (rule disjE)
assume "¬(P a)"
have "P a ⟶ Q a"
proof (rule impI)
assume "P a"
with `¬(P a)` show "Q a" by (rule notE)
qed
thus "∃x. P a ⟶ Q x" by (rule exI)
next
assume "P a"
with assms have "∃x. Q x" by (rule mp)
then obtain b where "Q b" by (rule exE)
have "P a ⟶ Q b"
proof (rule impI)
assume "P a"
note `Q b`
thus "Q b" by this
qed
thus "∃x. P a ⟶ Q x" by (rule exI)
qed
qed

text {* ---------------------------------------------------------------
Ejercicio 11. Demostrar
(∃x. P x) ⟶ Q a ⊢ ∀x. P x ⟶ Q a
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_11a:
"(∃x. P x) ⟶ Q a ⟹ ∀x. P x ⟶ Q a"
by auto

-- "La demostración estructurada es"
lemma ejercicio_11b:
assumes "(∃x. P x) ⟶ Q a"
shows "∀x. P x ⟶ Q a"
proof
fix b
show "P b ⟶ Q a"
proof
assume "P b"
hence "∃x. P x" ..
with assms show "Q a" ..
qed
qed

-- "La demostración detallada es"
lemma ejercicio_11c:
assumes "(∃x. P x) ⟶ Q a"
shows "∀x. P x ⟶ Q a"
proof (rule allI)
fix b
show "P b ⟶ Q a"
proof (rule impI)
assume "P b"
hence "∃x. P x" by (rule exI)
with assms show "Q a" by (rule mp)
qed
qed

text {* ---------------------------------------------------------------
Ejercicio 12. Demostrar
∀x. P x ⟶ Q a ⊢ ∃ x. P x ⟶ Q a
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_12a:
"∀x. P x ⟶ Q a ⟹ ∃x. P x ⟶ Q a"
by auto

-- "La demostración estructurada es"
lemma ejercicio_12b:
assumes "∀x. P x ⟶ Q a"
shows "∃x. P x ⟶ Q a"
proof -
have "P b ⟶ Q a" using assms ..
thus "∃x. P x ⟶ Q a" ..
qed

-- "La demostración detallada es"
lemma ejercicio_12c:
assumes "∀x. P x ⟶ Q a"
shows "∃x. P x ⟶ Q a"
proof -
have "P b ⟶ Q a" using assms by (rule allE)
thus "∃x. P x ⟶ Q a" by (rule exI)
qed

text {* ---------------------------------------------------------------
Ejercicio 13. Demostrar
(∀x. P x) ∨ (∀x. Q x) ⊢ ∀x. P x ∨ Q x
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_13a:
"(∀x. P x) ∨ (∀x. Q x) ⟹ ∀x. P x ∨ Q x"
by auto

-- "La demostración estructurada es"
lemma ejercicio_13b:
assumes "(∀x. P x) ∨ (∀x. Q x)"
shows "∀x. P x ∨ Q x"
proof
fix a
note assms
thus "P a ∨ Q a"
proof
assume "∀x. P x"
hence "P a" ..
thus "P a ∨ Q a" ..
next
assume "∀x. Q x"
hence "Q a" ..
thus "P a ∨ Q a" ..
qed
qed

-- "La demostración detallada es"
lemma ejercicio_13c:
assumes "(∀x. P x) ∨ (∀x. Q x)"
shows "∀x. P x ∨ Q x"
proof (rule allI)
fix a
note assms
thus "P a ∨ Q a"
proof (rule disjE)
assume "∀x. P x"
hence "P a" by (rule allE)
thus "P a ∨ Q a" by (rule disjI1)
next
assume "∀x. Q x"
hence "Q a" by (rule allE)
thus "P a ∨ Q a" by (rule disjI2)
qed
qed

text {* ---------------------------------------------------------------
Ejercicio 14. Demostrar
∃x. P x ∧ Q x ⊢ (∃x. P x) ∧ (∃x. Q x)
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_14a:
"∃x. P x ∧ Q x ⟹ (∃x. P x) ∧ (∃x. Q x)"
by auto

-- "La demostración estructurada es"
lemma ejercicio_14b:
assumes "∃x. P x ∧ Q x"
shows "(∃x. P x) ∧ (∃x. Q x)"
proof
obtain a where "P a ∧ Q a" using assms ..
hence "P a" ..
thus "∃x. P x" ..
next
obtain a where "P a ∧ Q a" using assms ..
hence "Q a" ..
thus "∃x. Q x" ..
qed

-- "La demostración detallada es"
lemma ejercicio_14c:
assumes "∃x. P x ∧ Q x"
shows "(∃x. P x) ∧ (∃x. Q x)"
proof (rule conjI)
obtain a where "P a ∧ Q a" using assms by (rule exE)
hence "P a" by (rule conjunct1)
thus "∃x. P x" by (rule exI)
next
obtain a where "P a ∧ Q a" using assms by (rule exE)
hence "Q a" by (rule conjunct2)
thus "∃x. Q x" by (rule exI)
qed

text {* ---------------------------------------------------------------
Ejercicio 15. Demostrar
∀x y. P y ⟶ Q x ⊢ (∃y. P y) ⟶ (∀x. Q x)
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_15a:
"∀x y. P y ⟶ Q x ⟹ (∃y. P y) ⟶ (∀x. Q x)"
by auto

-- "La demostración estructurada es"
lemma ejercicio_15b:
assumes "∀x y. P y ⟶ Q x"
shows "(∃y. P y) ⟶ (∀x. Q x)"
proof
assume "∃y. P y"
then obtain b where "P b" ..
show "∀x. Q x"
proof
fix a
have "∀y. P y ⟶ Q a" using assms ..
hence "P b ⟶ Q a" ..
thus "Q a" using `P b` ..
qed
qed

-- "La demostración detallada es"
lemma ejercicio_15c:
assumes "∀x y. P y ⟶ Q x"
shows "(∃y. P y) ⟶ (∀x. Q x)"
proof (rule impI)
assume "∃y. P y"
then obtain b where "P b" by (rule exE)
show "∀x. Q x"
proof (rule allI)
fix a
have "∀y. P y ⟶ Q a" using assms by (rule allE)
hence "P b ⟶ Q a" by (rule allE)
thus "Q a" using `P b` by (rule mp)
qed
qed

text {* ---------------------------------------------------------------
Ejercicio 16. Demostrar
¬(∀x. ¬(P x)) ⊢ ∃x. P x
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_16a:
"¬(∀x. ¬(P x)) ⟹ ∃x. P x"
by auto

-- "La demostración estructurada es"
lemma ejercicio_16b:
assumes "¬(∀x. ¬(P x))"
shows "∃x. P x"
proof (rule ccontr)
assume "¬(∃x. P x)"
have "∀x. ¬(P x)"
proof
fix a
show "¬(P a)"
proof
assume "P a"
hence "∃x. P x" ..
with `¬(∃x. P x)` show False ..
qed
qed
with assms show False ..
qed

-- "La demostración detallada es"
lemma ejercicio_16c:
assumes "¬(∀x. ¬(P x))"
shows "∃x. P x"
proof (rule ccontr)
assume "¬(∃x. P x)"
have "∀x. ¬(P x)"
proof (rule allI)
fix a
show "¬(P a)"
proof
assume "P a"
hence "∃x. P x" by (rule exI)
with `¬(∃x. P x)` show False by (rule notE)
qed
qed
with assms show False by (rule notE)
qed

text {* ---------------------------------------------------------------
Ejercicio 17. Demostrar
∀x. ¬(P x) ⊢ ¬(∃x. P x)
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_17a:
"∀x. ¬(P x) ⟹ ¬(∃x. P x)"
by auto

-- "La demostración estructurada es"
lemma ejercicio_17b:
assumes "∀x. ¬(P x)"
shows "¬(∃x. P x)"
proof
assume "∃x. P x"
then obtain a where "P a" ..
have "¬(P a)" using assms ..
thus False using `P a` ..
qed

-- "La demostración detallada es"
lemma ejercicio_17c:
assumes "∀x. ¬(P x)"
shows "¬(∃x. P x)"
proof (rule notI)
assume "∃x. P x"
then obtain a where "P a" by (rule exE)
have "¬(P a)" using assms by (rule allE)
thus False using `P a` by (rule notE)
qed

text {* ---------------------------------------------------------------
Ejercicio 18. Demostrar
∃x. P x ⊢ ¬(∀x. ¬(P x))
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_18a:
"∃x. P x ⟹ ¬(∀x. ¬(P x))"
by auto

-- "La demostración estructurada es"
lemma ejercicio_18b:
assumes "∃x. P x"
shows "¬(∀x. ¬(P x))"
proof
assume "∀x. ¬(P x)"
obtain a where "P a" using assms ..
have "¬(P a)" using `∀x. ¬(P x)` ..
thus False using `P a` ..
qed

-- "La demostración detallada es"
lemma ejercicio_18c:
assumes "∃x. P x"
shows "¬(∀x. ¬(P x))"
proof (rule notI)
assume "∀x. ¬(P x)"
obtain a where "P a" using assms by (rule exE)
have "¬(P a)" using `∀x. ¬(P x)` by (rule allE)
thus False using `P a` by (rule notE)
qed

text {* ---------------------------------------------------------------
Ejercicio 19. Demostrar
P a ⟶ (∀x. Q x) ⊢ ∀x. P a ⟶ Q x
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_19a:
"P a ⟶ (∀x. Q x) ⟹ ∀x. P a ⟶ Q x"
by auto

-- "La demostración estructurada es"
lemma ejercicio_19b:
assumes "P a ⟶ (∀x. Q x)"
shows "∀x. P a ⟶ Q x"
proof
fix b
show "P a ⟶ Q b"
proof
assume "P a"
with assms have "∀x. Q x" ..
thus "Q b" ..
qed
qed

-- "La demostración detallada es"
lemma ejercicio_19c:
assumes "P a ⟶ (∀x. Q x)"
shows "∀x. P a ⟶ Q x"
proof (rule allI)
fix b
show "P a ⟶ Q b"
proof (rule impI)
assume "P a"
with assms have "∀x. Q x" by (rule mp)
thus "Q b" by (rule allE)
qed
qed

text {* ---------------------------------------------------------------
Ejercicio 20. Demostrar
{∀x y z. R x y ∧ R y z ⟶ R x z,
∀x. ¬(R x x)}
⊢ ∀x y. R x y ⟶ ¬(R y x)
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_20a:
"⟦∀x y z. R x y ∧ R y z ⟶ R x z; ∀x. ¬(R x x)⟧ ⟹ ∀x y. R x y ⟶ ¬(R y x)"
by metis

-- "La demostración estructurada es"
lemma ejercicio_20b:
assumes "∀x y z. R x y ∧ R y z ⟶ R x z"
"∀x. ¬(R x x)"
shows "∀x y. R x y ⟶ ¬(R y x)"
proof (rule allI)+
fix a b
show "R a b ⟶ ¬(R b a)"
proof
assume "R a b"
show "¬(R b a)"
proof
assume "R b a"
show False
proof -
have "R a b ∧ R b a" using `R a b` `R b a` ..
have "∀y z. R a y ∧ R y z ⟶ R a z" using assms(1) ..
hence "∀z. R a b ∧ R b z ⟶ R a z" ..
hence "R a b ∧ R b a ⟶ R a a" ..
hence "R a a" using `R a b ∧ R b a` ..
have "¬(R a a)" using assms(2) ..
thus False using `R a a` ..
qed
qed
qed
qed

-- "La demostración detallada es"
lemma ejercicio_20c:
assumes "∀x y z. R x y ∧ R y z ⟶ R x z"
"∀x. ¬(R x x)"
shows "∀x y. R x y ⟶ ¬(R y x)"
proof (rule allI)+
fix a b
show "R a b ⟶ ¬(R b a)"
proof (rule impI)
assume "R a b"
show "¬(R b a)"
proof (rule notI)
assume "R b a"
show False
proof -
have "R a b ∧ R b a" using `R a b` `R b a` by (rule conjI)
have "∀y z. R a y ∧ R y z ⟶ R a z" using assms(1) by (rule allE)
hence "∀z. R a b ∧ R b z ⟶ R a z" by (rule allE)
hence "R a b ∧ R b a ⟶ R a a" by (rule allE)
hence "R a a" using `R a b ∧ R b a` by (rule mp)
have "¬(R a a)" using assms(2) by (rule allE)
thus False using `R a a` by (rule notE)
qed
qed
qed
qed

text {* ---------------------------------------------------------------
Ejercicio 21. Demostrar
{∀x. P x ∨ Q x, ∃x. ¬(Q x), ∀x. R x ⟶ ¬(P x)} ⊢ ∃x. ¬(R x)
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_21a:
"⟦∀x. P x ∨ Q x; ∃x. ¬(Q x); ∀x. R x ⟶ ¬(P x)⟧ ⟹ ∃x. ¬(R x)"
by auto

-- "La demostración estructurada es"
lemma ejercicio_21b:
assumes "∀x. P x ∨ Q x"
"∃x. ¬(Q x)"
"∀x. R x ⟶ ¬(P x)"
shows "∃x. ¬(R x)"
proof -
obtain a where "¬(Q a)" using assms(2) ..
have "P a ∨ Q a" using assms(1) ..
hence "P a"
proof
assume "P a"
thus "P a" .
next
assume "Q a"
with `¬(Q a)` show "P a" ..
qed
hence "¬¬(P a)" by (rule notnotI)
have "R a ⟶ ¬(P a)" using assms(3) ..
hence "¬(R a)" using `¬¬(P a)` by (rule mt)
thus "∃x. ¬(R x)" ..
qed

-- "La demostración detallada es"
lemma ejercicio_21c:
assumes "∀x. P x ∨ Q x"
"∃x. ¬(Q x)"
"∀x. R x ⟶ ¬(P x)"
shows "∃x. ¬(R x)"
proof -
obtain a where "¬(Q a)" using assms(2) by (rule exE)
have "P a ∨ Q a" using assms(1) by (rule allE)
hence "P a"
proof (rule disjE)
assume "P a"
thus "P a" by this
next
assume "Q a"
with `¬(Q a)` show "P a" by (rule notE)
qed
hence "¬¬(P a)" by (rule notnotI)
have "R a ⟶ ¬(P a)" using assms(3) by (rule allE)
hence "¬(R a)" using `¬¬(P a)` by (rule mt)
thus "∃x. ¬(R x)" by (rule exI)
qed

text {* ---------------------------------------------------------------
Ejercicio 22. Demostrar
{∀x. P x ⟶ Q x ∨ R x, ¬(∃x. P x ∧ R x)} ⊢ ∀x. P x ⟶ Q x
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_22a:
"⟦∀x. P x ⟶ Q x ∨ R x; ¬(∃x. P x ∧ R x)⟧ ⟹ ∀x. P x ⟶ Q x"
by auto

-- "La demostración estructurada es"
lemma ejercicio_22b:
assumes "∀x. P x ⟶ Q x ∨ R x"
"¬(∃x. P x ∧ R x)"
shows "∀x. P x ⟶ Q x"
proof
fix a
show "P a ⟶ Q a"
proof
assume "P a"
have "P a ⟶ Q a ∨ R a" using assms(1) ..
hence "Q a ∨ R a" using `P a` ..
thus "Q a"
proof
assume "Q a"
thus "Q a" .
next
assume "R a"
with `P a` have "P a ∧ R a" ..
hence "∃x. P x ∧ R x" ..
with assms(2) show "Q a" ..
qed
qed
qed

-- "La demostración detallada es"
lemma ejercicio_22c:
assumes "∀x. P x ⟶ Q x ∨ R x"
"¬(∃x. P x ∧ R x)"
shows "∀x. P x ⟶ Q x"
proof (rule allI)
fix a
show "P a ⟶ Q a"
proof (rule impI)
assume "P a"
have "P a ⟶ Q a ∨ R a" using assms(1) by (rule allE)
hence "Q a ∨ R a" using `P a` by (rule mp)
thus "Q a"
proof (rule disjE)
assume "Q a"
thus "Q a" by this
next
assume "R a"
with `P a` have "P a ∧ R a" by (rule conjI)
hence "∃x. P x ∧ R x" by (rule exI)
with assms(2) show "Q a" by (rule notE)
qed
qed
qed

text {* ---------------------------------------------------------------
Ejercicio 23. Demostrar
∃x y. R x y ∨ R y x ⊢ ∃x y. R x y
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_23a:
"∃x y. R x y ∨ R y x ⟹ ∃x y. R x y"
by auto

-- "La demostración estructurada es"
lemma ejercicio_23b:
assumes "∃x y. R x y ∨ R y x"
shows "∃x y. R x y"
proof -
obtain a where "∃y. R a y ∨ R y a" using assms ..
then obtain b where "R a b ∨ R b a" ..
thus "∃x y. R x y"
proof
assume "R a b"
hence "∃y. R a y" ..
thus "∃ x y. R x y" ..
next
assume "R b a"
hence "∃y. R b y" ..
thus "∃ x y. R x y" ..
qed
qed

-- "La demostración detallada es"
lemma ejercicio_23c:
assumes "∃x y. R x y ∨ R y x"
shows "∃x y. R x y"
proof -
obtain a where "∃y. R a y ∨ R y a" using assms by (rule exE)
then obtain b where "R a b ∨ R b a" by (rule exE)
thus "∃x y. R x y"
proof (rule disjE)
assume "R a b"
hence "∃y. R a y" by (rule exI)
thus "∃ x y. R x y" by (rule exI)
next
assume "R b a"
hence "∃y. R b y" by (rule exI)
thus "∃ x y. R x y" by (rule exI)
qed
qed

text {* ---------------------------------------------------------------
Ejercicio 24. Demostrar
(∃x. ∀y. P x y) ⟶ (∀y. ∃x. P x y)
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_24a: "(∃x. ∀y. P x y) ⟶ (∀y. ∃x. P x y)"
by auto

-- "La demostración estructurada es"
lemma ejercicio_24b: "(∃x. ∀y. P x y) ⟶ (∀y. ∃x. P x y)"
proof
assume "∃x. ∀y. P x y"
then obtain a where "∀y. P a y" ..
show "∀y. ∃x. P x y"
proof
fix b
have "P a b" using `∀y. P a y` ..
thus "∃x. P x b" ..
qed
qed

-- "La demostración detallada es"
lemma ejercicio_24c: "(∃x. ∀y. P x y) ⟶ (∀y. ∃x. P x y)"
proof (rule impI)
assume "∃x. ∀y. P x y"
then obtain a where "∀y. P a y" by (rule exE)
show "∀y. ∃x. P x y"
proof (rule allI)
fix b
have "P a b" using `∀y. P a y` by (rule allE)
thus "∃x. P x b" by (rule exI)
qed
qed

text {* ---------------------------------------------------------------
Ejercicio 25. Demostrar
(∀x. P x ⟶ Q) ⟷ ((∃x. P x) ⟶ Q)
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_25a: "(∀x. P x ⟶ Q) ⟷ ((∃x. P x) ⟶ Q)"
by auto

-- "La demostración estructurada es"
lemma ejercicio_25b: "(∀x. P x ⟶ Q) ⟷ ((∃x. P x) ⟶ Q)"
proof
assume "∀x. P x ⟶ Q"
show "(∃x. P x) ⟶ Q"
proof
assume "∃x. P x"
then obtain a where "P a" ..
have "P a ⟶ Q" using `∀x. P x ⟶ Q` ..
thus "Q" using `P a` ..
qed
next
assume "(∃x. P x) ⟶ Q"
show "∀x. P x ⟶ Q"
proof
fix b
show "P b ⟶ Q"
proof
assume "P b"
hence "∃x. P x" ..
with `(∃x. P x) ⟶ Q` show "Q" ..
qed
qed
qed

-- "La demostración detallada es"
lemma ejercicio_25c: "(∀x. P x ⟶ Q) ⟷ ((∃x. P x) ⟶ Q)"
proof (rule iffI)
assume "∀x. P x ⟶ Q"
show "(∃x. P x) ⟶ Q"
proof (rule impI)
assume "∃x. P x"
then obtain a where "P a" by (rule exE)
have "P a ⟶ Q" using `∀x. P x ⟶ Q` by (rule allE)
thus "Q" using `P a` by (rule mp)
qed
next
assume "(∃x. P x) ⟶ Q"
show "∀x. P x ⟶ Q"
proof (rule allI)
fix b
show "P b ⟶ Q"
proof (rule impI)
assume "P b"
hence "∃x. P x" by (rule exI)
with `(∃x. P x) ⟶ Q` show "Q" by (rule mp)
qed
qed
qed

text {* ---------------------------------------------------------------
Ejercicio 26. Demostrar
((∀x. P x) ∧ (∀x. Q x)) ⟷ (∀x. P x ∧ Q x)
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_26a: "((∀x. P x) ∧ (∀x. Q x)) ⟷ (∀x. P x ∧ Q x)"
by auto

-- "La demostración estructurada es"
lemma ejercicio_26b: "((∀x. P x) ∧ (∀x. Q x)) ⟷ (∀x. P x ∧ Q x)"
proof
assume "(∀x. P x) ∧ (∀x. Q x)"
show "∀x. P x ∧ Q x"
proof
fix a
have "∀x. P x" using `(∀x. P x) ∧ (∀x. Q x)` ..
have "∀x. Q x" using `(∀x. P x) ∧ (∀x. Q x)` ..
hence "Q a" ..
have "P a" using `∀x. P x` ..
thus "P a ∧ Q a" using `Q a` ..
qed
next
assume "∀x. P x ∧ Q x"
have "∀x. P x"
proof
fix a
have "P a ∧ Q a" using `∀x. P x ∧ Q x` ..
thus "P a" ..
qed
moreover have "∀x. Q x"
proof
fix a
have "P a ∧ Q a" using `∀x. P x ∧ Q x` ..
thus "Q a" ..
qed
ultimately show "(∀x. P x) ∧ (∀x. Q x)" ..
qed

-- "La demostración detallada es"
lemma ejercicio_26c: "((∀x. P x) ∧ (∀x. Q x)) = (∀x. P x ∧ Q x)"
proof (rule iffI)
assume "(∀x. P x) ∧ (∀x. Q x)"
show "∀x. P x ∧ Q x"
proof (rule allI)
fix a
have "∀x. P x" using `(∀x. P x) ∧ (∀x. Q x)` by (rule conjunct1)
have "∀x. Q x" using `(∀x. P x) ∧ (∀x. Q x)` by (rule conjunct2)
hence "Q a" by (rule allE)
have "P a" using `∀x. P x` by (rule allE)
thus "P a ∧ Q a" using `Q a` by (rule conjI)
qed
next
assume "∀x. P x ∧ Q x"
have "∀x. P x"
proof (rule allI)
fix a
have "P a ∧ Q a" using `∀x. P x ∧ Q x` by (rule allE)
thus "P a" by (rule conjunct1)
qed
moreover have "∀x. Q x"
proof (rule allI)
fix a
have "P a ∧ Q a" using `∀x. P x ∧ Q x` by (rule allE)
thus "Q a" by (rule conjunct2)
qed
ultimately show "(∀x. P x) ∧ (∀x. Q x)" by (rule conjI)
qed

text {* ---------------------------------------------------------------
Ejercicio 27. Demostrar o refutar
((∀x. P x) ∨ (∀x. Q x)) ⟷ (∀x. P x ∨ Q x)
------------------------------------------------------------------ *}

lemma ejercicio_27: "((∀x. P x) ∨ (∀x. Q x)) ⟷ (∀x. P x ∨ Q x)"
oops

(*
Auto Quickcheck found a counterexample:
P = {a\<^isub>1}
Q = {a\<^isub>2}
*)

text {* ---------------------------------------------------------------
Ejercicio 28. Demostrar o refutar
((∃x. P x) ∨ (∃x. Q x)) ⟷ (∃x. P x ∨ Q x)
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_28a:
"((∃x. P x) ∨ (∃x. Q x)) ⟷ (∃x. P x ∨ Q x)"
by auto

-- "La demostración estructurada es"
lemma ejercicio_28b:
"((∃x. P x) ∨ (∃x. Q x)) ⟷ (∃x. P x ∨ Q x)"
proof
assume "(∃x. P x) ∨ (∃x. Q x)"
thus "∃x. P x ∨ Q x"
proof
assume "∃x. P x"
then obtain a where "P a" ..
hence "P a ∨ Q a" ..
thus "∃x. P x ∨ Q x" ..
next
assume "∃x. Q x"
then obtain a where "Q a" ..
hence "P a ∨ Q a" ..
thus "∃x. P x ∨ Q x" ..
qed
next
assume "∃x. P x ∨ Q x"
then obtain a where "P a ∨ Q a" ..
thus "(∃x. P x) ∨ (∃x. Q x)"
proof
assume "P a"
hence "∃x. P x" ..
thus "(∃x. P x) ∨ (∃x. Q x)" ..
next
assume "Q a"
hence "∃x. Q x" ..
thus "(∃x. P x) ∨ (∃x. Q x)" ..
qed
qed

-- "La demostración detallada es"
lemma ejercicio_28c:
"((∃x. P x) ∨ (∃x. Q x)) ⟷ (∃x. P x ∨ Q x)"
proof (rule iffI)
assume "(∃x. P x) ∨ (∃x. Q x)"
thus "∃x. P x ∨ Q x"
proof (rule disjE)
assume "∃x. P x"
then obtain a where "P a" by (rule exE)
hence "P a ∨ Q a" by (rule disjI1)
thus "∃x. P x ∨ Q x" by (rule exI)
next
assume "∃x. Q x"
then obtain a where "Q a" by (rule exE)
hence "P a ∨ Q a" by (rule disjI2)
thus "∃x. P x ∨ Q x" by (rule exI)
qed
next
assume "∃x. P x ∨ Q x"
then obtain a where "P a ∨ Q a" by (rule exE)
thus "(∃x. P x) ∨ (∃x. Q x)"
proof (rule disjE)
assume "P a"
hence "∃x. P x" by (rule exI)
thus "(∃x. P x) ∨ (∃x. Q x)" by (rule disjI1)
next
assume "Q a"
hence "∃x. Q x" by (rule exI)
thus "(∃x. P x) ∨ (∃x. Q x)" by (rule disjI2)
qed
qed

text {* ---------------------------------------------------------------
Ejercicio 29. Demostrar o refutar
(∀x. ∃y. P x y) ⟶ (∃y. ∀x. P x y)
------------------------------------------------------------------ *}

lemma ejercicio_29:
"(∀x. ∃y. P x y) ⟶ (∃y. ∀x. P x y)"
quickcheck
(*
Quickcheck found a counterexample:

P = (λx. undefined)(a\<^isub> := {b}, b := {a})
*)
oops

text {* ---------------------------------------------------------------
Ejercicio 30. Demostrar o refutar
(¬(∀x. P x)) ⟷ (∃x. ¬P x)
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_30a:
"(¬(∀x. P x)) ⟷ (∃x. ¬P x)"
by auto

-- "La demostración estructurada es"
lemma ejercicio_30b:
"(¬(∀x. P x)) ⟷ (∃x. ¬P x)"
proof
assume "¬(∀x. P x)"
show "∃x. ¬P x"
proof (rule ccontr)
assume "¬(∃x. ¬P x)"
have "∀x. P x"
proof
fix a
show "P a"
proof (rule ccontr)
assume "¬P a"
hence "∃x. ¬P x" ..
with `¬(∃x. ¬P x)` show False ..
qed
qed
with `¬(∀x. P x)` show False ..
qed
next
assume "∃x. ¬P x"
then obtain a where "¬P a" ..
show "¬(∀x. P x)"
proof
assume "∀x. P x"
hence "P a" ..
with `¬P a` show False ..
qed
qed

-- "La demostración detallada es"
lemma ejercicio_30c:
"(¬(∀x. P x)) ⟷ (∃x. ¬P x)"
proof (rule iffI)
assume "¬(∀x. P x)"
show "∃x. ¬P x"
proof (rule ccontr)
assume "¬(∃x. ¬P x)"
have "∀x. P x"
proof (rule allI)
fix a
show "P a"
proof (rule ccontr)
assume "¬P a"
hence "∃x. ¬P x" by (rule exI)
with `¬(∃x. ¬P x)` show False by (rule notE)
qed
qed
with `¬(∀x. P x)` show False by (rule notE)
qed
next
assume "∃x. ¬P x"
then obtain a where "¬P a" by (rule exE)
show "¬(∀x. P x)"
proof (rule notI)
assume "∀x. P x"
hence "P a" by (rule allE)
show False using `¬P a` `P a` by (rule notE)
qed
qed

section {* Ejercicios sobre igualdad *}

text {* ---------------------------------------------------------------
Ejercicio 31. Demostrar o refutar
P a ⟹ ∀x. x = a ⟶ P x
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_31a:
"P a ⟹ ∀x. x = a ⟶ P x"
by auto

-- "La demostración estructurada es"
lemma ejercicio_31b:
assumes "P a"
shows "∀x. x = a ⟶ P x"
proof
fix b
show "b = a ⟶ P b"
proof
assume "b = a"
thus "P b" using assms by (rule ssubst)
qed
qed

-- "La demostración detallada es"
lemma ejercicio_31c:
assumes "P a"
shows "∀x. x = a ⟶ P x"
proof (rule allI)
fix b
show "b = a ⟶ P b"
proof (rule impI)
assume "b = a"
thus "P b" using assms by (rule ssubst)
qed
qed

text {* ---------------------------------------------------------------
Ejercicio 32. Demostrar o refutar
∃x y. R x y ∨ R y x; ¬(∃x. R x x)⟧ ⟹ ∃x y. x ≠ y
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_32a:
fixes R :: "'c ⇒ 'c ⇒ bool"
assumes "∃x y. R x y ∨ R y x"
"¬(∃x. R x x)"
shows "∃(x::'c) y. x ≠ y"
using assms
by metis

-- "La demostración estructurada es"
lemma ejercicio_32b:
fixes R :: "'c ⇒ 'c ⇒ bool"
assumes "∃x y. R x y ∨ R y x"
"¬(∃x. R x x)"
shows "∃(x::'c) y. x ≠ y"
proof -
obtain a where "∃y. R a y ∨ R y a" using assms(1) ..
then obtain b where "R a b ∨ R b a" ..
hence "a ≠ b"
proof
assume "R a b"
show "a ≠ b"
proof
assume "a = b"
hence "R b b" using `R a b` by (rule subst)
hence "∃x. R x x" ..
with assms(2) show False ..
qed
next
assume "R b a"
show "a ≠ b"
proof
assume "a = b"
hence "R a a" using `R b a` by (rule ssubst)
hence "∃x. R x x" ..
with assms(2) show False ..
qed
qed
hence "∃y. a ≠ y" ..
thus "∃(x::'c) y. x ≠ y" ..
qed

-- "La demostración detallada es"
lemma ejercicio_32c:
fixes R :: "'c ⇒ 'c ⇒ bool"
assumes "∃x y. R x y ∨ R y x"
"¬(∃x. R x x)"
shows "∃(x::'c) y. x ≠ y"
proof -
obtain a where "∃y. R a y ∨ R y a" using assms(1) by (rule exE)
then obtain b where "R a b ∨ R b a" by (rule exE)
hence "a ≠ b"
proof (rule disjE)
assume "R a b"
show "a ≠ b"
proof (rule notI)
assume "a = b"
hence "R b b" using `R a b` by (rule subst)
hence "∃x. R x x" by (rule exI)
with assms(2) show False by (rule notE)
qed
next
assume "R b a"
show "a ≠ b"
proof (rule notI)
assume "a = b"
hence "R a a" using `R b a` by (rule ssubst)
hence "∃x. R x x" by (rule exI)
with assms(2) show False by (rule notE)
qed
qed
hence "∃y. a ≠ y" by (rule exI)
thus "∃(x::'c) y. x ≠ y" by (rule exI)
qed

text {* ---------------------------------------------------------------
Ejercicio 33. Demostrar o refutar
{∀x. P a x x,
∀x y z. P x y z ⟶ P (f x) y (f z)}
⊢ P (f a) a (f a)
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_33a:
"⟦∀x. P a x x; ∀x y z. P x y z ⟶ P (f x) y (f z)⟧ ⟹ P (f a) a (f a)"
by auto

-- "La demostración estructura es"
lemma ejercicio_33b:
assumes "∀x. P a x x"
"∀x y z. P x y z ⟶ P (f x) y (f z)"
shows "P (f a) a (f a)"
proof -
have "P a a a" using assms(1) ..
have "∀y z. P a y z ⟶ P (f a) y (f z)" using assms(2) ..
hence "∀z. P a a z ⟶ P (f a) a (f z)" ..
hence "P a a a ⟶ P (f a) a (f a)" ..
thus "P (f a) a (f a)" using `P a a a` ..
qed

-- "La demostración detallada es"
lemma ejercicio_33c:
assumes "∀x. P a x x"
"∀x y z. P x y z ⟶ P (f x) y (f z)"
shows "P (f a) a (f a)"
proof -
have "P a a a" using assms(1) by (rule allE)
have "∀y z. P a y z ⟶ P (f a) y (f z)" using assms(2) by (rule allE)
hence "∀z. P a a z ⟶ P (f a) a (f z)" by (rule allE)
hence "P a a a ⟶ P (f a) a (f a)" by (rule allE)
thus "P (f a) a (f a)" using `P a a a` by (rule mp)
qed

text {* ---------------------------------------------------------------
Ejercicio 34. Demostrar o refutar
{∀x. P a x x,
∀x y z. P x y z ⟶ P (f x) y (f z)⟧
⊢ ∃z. P (f a) z (f (f a))
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_34a:
"⟦∀x. P a x x; ∀x y z. P x y z ⟶ P (f x) y (f z)⟧
⟹ ∃z. P (f a) z (f (f a))"
by metis

-- "La demostración estructura es"
lemma ejercicio_34b:
assumes "∀x. P a x x"
"∀x y z. P x y z ⟶ P (f x) y (f z)"
shows "∃z. P (f a) z (f (f a))"
proof -
have "P a (f a) (f a)" using assms(1) ..
have "∀y z. P a y z ⟶ P (f a) y (f z)" using assms(2) ..
hence "∀z. P a (f a) z ⟶ P (f a) (f a) (f z)" ..
hence "P a (f a) (f a) ⟶ P (f a) (f a) (f (f a))" ..
hence "P (f a) (f a) (f (f a))" using `P a (f a) (f a)` ..
thus "∃z. P (f a) z (f (f a))" ..
qed

-- "La demostración detallada es"
lemma ejercicio_34c:
assumes "∀x. P a x x"
"∀x y z. P x y z ⟶ P (f x) y (f z)"
shows "∃z. P (f a) z (f (f a))"
proof -
have "P a (f a) (f a)" using assms(1) by (rule allE)
have "∀y z. P a y z ⟶ P (f a) y (f z)" using assms(2) by (rule allE)
hence "∀z. P a (f a) z ⟶ P (f a) (f a) (f z)" by (rule allE)
hence "P a (f a) (f a) ⟶ P (f a) (f a) (f (f a))" by (rule allE)
hence "P (f a) (f a) (f (f a))" using `P a (f a) (f a)` by (rule mp)
thus "∃z. P (f a) z (f (f a))" by (rule exI)
qed

text {* ---------------------------------------------------------------
Ejercicio 35. Demostrar o refutar
{∀y. Q a y,
∀x y. Q x y ⟶ Q (s x) (s y)}
⊢ ∃z. Qa z ∧ Q z (s (s a))
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_35a:
"⟦∀y. Q a y; ∀x y. Q x y ⟶ Q (s x) (s y)⟧ ⟹ ∃z. Q a z ∧ Q z (s (s a))"
by auto

-- "La demostración estructura es"
lemma ejercicio_35b:
assumes "∀y. Q a y"
"∀x y. Q x y ⟶ Q (s x) (s y)"
shows "∃z. Q a z ∧ Q z (s (s a))"
proof -
have "Q a (s a)" using assms(1) ..
have "∀y. Q a y ⟶ Q (s a) (s y)" using assms(2) ..
hence "Q a (s a) ⟶ Q (s a) (s (s a))" ..
hence "Q (s a) (s (s a))" using `Q a (s a)` ..
with `Q a (s a)` have "Q a (s a) ∧ Q (s a) (s (s a))" ..
thus "∃z. Q a z ∧ Q z (s (s a))" ..
qed

-- "La demostración detallada es"
lemma ejercicio_35c:
assumes "∀y. Q a y"
"∀x y. Q x y ⟶ Q (s x) (s y)"
shows "∃z. Q a z ∧ Q z (s (s a))"
proof -
have "Q a (s a)" using assms(1) by (rule allE)
have "∀y. Q a y ⟶ Q (s a) (s y)" using assms(2) by (rule allE)
hence "Q a (s a) ⟶ Q (s a) (s (s a))" by (rule allE)
hence "Q (s a) (s (s a))" using `Q a (s a)` by (rule mp)
with `Q a (s a)` have "Q a (s a) ∧ Q (s a) (s (s a))" by (rule conjI)
thus "∃z. Q a z ∧ Q z (s (s a))" by (rule exI)
qed

text {* ---------------------------------------------------------------
Ejercicio 36. Demostrar o refutar
{x = f x, odd (f x)} ⊢ odd x
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_36a:
"⟦x = f x; odd (f x)⟧ ⟹ odd x"
by auto

-- "La demostración semiautomática es"
lemma ejercicio_36b:
"⟦x = f x; odd (f x)⟧ ⟹ odd x"
by (rule ssubst)

-- "La demostración estructurada es"
lemma ejercicio_36c:
assumes "x = f x"
"odd (f x)"
shows "odd x"
proof -
show "odd x" using assms by (rule ssubst)
qed

text {* ---------------------------------------------------------------
Ejercicio 37. Demostrar o refutar
{x = f x, triple (f x) (f x) x} ⊢ triple x x x
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_37a:
"⟦x = f x; triple (f x) (f x) x⟧ ⟹ triple x x x"
by auto

-- "La demostración semiautomática es"
lemma ejercicio_37b:
"⟦x = f x; triple (f x) (f x) x⟧ ⟹ triple x x x"
by (rule ssubst)

-- "La demostración estructurada es"
lemma ejercicio_37c:
assumes "x = f x"
"triple (f x) (f x) x"
shows "triple x x x"
proof -
show "triple x x x" using assms by (rule ssubst)
qed

end
</source>

Rel 2

2018-07-15T12:03:17Z

Jalonso: Texto reemplazado: «"isar"» por «"isabelle"»

<source lang="isabelle">
header {* Relación 2: Razonamiento sobre programas *}

theory R2_Razonamiento_sobre_programas
imports Main
begin

text {* ---------------------------------------------------------------
Ejercicio 1. Definir la función
sumaImpares :: nat ⇒ nat
tal que (sumaImpares n) es la suma de los n primeros números
impares. Por ejemplo,
sumaImpares 5 = 25
------------------------------------------------------------------ *}

fun sumaImpares :: "nat ⇒ nat" where
"sumaImpares n = undefined"

value "sumaImpares 5" -- "= 25"

text {* ---------------------------------------------------------------
Ejercicio 2. Demostrar que
sumaImpares n = n*n
------------------------------------------------------------------- *}

lemma "sumaImpares n = n*n"
oops

text {* ---------------------------------------------------------------
Ejercicio 3. Definir la función
sumaPotenciasDeDosMasUno :: nat ⇒ nat
tal que
(sumaPotenciasDeDosMasUno n) = 1 + 2^0 + 2^1 + 2^2 + ... + 2^n.
Por ejemplo,
sumaPotenciasDeDosMasUno 3 = 16
------------------------------------------------------------------ *}

fun sumaPotenciasDeDosMasUno :: "nat ⇒ nat" where
"sumaPotenciasDeDosMasUno n = undefined"

value "sumaPotenciasDeDosMasUno 3" -- "= 16"

text {* ---------------------------------------------------------------
Ejercicio 4. Demostrar que
sumaPotenciasDeDosMasUno n = 2^(n+1)
------------------------------------------------------------------- *}

lemma "sumaPotenciasDeDosMasUno n = 2^(n+1)"
oops

text {* ---------------------------------------------------------------
Ejercicio 5. Definir la función
copia :: nat ⇒ 'a ⇒ 'a list
tal que (copia n x) es la lista formado por n copias del elemento
x. Por ejemplo,
copia 3 x = [x,x,x]
------------------------------------------------------------------ *}

fun copia :: "nat ⇒ 'a ⇒ 'a list" where
"copia n x = undefined"

value "copia 3 x" -- "= [x,x,x]"

text {* ---------------------------------------------------------------
Ejercicio 6. Definir la función
todos :: ('a ⇒ bool) ⇒ 'a list ⇒ bool
tal que (todos p xs) se verifica si todos los elementos de xs cumplen
la propiedad p. Por ejemplo,
todos (λx. x>(1::nat)) [2,6,4] = True
todos (λx. x>(2::nat)) [2,6,4] = False
Nota: La conjunción se representa por ∧
----------------------------------------------------------------- *}

fun todos :: "('a ⇒ bool) ⇒ 'a list ⇒ bool" where
"todos p xs = undefined"

value "todos (λx. x>(1::nat)) [2,6,4]" -- "= True"
value "todos (λx. x>(2::nat)) [2,6,4]" -- "= False"

text {* ---------------------------------------------------------------
Ejercicio 7. Demostrar que todos los elementos de (copia n x) son
iguales a x.
------------------------------------------------------------------- *}

lemma "todos (λy. y=x) (copia n x)"
oops

text {* ---------------------------------------------------------------
Ejercicio 8. Definir la función
factR :: nat ⇒ nat
tal que (factR n) es el factorial de n. Por ejemplo,
factR 4 = 24
------------------------------------------------------------------ *}

fun factR :: "nat ⇒ nat" where
"factR n = undefined"

value "factR 4" -- "= 24"

text {* ---------------------------------------------------------------
Ejercicio 9. Se considera la siguiente definición iterativa de la
función factorial
factI :: "nat ⇒ nat" where
factI n = factI' n 1

factI' :: nat ⇒ nat ⇒ nat" where
factI' 0 x = x
factI' (Suc n) x = factI' n (Suc n)*x
Demostrar que, para todo n y todo x, se tiene
factI' n x = x * factR n
------------------------------------------------------------------- *}

fun factI' :: "nat ⇒ nat ⇒ nat" where
"factI' 0 x = x"
| "factI' (Suc n) x = factI' n (Suc n)*x"

fun factI :: "nat ⇒ nat" where
"factI n = factI' n 1"

value "factI 4" -- "= 24"

lemma fact: "factI' n x = x * factR n"
oops

text {* ---------------------------------------------------------------
Ejercicio 10. Demostrar que
factI n = factR n
------------------------------------------------------------------- *}

corollary "factI n = factR n"
oops

text {* ---------------------------------------------------------------
Ejercicio 11. Definir, recursivamente y sin usar (@), la función
amplia :: 'a list ⇒ 'a ⇒ 'a list
tal que (amplia xs y) es la lista obtenida añadiendo el elemento y al
final de la lista xs. Por ejemplo,
amplia [d,a] t = [d,a,t]
------------------------------------------------------------------ *}

fun amplia :: "'a list ⇒ 'a ⇒ 'a list" where
"amplia xs y = undefined"

value "amplia [d,a] t" -- "= [d,a,t]"

text {* ---------------------------------------------------------------
Ejercicio 12. Demostrar que
amplia xs y = xs @ [y]
------------------------------------------------------------------- *}

lemma "amplia xs y = xs @ [y]"
oops

end
</source>

RA12 Relación 9

2018-07-15T12:03:07Z

Jalonso:

<source lang="isabelle">
header {* R9: Cons inverso *}

theory R9
imports Main
begin

text {*
---------------------------------------------------------------------
Ejercicio 1. Definir recursivamente la función
snoc :: "'a list ⇒ 'a ⇒ 'a list"
tal que (snoc xs a) es la lista obtenida al añadir el elemento a al
final de la lista xs. Por ejemplo,
value "snoc [2,5] (3::int)" == [2,5,3]

Nota: No usar @.
---------------------------------------------------------------------
*}

fun snoc :: "'a list ⇒ 'a ⇒ 'a list" where
"snoc xs a = undefined"

text {*
---------------------------------------------------------------------
Ejercicio 2. Demostrar el siguiente teorema
snoc xs a = xs @ [a]
---------------------------------------------------------------------
*}

lemma snoc_append:
"snoc xs a = xs @ [a]"
oops

text {*
---------------------------------------------------------------------
Ejercicio 3. Demostrar el siguiente teorema
rev (x # xs) = snoc (rev xs) x"
---------------------------------------------------------------------
*}

theorem rev_cons:
"rev (x # xs) = snoc (rev xs) x"
oops

end
</source>

RA12 Relación 6

2018-07-15T12:02:24Z

Jalonso:

<source lang="isabelle">
header {* R6: Argumentación en lógica de primer orden con igualdad *}

theory R6
imports Main
begin

text {*
---------------------------------------------------------------------
El objetivo de esta relación es formalizar y decidir la corrección
de los argumentos. En el caso de que sea correcto, demostrarlo usando
sólo las reglas básicas de deducción natural de la lógica de primer
orden (sin usar el método auto). En el caso de que sea incorrecto,
calcular un contraejemplo con QuickCheck.

Las reglas básicas de la deducción natural son las siguientes:
· conjI: ⟦P; Q⟧ ⟹ P ∧ Q
· conjunct1: P ∧ Q ⟹ P
· conjunct2: P ∧ Q ⟹ Q
· notnotD: ¬¬ P ⟹ P
· notnotI: P ⟹ ¬¬ P
· mp: ⟦P ⟶ Q; P⟧ ⟹ Q
· mt: ⟦F ⟶ G; ¬G⟧ ⟹ ¬F
· impI: (P ⟹ Q) ⟹ P ⟶ Q
· disjI1: P ⟹ P ∨ Q
· disjI2: Q ⟹ P ∨ Q
· disjE: ⟦P ∨ Q; P ⟹ R; Q ⟹ R⟧ ⟹ R
· FalseE: False ⟹ P
· notE: ⟦¬P; P⟧ ⟹ R
· notI: (P ⟹ False) ⟹ ¬P
· iffI: ⟦P ⟹ Q; Q ⟹ P⟧ ⟹ P = Q
· iffD1: ⟦Q = P; Q⟧ ⟹ P
· iffD2: ⟦P = Q; Q⟧ ⟹ P
· ccontr: (¬P ⟹ False) ⟹ P
· excluded_middle: ¬P ∨ P

· allI: ⟦∀x. P x; P x ⟹ R⟧ ⟹ R
· allE: (⋀x. P x) ⟹ ∀x. P x
· exI: P x ⟹ ∃x. P x
· exE: ⟦∃x. P x; ⋀x. P x ⟹ Q⟧ ⟹ Q

· refl: t = t
· subst: ⟦s = t; P s⟧ ⟹ P t

· trans: ⟦r = s; s = t⟧ ⟹ r = t
· sym: s = t ⟹ t = s
· not_sym: t ≠ s ⟹ s ≠ t
· ssubst: ⟦t = s; P s⟧ ⟹ P t
· box_equals: ⟦a = b; a = c; b = d⟧ ⟹ a: = d
· arg_cong: x = y ⟹ f x = f y
· fun_cong: f = g ⟹ f x = g x
· cong: ⟦f = g; x = y⟧ ⟹ f x = g y
---------------------------------------------------------------------
*}

text {*
Se usarán, además, siquientes reglas que demostramos a continuación.
*}

text {* ---------------------------------------------------------------
Ejercicio 1. Formalizar, y decidir la corrección, del siguiente
argumento
Rosa ama a Curro. Paco no simpatiza con Ana. Quien no simpatiza con
Ana ama a Rosa. Si una persona ama a otra, la segunda ama a la
primera. Hay como máximo una persona que ama a Rosa. Por tanto,
Paco es Curro.
Usar A(x,y) para x ama a y
S(x,y) para x simpatiza con y
a para Ana
c para Curro
p para Paco
r para Rosa
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 2. Formalizar, y decidir la corrección, del siguiente
argumento
Sólo hay un sofista que enseña gratuitamente, y éste es
Sócrates. Sócrates argumenta mejor que ningún otro sofista. Platón
argumenta mejor que algún sofista que enseña gratuitamente. Si una
persona argumenta mejor que otra segunda, entonces la segunda no
argumenta mejor que la primera. Por consiguiente, Platón no es un
sofista.
Usar G(x) para x enseña gratuitamente
M(x,y) para x argumenta mejor que y
S(x) para x es un sofista
p para Platón
s para Sócrates
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 3. Formalizar, y decidir la corrección, del siguiente
argumento
Todos los filósofos se han preguntado qué es la filosofía. Los que
se preguntan qué es la filosofía se vuelven locos. Nietzsche es
filósofo. El maestro de Nietzsche no acabó loco. Por tanto,
Nietzsche y su maestro son diferentes personas.
Usar F(x) para x es filósofo
L(x) para x se vuelve loco
P(x) para x se ha preguntado qué es la filosofía.
m para el maestro de Nietzsche
n para Nietzsche
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 4. Formalizar, y decidir la corrección, del siguiente
argumento
Los padres son mayores que los hijos. Juan es el padre de Luis. Por
tanto, Juan es mayor que Luis.
Usar M(x,y) para x es mayor que y
p(x) para el padre de x
j para Juan
l para Luis
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 5. Formalizar, y decidir la corrección, del siguiente
argumento
El esposo de la hermana de Toni es Roberto. La hermana de Toni es
María. Por tanto, el esposo de María es Roberto.
Usar e(x) para el esposo de x
h para la hermana de Toni
m para María
r para Roberto
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 6. Formalizar, y decidir la corrección, del siguiente
argumento
Luis y Jaime tienen el mismo padre. La madre de Rosa es
Eva. Eva ama a Carlos. Carlos es el padre de Jaime. Por tanto,
la madre de Rosa ama al padre de Luis.
Usar A(x,y) para x ama a y
m(x) para la madre de x
p(x) para el padre de x
c para Carlos
e para Eva
j para Jaime
l para Luis
r para Rosa
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 7. Formalizar, y decidir la corrección, del siguiente
argumento
Si dos personas son hermanos, entonces tienen la misma madre y el
mismo padre. Juan es hermano de Luis. Por tanto, la madre del padre
de Juan es la madre del padre de Luis.
Usar H(x,y) para x es hermano de y
m(x) para la madre de x
p(x) para el padre de x
j para Juan
l para Luis
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 8. Formalizar, y decidir la corrección, del siguiente
argumento
Todos los miembros del claustro son asturianos. El secretario forma
parte del claustro. El señor Martínez es el secretario. Por tanto,
el señor Martínez es asturiano.
Usar C(x) para x es miembro del claustro
A(x) para x es asturiano
s para el secretario
m para el señor Martínez
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 9. Formalizar, y decidir la corrección, del siguiente
argumento
Eduardo pudo haber visto al asesino. Antonio fue el primer testigo
de la defensa. O Eduardo estaba en clase o Antonio dio falso
testimonio. Nadie en clase pudo haber visto al asesino. Luego, el
primer testigo de la defensa dio falso testimonio.
Usar C(x) para x estaba en clase
F(x) para x dio falso testimonio
V(x) para x pudo haber visto al asesino
a para Antonio
e para Eduardo
p para el primer testigo de la defensa
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 10. Formalizar, y decidir la corrección, del siguiente
argumento
La luna hoy es redonda. La luna de hace dos semanas tenía forma de
cuarto creciente. Luna no hay más que una, es decir, siempre es la
misma. Luego existe algo que es a la vez redondo y con forma de
cuarto creciente.
Usar L(x) para la luna del momento x
R(x) para x es redonda
C(x) para x tiene forma de cuarto creciente
h para hoy
d para hace dos semanas
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 11. Formalizar, y decidir la corrección, del siguiente
argumento
Juana sólo tiene un marido. Juana está casada con Tomás. Tomás es
delgado y Guillermo no. Luego, Juana no está casada con Guillermo.
Usar D(x) para x es delgado
C(x,y) para x está casada con y
g para Guillermo
j para Juana
t para Tomás
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 12. Formalizar, y decidir la corrección, del siguiente
argumento
Sultán no es Chitón. Sultán no obtendrá un plátano a menos que
pueda resolver cualquier problema. Si el chimpancé Chitón trabaja
más que Sultán resolverá problemas que Sultán no puede resolver.
Todos los chimpancés distintos de Sultán trabajan más que Sultán.
Por consiguiente, Sultán no obtendrá un plátano.
Usar Pl(x) para x obtiene el plátano
Pr(x) para x es un problema
R(x,y) para x resuelve y
T(x,y) para x trabaja más que y
c para Chitón
s para Sultán
------------------------------------------------------------------ *}

end
</source>

GLC T1R1

2018-07-15T12:01:30Z

Jalonso: Texto reemplazado: «"isar"» por «"isabelle"»

<source lang="isabelle">
header {* T1R1: Deducción natural proposicional *}

theory T1R1
imports Main
begin

text {*
---------------------------------------------------------------------
El objetivo de esta relación es lemas usando sólo las reglas básicas
de deducción natural de la lógica proposicional.

Los ejercicios son los de la asignatura de "Lógica informática" que se
encuentran en http://goo.gl/yrPLn

Las reglas básicas de la deducción natural son las siguientes:
· conjI: ⟦P; Q⟧ ⟹ P ∧ Q
· conjunct1: P ∧ Q ⟹ P
· conjunct2: P ∧ Q ⟹ Q
· notnotD: ¬¬ P ⟹ P
· notnotI: P ⟹ ¬¬ P
· mp: ⟦P ⟶ Q; P⟧ ⟹ Q
· mt: ⟦F ⟶ G; ¬G⟧ ⟹ ¬F
· impI: (P ⟹ Q) ⟹ P ⟶ Q
· disjI1: P ⟹ P ∨ Q
· disjI2: Q ⟹ P ∨ Q
· disjE: ⟦P ∨ Q; P ⟹ R; Q ⟹ R⟧ ⟹ R
· FalseE: False ⟹ P
· notE: ⟦¬P; P⟧ ⟹ R
· notI: (P ⟹ False) ⟹ ¬P
· iffI: ⟦P ⟹ Q; Q ⟹ P⟧ ⟹ P = Q
· iffD1: ⟦Q = P; Q⟧ ⟹ P
· iffD2: ⟦P = Q; Q⟧ ⟹ P
· ccontr: (¬P ⟹ False) ⟹ P
· excluded_middle: ¬P ∨ P
---------------------------------------------------------------------
*}

text {*
Se usarán las reglas notnotI y mt que demostramos a continuación.
*}

lemma notnotI: "P ⟹ ¬¬ P"
by auto

lemma mt: "⟦F ⟶ G; ¬G⟧ ⟹ ¬F"
by auto

section {* Implicaciones *}

text {* ---------------------------------------------------------------
Ejercicio 1. Demostrar
p ⟶ q, p ⊢ q
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_1_1:
assumes 1: "p ⟶ q" and
2: "p"
shows "q"
proof -
show "q" using 1 2 by (rule mp)
qed

-- "La demostración estructurada es"
lemma ejercicio_1_2:
assumes "p ⟶ q"
"p"
shows "q"
proof -
show "q" using assms ..
qed

-- "La demostración automática es"
lemma ejercicio_1_3:
assumes "p ⟶ q"
"p"
shows "q"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 2. Demostrar
p ⟶ q, q ⟶ r, p ⊢ r
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_2_1:
assumes 1: "p ⟶ q" and
2: "q ⟶ r" and
3: "p"
shows "r"
proof -
have 4: "q" using 1 3 by (rule mp)
show "r" using 2 4 by (rule mp)
qed

-- "La demostración estructurada es"
lemma ejercicio_2_2:
assumes "p ⟶ q"
"q ⟶ r"
"p"
shows "r"
proof -
have "q" using assms(1,3) ..
show "r" using assms(2) `q` ..
qed

-- "La demostración automática es"
lemma ejercicio_2_3:
assumes "p ⟶ q"
"q ⟶ r"
"p"
shows "r"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 3. Demostrar
p ⟶ (q ⟶ r), p ⟶ q, p ⊢ r
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_3_1:
assumes 1: "p ⟶ (q ⟶ r)" and
2: "p ⟶ q" and
3: "p"
shows "r"
proof -
have 4: "q" using 2 3 by (rule mp)
have 5: "q ⟶ r" using 1 3 by (rule mp)
show "r" using 5 4 by (rule mp)
qed

-- "La demostración estructurada es"
lemma ejercicio_3_2:
assumes "p ⟶ (q ⟶ r)"
"p ⟶ q"
"p"
shows "r"
proof -
have "q" using assms(2,3) ..
have "q ⟶ r" using assms(1,3) ..
thus "r" using `q` ..
qed

-- "La demostración automática es"
lemma ejercicio_3_3:
assumes "p ⟶ (q ⟶ r)"
"p ⟶ q"
"p"
shows "r"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 4. Demostrar
p ⟶ q, q ⟶ r ⊢ p ⟶ r
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_4_1:
assumes 1: "p ⟶ q" and
2: "q ⟶ r"
shows "p ⟶ r"
proof (rule impI)
assume 3: "p"
have 4: "q" using 1 3 by (rule mp)
show "r" using 2 4 by (rule mp)
qed

-- "La demostración estructurada es"
lemma ejercicio_4_2:
assumes "p ⟶ q"
"q ⟶ r"
shows "p ⟶ r"
proof
assume "p"
with assms(1) have "q" ..
with assms(2) show "r" ..
qed

-- "La demostración automática es"
lemma ejercicio_4_3:
assumes "p ⟶ q"
"q ⟶ r"
shows "p ⟶ r"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 5. Demostrar
p ⟶ (q ⟶ r) ⊢ q ⟶ (p ⟶ r)
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_5_1:
assumes 1: "p ⟶ (q ⟶ r)"
shows "q ⟶ (p ⟶ r)"
proof (rule impI)
assume 2: "q"
show "p ⟶ r"
proof (rule impI)
assume 3: "p"
have "q ⟶ r" using 1 3 by (rule mp)
thus "r" using 2 by (rule mp)
qed
qed

-- "La demostración estructurada es"
lemma ejercicio_5_2:
assumes "p ⟶ (q ⟶ r)"
shows "q ⟶ (p ⟶ r)"
proof
assume "q"
show "p ⟶ r"
proof
assume "p"
with assms(1) have "q ⟶ r" ..
thus "r" using `q` ..
qed
qed

-- "La demostración automática es"
lemma ejercicio_5_3:
assumes "p ⟶ (q ⟶ r)"
shows "q ⟶ (p ⟶ r)"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 6. Demostrar
p ⟶ (q ⟶ r) ⊢ (p ⟶ q) ⟶ (p ⟶ r)
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_6_1:
assumes 1: "p ⟶ (q ⟶ r)"
shows "(p ⟶ q) ⟶ (p ⟶ r)"
proof (rule impI)
assume 2: "p ⟶ q"
show "p ⟶ r"
proof (rule impI)
assume 3: "p"
have 4: "q" using 2 3 by (rule mp)
have 5: "q ⟶ r" using 1 3 by (rule mp)
show "r" using 5 4 by (rule mp)
qed
qed

-- "La demostración estructurada es"
lemma ejercicio_6_2:
assumes "p ⟶ (q ⟶ r)"
shows "(p ⟶ q) ⟶ (p ⟶ r)"
proof
assume "p ⟶ q"
show "p ⟶ r"
proof
assume "p"
with `p ⟶ q` have "q" ..
have "q ⟶ r" using assms(1) `p` ..
thus "r" using `q` ..
qed
qed

-- "La demostración automática es"
lemma ejercicio_6_3:
assumes "p ⟶ (q ⟶ r)"
shows "(p ⟶ q) ⟶ (p ⟶ r)"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 7. Demostrar
p ⊢ q ⟶ p
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_7_1:
assumes 1: "p"
shows "q ⟶ p"
proof (rule impI)
assume 2: "q"
show "p" using 1 by this
qed

-- "La demostración estructurada es"
lemma ejercicio_7_2:
assumes "p"
shows "q ⟶ p"
proof
assume "q"
show "p" using assms(1) .
qed

-- "La demostración automática es"
lemma ejercicio_7_3:
assumes "p"
shows "q ⟶ p"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 8. Demostrar
⊢ p ⟶ (q ⟶ p)
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_8_1:
"p ⟶ (q ⟶ p)"
proof (rule impI)
assume 1: "p"
show "q ⟶ p"
proof (rule impI)
assume 2: "q"
show "p" using 1 by this
qed
qed

-- "La demostración estructurada es"
lemma ejercicio_8_2:
"p ⟶ (q ⟶ p)"
proof
assume "p"
show "q ⟶ p"
proof
assume "q"
show "p" using `p` .
qed
qed

-- "La demostración automática es"
lemma ejercicio_8_3:
"p ⟶ (q ⟶ p)"
by auto

text {* ---------------------------------------------------------------
Ejercicio 9. Demostrar
p ⟶ q ⊢ (q ⟶ r) ⟶ (p ⟶ r)
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_9_1:
assumes 1: "p ⟶ q"
shows "(q ⟶ r) ⟶ (p ⟶ r)"
proof (rule impI)
assume 2: "q ⟶ r"
show "p ⟶ r"
proof (rule impI)
assume 3: "p"
have 4: "q" using 1 3 by (rule mp)
show "r" using 2 4 by (rule mp)
qed
qed

-- "La demostración estructurada es"
lemma ejercicio_9_2:
assumes "p ⟶ q"
shows "(q ⟶ r) ⟶ (p ⟶ r)"
proof
assume "q ⟶ r"
show "p ⟶ r"
proof
assume "p"
with assms(1) have "q" ..
with `q ⟶ r` show "r" ..
qed
qed

-- "La demostración automática es"
lemma ejercicio_9_3:
assumes "p ⟶ q"
shows "(q ⟶ r) ⟶ (p ⟶ r)"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 10. Demostrar
p ⟶ (q ⟶ (r ⟶ s)) ⊢ r ⟶ (q ⟶ (p ⟶ s))
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_10_1:
assumes 1: "p ⟶ (q ⟶ (r ⟶ s))"
shows "r ⟶ (q ⟶ (p ⟶ s))"
proof -
{ assume 2: "r"
{ assume 3: "q"
{ assume 4: "p"
have 5: "q ⟶ (r ⟶ s)" using 1 4 by (rule mp)
have 6: "r ⟶ s" using 5 3 by (rule mp)
have 7: "s" using 6 2 by (rule mp) }
hence 8: "p ⟶ s" by (rule impI) }
hence 9: "q ⟶ (p ⟶ s)" by (rule impI) }
thus 10: "r ⟶ (q ⟶ (p ⟶ s))" by (rule impI)
qed

-- "Una variante de la demostración anterior es"
lemma ejercicio_10_1b:
assumes 1: "p ⟶ (q ⟶ (r ⟶ s))"
shows "r ⟶ (q ⟶ (p ⟶ s))"
proof (rule impI)
assume 2: "r"
show "q ⟶ (p ⟶ s)"
proof (rule impI)
assume 3: "q"
show "p ⟶ s"
proof (rule impI)
assume 4: "p"
have 5: "q ⟶ (r ⟶ s)" using 1 4 by (rule mp)
have 6: "r ⟶ s" using 5 3 by (rule mp)
show "s" using 6 2 by (rule mp)
qed
qed
qed

-- "La demostración estructurada es"
lemma ejercicio_10_2:
assumes "p ⟶ (q ⟶ (r ⟶ s))"
shows "r ⟶ (q ⟶ (p ⟶ s))"
proof
assume "r"
show "q ⟶ (p ⟶ s)"
proof
assume "q"
show "p ⟶ s"
proof
assume "p"
with assms(1) have "q ⟶ (r ⟶ s)" ..
hence "r ⟶ s" using `q` ..
thus "s" using `r` ..
qed
qed
qed

-- "La demostración automática es"
lemma ejercicio_10_3:
assumes "p ⟶ (q ⟶ (r ⟶ s))"
shows "r ⟶ (q ⟶ (p ⟶ s))"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 11. Demostrar
⊢ (p ⟶ (q ⟶ r)) ⟶ ((p ⟶ q) ⟶ (p ⟶ r))
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_11_1:
"(p ⟶ (q ⟶ r)) ⟶ ((p ⟶ q) ⟶ (p ⟶ r))"
proof -
{ assume 1: "p ⟶ (q ⟶ r)"
{ assume 2: "p ⟶ q"
{ assume 3: "p"
have 4: "q" using 2 3 by (rule mp)
have 5: "q ⟶ r" using 1 3 by (rule mp)
have 6: "r" using 5 4 by (rule mp) }
hence 7: "p ⟶ r" by (rule impI) }
hence 8: "(p ⟶ q) ⟶ (p ⟶ r)" by (rule impI) }
thus "(p ⟶ (q ⟶ r)) ⟶ ((p ⟶ q) ⟶ (p ⟶ r))" by (rule impI)
qed

-- "La demostración estructurada es"
lemma ejercicio_11_2:
"(p ⟶ (q ⟶ r)) ⟶ ((p ⟶ q) ⟶ (p ⟶ r))"
proof
assume "p ⟶ (q ⟶ r)"
{ assume "p ⟶ q"
{ assume "p"
with `p ⟶ q` have "q" ..
have "q ⟶ r" using `p ⟶ (q ⟶ r)` `p` ..
hence "r" using `q` .. }
hence "p ⟶ r" .. }
thus "(p ⟶ q) ⟶ (p ⟶ r)" ..
qed

-- "La demostración automática es"
lemma ejercicio_11_3:
"(p ⟶ (q ⟶ r)) ⟶ ((p ⟶ q) ⟶ (p ⟶ r))"
by auto

text {* ---------------------------------------------------------------
Ejercicio 12. Demostrar
(p ⟶ q) ⟶ r ⊢ p ⟶ (q ⟶ r)
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_12_1:
assumes 1: "(p ⟶ q) ⟶ r"
shows "p ⟶ (q ⟶ r)"
proof -
{ assume 2: "p"
{ assume 3: "q"
{ assume 4: "p"
have 5: "q" using 3 by this }
hence 6: "p ⟶ q" by (rule impI)
have 7: "r" using 1 6 by (rule mp) }
hence 8: "q ⟶ r" by (rule impI) }
thus 9: "p ⟶ (q ⟶ r)" by (rule impI)
qed

-- "La demostración estructurada es"
lemma ejercicio_12_2:
assumes "(p ⟶ q) ⟶ r"
shows "p ⟶ (q ⟶ r)"
proof
assume "p"
{ assume "q"
{ assume "p"
have "q" using `q` . }
hence "p ⟶ q" ..
with assms(1) have "r" .. }
thus "q ⟶ r" ..
qed

-- "La demostración automática es"
lemma ejercicio_12_3:
assumes "(p ⟶ q) ⟶ r"
shows "p ⟶ (q ⟶ r)"
using assms
by auto

section {* Conjunciones *}

text {* ---------------------------------------------------------------
Ejercicio 13. Demostrar
p, q ⊢ p ∧ q
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_13_1:
assumes 1: "p" and
2: "q"
shows "p ∧ q"
proof -
show "p ∧ q" using assms by (rule conjI)
qed

-- "La demostración estructurada es"
lemma ejercicio_13_2:
assumes "p"
"q"
shows "p ∧ q"
proof
show "p" using assms(1) .
next
show "q" using assms(2) .
qed

-- "La demostración automática es"
lemma ejercicio_13_3:
assumes "p"
"q"
shows "p ∧ q"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 14. Demostrar
p ∧ q ⊢ p
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_14_1:
assumes 1: "p ∧ q"
shows "p"
proof -
show "p" using 1 by (rule conjunct1)
qed

-- "La demostración estructurada es"
lemma ejercicio_14_2:
assumes "p ∧ q"
shows "p"
proof -
show "p" using assms ..
qed

-- "La demostración automática es"
lemma ejercicio_14_3:
assumes "p ∧ q"
shows "p"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 15. Demostrar
p ∧ q ⊢ q
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_15_1:
assumes 1: "p ∧ q"
shows "q"
proof -
show "q" using 1 by (rule conjunct2)
qed

-- "La demostración estructurada es"
lemma ejercicio_15_2:
assumes "p ∧ q"
shows "q"
proof -
show "q" using assms ..
qed

-- "La demostración automática es"
lemma ejercicio_15_3:
assumes "p ∧ q"
shows "q"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 16. Demostrar
p ∧ (q ∧ r) ⊢ (p ∧ q) ∧ r
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_16_1:
assumes 1: "p ∧ (q ∧ r)"
shows "(p ∧ q) ∧ r"
proof -
have 2: "p" using 1 by (rule conjunct1)
have 3: "q ∧ r" using 1 by (rule conjunct2)
have 4: "q" using 3 by (rule conjunct1)
have 5: "p ∧ q" using 2 4 by (rule conjI)
have 6: "r" using 3 by (rule conjunct2)
show 7: "(p ∧ q) ∧ r" using 5 6 by (rule conjI)
qed

-- "La demostración estructurada es"
lemma ejercicio_16_2:
assumes "p ∧ (q ∧ r)"
shows "(p ∧ q) ∧ r"
proof
show "p ∧ q"
proof
show "p" using assms ..
next
have "q ∧ r" using assms ..
thus "q" ..
qed
next
have "q ∧ r" using assms ..
thus "r" ..
qed

-- "La demostración automática es"
lemma ejercicio_16_3:
assumes "p ∧ (q ∧ r)"
shows "(p ∧ q) ∧ r"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 17. Demostrar
(p ∧ q) ∧ r ⊢ p ∧ (q ∧ r)
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_17_1:
assumes 1: "(p ∧ q) ∧ r"
shows "p ∧ (q ∧ r)"
proof -
have 2: "p ∧ q" using 1 by (rule conjunct1)
have 3: "p" using 2 by (rule conjunct1)
have 4: "q" using 2 by (rule conjunct2)
have 5: "r" using 1 by (rule conjunct2)
have 6: "q ∧ r" using 4 5 by (rule conjI)
show 7: "p ∧ (q ∧ r)" using 3 6 by (rule conjI)
qed

-- "La demostración estructurada es"
lemma ejercicio_17_2:
assumes "(p ∧ q) ∧ r"
shows "p ∧ (q ∧ r)"
proof
have "p ∧ q" using assms ..
thus "p" ..
next
show "q ∧ r"
proof
have "p ∧ q" using assms ..
thus "q" ..
next
show "r" using assms ..
qed
qed

-- "La demostración automática es"
lemma ejercicio_17_3:
assumes "(p ∧ q) ∧ r"
shows "p ∧ (q ∧ r)"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 18. Demostrar
p ∧ q ⊢ p ⟶ q
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_18_1:
assumes 1: "p ∧ q"
shows "p ⟶ q"
proof (rule impI)
assume 2: "p"
show "q" using 1 by (rule conjunct2)
qed

-- "La demostración estructurada es"
lemma ejercicio_18_2:
assumes "p ∧ q"
shows "p ⟶ q"
proof
assume "p"
show "q" using assms ..
qed

-- "La demostración automática es"
lemma ejercicio_18_3:
assumes "p ∧ q"
shows "p ⟶ q"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 19. Demostrar
(p ⟶ q) ∧ (p ⟶ r) ⊢ p ⟶ q ∧ r
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_19_1:
assumes 1: "(p ⟶ q) ∧ (p ⟶ r)"
shows "p ⟶ q ∧ r"
proof (rule impI)
assume 2: "p"
have 3: "p ⟶ q" using 1 by (rule conjunct1)
have 4: "q" using 3 2 by (rule mp)
have 5: "p ⟶ r" using 1 by (rule conjunct2)
have 6: "r" using 5 2 by (rule mp)
show 7: "q ∧ r" using 4 6 by (rule conjI)
qed

-- "La demostración estructurada es"
lemma ejercicio_19_2:
assumes "(p ⟶ q) ∧ (p ⟶ r)"
shows "p ⟶ q ∧ r"
proof
assume "p"
show "q ∧ r"
proof
have "p ⟶ q" using assms ..
thus "q" using `p` ..
next
have "p ⟶ r" using assms ..
thus "r" using `p` ..
qed
qed

-- "La demostración automática es"
lemma ejercicio_19_3:
assumes "(p ⟶ q) ∧ (p ⟶ r)"
shows "p ⟶ q ∧ r"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 20. Demostrar
p ⟶ q ∧ r ⊢ (p ⟶ q) ∧ (p ⟶ r)
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_20_1:
assumes 1: "p ⟶ q ∧ r"
shows "(p ⟶ q) ∧ (p ⟶ r)"
proof (rule conjI)
show "p ⟶ q"
proof (rule impI)
assume 2: "p"
have "q ∧ r" using 1 2 by (rule mp)
thus "q" by (rule conjunct1)
qed
next
show "p ⟶ r"
proof (rule impI)
assume 3: "p"
have "q ∧ r" using 1 3 by (rule mp)
thus "r" by (rule conjunct2)
qed
qed

-- "La demostración estructurada es"
lemma ejercicio_20_2:
assumes "p ⟶ q ∧ r"
shows "(p ⟶ q) ∧ (p ⟶ r)"
proof
show "p ⟶ q"
proof
assume "p"
have "q ∧ r" using assms `p` ..
thus "q" ..
qed
next
show "p ⟶ r"
proof
assume "p"
have "q ∧ r" using assms `p` ..
thus "r" ..
qed
qed

-- "La demostración automática es"
lemma ejercicio_20_3:
assumes "p ⟶ q ∧ r"
shows "(p ⟶ q) ∧ (p ⟶ r)"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 21. Demostrar
p ⟶ (q ⟶ r) ⊢ p ∧ q ⟶ r
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_21_1:
assumes 1: "p ⟶ (q ⟶ r)"
shows "p ∧ q ⟶ r"
proof (rule impI)
assume 2: "p ∧ q"
have 3: "p" using 2 by (rule conjunct1)
have 4: "q" using 2 by (rule conjunct2)
have 5: "q ⟶ r" using 1 3 by (rule mp)
show 6: "r" using 5 4 by (rule mp)
qed

-- "La demostración estructurada es"
lemma ejercicio_21_2:
assumes "p ⟶ (q ⟶ r)"
shows "p ∧ q ⟶ r"
proof
assume "p ∧ q"
hence "p" ..
have "q" using `p ∧ q` ..
have "q ⟶ r" using assms(1) `p` ..
thus "r" using `q` ..
qed

-- "La demostración automática es"
lemma ejercicio_21_3:
assumes "p ⟶ (q ⟶ r)"
shows "p ∧ q ⟶ r"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 22. Demostrar
p ∧ q ⟶ r ⊢ p ⟶ (q ⟶ r)
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_22_1:
assumes 1: "p ∧ q ⟶ r"
shows "p ⟶ (q ⟶ r)"
proof (rule impI)
assume 2: "p"
{ assume 3: "q"
have 4: "p ∧ q" using 2 3 by (rule conjI)
have "r" using 1 4 by (rule mp) }
thus "q ⟶ r" by (rule impI)
qed

-- "La demostración estructurada es"
lemma ejercicio_22_2:
assumes "p ∧ q ⟶ r"
shows "p ⟶ (q ⟶ r)"
proof
assume "p"
show "q ⟶ r"
proof
assume "q"
with `p` have "p ∧ q" ..
with assms(1) show "r" ..
qed
qed

-- "La demostración automática es"
lemma ejercicio_22_3:
assumes "p ∧ q ⟶ r"
shows "p ⟶ (q ⟶ r)"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 23. Demostrar
(p ⟶ q) ⟶ r ⊢ p ∧ q ⟶ r
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_23_1:
assumes 1: "(p ⟶ q) ⟶ r"
shows "p ∧ q ⟶ r"
proof (rule impI)
assume 2: "p ∧ q"
have 3: "p ⟶ q"
proof (rule impI)
assume 4: "p"
show "q" using 2 by (rule conjunct2)
qed
show "r" using 1 3 by (rule mp)
qed

-- "La demostración estructurada es"
lemma ejercicio_23_2:
assumes "(p ⟶ q) ⟶ r"
shows "p ∧ q ⟶ r"
proof
assume "p ∧ q"
have "p ⟶ q"
proof
assume "p"
show "q" using `p ∧ q` ..
qed
with assms show "r" ..
qed

-- "La demostración automática es"
lemma ejercicio_23_3:
assumes "(p ⟶ q) ⟶ r"
shows "p ∧ q ⟶ r"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 24. Demostrar
p ∧ (q ⟶ r) ⊢ (p ⟶ q) ⟶ r
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_24_1:
assumes 1: "p ∧ (q ⟶ r)"
shows "(p ⟶ q) ⟶ r"
proof (rule impI)
assume 2: "p ⟶ q"
have 3: "p" using 1 by (rule conjunct1)
have 4: "q" using 2 3 by (rule mp)
have 5: "q ⟶ r" using 1 by (rule conjunct2)
thus "r" using 4 by (rule mp)
qed

-- "La demostración estructurada es"
lemma ejercicio_24_2:
assumes "p ∧ (q ⟶ r)"
shows "(p ⟶ q) ⟶ r"
proof
assume "p ⟶ q"
have "p" using assms ..
with `p ⟶ q` have "q" ..
have "q ⟶ r" using assms ..
thus "r" using `q` ..
qed

-- "La demostración automática es"
lemma ejercicio_24_3:
assumes "p ∧ (q ⟶ r)"
shows "(p ⟶ q) ⟶ r"
using assms
by auto

section {* Disyunciones *}

text {* ---------------------------------------------------------------
Ejercicio 25. Demostrar
p ⊢ p ∨ q
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_25_1:
assumes 1: "p"
shows "p ∨ q"
proof -
show "p ∨ q" using 1 by (rule disjI1)
qed

-- "La demostración estructurada es"
lemma ejercicio_25_2:
assumes "p"
shows "p ∨ q"
proof -
show "p ∨ q" using assms ..
qed

-- "La demostración estructurada es"
lemma ejercicio_25_3:
assumes "p"
shows "p ∨ q"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 26. Demostrar
q ⊢ p ∨ q
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_26_1:
assumes 1: "q"
shows "p ∨ q"
proof -
show "p ∨ q" using 1 by (rule disjI2)
qed

-- "La demostración estructurada es"
lemma ejercicio_26_2:
assumes "q"
shows "p ∨ q"
proof -
show "p ∨ q" using assms ..
qed

-- "La demostración estructurada es"
lemma ejercicio_26_3:
assumes "q"
shows "p ∨ q"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 27. Demostrar
p ∨ q ⊢ q ∨ p
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_27_1:
assumes 1: "p ∨ q"
shows "q ∨ p"
using 1
proof (rule disjE)
assume "p"
thus "q ∨ p" by (rule disjI2)
next
assume "q"
thus "q ∨ p" by (rule disjI1)
qed

-- "La demostración estructurada es"
lemma ejercicio_27_2:
assumes "p ∨ q"
shows "q ∨ p"
using assms
proof
assume "p"
thus "q ∨ p" ..
next
assume "q"
thus "q ∨ p" ..
qed

-- "La demostración estructurada es"
lemma ejercicio_27_3:
assumes "p ∨ q"
shows "q ∨ p"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 28. Demostrar
q ⟶ r ⊢ p ∨ q ⟶ p ∨ r
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_28_1:
assumes 1: "q ⟶ r"
shows "p ∨ q ⟶ p ∨ r"
proof (rule impI)
assume "p ∨ q"
thus "p ∨ r"
proof (rule disjE)
assume "p"
thus "p ∨ r" by (rule disjI1)
next
assume "q"
have "r" using assms `q` by (rule mp)
thus "p ∨ r" by (rule disjI2)
qed
qed

-- "La demostración estructurada es"
lemma ejercicio_28_2:
assumes "q ⟶ r"
shows "p ∨ q ⟶ p ∨ r"
proof
assume "p ∨ q"
thus "p ∨ r"
proof
assume "p"
thus "p ∨ r" ..
next
assume "q"
have "r" using assms `q` ..
thus "p ∨ r" ..
qed
qed

-- "La demostración automática es"
lemma ejercicio_28_3:
assumes "q ⟶ r"
shows "p ∨ q ⟶ p ∨ r"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 29. Demostrar
p ∨ p ⊢ p
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_29_1:
assumes 1: "p ∨ p"
shows "p"
using 1
proof (rule disjE)
assume "p"
thus "p" by this
next
assume "p"
thus "p" by this
qed

-- "La demostración estructurada es"
lemma ejercicio_29_2:
assumes "p ∨ p"
shows "p"
using assms
proof
assume "p"
thus "p" .
next
assume "p"
thus "p" .
qed

-- "La demostración estructurada es"
lemma ejercicio_29_3:
assumes "p ∨ p"
shows "p"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 30. Demostrar
p ⊢ p ∨ p
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_30_1:
assumes 1: "p"
shows "p ∨ p"
proof -
show "p ∨ p" using 1 by (rule disjI1)
qed

-- "La demostración estructurada es"
lemma ejercicio_30_2:
assumes "p"
shows "p ∨ p"
proof -
show "p ∨ p" using assms ..
qed

-- "La demostración estructurada es"
lemma ejercicio_30_3:
assumes "p"
shows "p ∨ p"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 31. Demostrar
p ∨ (q ∨ r) ⊢ (p ∨ q) ∨ r
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_31_1:
assumes 1: "p ∨ (q ∨ r)"
shows "(p ∨ q) ∨ r"
using 1
proof (rule disjE)
assume "p"
hence "p ∨ q" by (rule disjI1)
thus "(p ∨ q) ∨ r" by (rule disjI1)
next
assume "q ∨ r"
thus "(p ∨ q) ∨ r"
proof (rule disjE)
assume "q"
hence "p ∨ q" by (rule disjI2)
thus "(p ∨ q) ∨ r" by (rule disjI1)
next
assume "r"
thus "(p ∨ q) ∨ r" by (rule disjI2)
qed
qed

-- "La demostración estructurada es"
lemma ejercicio_31_2:
assumes "p ∨ (q ∨ r)"
shows "(p ∨ q) ∨ r"
using assms
proof
assume "p"
hence "p ∨ q" ..
thus "(p ∨ q) ∨ r" ..
next
assume "q ∨ r"
thus "(p ∨ q) ∨ r"
proof
assume "q"
hence "p ∨ q" ..
thus "(p ∨ q) ∨ r" ..
next
assume "r"
thus "(p ∨ q) ∨ r" ..
qed
qed

-- "La demostración estructurada es"
lemma ejercicio_31_3:
assumes "p ∨ (q ∨ r)"
shows "(p ∨ q) ∨ r"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 32. Demostrar
(p ∨ q) ∨ r ⊢ p ∨ (q ∨ r)
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_32_1:
assumes 1: "(p ∨ q) ∨ r"
shows "p ∨ (q ∨ r)"
using 1
proof (rule disjE)
assume "p ∨ q"
thus "p ∨ (q ∨ r)"
proof (rule disjE)
assume "p"
thus "p ∨ (q ∨ r)" by (rule disjI1)
next
assume "q"
hence "q ∨ r" by (rule disjI1)
thus "p ∨ (q ∨ r)" by (rule disjI2)
qed
next
assume "r"
hence "q ∨ r" by (rule disjI2)
thus "p ∨ (q ∨ r)" by (rule disjI2)
qed

-- "La demostración estructurada es"
lemma ejercicio_32_2:
assumes "(p ∨ q) ∨ r"
shows "p ∨ (q ∨ r)"
using assms
proof
assume "p ∨ q"
thus "p ∨ (q ∨ r)"
proof
assume "p"
thus "p ∨ (q ∨ r)" ..
next
assume "q"
hence "q ∨ r" ..
thus "p ∨ (q ∨ r)" ..
qed
next
assume "r"
hence "q ∨ r" ..
thus "p ∨ (q ∨ r)" ..
qed

-- "La demostración estructurada es"
lemma ejercicio_32_3:
assumes "(p ∨ q) ∨ r"
shows "p ∨ (q ∨ r)"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 33. Demostrar
p ∧ (q ∨ r) ⊢ (p ∧ q) ∨ (p ∧ r)
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_33_1:
assumes 1: "p ∧ (q ∨ r)"
shows "(p ∧ q) ∨ (p ∧ r)"
proof -
have 2: "p" using 1 by (rule conjunct1)
have 3: "q ∨ r" using 1 by (rule conjunct2)
thus "(p ∧ q) ∨ (p ∧ r)"
proof (rule disjE)
assume 4: "q"
have "p ∧ q" using 2 4 by (rule conjI)
thus "(p ∧ q) ∨ (p ∧ r)" by (rule disjI1)
next
assume 5: "r"
have "q ∨ r" using 1 by (rule conjunct2)
thus "(p ∧ q) ∨ (p ∧ r)"
proof (rule disjE)
assume "q"
have "p ∧ q" using `p` `q` by (rule conjI)
thus "(p ∧ q) ∨ (p ∧ r)" by (rule disjI1)
next
assume "r"
have "p ∧ r" using `p` `r` by (rule conjI)
thus "(p ∧ q) ∨ (p ∧ r)" by (rule disjI2)
qed
qed
qed

-- "La demostración estructurada es"
lemma ejercicio_33_2:
assumes "p ∧ (q ∨ r)"
shows "(p ∧ q) ∨ (p ∧ r)"
proof -
have "p" using assms ..
have "q ∨ r" using assms ..
thus "(p ∧ q) ∨ (p ∧ r)"
proof
assume "q"
with `p` have "p ∧ q" ..
thus "(p ∧ q) ∨ (p ∧ r)" ..
next
assume "r"
hence "q ∨ r" ..
thus "(p ∧ q) ∨ (p ∧ r)"
proof
assume "q"
with `p` have "p ∧ q" ..
thus "(p ∧ q) ∨ (p ∧ r)" ..
next
assume "r"
with `p` have "p ∧ r" ..
thus "(p ∧ q) ∨ (p ∧ r)" ..
qed
qed
qed

-- "La demostración automática es"
lemma ejercicio_33_3:
assumes "p ∧ (q ∨ r)"
shows "(p ∧ q) ∨ (p ∧ r)"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 34. Demostrar
(p ∧ q) ∨ (p ∧ r) ⊢ p ∧ (q ∨ r)
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_34_1:
assumes "(p ∧ q) ∨ (p ∧ r)"
shows "p ∧ (q ∨ r)"
using assms
proof (rule disjE)
assume 1: "p ∧ q"
show "p ∧ (q ∨ r)"
proof (rule conjI)
show "p" using 1 by (rule conjunct1)
next
have "q" using 1 by (rule conjunct2)
thus "q ∨ r" by (rule disjI1)
qed
next
assume 2: "p ∧ r"
hence 3: "p" by (rule conjunct1)
have "r" using 2 by (rule conjunct2)
hence 4: "q ∨ r" by (rule disjI2)
show "p ∧ (q ∨ r)" using 3 4 by (rule conjI)
qed

-- "La demostración estructurada es"
lemma ejercicio_34_2:
assumes "(p ∧ q) ∨ (p ∧ r)"
shows "p ∧ (q ∨ r)"
using assms
proof
assume "p ∧ q"
show "p ∧ (q ∨ r)"
proof
show "p" using `p ∧ q` ..
next
have "q" using `p ∧ q` ..
thus "q ∨ r" ..
qed
next
assume "p ∧ r"
hence "p" ..
have "r" using `p ∧ r` ..
hence "q ∨ r" ..
with `p` show "p ∧ (q ∨ r)" ..
qed

-- "La demostración estructurada es"
lemma ejercicio_34_3:
assumes "(p ∧ q) ∨ (p ∧ r)"
shows "p ∧ (q ∨ r)"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 35. Demostrar
p ∨ (q ∧ r) ⊢ (p ∨ q) ∧ (p ∨ r)
------------------------------------------------------------------ *}

-- "La demostración estructurada es"
lemma ejercicio_35_1:
assumes "p ∨ (q ∧ r)"
shows "(p ∨ q) ∧ (p ∨ r)"
using assms
proof
assume "p"
show "(p ∨ q) ∧ (p ∨ r)"
proof
show "p ∨ q" using `p` ..
next
show "p ∨ r" using `p` ..
qed
next
assume "q ∧ r"
show "(p ∨ q) ∧ (p ∨ r)"
proof
have "q" using `q ∧ r` ..
thus "p ∨ q" ..
next
have "r" using `q ∧ r` ..
thus "p ∨ r" ..
qed
qed

-- "La demostración detallada es"
lemma ejercicio_35_2:
assumes "p ∨ (q ∧ r)"
shows "(p ∨ q) ∧ (p ∨ r)"
using assms
proof (rule disjE)
assume "p"
show "(p ∨ q) ∧ (p ∨ r)"
proof (rule conjI)
show "p ∨ q" using `p` by (rule disjI1)
next
show "p ∨ r" using `p` by (rule disjI1)
qed
next
assume "q ∧ r"
show "(p ∨ q) ∧ (p ∨ r)"
proof (rule conjI)
have "q" using `q ∧ r` ..
thus "p ∨ q" by (rule disjI2)
next
have "r" using `q ∧ r` by (rule conjunct2)
thus "p ∨ r" by (rule disjI2)
qed
qed

-- "La demostración automática es"
lemma ejercicio_35_3:
assumes "p ∨ (q ∧ r)"
shows "(p ∨ q) ∧ (p ∨ r)"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 36. Demostrar
(p ∨ q) ∧ (p ∨ r) ⊢ p ∨ (q ∧ r)
------------------------------------------------------------------ *}

-- "La demostración estructurada es"
lemma ejercicio_36_1:
assumes "(p ∨ q) ∧ (p ∨ r)"
shows "p ∨ (q ∧ r)"
proof -
have "p ∨ q" using assms ..
thus "p ∨ (q ∧ r)"
proof
assume "p"
thus "p ∨ (q ∧ r)" ..
next
assume "q"
have "p ∨ r" using assms ..
thus "p ∨ (q ∧ r)"
proof
assume "p"
thus "p ∨ (q ∧ r)" ..
next
assume "r"
with `q` have "q ∧ r" ..
thus "p ∨ (q ∧ r)" ..
qed
qed
qed

-- "La demostración detallada es"
lemma ejercicio_36_2:
assumes "(p ∨ q) ∧ (p ∨ r)"
shows "p ∨ (q ∧ r)"
proof -
have "p ∨ q" using assms by (rule conjunct1)
thus "p ∨ (q ∧ r)"
proof (rule disjE)
assume "p"
thus "p ∨ (q ∧ r)" by (rule disjI1)
next
assume "q"
have "p ∨ r" using assms by (rule conjunct2)
thus "p ∨ (q ∧ r)"
proof (rule disjE)
assume "p"
thus "p ∨ (q ∧ r)" by (rule disjI1)
next
assume "r"
have "q ∧ r" using `q` `r` by (rule conjI)
thus "p ∨ (q ∧ r)" by (rule disjI2)
qed
qed
qed

-- "La demostración automática es"
lemma ejercicio_36_3:
assumes "(p ∨ q) ∧ (p ∨ r)"
shows "p ∨ (q ∧ r)"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 37. Demostrar
(p ⟶ r) ∧ (q ⟶ r) ⊢ p ∨ q ⟶ r
------------------------------------------------------------------ *}

-- "La demostración estructurada es"
lemma ejercicio_37_1:
assumes "(p ⟶ r) ∧ (q ⟶ r)"
shows "p ∨ q ⟶ r"
proof
assume "p ∨ q"
thus "r"
proof
assume "p"
have "p ⟶ r" using assms ..
thus "r" using `p` ..
next
assume "q"
have "q ⟶ r" using assms ..
thus "r" using `q` ..
qed
qed

-- "La demostración detallada es"
lemma ejercicio_37_2:
assumes "(p ⟶ r) ∧ (q ⟶ r)"
shows "p ∨ q ⟶ r"
proof (rule impI)
assume "p ∨ q"
thus "r"
proof (rule disjE)
assume "p"
have "p ⟶ r" using assms by (rule conjunct1)
thus "r" using `p` by (rule mp)
next
assume "q"
have "q ⟶ r" using assms by (rule conjunct2)
thus "r" using `q` by (rule mp)
qed
qed

-- "La demostración automática es"
lemma ejercicio_37_3:
assumes "(p ⟶ r) ∧ (q ⟶ r)"
shows "p ∨ q ⟶ r"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 38. Demostrar
p ∨ q ⟶ r ⊢ (p ⟶ r) ∧ (q ⟶ r)
------------------------------------------------------------------ *}

-- "La demostración estructurada es"
lemma ejercicio_38_1:
assumes "p ∨ q ⟶ r"
shows "(p ⟶ r) ∧ (q ⟶ r)"
proof
show "p ⟶ r"
proof
assume "p"
hence "p ∨ q" ..
with assms show "r" ..
qed
next
show "q ⟶ r"
proof
assume "q"
hence "p ∨ q" ..
with assms show "r" ..
qed
qed

-- "La demostración detallada es"
lemma ejercicio_38_2:
assumes "p ∨ q ⟶ r"
shows "(p ⟶ r) ∧ (q ⟶ r)"
proof (rule conjI)
show "p ⟶ r"
proof (rule impI)
assume "p"
hence "p ∨ q" by (rule disjI1)
show "r" using assms `p ∨ q` by (rule mp)
qed
next
show "q ⟶ r"
proof (rule impI)
assume "q"
hence "p ∨ q" by (rule disjI2)
show "r" using assms `p ∨ q` by (rule mp)
qed
qed

-- "La demostración automática es"
lemma ejercicio_38_3:
assumes "p ∨ q ⟶ r"
shows "(p ⟶ r) ∧ (q ⟶ r)"
using assms
by auto

section {* Negación *}

text {* ---------------------------------------------------------------
Ejercicio 39. Demostrar
p ⊢ ¬¬p
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_39_1:
assumes "p"
shows "¬¬p"
proof -
show "¬¬p" using assms by (rule notnotI)
qed

-- "La demostración automática es"
lemma ejercicio_39_2:
assumes "p"
shows "¬¬p"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 40. Demostrar
¬p ⊢ p ⟶ q
------------------------------------------------------------------ *}

-- "La demostración estructurada es"
lemma ejercicio_40_1:
assumes "¬p"
shows "p ⟶ q"
proof
assume "p"
with assms(1) show "q" ..
qed

-- "La demostración detallada es"
lemma ejercicio_40_2:
assumes "¬p"
shows "p ⟶ q"
proof (rule impI)
assume "p"
show "q" using assms(1) `p` by (rule notE)
qed

-- "La demostración automática es"
lemma ejercicio_40_3:
assumes "¬p"
shows "p ⟶ q"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 41. Demostrar
p ⟶ q ⊢ ¬q ⟶ ¬p
------------------------------------------------------------------ *}

-- "La demostración estructurada es"
lemma ejercicio_41_1:
assumes "p ⟶ q"
shows "¬q ⟶ ¬p"
proof
assume "¬q"
with assms(1) show "¬p" by (rule mt)
qed

-- "La demostración detallada es"
lemma ejercicio_41_2:
assumes "p ⟶ q"
shows "¬q ⟶ ¬p"
proof (rule impI)
assume "¬q"
show "¬p" using assms(1) `¬q` by (rule mt)
qed

-- "La demostración automática es"
lemma ejercicio_41_3:
assumes "p ⟶ q"
shows "¬q ⟶ ¬p"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 42. Demostrar
p ∨ q, ¬q ⊢ p
------------------------------------------------------------------ *}

-- "La demostración estructurada es"
lemma ejercicio_42_1:
assumes "p ∨ q"
"¬q"
shows "p"
using assms(1)
proof
assume "p"
thus "p" .
next
assume "q"
with assms(2) show "p" ..
qed

-- "La demostración detallada es"
lemma ejercicio_42_2:
assumes "p ∨ q"
"¬q"
shows "p"
using assms(1)
proof (rule disjE)
assume "p"
thus "p" by this
next
assume "q"
show "p" using assms(2) `q` by (rule notE)
qed

-- "La demostración automática es"
lemma ejercicio_42_3:
assumes "p ∨ q"
"¬q"
shows "p"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 42. Demostrar
p ∨ q, ¬p ⊢ q
------------------------------------------------------------------ *}

-- "La demostración estructurada es"
lemma ejercicio_43_1:
assumes "p ∨ q"
"¬p"
shows "q"
using assms(1)
proof
assume "p"
with assms(2) show "q" ..
next
assume "q"
thus "q" .
qed

-- "La demostración detallada es"
lemma ejercicio_43_2:
assumes "p ∨ q"
"¬p"
shows "q"
using assms(1)
proof (rule disjE)
assume "p"
show "q" using assms(2) `p` by (rule notE)
next
assume "q"
thus "q" by this
qed

-- "La demostración automática es"
lemma ejercicio_43_3:
assumes "p ∨ q"
"¬p"
shows "q"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 44. Demostrar
p ∨ q ⊢ ¬(¬p ∧ ¬q)
------------------------------------------------------------------ *}

-- "La demostración estructurada es"
lemma ejercicio_44_1:
assumes "p ∨ q"
shows "¬(¬p ∧ ¬q)"
proof
assume "¬p ∧ ¬q"
note `p ∨ q`
thus "False"
proof
assume "p"
have "¬p" using `¬p ∧ ¬q` ..
thus "False" using `p` ..
next
assume "q"
have "¬q" using `¬p ∧ ¬q` ..
thus "False" using `q` ..
qed
qed

-- "La demostración detallada es"
lemma ejercicio_44_2:
assumes "p ∨ q"
shows "¬(¬p ∧ ¬q)"
proof (rule notI)
assume "¬p ∧ ¬q"
note `p ∨ q`
thus "False"
proof
assume "p"
have "¬p" using `¬p ∧ ¬q` by (rule conjunct1)
thus "False" using `p` by (rule notE)
next
assume "q"
have "¬q" using `¬p ∧ ¬q` by (rule conjunct2)
thus "False" using `q` by (rule notE)
qed
qed

-- "La demostración automática es"
lemma ejercicio_44_3:
assumes "p ∨ q"
shows "¬(¬p ∧ ¬q)"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 45. Demostrar
p ∧ q ⊢ ¬(¬p ∨ ¬q)
------------------------------------------------------------------ *}

-- "La demostración estructurada es"
lemma ejercicio_45_1:
assumes "p ∧ q"
shows "¬(¬p ∨ ¬q)"
proof
assume "¬p ∨ ¬q"
thus "False"
proof
assume "¬p"
have "p" using assms ..
with `¬p` show "False" ..
next
assume "¬q"
have "q" using assms ..
with `¬q` show "False" ..
qed
qed

-- "La demostración detallada es"
lemma ejercicio_45_2:
assumes "p ∧ q"
shows "¬(¬p ∨ ¬q)"
proof (rule notI)
assume "¬p ∨ ¬q"
thus "False"
proof
assume "¬p"
have "p" using assms by (rule conjunct1)
show "False" using `¬p` `p` by (rule notE)
next
assume "¬q"
have "q" using assms by (rule conjunct2)
show "False" using `¬q` `q` by (rule notE)
qed
qed

-- "La demostración automática es"
lemma ejercicio_45_3:
assumes "p ∧ q"
shows "¬(¬p ∨ ¬q)"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 46. Demostrar
¬(p ∨ q) ⊢ ¬p ∧ ¬q
------------------------------------------------------------------ *}

-- "La demostración estructurada es"
lemma ejercicio_46_1:
assumes "¬(p ∨ q)"
shows "¬p ∧ ¬q"
proof
show "¬p"
proof
assume "p"
hence "p ∨ q" ..
with assms show "False" ..
qed
next
show "¬q"
proof
assume "q"
hence "p ∨ q" ..
with assms show "False" ..
qed
qed

-- "La demostración detallada es"
lemma ejercicio_46_2:
assumes "¬(p ∨ q)"
shows "¬p ∧ ¬q"
proof (rule conjI)
show "¬p"
proof (rule notI)
assume "p"
hence "p ∨ q" by (rule disjI1)
show "False" using assms `p ∨ q` by (rule notE)
qed
next
show "¬q"
proof (rule notI)
assume "q"
hence "p ∨ q" by (rule disjI2)
show "False" using assms `p ∨ q` by (rule notE)
qed
qed

-- "La demostración automática es"
lemma ejercicio_46_3:
assumes "¬(p ∨ q)"
shows "¬p ∧ ¬q"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 47. Demostrar
¬p ∧ ¬q ⊢ ¬(p ∨ q)
------------------------------------------------------------------ *}

-- "La demostración estructurada es"
lemma ejercicio_47_1:
assumes "¬p ∧ ¬q"
shows "¬(p ∨ q)"
proof
assume "p ∨ q"
thus False
proof
assume "p"
have "¬p" using assms ..
thus False using `p` ..
next
assume "q"
have "¬q" using assms ..
thus False using `q` ..
qed
qed

-- "La demostración detallada es"
lemma ejercicio_47_2:
assumes "¬p ∧ ¬q"
shows "¬(p ∨ q)"
proof (rule notI)
assume "p ∨ q"
thus False
proof (rule disjE)
assume "p"
have "¬p" using assms by (rule conjunct1)
thus False using `p` by (rule notE)
next
assume "q"
have "¬q" using assms by (rule conjunct2)
thus False using `q` by (rule notE)
qed
qed

-- "La demostración automática es"
lemma ejercicio_47_3:
assumes "¬p ∧ ¬q"
shows "¬(p ∨ q)"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 48. Demostrar
¬p ∨ ¬q ⊢ ¬(p ∧ q)
------------------------------------------------------------------ *}

-- "La demostración estructurada es"
lemma ejercicio_48_1:
assumes "¬p ∨ ¬q"
shows "¬(p ∧ q)"
proof
assume "p ∧ q"
note `¬p ∨ ¬ q`
thus False
proof
assume "¬p"
have "p" using `p ∧ q` ..
with `¬p` show False ..
next
assume "¬q"
have "q" using `p ∧ q` ..
with `¬q` show False ..
qed
qed

-- "La demostración detallada es"
lemma ejercicio_48_2:
assumes "¬p ∨ ¬q"
shows "¬(p ∧ q)"
proof (rule notI)
assume "p ∧ q"
note `¬p ∨ ¬ q`
thus False
proof (rule disjE)
assume "¬p"
have "p" using `p ∧ q` by (rule conjunct1)
show False using `¬p` `p` by (rule notE)
next
assume "¬q"
have "q" using `p ∧ q` by (rule conjunct2)
show False using `¬q` `q` by (rule notE)
qed
qed

-- "La demostración automática es"
lemma ejercicio_48_3:
assumes "¬p ∨ ¬q"
shows "¬(p ∧ q)"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 49. Demostrar
⊢ ¬(p ∧ ¬p)
------------------------------------------------------------------ *}

-- "La demostración estructurada es"
lemma ejercicio_49_1:
"¬(p ∧ ¬p)"
proof
assume "p ∧ ¬p"
hence "p" ..
have "¬p" using `p ∧ ¬p` ..
thus False using `p` ..
qed

-- "La demostración detallada es"
lemma ejercicio_49_2:
"¬(p ∧ ¬p)"
proof (rule notI)
assume "p ∧ ¬p"
hence "p" by (rule conjunct1)
have "¬p" using `p ∧ ¬p` by (rule conjunct2)
thus False using `p` by (rule notE)
qed

-- "La demostración automática es"
lemma ejercicio_49_3:
"¬(p ∧ ¬p)"
by auto

text {* ---------------------------------------------------------------
Ejercicio 50. Demostrar
p ∧ ¬p ⊢ q
------------------------------------------------------------------ *}

-- "La demostración estructurada es"
lemma ejercicio_50_1:
assumes "p ∧ ¬p"
shows "q"
proof -
have "p" using assms ..
have "¬p" using assms ..
thus "q" using `p` ..
qed

-- "La demostración detallada es"
lemma ejercicio_50_2:
assumes "p ∧ ¬p"
shows "q"
proof -
have "p" using assms by (rule conjunct1)
have "¬p" using assms by (rule conjunct2)
thus "q" using `p` by (rule notE)
qed

-- "La demostración automática es"
lemma ejercicio_50_3:
assumes "p ∧ ¬p"
shows "q"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 51. Demostrar
¬¬p ⊢ p
------------------------------------------------------------------ *}

-- "La demostración detallada es"
lemma ejercicio_51_1:
assumes "¬¬p"
shows "p"
using assms
by (rule notnotD)

-- "La demostración automática es"
lemma ejercicio_51_2:
assumes "¬¬p"
shows "p"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 52. Demostrar
⊢ p ∨ ¬p
------------------------------------------------------------------ *}

-- "La demostración estructurada es"
lemma ejercicio_52_1:
"p ∨ ¬p"
proof -
have "¬¬p ∨ ¬p" ..
thus "p ∨ ¬p" by simp
qed

-- "La demostración detallada es"
lemma ejercicio_52_2:
"p ∨ ¬p"
proof -
have "¬¬p ∨ ¬p" by (rule excluded_middle)
thus "p ∨ ¬p" by simp
qed

-- "La demostración automática es"
lemma ejercicio_52_3:
"p ∨ ¬p"
by auto

text {* ---------------------------------------------------------------
Ejercicio 53. Demostrar
⊢ ((p ⟶ q) ⟶ p) ⟶ p
------------------------------------------------------------------ *}

-- "La demostración estructurada es"
lemma ejercicio_53_1:
"((p ⟶ q) ⟶ p) ⟶ p"
proof
assume "(p ⟶ q) ⟶ p"
show "p"
proof (rule ccontr)
assume "¬p"
have "¬(p ⟶ q)" using `(p ⟶ q) ⟶ p` `¬p` by (rule mt)
have "p ⟶ q"
proof
assume "p"
with `¬p` show "q" ..
qed
show False using `¬(p ⟶ q)` `p ⟶ q` ..
qed
qed

-- "La demostración detallada es"
lemma ejercicio_53_2:
"((p ⟶ q) ⟶ p) ⟶ p"
proof (rule impI)
assume "(p ⟶ q) ⟶ p"
show "p"
proof (rule ccontr)
assume "¬p"
have "¬(p ⟶ q)" using `(p ⟶ q) ⟶ p` `¬p` by (rule mt)
have "p ⟶ q"
proof (rule impI)
assume "p"
show "q" using `¬p` `p` by (rule notE)
qed
show False using `¬(p ⟶ q)` `p ⟶ q` by (rule notE)
qed
qed

-- "La demostración automática es"
lemma ejercicio_53_3:
"((p ⟶ q) ⟶ p) ⟶ p"
by auto

text {* ---------------------------------------------------------------
Ejercicio 54. Demostrar
¬q ⟶ ¬p ⊢ p ⟶ q
------------------------------------------------------------------ *}

-- "La demostración estructurada es"
lemma ejercicio_54_1:
assumes "¬q ⟶ ¬p"
shows "p ⟶ q"
proof
assume "p"
show "q"
proof (rule ccontr)
assume "¬q"
with assms have "¬p" ..
thus False using `p` ..
qed
qed

-- "La demostración detallada es"
lemma ejercicio_54_2:
assumes "¬q ⟶ ¬p"
shows "p ⟶ q"
proof (rule impI)
assume "p"
show "q"
proof (rule ccontr)
assume "¬q"
have "¬p" using assms `¬q` by (rule mp)
thus False using `p` by (rule notE)
qed
qed

-- "La demostración automática es"
lemma ejercicio_54_3:
assumes "¬q ⟶ ¬p"
shows "p ⟶ q"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 55. Demostrar
¬(¬p ∧ ¬q) ⊢ p ∨ q
------------------------------------------------------------------ *}

-- "La demostración estructurada es"
lemma ejercicio_55_1:
assumes "¬(¬p ∧ ¬q)"
shows "p ∨ q"
proof -
have "¬p ∨ p" ..
thus "p ∨ q"
proof
assume "¬p"
have "¬q ∨ q" ..
thus "p ∨ q"
proof
assume "¬q"
with `¬p` have "¬p ∧ ¬q" ..
with assms show "p ∨ q" ..
next
assume "q"
thus "p ∨ q" ..
qed
next
assume "p"
thus "p ∨ q" ..
qed
qed

-- "La demostración detallada es"
lemma ejercicio_55_2:
assumes "¬(¬p ∧ ¬q)"
shows "p ∨ q"
proof -
have "¬p ∨ p" by (rule excluded_middle)
thus "p ∨ q"
proof
assume "¬p"
have "¬q ∨ q" by (rule excluded_middle)
thus "p ∨ q"
proof
assume "¬q"
have "¬p ∧ ¬q" using `¬p` `¬q` by (rule conjI)
show "p ∨ q" using assms `¬p ∧ ¬q` by (rule notE)
next
assume "q"
thus "p ∨ q" by (rule disjI2)
qed
next
assume "p"
thus "p ∨ q" by (rule disjI1)
qed
qed

-- "La demostración automática es"
lemma ejercicio_55_3:
assumes "¬(¬p ∧ ¬q)"
shows "p ∨ q"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 56. Demostrar
¬(¬p ∨ ¬q) ⊢ p ∧ q
------------------------------------------------------------------ *}

-- "La demostración estructurada es"
lemma ejercicio_56_1:
assumes "¬(¬p ∨ ¬q)"
shows "p ∧ q"
proof
show "p"
proof (rule ccontr)
assume "¬p"
hence "¬p ∨ ¬q" ..
with assms show False ..
qed
next
show "q"
proof (rule ccontr)
assume "¬q"
hence "¬p ∨ ¬q" ..
with assms show False ..
qed
qed

-- "La demostración detallada es"
lemma ejercicio_56_2:
assumes "¬(¬p ∨ ¬q)"
shows "p ∧ q"
proof (rule conjI)
show "p"
proof (rule ccontr)
assume "¬p"
hence "¬p ∨ ¬q" by (rule disjI1)
show False using assms `¬p ∨ ¬q` by (rule notE)
qed
next
show "q"
proof (rule ccontr)
assume "¬q"
hence "¬p ∨ ¬q" by (rule disjI2)
show False using assms `¬p ∨ ¬q` by (rule notE)
qed
qed

-- "La demostración automática es"
lemma ejercicio_56_3:
assumes "¬(¬p ∨ ¬q)"
shows "p ∧ q"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 57. Demostrar
¬(p ∧ q) ⊢ ¬p ∨ ¬q
------------------------------------------------------------------ *}

-- "La demostración estructurada es"
lemma ejercicio_57_1:
assumes "¬(p ∧ q)"
shows "¬p ∨ ¬q"
proof -
have "¬p ∨ p" ..
thus "¬p ∨ ¬q"
proof
assume "¬p"
thus "¬p ∨ ¬q" ..
next
assume "p"
have "¬q ∨ q" ..
thus "¬p ∨ ¬q"
proof
assume "¬q"
thus "¬p ∨ ¬q" ..
next
assume "q"
with `p` have "p ∧ q" ..
with assms show "¬p ∨ ¬q" ..
qed
qed
qed

-- "La demostración detallada es"
lemma ejercicio_57_2:
assumes "¬(p ∧ q)"
shows "¬p ∨ ¬q"
proof -
have "¬p ∨ p" by (rule excluded_middle)
thus "¬p ∨ ¬q"
proof (rule disjE)
assume "¬p"
thus "¬p ∨ ¬q" by (rule disjI1)
next
assume "p"
have "¬q ∨ q" by (rule excluded_middle)
thus "¬p ∨ ¬q"
proof
assume "¬q"
thus "¬p ∨ ¬q" by (rule disjI2)
next
assume "q"
have "p ∧ q" using `p` `q` by (rule conjI)
show "¬p ∨ ¬q" using assms `p ∧ q` by (rule notE)
qed
qed
qed

-- "La demostración automática es"
lemma ejercicio_57_3:
assumes "¬(p ∧ q)"
shows "¬p ∨ ¬q"
using assms
by auto

text {* ---------------------------------------------------------------
Ejercicio 58. Demostrar
⊢ (p ⟶ q) ∨ (q ⟶ p)
------------------------------------------------------------------ *}

-- "La demostración estructurada es"
lemma ejercicio_58_1:
"(p ⟶ q) ∨ (q ⟶ p)"
proof -
have "¬p ∨ p" ..
thus "(p ⟶ q) ∨ (q ⟶ p)"
proof
assume "¬p"
have "p ⟶ q"
proof
assume "p"
with `¬p` show "q" ..
qed
thus "(p ⟶ q) ∨ (q ⟶ p)" ..
next
assume "p"
have "q ⟶ p"
proof
assume "q"
show "p" using `p` .
qed
thus "(p ⟶ q) ∨ (q ⟶ p)" ..
qed
qed

-- "La demostración detallada es"
lemma ejercicio_58_2:
"(p ⟶ q) ∨ (q ⟶ p)"
proof -
have "¬p ∨ p" by (rule excluded_middle)
thus "(p ⟶ q) ∨ (q ⟶ p)"
proof
assume "¬p"
have "p ⟶ q"
proof (rule impI)
assume "p"
show "q" using `¬p` `p` by (rule notE)
qed
thus "(p ⟶ q) ∨ (q ⟶ p)" by (rule disjI1)
next
assume "p"
have "q ⟶ p"
proof
assume "q"
show "p" using `p` by this
qed
thus "(p ⟶ q) ∨ (q ⟶ p)" by (rule disjI2)
qed
qed

-- "La demostración automática es"
lemma ejercicio_58_3:
"(p ⟶ q) ∨ (q ⟶ p)"
by auto

end
</source>

RA12 Relación 8

2018-07-15T12:00:39Z

Jalonso: Texto reemplazado: «"isar"» por «"isabelle"»

<source lang="isabelle">
header {* R8: Razonamiento sobre programas en Isabelle/HOL *}

theory R8
imports Main
begin

text {* ---------------------------------------------------------------
Ejercicio 1. Definir la función
sumaImpares :: nat ⇒ nat
tal que (sumaImpares n) es la suma de los n primeros números
impares. Por ejemplo,
sumaImpares 5 = 25
------------------------------------------------------------------ *}

fun sumaImpares :: "nat ⇒ nat" where
"sumaImpares n = undefined"

value "sumaImpares 5" -- "= 25"

text {* ---------------------------------------------------------------
Ejercicio 2. Demostrar que
sumaImpares n = n*n
------------------------------------------------------------------- *}

lemma "sumaImpares n = n*n"
oops

text {* ---------------------------------------------------------------
Ejercicio 3. Definir la función
sumaPotenciasDeDosMasUno :: nat ⇒ nat
tal que
(sumaPotenciasDeDosMasUno n) = 1 + 2^0 + 2^1 + 2^2 + ... + 2^n.
Por ejemplo,
sumaPotenciasDeDosMasUno 3 = 16
------------------------------------------------------------------ *}

fun sumaPotenciasDeDosMasUno :: "nat ⇒ nat" where
"sumaPotenciasDeDosMasUno n = undefined"

value "sumaPotenciasDeDosMasUno 3" -- "= 16"

text {* ---------------------------------------------------------------
Ejercicio 4. Demostrar que
sumaPotenciasDeDosMasUno n = 2^(n+1)
------------------------------------------------------------------- *}

lemma "sumaPotenciasDeDosMasUno n = 2^(n+1)"
oops

text {* ---------------------------------------------------------------
Ejercicio 5. Definir la función
copia :: nat ⇒ 'a ⇒ 'a list
tal que (copia n x) es la lista formado por n copias del elemento
x. Por ejemplo,
copia 3 x = [x,x,x]
------------------------------------------------------------------ *}

fun copia :: "nat ⇒ 'a ⇒ 'a list" where
"copia n x = undefined"

value "copia 3 x" -- "= [x,x,x]"

text {* ---------------------------------------------------------------
Ejercicio 6. Definir la función
todos :: ('a ⇒ bool) ⇒ 'a list ⇒ bool
tal que (todos p xs) se verifica si todos los elementos de xs cumplen
la propiedad p. Por ejemplo,
todos (λx. x>(1::nat)) [2,6,4] = True
todos (λx. x>(2::nat)) [2,6,4] = False
Nota: La conjunción se representa por ∧
----------------------------------------------------------------- *}

fun todos :: "('a ⇒ bool) ⇒ 'a list ⇒ bool" where
"todos p xs = undefined"

value "todos (λx. x>(1::nat)) [2,6,4]" -- "= True"
value "todos (λx. x>(2::nat)) [2,6,4]" -- "= False"

text {* ---------------------------------------------------------------
Ejercicio 7. Demostrar que todos los elementos de (copia n x) son
iguales a x.
------------------------------------------------------------------- *}

lemma "todos (λy. y=x) (copia n x)"
oops

text {* ---------------------------------------------------------------
Ejercicio 8. Definir la función
factR :: nat ⇒ nat
tal que (factR n) es el factorial de n. Por ejemplo,
factR 4 = 24
------------------------------------------------------------------ *}

fun factR :: "nat ⇒ nat" where
"factR n = undefined"

value "factR 4" -- "= 24"

text {* ---------------------------------------------------------------
Ejercicio 9. Se considera la siguiente definición iterativa de la
función factorial
factI :: "nat ⇒ nat" where
factI n = factI' n 1

factI' :: nat ⇒ nat ⇒ nat" where
factI' 0 x = x
factI' (Suc n) x = factI' n (Suc n)*x
Demostrar que, para todo n y todo x, se tiene
factI' n x = x * factR n
------------------------------------------------------------------- *}

fun factI' :: "nat ⇒ nat ⇒ nat" where
"factI' 0 x = x"
| "factI' (Suc n) x = factI' n (Suc n)*x"

fun factI :: "nat ⇒ nat" where
"factI n = factI' n 1"

value "factI 4" -- "= 24"

lemma fact: "factI' n x = x * factR n"
oops

text {* ---------------------------------------------------------------
Ejercicio 10. Demostrar que
factI n = factR n
------------------------------------------------------------------- *}

corollary "factI n = factR n"
oops

text {* ---------------------------------------------------------------
Ejercicio 11. Definir, recursivamente y sin usar (@), la función
amplia :: 'a list ⇒ 'a ⇒ 'a list
tal que (amplia xs y) es la lista obtenida añadiendo el elemento y al
final de la lista xs. Por ejemplo,
amplia [d,a] t = [d,a,t]
------------------------------------------------------------------ *}

fun amplia :: "'a list ⇒ 'a ⇒ 'a list" where
"amplia xs y = undefined"

value "amplia [d,a] t" -- "= [d,a,t]"

text {* ---------------------------------------------------------------
Ejercicio 12. Demostrar que
amplia xs y = xs @ [y]
------------------------------------------------------------------- *}

lemma "amplia xs y = xs @ [y]"
oops

end
</source>

RA12 Relación 12

2018-07-15T12:00:38Z

Jalonso: Texto reemplazado: «"isar"» por «"isabelle"»

<source lang="isabelle">
header {* R12: Menor posición válida *}

theory R12
imports Main
begin

text {*
---------------------------------------------------------------------
Ejercicio 1. Definir la función
menorValida :: "('a ⇒ bool) ⇒ 'a list ⇒ nat"
tal que (menorValida p xs) es el índice del primer elemento de una
lista xs que satisface el predicado p y es la longitud de xs si
ningún elemento satisface el predicado p. Por ejemplo,
menorValida (λx. 4<x) [1::nat, 3, 5, 3, 1] = 2
menorValida (λx. 6<x) [1::nat, 3, 5, 3, 1] = 5
menorValida (λx. 1<length x) [[], [1, 2], [3]] = 1
---------------------------------------------------------------------
*}

fun menorValida :: "('a ⇒ bool) ⇒ 'a list ⇒ nat" where
"menorValida P xs = undefined"

text {*
---------------------------------------------------------------------
Ejercicio 2. Demostrar que menorValida devuelve la longitud de la
lista syss ningún elemento satisface el predicado dado.
---------------------------------------------------------------------
*}

lemma "(menorValida P xs = length xs) = list_all (λ x. (¬ P x)) xs"
oops

text {*
---------------------------------------------------------------------
Ejercicio 3. Demostrar si n es el valor de (menorValida P xs),
entonces ninguno de los primeros n elementos de la lista xs verifica
la propiedad P.
---------------------------------------------------------------------
*}

lemma "list_all (λx. ¬ P x) (take (menorValida P xs) xs)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 4. ¿Cómo se puede relacionar
"menorValida (λx. P x ∨ Q x) xs"
con
"menorValida P xs" y "menorValida Q xs"?
¿Se puede decir algo parecido con la conjunción de P y Q?
Prueba tus conjeturas.
---------------------------------------------------------------------
*}

text {*
---------------------------------------------------------------------
Ejercicio 5. Si P implica Q, ¿qué relación puede deducirse entre
"menorValida P xs" y "menorValida Q xs"? Prueba tu conjetura.
---------------------------------------------------------------------
*}

end
</source>

Rel 3

2018-07-15T12:00:21Z

Jalonso: Texto reemplazado: «lang="isar"» por «lang="isabelle"»

<source lang="isabelle">
header {* T3R1: Deducción natural proposicional *}

theory T3R1
imports Main
begin

text {*
---------------------------------------------------------------------
El objetivo de esta relación es demostrar cada uno de los ejercicios
usando sólo las reglas básicas de deducción natural de la lógica
proposicional (sin usar el método auto).

Las reglas básicas de la deducción natural son las siguientes:
· conjI: ⟦P; Q⟧ ⟹ P ∧ Q
· conjunct1: P ∧ Q ⟹ P
· conjunct2: P ∧ Q ⟹ Q
· notnotD: ¬¬ P ⟹ P
· notnotI: P ⟹ ¬¬ P
· mp: ⟦P ⟶ Q; P⟧ ⟹ Q
· mt: ⟦F ⟶ G; ¬G⟧ ⟹ ¬F
· impI: (P ⟹ Q) ⟹ P ⟶ Q
· disjI1: P ⟹ P ∨ Q
· disjI2: Q ⟹ P ∨ Q
· disjE: ⟦P ∨ Q; P ⟹ R; Q ⟹ R⟧ ⟹ R
· FalseE: False ⟹ P
· notE: ⟦¬P; P⟧ ⟹ R
· notI: (P ⟹ False) ⟹ ¬P
· iffI: ⟦P ⟹ Q; Q ⟹ P⟧ ⟹ P = Q
· iffD1: ⟦Q = P; Q⟧ ⟹ P
· iffD2: ⟦P = Q; Q⟧ ⟹ P
· ccontr: (¬P ⟹ False) ⟹ P
---------------------------------------------------------------------
*}

text {*
Se usarán las reglas notnotI y mt que demostramos a continuación. *}

lemma notnotI: "P ⟹ ¬¬ P"
by auto

lemma mt: "⟦F ⟶ G; ¬G⟧ ⟹ ¬F"
by auto

section {* Implicaciones *}

text {* ---------------------------------------------------------------
Ejercicio 1. Demostrar
p ⟶ q, p ⊢ q
------------------------------------------------------------------ *}

lemma ejercicio_1:
assumes "p ⟶ q"
"p"
shows "q"
oops

text {* ---------------------------------------------------------------
Ejercicio 2. Demostrar
p ⟶ q, q ⟶ r, p ⊢ r
------------------------------------------------------------------ *}

lemma ejercicio_2:
assumes "p ⟶ q"
"q ⟶ r"
"p"
shows "r"
oops

text {* ---------------------------------------------------------------
Ejercicio 3. Demostrar
p ⟶ (q ⟶ r), p ⟶ q, p ⊢ r
------------------------------------------------------------------ *}

lemma ejercicio_3:
assumes "p ⟶ (q ⟶ r)"
"p ⟶ q"
"p"
shows "r"
oops

text {* ---------------------------------------------------------------
Ejercicio 4. Demostrar
p ⟶ q, q ⟶ r ⊢ p ⟶ r
------------------------------------------------------------------ *}

lemma ejercicio_4:
assumes "p ⟶ q"
"q ⟶ r"
shows "p ⟶ r"
oops

text {* ---------------------------------------------------------------
Ejercicio 5. Demostrar
p ⟶ (q ⟶ r) ⊢ q ⟶ (p ⟶ r)
------------------------------------------------------------------ *}

lemma ejercicio_5:
assumes "p ⟶ (q ⟶ r)"
shows "q ⟶ (p ⟶ r)"
oops

text {* ---------------------------------------------------------------
Ejercicio 6. Demostrar
p ⟶ (q ⟶ r) ⊢ (p ⟶ q) ⟶ (p ⟶ r)
------------------------------------------------------------------ *}

lemma ejercicio_6:
assumes "p ⟶ (q ⟶ r)"
shows "(p ⟶ q) ⟶ (p ⟶ r)"
oops

text {* ---------------------------------------------------------------
Ejercicio 7. Demostrar
p ⊢ q ⟶ p
------------------------------------------------------------------ *}

lemma ejercicio_7:
assumes "p"
shows "q ⟶ p"
oops

text {* ---------------------------------------------------------------
Ejercicio 8. Demostrar
⊢ p ⟶ (q ⟶ p)
------------------------------------------------------------------ *}

lemma ejercicio_8:
"p ⟶ (q ⟶ p)"
oops

text {* ---------------------------------------------------------------
Ejercicio 9. Demostrar
p ⟶ q ⊢ (q ⟶ r) ⟶ (p ⟶ r)
------------------------------------------------------------------ *}

lemma ejercicio_9:
assumes "p ⟶ q"
shows "(q ⟶ r) ⟶ (p ⟶ r)"
oops

text {* ---------------------------------------------------------------
Ejercicio 10. Demostrar
p ⟶ (q ⟶ (r ⟶ s)) ⊢ r ⟶ (q ⟶ (p ⟶ s))
------------------------------------------------------------------ *}

lemma ejercicio_10:
assumes "p ⟶ (q ⟶ (r ⟶ s))"
shows "r ⟶ (q ⟶ (p ⟶ s))"
oops

text {* ---------------------------------------------------------------
Ejercicio 11. Demostrar
⊢ (p ⟶ (q ⟶ r)) ⟶ ((p ⟶ q) ⟶ (p ⟶ r))
------------------------------------------------------------------ *}

lemma ejercicio_11:
"(p ⟶ (q ⟶ r)) ⟶ ((p ⟶ q) ⟶ (p ⟶ r))"
oops

text {* ---------------------------------------------------------------
Ejercicio 12. Demostrar
(p ⟶ q) ⟶ r ⊢ p ⟶ (q ⟶ r)
------------------------------------------------------------------ *}

lemma ejercicio_12:
assumes "(p ⟶ q) ⟶ r"
shows "p ⟶ (q ⟶ r)"
oops

section {* Conjunciones *}

text {* ---------------------------------------------------------------
Ejercicio 13. Demostrar
p, q ⊢ p ∧ q
------------------------------------------------------------------ *}

lemma ejercicio_13:
assumes "p"
"q"
shows "p ∧ q"
oops

text {* ---------------------------------------------------------------
Ejercicio 14. Demostrar
p ∧ q ⊢ p
------------------------------------------------------------------ *}

lemma ejercicio_14:
assumes "p ∧ q"
shows "p"
oops

text {* ---------------------------------------------------------------
Ejercicio 15. Demostrar
p ∧ q ⊢ q
------------------------------------------------------------------ *}

lemma ejercicio_15:
assumes "p ∧ q"
shows "q"
oops

text {* ---------------------------------------------------------------
Ejercicio 16. Demostrar
p ∧ (q ∧ r) ⊢ (p ∧ q) ∧ r
------------------------------------------------------------------ *}

lemma ejercicio_16:
assumes "p ∧ (q ∧ r)"
shows "(p ∧ q) ∧ r"
oops

text {* ---------------------------------------------------------------
Ejercicio 17. Demostrar
(p ∧ q) ∧ r ⊢ p ∧ (q ∧ r)
------------------------------------------------------------------ *}

lemma ejercicio_17:
assumes "(p ∧ q) ∧ r"
shows "p ∧ (q ∧ r)"
oops

text {* ---------------------------------------------------------------
Ejercicio 18. Demostrar
p ∧ q ⊢ p ⟶ q
------------------------------------------------------------------ *}

lemma ejercicio_18:
assumes "p ∧ q"
shows "p ⟶ q"
oops

text {* ---------------------------------------------------------------
Ejercicio 19. Demostrar
(p ⟶ q) ∧ (p ⟶ r) ⊢ p ⟶ q ∧ r
------------------------------------------------------------------ *}

lemma ejercicio_19:
assumes "(p ⟶ q) ∧ (p ⟶ r)"
shows "p ⟶ q ∧ r"
oops

text {* ---------------------------------------------------------------
Ejercicio 20. Demostrar
p ⟶ q ∧ r ⊢ (p ⟶ q) ∧ (p ⟶ r)
------------------------------------------------------------------ *}

lemma ejercicio_20:
assumes "p ⟶ q ∧ r"
shows "(p ⟶ q) ∧ (p ⟶ r)"
oops

text {* ---------------------------------------------------------------
Ejercicio 21. Demostrar
p ⟶ (q ⟶ r) ⊢ p ∧ q ⟶ r
------------------------------------------------------------------ *}

lemma ejercicio_21:
assumes "p ⟶ (q ⟶ r)"
shows "p ∧ q ⟶ r"
oops

text {* ---------------------------------------------------------------
Ejercicio 22. Demostrar
p ∧ q ⟶ r ⊢ p ⟶ (q ⟶ r)
------------------------------------------------------------------ *}

lemma ejercicio_22:
assumes "p ∧ q ⟶ r"
shows "p ⟶ (q ⟶ r)"
oops

text {* ---------------------------------------------------------------
Ejercicio 23. Demostrar
(p ⟶ q) ⟶ r ⊢ p ∧ q ⟶ r
------------------------------------------------------------------ *}

lemma ejercicio_23:
assumes "(p ⟶ q) ⟶ r"
shows "p ∧ q ⟶ r"
oops

text {* ---------------------------------------------------------------
Ejercicio 24. Demostrar
p ∧ (q ⟶ r) ⊢ (p ⟶ q) ⟶ r
------------------------------------------------------------------ *}

lemma ejercicio_24:
assumes "p ∧ (q ⟶ r)"
shows "(p ⟶ q) ⟶ r"
oops

section {* Disyunciones *}

text {* ---------------------------------------------------------------
Ejercicio 25. Demostrar
p ⊢ p ∨ q
------------------------------------------------------------------ *}

lemma ejercicio_25:
assumes "p"
shows "p ∨ q"
oops

text {* ---------------------------------------------------------------
Ejercicio 26. Demostrar
q ⊢ p ∨ q
------------------------------------------------------------------ *}

lemma ejercicio_26:
assumes "q"
shows "p ∨ q"
oops

text {* ---------------------------------------------------------------
Ejercicio 27. Demostrar
p ∨ q ⊢ q ∨ p
------------------------------------------------------------------ *}

lemma ejercicio_27:
assumes "p ∨ q"
shows "q ∨ p"
oops

text {* ---------------------------------------------------------------
Ejercicio 28. Demostrar
q ⟶ r ⊢ p ∨ q ⟶ p ∨ r
------------------------------------------------------------------ *}

lemma ejercicio_28:
assumes "q ⟶ r"
shows "p ∨ q ⟶ p ∨ r"
oops

text {* ---------------------------------------------------------------
Ejercicio 29. Demostrar
p ∨ p ⊢ p
------------------------------------------------------------------ *}

lemma ejercicio_29:
assumes "p ∨ p"
shows "p"
oops

text {* ---------------------------------------------------------------
Ejercicio 30. Demostrar
p ⊢ p ∨ p
------------------------------------------------------------------ *}

lemma ejercicio_30:
assumes "p"
shows "p ∨ p"
oops

text {* ---------------------------------------------------------------
Ejercicio 31. Demostrar
p ∨ (q ∨ r) ⊢ (p ∨ q) ∨ r
------------------------------------------------------------------ *}

lemma ejercicio_31:
assumes "p ∨ (q ∨ r)"
shows "(p ∨ q) ∨ r"
oops

text {* ---------------------------------------------------------------
Ejercicio 32. Demostrar
(p ∨ q) ∨ r ⊢ p ∨ (q ∨ r)
------------------------------------------------------------------ *}

lemma ejercicio_32:
assumes "(p ∨ q) ∨ r"
shows "p ∨ (q ∨ r)"
oops

text {* ---------------------------------------------------------------
Ejercicio 33. Demostrar
p ∧ (q ∨ r) ⊢ (p ∧ q) ∨ (p ∧ r)
------------------------------------------------------------------ *}

lemma ejercicio_33:
assumes "p ∧ (q ∨ r)"
shows "(p ∧ q) ∨ (p ∧ r)"
oops

text {* ---------------------------------------------------------------
Ejercicio 34. Demostrar
(p ∧ q) ∨ (p ∧ r) ⊢ p ∧ (q ∨ r)
------------------------------------------------------------------ *}

lemma ejercicio_34:
assumes "(p ∧ q) ∨ (p ∧ r)"
shows "p ∧ (q ∨ r)"
oops

text {* ---------------------------------------------------------------
Ejercicio 35. Demostrar
p ∨ (q ∧ r) ⊢ (p ∨ q) ∧ (p ∨ r)
------------------------------------------------------------------ *}

lemma ejercicio_35:
assumes "p ∨ (q ∧ r)"
shows "(p ∨ q) ∧ (p ∨ r)"
oops

text {* ---------------------------------------------------------------
Ejercicio 36. Demostrar
(p ∨ q) ∧ (p ∨ r) ⊢ p ∨ (q ∧ r)
------------------------------------------------------------------ *}

lemma ejercicio_36:
assumes "(p ∨ q) ∧ (p ∨ r)"
shows "p ∨ (q ∧ r)"
oops

text {* ---------------------------------------------------------------
Ejercicio 37. Demostrar
(p ⟶ r) ∧ (q ⟶ r) ⊢ p ∨ q ⟶ r
------------------------------------------------------------------ *}

lemma ejercicio_37:
assumes "(p ⟶ r) ∧ (q ⟶ r)"
shows "p ∨ q ⟶ r"
oops

text {* ---------------------------------------------------------------
Ejercicio 38. Demostrar
p ∨ q ⟶ r ⊢ (p ⟶ r) ∧ (q ⟶ r)
------------------------------------------------------------------ *}

lemma ejercicio_38:
assumes "p ∨ q ⟶ r"
shows "(p ⟶ r) ∧ (q ⟶ r)"
oops

section {* Negaciones *}

text {* ---------------------------------------------------------------
Ejercicio 39. Demostrar
p ⊢ ¬¬p
------------------------------------------------------------------ *}

lemma ejercicio_39:
assumes "p"
shows "¬¬p"
oops

text {* ---------------------------------------------------------------
Ejercicio 40. Demostrar
¬p ⊢ p ⟶ q
------------------------------------------------------------------ *}

lemma ejercicio_40:
assumes "¬p"
shows "p ⟶ q"
oops

text {* ---------------------------------------------------------------
Ejercicio 41. Demostrar
p ⟶ q ⊢ ¬q ⟶ ¬p
------------------------------------------------------------------ *}

lemma ejercicio_41:
assumes "p ⟶ q"
shows "¬q ⟶ ¬p"
oops

text {* ---------------------------------------------------------------
Ejercicio 42. Demostrar
p∨q, ¬q ⊢ p
------------------------------------------------------------------ *}

lemma ejercicio_42:
assumes "p∨q"
"¬q"
shows "p"
oops

text {* ---------------------------------------------------------------
Ejercicio 42. Demostrar
p ∨ q, ¬p ⊢ q
------------------------------------------------------------------ *}

lemma ejercicio_43:
assumes "p ∨ q"
"¬p"
shows "q"
oops

text {* ---------------------------------------------------------------
Ejercicio 40. Demostrar
p ∨ q ⊢ ¬(¬p ∧ ¬q)
------------------------------------------------------------------ *}

lemma ejercicio_44:
assumes "p ∨ q"
shows "¬(¬p ∧ ¬q)"
oops

text {* ---------------------------------------------------------------
Ejercicio 45. Demostrar
p ∧ q ⊢ ¬(¬p ∨ ¬q)
------------------------------------------------------------------ *}

lemma ejercicio_45:
assumes "p ∧ q"
shows "¬(¬p ∨ ¬q)"
oops

text {* ---------------------------------------------------------------
Ejercicio 46. Demostrar
¬(p ∨ q) ⊢ ¬p ∧ ¬q
------------------------------------------------------------------ *}

lemma ejercicio_46:
assumes "¬(p ∨ q)"
shows "¬p ∧ ¬q"
oops

text {* ---------------------------------------------------------------
Ejercicio 47. Demostrar
¬p ∧ ¬q ⊢ ¬(p ∨ q)
------------------------------------------------------------------ *}

lemma ejercicio_47:
assumes "¬p ∧ ¬q"
shows "¬(p ∨ q)"
oops

text {* ---------------------------------------------------------------
Ejercicio 48. Demostrar
¬p ∨ ¬q ⊢ ¬(p ∧ q)
------------------------------------------------------------------ *}

lemma ejercicio_48:
assumes "¬p ∨ ¬q"
shows "¬(p ∧ q)"
oops

text {* ---------------------------------------------------------------
Ejercicio 49. Demostrar
⊢ ¬(p ∧ ¬p)
------------------------------------------------------------------ *}

lemma ejercicio_49:
"¬(p ∧ ¬p)"
oops

text {* ---------------------------------------------------------------
Ejercicio 50. Demostrar
p ∧ ¬p ⊢ q
------------------------------------------------------------------ *}

lemma ejercicio_50:
assumes "p ∧ ¬p"
shows "q"
oops

text {* ---------------------------------------------------------------
Ejercicio 51. Demostrar
¬¬p ⊢ p
------------------------------------------------------------------ *}

lemma ejercicio_51:
assumes "¬¬p"
shows "p"
oops

text {* ---------------------------------------------------------------
Ejercicio 52. Demostrar
⊢ p ∨ ¬p
------------------------------------------------------------------ *}

lemma ejercicio_52:
"p ∨ ¬p"
oops

text {* ---------------------------------------------------------------
Ejercicio 53. Demostrar
⊢ ((p ⟶ q) ⟶ p) ⟶ p
------------------------------------------------------------------ *}

lemma ejercicio_53:
"((p ⟶ q) ⟶ p) ⟶ p"
oops

text {* ---------------------------------------------------------------
Ejercicio 54. Demostrar
¬q ⟶ ¬p ⊢ p ⟶ q
------------------------------------------------------------------ *}

lemma ejercicio_54:
assumes "¬q ⟶ ¬p"
shows "p ⟶ q"
oops

text {* ---------------------------------------------------------------
Ejercicio 55. Demostrar
¬(¬p ∧ ¬q) ⊢ p ∨ q
------------------------------------------------------------------ *}

lemma ejercicio_55:
assumes "¬(¬p ∧ ¬q)"
shows "p ∨ q"
oops

text {* ---------------------------------------------------------------
Ejercicio 56. Demostrar
¬(¬p ∨ ¬q) ⊢ p ∧ q
------------------------------------------------------------------ *}

lemma ejercicio_56:
assumes "¬(¬p ∨ ¬q)"
shows "p ∧ q"
oops

text {* ---------------------------------------------------------------
Ejercicio 57. Demostrar
¬(p ∧ q) ⊢ ¬p ∨ ¬q
------------------------------------------------------------------ *}

lemma ejercicio_57:
assumes "¬(p ∧ q)"
shows "¬p ∨ ¬q"
oops

text {* ---------------------------------------------------------------
Ejercicio 58. Demostrar
⊢ (p ⟶ q) ∨ (q ⟶ p)
------------------------------------------------------------------ *}

lemma ejercicio_58:
"(p ⟶ q) ∨ (q ⟶ p)"
oops

end
</source>

GLC T1R2

2018-07-15T12:00:12Z

Jalonso: Texto reemplazado: «"isar"» por «"isabelle"»

<source lang="isabelle">
header {* T1R2: Argumentación proposicional *}

theory T1R2
imports Main
begin

text {*
---------------------------------------------------------------------
El objetivo de esta es relación formalizar y demostrar la corrección
de los argumentos usando sólo las reglas básicas de deducción natural
de la lógica proposicional (sin usar el método auto).

Las reglas básicas de la deducción natural son las siguientes:
· conjI: ⟦P; Q⟧ ⟹ P ∧ Q
· conjunct1: P ∧ Q ⟹ P
· conjunct2: P ∧ Q ⟹ Q
· notnotD: ¬¬ P ⟹ P
· notnotI: P ⟹ ¬¬ P
· mp: ⟦P ⟶ Q; P⟧ ⟹ Q
· mt: ⟦F ⟶ G; ¬G⟧ ⟹ ¬F
· impI: (P ⟹ Q) ⟹ P ⟶ Q
· disjI1: P ⟹ P ∨ Q
· disjI2: Q ⟹ P ∨ Q
· disjE: ⟦P ∨ Q; P ⟹ R; Q ⟹ R⟧ ⟹ R
· FalseE: False ⟹ P
· notE: ⟦¬P; P⟧ ⟹ R
· notI: (P ⟹ False) ⟹ ¬P
· iffI: ⟦P ⟹ Q; Q ⟹ P⟧ ⟹ P = Q
· iffD1: ⟦Q = P; Q⟧ ⟹ P
· iffD2: ⟦P = Q; Q⟧ ⟹ P
· ccontr: (¬P ⟹ False) ⟹ P
---------------------------------------------------------------------
*}

text {*
Se usarán las reglas notnotI y mt que demostramos a continuación.
*}

lemma notnotI: "P ⟹ ¬¬ P"
by auto

lemma mt: "⟦F ⟶ G; ¬G⟧ ⟹ ¬F"
by auto

text {* ---------------------------------------------------------------
Ejercicio 1. Formalizar, y demostrar la corrección, del siguiente
argumento
Cuando tanto la temperatura como la presión atmosférica permanecen
contantes, no llueve. La temperatura permanece constante. Por lo
tanto, en caso de que llueva, la presión atmosférica no permanece
constante.
Usar T para "La temperatura permanece constante",
P para "La presión atmosférica permanece constante" y
L para "Llueve".
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_1_1:
"⟦T ∧ P ⟶ ¬L; T⟧ ⟹ L ⟶ ¬P"
by auto

-- "La demostración estructurada es"
lemma ejercicio_1_2:
assumes "T ∧ P ⟶ ¬L"
"T"
shows "L ⟶ ¬P"
proof
assume "L"
show "¬P"
proof
assume "P"
with `T` have "T ∧ P" ..
with assms(1) have "¬L" ..
thus "False" using `L` ..
qed
qed

-- "La demostración detallada es"
lemma ejercicio_1_3:
assumes "T ∧ P ⟶ ¬L"
"T"
shows "L ⟶ ¬P"
proof (rule impI)
assume "L"
show "¬P"
proof
assume "P"
with `T` have "T ∧ P" by (rule conjI)
with assms(1) have "¬L" by (rule mp)
thus "False" using `L` by (rule notE)
qed
qed

text {* ---------------------------------------------------------------
Ejercicio 2. Formalizar, y demostrar la corrección, del siguiente
argumento
Siempre que un número x es divisible por 10, acaba en 0. El número
x no acaba en 0. Por lo tanto, x no es divisible por 10.
Usar D para "el número es divisible por 10" y
C para "el número acaba en cero".
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_2_1:
"⟦C ⟶ D; ¬D⟧ ⟹ ¬C"
by auto

-- "La demostración estructurada es"
lemma ejercicio_2_2:
assumes "C ⟶ D"
"¬D"
shows "¬C"
proof
assume "C"
with assms(1) have "D" ..
with assms(2) show False ..
qed

-- "La demostración detallada es"
lemma ejercicio_2_3:
assumes "C ⟶ D"
"¬D"
shows "¬C"
proof
assume "C"
with assms(1) have "D" by (rule mp)
with assms(2) show False by (rule notE)
qed

text {* ---------------------------------------------------------------
Ejercicio 3. Formalizar, y demostrar la corrección, del siguiente
argumento
En cierto experimento, cuando hemos empleado un fármaco A, el
paciente ha mejorado considerablemente en el caso, y sólo en el
caso, en que no se haya empleado también un fármaco B. Además, o se
ha empleado el fármaco A o se ha empleado el fármaco B. En
consecuencia, podemos afirmar que si no hemos empleado el fármaco
B, el paciente ha mejorado considerablemente.
Usar A: Hemos empleado el fármaco A.
B: Hemos empleado el fármaco B.
M: El paciente ha mejorado notablemente.
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_3_1:
assumes "A ⟶ (M ⟷ ¬B)"
"A ∨ B"
shows "¬B ⟶ M"
using assms
by auto

-- "La demostración estructurada es"
lemma ejercicio_3_2:
assumes "A ⟶ (M ⟷ ¬B)"
"A ∨ B"
shows "¬B ⟶ M"
proof
assume "¬B"
note `A ∨ B`
hence "A"
proof
assume "A"
thus "A" .
next
assume "B"
with `¬B` show "A" ..
qed
have "M ⟷ ¬B" using assms(1) `A` ..
thus "M" using `¬B` ..
qed

-- "La demostración detallada es"
lemma ejercicio_3_3:
assumes "A ⟶ (M ⟷ ¬B)"
"A ∨ B"
shows "¬B ⟶ M"
proof (rule impI)
assume "¬B"
note `A ∨ B`
hence "A"
proof (rule disjE)
assume "A"
thus "A" by this
next
assume "B"
with `¬B` show "A" by (rule notE)
qed
have "M ⟷ ¬B" using assms(1) `A` by (rule mp)
thus "M" using `¬B` by (rule iffD2)
qed

text {* ---------------------------------------------------------------
Ejercicio 4. Formalizar, y demostrar la corrección, del siguiente
argumento
Si no está el mañana ni el ayer escrito, entonces no está el mañana
escrito.
Usar M: El mañana está escrito.
A: El ayer está escrito.
------------------------------------------------------------------ *}

-- "La demostración automática es:"
lemma ejercicio_4_1:
"¬M ∧ ¬A ⟹ ¬M"
by auto

-- "La demostración estructurada es:"
lemma ejercicio_4_2:
assumes "¬M ∧ ¬A"
shows "¬M"
using assms ..

-- "La demostración detallada es:"
lemma ejercicio_4_3:
assumes "¬M ∧ ¬A"
shows "¬M"
using assms by (rule conjunct1)

text {* ---------------------------------------------------------------
Ejercicio 5. Formalizar, y demostrar la corrección, del siguiente
argumento
Me matan si no trabajo y si trabajo me matan. Me matan siempre me
matan.
Usar M: Me matan.
T: Trabajo.
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_5_1:
"(¬T ⟶ M) ∧ (T ⟶ M) ⟹ M"
by auto

-- "La demostración estructurada es"
lemma ejercicio_5_2:
assumes "(¬T ⟶ M) ∧ (T ⟶ M)"
shows "M"
proof -
have "¬T ∨ T" ..
thus "M"
proof
assume "¬T"
have "¬T ⟶ M" using assms ..
thus "M" using `¬T` ..
next
assume "T"
have "T ⟶ M" using assms ..
thus "M" using `T` ..
qed
qed

-- "La demostración detallada es"
lemma ejercicio_5_3:
assumes "(¬T ⟶ M) ∧ (T ⟶ M)"
shows "M"
proof -
have "¬T ∨ T" by (rule excluded_middle)
thus "M"
proof (rule disjE)
assume "¬T"
have "¬T ⟶ M" using assms by (rule conjunct1)
thus "M" using `¬T` by (rule mp)
next
assume "T"
have "T ⟶ M" using assms by (rule conjunct2)
thus "M" using `T` by (rule mp)
qed
qed

text {* ---------------------------------------------------------------
Ejercicio 6. Formalizar, y demostrar la corrección, del siguiente
argumento
Si te llamé por teléfono, entonces recibiste mi llamada y no es
cierto que no te avisé del peligro que corrías. Por consiguiente,
como te llamé, es cierto que te avisé del peligro que corrías.
Usar T: Te llamé por teléfono.
R: Recibiste mi llamada.
P: Te avisé del peligro que corrías.
------------------------------------------------------------------ *}

-- "La demostración automática es:"
lemma ejercicio_6_1:
"T ⟶ R ∧ ¬¬A ⟹ T ⟶ A"
by auto

-- "La demostración estructurada es:"
lemma ejercicio_6_2:
assumes "T ⟶ R ∧ ¬¬A"
shows "T ⟶ A"
proof
assume "T"
with assms have "R ∧ ¬¬A" ..
hence "¬¬A" ..
thus "A" by (rule notnotD)
qed

-- "La demostración detallada es:"
lemma ejercicio_6_3:
assumes "T ⟶ R ∧ ¬¬A"
shows "T ⟶ A"
proof (rule impI)
assume "T"
with assms(1) have "R ∧ ¬¬A" by (rule mp)
hence "¬¬A" by (rule conjunct2)
thus "A" by (rule notnotD)
qed

text {* ---------------------------------------------------------------
Ejercicio 7. Formalizar, y demostrar la corrección, del siguiente
argumento
Si no hay control de nacimientos, entonces la población crece
ilimitadamente; pero si la población crece ilimitadamente,
aumentará el índice de pobreza. Por consiguiente, si no hay control
de nacimientos, aumentará el índice de pobreza.
Usar N: Hay control de nacimientos.
P: La población crece ilimitadamente,
I: Aumentará el índice de pobreza.
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_7_1:
"⟦¬N ⟶ P; P ⟶ I⟧ ⟹ ¬N ⟶ I"
by auto

-- "La demostración estructurada es"
lemma ejercicio_7_2:
assumes "¬N ⟶ P"
"P ⟶ I"
shows "¬N ⟶ I"
proof
assume "¬N"
with assms(1) have "P" ..
with assms(2) show "I" ..
qed

-- "La demostración detallada es"
lemma ejercicio_7_3:
assumes "¬N ⟶ P"
"P ⟶ I"
shows "¬N ⟶ I"
proof (rule impI)
assume "¬N"
with assms(1) have "P" by (rule mp)
with assms(2) show "I" by (rule mp)
qed

text {* ---------------------------------------------------------------
Ejercicio 8. Formalizar, y demostrar la corrección, del siguiente
argumento
Si el general era leal, hubiera obedecido las órdenes, y si era
inteligente las hubiera comprendido. O el general desobedeció las
órdenes o no las comprendió. Luego, el general era desleal o no era
inteligente.
Usar L: El general es leal.
Ob: El general obedece las órdenes.
I: El general es inteligente.
C: El general comprende las órdenes.
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_8_1:
"⟦(L ⟶ Ob) ∧ (I ⟶ C); ¬Ob ∨ ¬C⟧ ⟹ ¬L ∨ ¬I"
by auto

-- "La demostración estructurada es"
lemma ejercicio_8_2:
assumes "(L ⟶ Ob) ∧ (I ⟶ C)"
"¬Ob ∨ ¬C"
shows "¬L ∨ ¬I"
using assms(2)
proof
assume "¬Ob"
have "L ⟶ Ob" using assms(1) ..
hence "¬L" using `¬Ob` by (rule mt)
thus "¬L ∨ ¬I" ..
next
assume "¬C"
have "I ⟶ C" using assms(1) ..
hence "¬I" using `¬C` by (rule mt)
thus "¬L ∨ ¬I" ..
qed

-- "La demostración detallada es"
lemma ejercicio_8_3:
assumes "(L ⟶ Ob) ∧ (I ⟶ C)"
"¬Ob ∨ ¬C"
shows "¬L ∨ ¬I"
using assms(2)
proof (rule disjE)
assume "¬Ob"
have "L ⟶ Ob" using assms(1) by (rule conjunct1)
hence "¬L" using `¬Ob` by (rule mt)
thus "¬L ∨ ¬I" by (rule disjI1)
next
assume "¬C"
have "I ⟶ C" using assms(1) by (rule conjunct2)
hence "¬I" using `¬C` by (rule mt)
thus "¬L ∨ ¬I" by (rule disjI2)
qed

text {* ---------------------------------------------------------------
Ejercicio 9. Formalizar, y demostrar la corrección, del siguiente
argumento
Si Dios fuera capaz de evitar el mal y quisiera hacerlo, lo
haría. Si Dios fuera incapaz de evitar el mal, no sería
omnipotente; si no quisiera evitar el mal sería malévolo. Dios no
evita el mal. Si Dios existe, es omnipotente y no es
malévolo. Luego, Dios no existe.
Usar C: Dios es capaz de evitar el mal.
Q: Dios quiere evitar el mal.
Om: Dios es omnipotente.
M: Dios es malévolo.
P: Dios evita el mal.
E: Dios existe.
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_9_1:
"⟦C ∧ Q ⟶ P; (¬C ⟶ ¬Om) ∧ (¬Q ⟶ M); ¬P; E ⟶ Om ∧ ¬M⟧ ⟹ ¬E"
by auto

-- "La demostración estructurada es"
lemma ejercicio_9_2:
assumes "C ∧ Q ⟶ P"
"(¬C ⟶ ¬Om) ∧ (¬Q ⟶ M)"
"¬P"
"E ⟶ Om ∧ ¬M"
shows "¬E"
proof
assume "E"
have "Om ∧ ¬M" using assms(4) `E` ..
hence "Om" ..
hence "¬¬Om" by (rule notnotI)
have "¬C ⟶ ¬Om" using assms(2) ..
hence "¬¬C" using `¬¬Om` by (rule mt)
hence "C" by (rule notnotD)
have "¬M" using `Om ∧ ¬M` ..
have "¬Q ⟶ M" using assms(2) ..
hence "¬¬Q" using `¬M` by (rule mt)
hence "Q" by (rule notnotD)
with `C` have "C ∧ Q" ..
with assms(1) have "P" ..
with assms(3) show False ..
qed

-- "La demostración detallada es"
lemma ejercicio_9_3:
assumes "C ∧ Q ⟶ P"
"(¬C ⟶ ¬Om) ∧ (¬Q ⟶ M)"
"¬P"
"E ⟶ Om ∧ ¬M"
shows "¬E"
proof (rule notI)
assume "E"
with assms(4) have "Om ∧ ¬M" by (rule mp)
hence "Om" by (rule conjunct1)
hence "¬¬Om" by (rule notnotI)
have "¬C ⟶ ¬Om" using assms(2) by (rule conjunct1)
hence "¬¬C" using `¬¬Om` by (rule mt)
hence "C" by (rule notnotD)
have "¬M" using `Om ∧ ¬M` by (rule conjunct2)
have "¬Q ⟶ M" using assms(2) by (rule conjunct2)
hence "¬¬Q" using `¬M` by (rule mt)
hence "Q" by (rule notnotD)
with `C` have "C ∧ Q" by (rule conjI)
with assms(1) have "P" by (rule mp)
with assms(3) show False by (rule notE)
qed

text {* ---------------------------------------------------------------
Ejercicio 10. Formalizar, y demostrar la corrección, del siguiente
argumento
Si la válvula está abierta o la monitorización está preparada,
entonces se envía una señal de reconocimiento y un mensaje de
funcionamiento al controlador del ordenador. Si se envía un mensaje
de funcionamiento al controlador del ordenador o el sistema está en
estado normal, entonces se aceptan las órdenes del operador. Por lo
tanto, si la válvula está abierta, entonces se aceptan las órdenes
del operador.
Usar A : La válvula está abierta.
P : La monitorización está preparada.
R : Envía una señal de reconocimiento.
F : Envía un mensaje de funcionamiento.
N : El sistema está en estado normal.
O : Se aceptan órdenes del operador.
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_10_1:
"⟦A ∨ P ⟶ R ∧ F; F ∨ N ⟶ Or⟧ ⟹ A ⟶ Or"
by auto

-- "La demostración estructurada es"
lemma ejercicio_10_2:
assumes "A ∨ P ⟶ R ∧ F"
"F ∨ N ⟶ Or"
shows "A ⟶ Or"
proof
assume "A"
hence "A ∨ P" ..
with assms(1) have "R ∧ F" ..
hence "F" ..
hence "F ∨ N" ..
with assms(2) show "Or" ..
qed

-- "La demostración detallada es"
lemma ejercicio_10_3:
assumes "A ∨ P ⟶ R ∧ F"
"F ∨ N ⟶ Or"
shows "A ⟶ Or"
proof (rule impI)
assume "A"
hence "A ∨ P" by (rule disjI1)
with assms(1) have "R ∧ F" by (rule mp)
hence "F" by (rule conjunct2)
hence "F ∨ N" by (rule disjI1)
with assms(2) show "Or" by (rule mp)
qed

text {* ---------------------------------------------------------------
Ejercicio 11. Formalizar, y demostrar la corrección, del siguiente
argumento
Si trabajo gano dinero, pero si no trabajo gozo de la vida. Sin
embargo, si trabajo no gozo de la vida, mientras que si no trabajo
no gano dinero. Por lo tanto, gozo de la vida si y sólo si no gano
dinero.
Usar p: Trabajo
q: Gano dinero.
r: Gozo de la vida.
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_11_1:
"⟦(p ⟶ q) ∧ (¬p ⟶ r); (p ⟶ ¬r) ∧ (¬p ⟶ ¬q)⟧ ⟹ r ⟷ ¬q"
by auto

-- "La demostración estructurada es"
lemma ejercicio_11_2:
assumes "(p ⟶ q) ∧ (¬p ⟶ r)"
"(p ⟶ ¬r) ∧ (¬p ⟶ ¬q)"
shows "r ⟷ ¬q"
proof
assume "r"
hence "¬¬r" by (rule notnotI)
have "p ⟶ ¬r" using assms(2) ..
hence "¬p" using `¬¬r` by (rule mt)
have "¬p ⟶ ¬q" using assms(2) ..
thus "¬q" using `¬p` ..
next
assume "¬q"
have "p ⟶ q" using assms(1) ..
hence "¬p" using `¬q` by (rule mt)
have "¬p ⟶ r" using assms(1) ..
thus "r" using `¬p` ..
qed

-- "La demostración detallada es"
lemma ejercicio_11_3:
assumes "(p ⟶ q) ∧ (¬p ⟶ r)"
"(p ⟶ ¬r) ∧ (¬p ⟶ ¬q)"
shows "r ⟷ ¬q"
proof (rule iffI)
assume "r"
hence "¬¬r" by (rule notnotI)
have "p ⟶ ¬r" using assms(2) by (rule conjunct1)
hence "¬p" using `¬¬r` by (rule mt)
have "¬p ⟶ ¬q" using assms(2) by (rule conjunct2)
thus "¬q" using `¬p` by (rule mp)
next
assume "¬q"
have "p ⟶ q" using assms(1) by (rule conjunct1)
hence "¬p" using `¬q` by (rule mt)
have "¬p ⟶ r" using assms(1) by (rule conjunct2)
thus "r" using `¬p` by (rule mp)
qed

end
</source>

RA12 Relación 19

2018-07-15T11:59:17Z

Jalonso: Texto reemplazado: «lang="isar"» por «lang="isabelle"»

<source lang="isabelle">
header {* R19: Recorridos de árboles *}

theory R19
imports Main
begin

text {*
---------------------------------------------------------------------
Ejercicio 1. Definir el tipo de datos arbol para representar los
árboles binarios que tiene información en los nodos y en las hojas.
Por ejemplo, el árbol
e
/ \
/ \
c g
/ \ / \
a d f h
se representa por "N e (N c (H a) (H d)) (N g (H f) (H h))".
---------------------------------------------------------------------
*}

datatype 'a arbol = H "'a" | N "'a" "'a arbol" "'a arbol"

value "N e (N c (H a) (H d)) (N g (H f) (H h))"

text {*
---------------------------------------------------------------------
Ejercicio 2. Definir la función
preOrden :: "'a arbol ⇒ 'a list"
tal que (preOrden a) es el recorrido pre orden del árbol a. Por
ejemplo,
preOrden (N e (N c (H a) (H d)) (N g (H f) (H h)))
= [e,c,a,d,g,f,h]
---------------------------------------------------------------------
*}

fun preOrden :: "'a arbol ⇒ 'a list" where
"preOrden t = undefined"

value "preOrden (N e (N c (H a) (H d)) (N g (H f) (H h)))"
-- "= [e,c,a,d,g,f,h]"

text {*
---------------------------------------------------------------------
Ejercicio 3. Definir la función
postOrden :: "'a arbol ⇒ 'a list"
tal que (postOrden a) es el recorrido post orden del árbol a. Por
ejemplo,
postOrden (N e (N c (H a) (H d)) (N g (H f) (H h)))
= [e,c,a,d,g,f,h]
---------------------------------------------------------------------
*}

fun postOrden :: "'a arbol ⇒ 'a list" where
"postOrden t = undefined"

value "postOrden (N e (N c (H a) (H d)) (N g (H f) (H h)))"
-- "[a,d,c,f,h,g,e]"

text {*
---------------------------------------------------------------------
Ejercicio 4. Definir la función
inOrden :: "'a arbol ⇒ 'a list"
tal que (inOrden a) es el recorrido in orden del árbol a. Por
ejemplo,
inOrden (N e (N c (H a) (H d)) (N g (H f) (H h)))
= [a,c,d,e,f,g,h]
---------------------------------------------------------------------
*}

fun inOrden :: "'a arbol ⇒ 'a list" where
"inOrden t = undefined"

value "inOrden (N e (N c (H a) (H d)) (N g (H f) (H h)))"
-- "[a,c,d,e,f,g,h]"

text {*
---------------------------------------------------------------------
Ejercicio 5. Definir la función
espejo :: "'a arbol ⇒ 'a arbol"
tal que (espejo a) es la imagen especular del árbol a. Por ejemplo,
espejo (N e (N c (H a) (H d)) (N g (H f) (H h)))
= N e (N g (H h) (H f)) (N c (H d) (H a))
---------------------------------------------------------------------
*}

fun espejo :: "'a arbol ⇒ 'a arbol" where
"espejo t = undefined"

value "espejo (N e (N c (H a) (H d)) (N g (H f) (H h)))"
-- "N e (N g (H h) (H f)) (N c (H d) (H a))"

text {*
---------------------------------------------------------------------
Ejercicio 6. Demostrar que
preOrden (espejo a) = rev (postOrden a)
---------------------------------------------------------------------
*}

lemma "preOrden (espejo a) = rev (postOrden a)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 7. Demostrar que
postOrden (espejo a) = rev (preOrden a)
---------------------------------------------------------------------
*}

lemma "postOrden (espejo a) = rev (preOrden a)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 8. Demostrar que
inOrden (espejo a) = rev (inOrden a)
---------------------------------------------------------------------
*}

theorem "inOrden (espejo a) = rev (inOrden a)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 9. Definir la función
raiz :: "'a arbol ⇒ 'a"
tal que (raiz a) es la raiz del árbol a. Por ejemplo,
raiz (N e (N c (H a) (H d)) (N g (H f) (H h))) = e
---------------------------------------------------------------------
*}

fun raiz :: "'a arbol ⇒ 'a" where
"raiz t = undefined"

value "raiz (N e (N c (H a) (H d)) (N g (H f) (H h)))" -- "= e"

text {*
---------------------------------------------------------------------
Ejercicio 10. Definir la función
extremo_izquierda :: "'a arbol ⇒ 'a"
tal que (extremo_izquierda a) es el nodo más a la izquierda del árbol
a. Por ejemplo,
extremo_izquierda (N e (N c (H a) (H d)) (N g (H f) (H h))) = a
---------------------------------------------------------------------
*}

fun extremo_izquierda :: "'a arbol ⇒ 'a" where
"extremo_izquierda t = undefined"

value "extremo_izquierda (N e (N c (H a) (H d)) (N g (H f) (H h)))" -- "= a"

text {*
---------------------------------------------------------------------
Ejercicio 11. Definir la función
extremo_derecha :: "'a arbol ⇒ 'a"
tal que (extremo_derecha a) es el nodo más a la derecha del árbol
a. Por ejemplo,
extremo_derecha (N e (N c (H a) (H d)) (N g (H f) (H h))) = h
---------------------------------------------------------------------
*}

fun extremo_derecha :: "'a arbol ⇒ 'a" where
"extremo_derecha t = undefined"

value "extremo_derecha (N e (N c (H a) (H d)) (N g (H f) (H h)))" -- "= h"

text {*
---------------------------------------------------------------------
Ejercicio 12. Demostrar o refutar
last (inOrden a) = extremo_derecha a
---------------------------------------------------------------------
*}

theorem "last (inOrden a) = extremo_derecha a"
oops

text {*
---------------------------------------------------------------------
Ejercicio 13. Demostrar o refutar
hd (inOrden a) = extremo_izquierda a
---------------------------------------------------------------------
*}

theorem "hd (inOrden a) = extremo_izquierda a"
oops

text {*
---------------------------------------------------------------------
Ejercicio 14. Demostrar o refutar
hd (preOrden a) = last (postOrden a)
---------------------------------------------------------------------
*}

theorem "hd (preOrden a) = last (postOrden a)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 15. Demostrar o refutar
hd (preOrden a) = raiz a
---------------------------------------------------------------------
*}

theorem "hd (preOrden a) = raiz a"
oops

text {*
---------------------------------------------------------------------
Ejercicio 16. Demostrar o refutar
hd (inOrden a) = raiz a
---------------------------------------------------------------------
*}

theorem "hd (inOrden a) = raiz a"
oops

text {*
---------------------------------------------------------------------
Ejercicio 17. Demostrar o refutar
last (postOrden a) = raiz a
---------------------------------------------------------------------
*}

theorem "last (postOrden a) = raiz a"
oops

end
</source>

RA12 Relación 7

2018-07-15T11:58:36Z

Jalonso: Texto reemplazado: «"isar"» por «"isabelle"»

<source lang="isabelle">
header {* R7: Programación funcional en Isabelle/HOL *}

theory R7
imports Main
begin

text {* ----------------------------------------------------------------
Ejercicio 1. Definir, por recursión, la función
longitud :: 'a list ⇒ nat
tal que (longitud xs) es la longitud de la listas xs. Por ejemplo,
longitud [4,2,5] = 3
------------------------------------------------------------------- *}

fun longitud :: "'a list ⇒ nat" where
"longitud xs = undefined"

value "longitud [4,2,5]" -- "= 3"

text {* ---------------------------------------------------------------
Ejercicio 2. Definir la función
fun intercambia :: 'a × 'b ⇒ 'b × 'a
tal que (intercambia p) es el par obtenido intercambiando las
componentes del par p. Por ejemplo,
intercambia (u,v) = (v,u)
------------------------------------------------------------------ *}

fun intercambia :: "'a × 'b ⇒ 'b × 'a" where
"intercambia (x,y) = undefined"

value "intercambia (u,v)" -- "= (v,u)"

text {* ---------------------------------------------------------------
Ejercicio 3. Definir, por recursión, la función
inversa :: 'a list ⇒ 'a list
tal que (inversa xs) es la lista obtenida invirtiendo el orden de los
elementos de xs. Por ejemplo,
inversa [a,d,c] = [c,d,a]
------------------------------------------------------------------ *}

fun inversa :: "'a list ⇒ 'a list" where
"inversa xs = undefined"

value "inversa [a,d,c]" -- "= [c,d,a]"

text {* ---------------------------------------------------------------
Ejercicio 4. Definir la función
repite :: nat ⇒ 'a ⇒ 'a list
tal que (repite n x) es la lista formada por n copias del elemento
x. Por ejemplo,
repite 3 a = [a,a,a]
------------------------------------------------------------------ *}

fun repite :: "nat ⇒ 'a ⇒ 'a list" where
"repite n x = undefined"

value "repite 3 a" -- "= [a,a,a]"

text {* ---------------------------------------------------------------
Ejercicio 5. Definir la función
conc :: 'a list ⇒ 'a list ⇒ 'a list
tal que (conc xs ys) es la concatención de las listas xs e ys. Por
ejemplo,
conc [a,d] [b,d,a,c] = [a,d,b,d,a,c]
------------------------------------------------------------------ *}

fun conc :: "'a list ⇒ 'a list ⇒ 'a list" where
"conc xs ys = undefined"

value "conc [a,d] [b,d,a,c]" -- "= [a,d,b,d,a,c]"

text {* ---------------------------------------------------------------
Ejercicio 6. Definir la función
coge :: nat ⇒ 'a list ⇒ 'a list
tal que (coge n xs) es la lista de los n primeros elementos de xs. Por
ejemplo,
coge 2 [a,c,d,b,e] = [a,c]
------------------------------------------------------------------ *}

fun coge :: "nat ⇒ 'a list ⇒ 'a list" where
"coge n xs = undefined"

value "coge 2 [a,c,d,b,e]" -- "= [a,c]"

text {* ---------------------------------------------------------------
Ejercicio 7. Definir la función
elimina :: nat ⇒ 'a list ⇒ 'a list
tal que (elimina n xs) es la lista obtenida eliminando los n primeros
elementos de xs. Por ejemplo,
elimina 2 [a,c,d,b,e] = [d,b,e]
------------------------------------------------------------------ *}

fun elimina :: "nat ⇒ 'a list ⇒ 'a list" where
"elimina n xs = undefined"

value "elimina 2 [a,c,d,b,e]" -- "= [d,b,e]"

text {* ---------------------------------------------------------------
Ejercicio 8. Definir la función
esVacia :: 'a list ⇒ bool
tal que (esVacia xs) se verifica si xs es la lista vacía. Por ejemplo,
esVacia [] = True
esVacia [1] = False
------------------------------------------------------------------ *}

fun esVacia :: "'a list ⇒ bool" where
"esVacia xs = undefined"

value "esVacia []" -- "= True"
value "esVacia [1]" -- "= False"

text {* ---------------------------------------------------------------
Ejercicio 9. Definir la función
inversaAc :: 'a list ⇒ 'a list
tal que (inversaAc xs) es a inversa de xs calculada usando
acumuladores. Por ejemplo,
inversaAc [a,c,b,e] = [e,b,c,a]
------------------------------------------------------------------ *}

fun inversaAcAux :: "'a list ⇒ 'a list ⇒ 'a list" where
"inversaAcAux xs ys = undefined"

fun inversaAc :: "'a list ⇒ 'a list" where
"inversaAc xs = undefined"

value "inversaAc [a,c,b,e]" -- "= [e,b,c,a]"

text {* ---------------------------------------------------------------
Ejercicio 10. Definir la función
sum :: nat list ⇒ nat
tal que (sum xs) es la suma de los elementos de xs. Por ejemplo,
sum [3,2,5] = 10
------------------------------------------------------------------ *}

fun sum :: "nat list ⇒ nat" where
"sum xs = undefined"

value "sum [3,2,5]" -- "= 10"

text {* ---------------------------------------------------------------
Ejercicio 11. Definir la función
map :: ('a ⇒ 'b) ⇒ 'a list ⇒ 'b list
tal que (map f xs) es la lista obtenida aplicando la función f a los
elementos de xs. Por ejemplo,
map (λx. 2*x) [3,2,5] = [6,4,10]
------------------------------------------------------------------ *}

fun map :: "('a ⇒ 'b) ⇒ 'a list ⇒ 'b list" where
"map f xs = undefined"

value "map (λx. 2*x) [3::nat,2,5]" -- "= [6,4,10]"

end
</source>

GLC T2R2a

2018-07-15T11:58:29Z

Jalonso: Texto reemplazado: «"isar"» por «"isabelle"»

<source lang="isabelle">
header {* T2R2a: Argumentación en lógica de primer orden *}

theory T2R2a
imports Main
begin

text {*
---------------------------------------------------------------------
El objetivo de esta relación es formalizar y demostrar la corrección
de los argumentos usando sólo las reglas básicas de deducción natural
de la lógica de primer orden (sin usar el método auto).

Las reglas básicas de la deducción natural son las siguientes:
· conjI: ⟦P; Q⟧ ⟹ P ∧ Q
· conjunct1: P ∧ Q ⟹ P
· conjunct2: P ∧ Q ⟹ Q
· notnotD: ¬¬ P ⟹ P
· notnotI: P ⟹ ¬¬ P
· mp: ⟦P ⟶ Q; P⟧ ⟹ Q
· mt: ⟦F ⟶ G; ¬G⟧ ⟹ ¬F
· impI: (P ⟹ Q) ⟹ P ⟶ Q
· disjI1: P ⟹ P ∨ Q
· disjI2: Q ⟹ P ∨ Q
· disjE: ⟦P ∨ Q; P ⟹ R; Q ⟹ R⟧ ⟹ R
· FalseE: False ⟹ P
· notE: ⟦¬P; P⟧ ⟹ R
· notI: (P ⟹ False) ⟹ ¬P
· iffI: ⟦P ⟹ Q; Q ⟹ P⟧ ⟹ P = Q
· iffD1: ⟦Q = P; Q⟧ ⟹ P
· iffD2: ⟦P = Q; Q⟧ ⟹ P
· ccontr: (¬P ⟹ False) ⟹ P
· excluded_middle: ¬P ∨ P

· allI: ⟦∀x. P x; P x ⟹ R⟧ ⟹ R
· allE: (⋀x. P x) ⟹ ∀x. P x
· exI: P x ⟹ ∃x. P x
· exE: ⟦∃x. P x; ⋀x. P x ⟹ Q⟧ ⟹ Q

---------------------------------------------------------------------
*}

text {*
Se usarán las reglas notnotI y mt que demostramos a continuación.
*}

lemma notnotI: "P ⟹ ¬¬ P"
by auto

lemma mt: "⟦F ⟶ G; ¬G⟧ ⟹ ¬F"
by auto

lemma no_ex: "¬(∃x. P(x)) ⟹ ∀x. ¬P(x)"
by auto

lemma no_para_todo: "¬(∀x. P(x)) ⟹ ∃x. ¬P(x)"
by auto

text {* ---------------------------------------------------------------
Ejercicio 1. Formalizar, y demostrar la corrección, del siguiente
argumento
Sócrates es un hombre.
Los hombres son mortales.
Luego, Sócrates es mortal.
Usar s para Sócrates
H(x) para x es un hombre
M(x) para x es mortal
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_1a:
"⟦H(s); ∀x. H(x) ⟶ M(x)⟧ ⟹ M(s)"
by auto

-- "La demostración estructurada es"
lemma ejercicio_1b:
assumes "H(s)"
"∀x. H(x) ⟶ M(x)"
shows "M(s)"
proof -
have "H(s) ⟶ M(s)" using assms(2) ..
thus "M(s)" using assms(1) ..
qed

-- "La demostración detallada es"
lemma ejercicio_1c:
assumes "H(s)"
"∀x. H(x) ⟶ M(x)"
shows "M(s)"
proof -
have "H(s) ⟶ M(s)" using assms(2) by (rule allE)
thus "M(s)" using assms(1) by (rule mp)
qed

text {* ---------------------------------------------------------------
Ejercicio 2. Formalizar, y decidir la corrección, del siguiente
argumento
Hay estudiantes inteligentes y hay estudiantes trabajadores. Por
tanto, hay estudiantes inteligentes y trabajadores.
Usar I(x) para x es inteligente
T(x) para x es trabajador
------------------------------------------------------------------ *}

-- "La refutación automática es"
lemma ejercicio_2a:
"(∃x. I(x)) ∧ (∃x. T(x)) ⟹ ∃x. I(x) ∧ T(x)"
quickcheck
oops

text {*
El argumento es incorrecto como muestra el siguiente contraejemplo:
I = {a1}
T = {a2}
*}

text {* ---------------------------------------------------------------
Ejercicio 3. Formalizar, y decidir la corrección, del siguiente
argumento
Todos los participantes son vencedores. Hay como máximo un
vencedor. Hay como máximo un participante. Por lo tanto, hay
exactamente un participante.
Usar P(x) para x es un participante
V(x) para x es un vencedor
------------------------------------------------------------------ *}

-- "La refutación automática es"
lemma ejercicio_3a:
"⟦∀x. P(x) ⟶ V(x);
∀x y. V(x) ∧ V(y) ⟶ x=y;
∀x y. P(x) ∧ P(y) ⟶ x=y⟧
⟹ ∃x. P(x) ∧ (∀y. P(y) ⟶ x=y)"
quickcheck
oops

text {*
El argumento es incorrecto como muestra el siguiente contraejemplo:
V = {}
P = {}
*}

text {* ---------------------------------------------------------------
Ejercicio 4. Formalizar, y decidir la corrección, del siguiente
argumento
Todo aquel que entre en el país y no sea un VIP será cacheado por
un aduanero. Hay un contrabandista que entra en el país y que solo
podrá ser cacheado por contrabandistas. Ningún contrabandista es un
VIP. Por tanto, algún aduanero es contrabandista.
Usar A(x) para x es aduanero
Ca(x,y) para x cachea a y
Co(x) para x es contrabandista
E(x) para x entra en el pais
V(x) para x es un VIP
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_4a:
"⟦∀x. E(x) ∧ ¬V(x) ⟶ (∃y. A(y) ∧ Ca(y,x));
∃x. Co(x) ∧ E(x) ∧ (∀y. Ca(y,x) ⟶ Co(y));
¬(∃x. Co(x) ∧ V(x))⟧
⟹ ∃x. A(x) ∧ Co(x)"
by metis

-- "La demostración estructurada es"
lemma ejercicio_4b:
assumes "∀x. E(x) ∧ ¬V(x) ⟶ (∃y. A(y) ∧ Ca(y,x))"
"∃x. Co(x) ∧ E(x) ∧ (∀y. Ca(y,x) ⟶ Co(y))"
"¬(∃x. Co(x) ∧ V(x))"
shows "∃x. A(x) ∧ Co(x)"
proof -
obtain a where a: "Co(a) ∧ E(a) ∧ (∀y. Ca(y,a) ⟶ Co(y))"
using assms(2) ..
have "∃y. A(y) ∧ Ca(y,a)"
proof -
have "E(a) ∧ ¬V(a) ⟶ (∃y. A(y) ∧ Ca(y,a))" using assms(1) ..
moreover
have "E(a) ∧ ¬V(a)"
proof
have "E(a) ∧ (∀y. Ca(y,a) ⟶ Co(y))" using a ..
thus "E(a)" ..
next
have "∀x. ¬(Co(x) ∧ V(x))" using assms(3) by (rule no_ex)
hence "¬(Co(a) ∧ V(a))" ..
have "Co(a)" using a ..
show "¬V(a)"
proof
assume "V(a)"
with `Co(a)` have "Co(a) ∧ V(a)" ..
with `¬(Co(a) ∧ V(a))` show False ..
qed
qed
ultimately show "∃y. A(y) ∧ Ca(y,a)" ..
qed
then obtain b where "A(b) ∧ Ca(b,a)" ..
hence "A(b)" ..
moreover
have "Co(b)"
proof -
have "E(a) ∧ (∀y. Ca(y,a) ⟶ Co(y))" using a ..
hence "∀y. Ca(y,a) ⟶ Co(y)" ..
hence "Ca(b,a) ⟶ Co(b)" ..
have "Ca(b,a)" using `A(b) ∧ Ca(b,a)` ..
with `Ca(b,a) ⟶ Co(b)` show "Co(b)" ..
qed
ultimately have "A(b) ∧ Co(b)" ..
thus "∃x. A(x) ∧ Co(x)" ..
qed

-- "La demostración detallada es"
lemma ejercicio_4c:
assumes "∀x. E(x) ∧ ¬V(x) ⟶ (∃y. A(y) ∧ Ca(y,x))"
"∃x. Co(x) ∧ E(x) ∧ (∀y. Ca(y,x) ⟶ Co(y))"
"¬(∃x. Co(x) ∧ V(x))"
shows "∃x. A(x) ∧ Co(x)"
proof -
obtain a where a: "Co(a) ∧ E(a) ∧ (∀y. Ca(y,a) ⟶ Co(y))"
using assms(2) by (rule exE)
have "∃y. A(y) ∧ Ca(y,a)"
proof -
have "E(a) ∧ ¬V(a) ⟶ (∃y. A(y) ∧ Ca(y,a))" using assms(1) by (rule allE)
moreover
have "E(a) ∧ ¬V(a)"
proof
have "E(a) ∧ (∀y. Ca(y,a) ⟶ Co(y))" using a by (rule conjunct2)
thus "E(a)" by (rule conjunct1)
next
have "∀x. ¬(Co(x) ∧ V(x))" using assms(3) by (rule no_ex)
hence "¬(Co(a) ∧ V(a))" by (rule allE)
have "Co(a)" using a by (rule conjunct1)
show "¬V(a)"
proof (rule notI)
assume "V(a)"
with `Co(a)` have "Co(a) ∧ V(a)" by (rule conjI)
with `¬(Co(a) ∧ V(a))` show False by (rule notE)
qed
qed
ultimately show "∃y. A(y) ∧ Ca(y,a)" by (rule mp)
qed
then obtain b where "A(b) ∧ Ca(b,a)" by (rule exE)
hence "A(b)" by (rule conjunct1)
moreover
have "Co(b)"
proof -
have "E(a) ∧ (∀y. Ca(y,a) ⟶ Co(y))" using a by (rule conjunct2)
hence "∀y. Ca(y,a) ⟶ Co(y)" by (rule conjunct2)
hence "Ca(b,a) ⟶ Co(b)" by (rule allE)
have "Ca(b,a)" using `A(b) ∧ Ca(b,a)` by (rule conjunct2)
with `Ca(b,a) ⟶ Co(b)` show "Co(b)" by (rule mp)
qed
ultimately have "A(b) ∧ Co(b)" by (rule conjI)
thus "∃x. A(x) ∧ Co(x)" by (rule exI)
qed

text {* ---------------------------------------------------------------
Ejercicio 5. Formalizar, y decidir la corrección, del siguiente
argumento
Juan teme a María. Pedro es temido por Juan. Luego, alguien teme a
María y a Pedro.
Usar j para Juan
m para María
p para Pedro
T(x,y) para x teme a y
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_5a:
"⟦T(j,m); T(j,p)⟧ ⟹ ∃x. T(x,m) ∧ T(x,p)"
by auto

-- "La demostración estructurada es"
lemma ejercicio_5b:
assumes "T(j,m)"
"T(j,p)"
shows "∃x. T(x,m) ∧ T(x,p)"
proof
show "T(j,m) ∧ T(j,p)" using assms ..
qed

-- "La demostración detallada es"
lemma ejercicio_5c:
assumes "T(j,m)"
"T(j,p)"
shows "∃x. T(x,m) ∧ T(x,p)"
proof (rule exI)
show "T(j,m) ∧ T(j,p)" using assms by (rule conjI)
qed

text {* ---------------------------------------------------------------
Ejercicio 6. Formalizar, y decidir la corrección, del siguiente
argumento
Los hermanos tienen el mismo padre. Juan es hermano de Luis. Carlos
es padre de Luis. Por tanto, Carlos es padre de Juan.
Usar H(x,y) para x es hermano de y
P(x,y) para x es padre de y
j para Juan
l para Luis
c para Carlos
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_6a:
assumes "∀x y. H(x,y) ⟶ H(y,x)"
"∀x y z. H(x,y) ∧ P(z,x) ⟶ P(z,y)"
"H(j,l)"
"P(c,l)"
shows "P(c,j)"
using assms
by metis

-- "La demostración estructurada es"
lemma ejercicio_6b:
fixes H P :: "'a × 'a ⇒ bool"
assumes "∀x y. H(x,y) ⟶ H(y,x)"
"∀x y z. H(x,y) ∧ P(z,x) ⟶ P(z,y)"
"H(j,l)"
"P(c,l)"
shows "P(c,j)"
proof -
have "H(l,j) ∧ P(c,l) ⟶ P(c,j)"
proof -
have "∀y z. H(l,y) ∧ P(z,l) ⟶ P(z,y)" using assms(2) ..
hence "∀z. H(l,j) ∧ P(z,l) ⟶ P(z,j)" ..
thus "H(l,j) ∧ P(c,l) ⟶ P(c,j)" ..
qed
moreover
have "H(l,j) ∧ P(c,l)"
proof
have "∀y. H(j,y) ⟶ H(y,j)" using assms(1) ..
hence "H(j,l) ⟶ H(l,j)" ..
thus "H(l,j)" using assms(3) ..
next
show "P(c,l)" using assms(4) .
qed
ultimately show "P(c,j)" ..
qed

-- "La demostración detallada es"
lemma ejercicio_6c:
fixes H P :: "'a × 'a ⇒ bool"
assumes "∀x y. H(x,y) ⟶ H(y,x)"
"∀x y z. H(x,y) ∧ P(z,x) ⟶ P(z,y)"
"H(j,l)"
"P(c,l)"
shows "P(c,j)"
proof -
have "H(l,j) ∧ P(c,l) ⟶ P(c,j)"
proof -
have "∀y z. H(l,y) ∧ P(z,l) ⟶ P(z,y)" using assms(2) by (rule allE)
hence "∀z. H(l,j) ∧ P(z,l) ⟶ P(z,j)" by (rule allE)
thus "H(l,j) ∧ P(c,l) ⟶ P(c,j)" by (rule allE)
qed
moreover
have "H(l,j) ∧ P(c,l)"
proof (rule conjI)
have "∀y. H(j,y) ⟶ H(y,j)" using assms(1) by (rule allE)
hence "H(j,l) ⟶ H(l,j)" by (rule allE)
thus "H(l,j)" using assms(3) by (rule mp)
next
show "P(c,l)" using assms(4) by this
qed
ultimately show "P(c,j)" by (rule mp)
qed

text {* ---------------------------------------------------------------
Ejercicio 7. Formalizar, y decidir la corrección, del siguiente
argumento
La existencia de algún canal de TV pública, supone un acicate para
cualquier canal de TV privada; el que un canal de TV tenga un
acicate, supone una gran satisfacción para cualquiera de sus
directivos; en Madrid hay varios canales públicos de TV; TV5 es un
canal de TV privada; por tanto, todos los directivos de TV5 están
satisfechos.
Usar Pu(x) para x es un canal de TV pública
Pr(x) para x es un canal de TV privada
A(x) para x posee un acicate
D(x,y) para x es un directivo del canal y
S(x) para x está satisfecho
t para TV5
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_7a:
assumes "(∃x. Pu(x)) ⟶ (∀x. Pr(x) ⟶ A(x))"
"∀x. A(x) ⟶ (∀y. D(y,x) ⟶ S(y))"
"∃x. Pu(x)"
"Pr(t)"
shows "∀x. D(x,t) ⟶ S(x)"
using assms
by auto

-- "La demostración estructurada es"
lemma ejercicio_7b:
assumes "(∃x. Pu(x)) ⟶ (∀x. Pr(x) ⟶ A(x))"
"∀x. A(x) ⟶ (∀y. D(y,x) ⟶ S(y))"
"∃x. Pu(x)"
"Pr(t)"
shows "∀x. D(x,t) ⟶ S(x)"
proof
fix a
show "D(a,t) ⟶ S(a)"
proof
assume "D(a,t)"
have "∀x. Pr(x) ⟶ A(x)" using assms(1) assms(3) ..
hence "Pr(t) ⟶ A(t)" ..
hence "A(t)" using assms(4) ..
have "A(t) ⟶ (∀y. D(y,t) ⟶ S(y))" using assms(2) ..
hence "∀y. D(y,t) ⟶ S(y)" using `A(t)` ..
hence "D(a,t) ⟶ S(a)" ..
thus "S(a)" using `D(a,t)` ..
qed
qed

-- "La demostración detallada es"
lemma ejercicio_7c:
assumes "(∃x. Pu(x)) ⟶ (∀x. Pr(x) ⟶ A(x))"
"∀x. A(x) ⟶ (∀y. D(y,x) ⟶ S(y))"
"∃x. Pu(x)"
"Pr(t)"
shows "∀x. D(x,t) ⟶ S(x)"
proof (rule allI)
fix a
show "D(a,t) ⟶ S(a)"
proof (rule impI)
assume "D(a,t)"
have "∀x. Pr(x) ⟶ A(x)" using assms(1) assms(3) by (rule mp)
hence "Pr(t) ⟶ A(t)" by (rule allE)
hence "A(t)" using assms(4) by (rule mp)
have "A(t) ⟶ (∀y. D(y,t) ⟶ S(y))" using assms(2) by (rule allE)
hence "∀y. D(y,t) ⟶ S(y)" using `A(t)` by (rule mp)
hence "D(a,t) ⟶ S(a)" by (rule allE)
thus "S(a)" using `D(a,t)` by (rule mp)
qed
qed

text {* ---------------------------------------------------------------
Ejercicio 8. Formalizar, y decidir la corrección, del siguiente
argumento
Quien intente entrar en un país y no tenga pasaporte, encontrará
algún aduanero que le impida el paso. A algunas personas
motorizadas que intentan entrar en un país le impiden el paso
únicamente personas motorizadas. Ninguna persona motorizada tiene
pasaporte. Por tanto, ciertos aduaneros están motorizados.
Usar E(x) para x entra en un país
P(x) para x tiene pasaporte
A(x) para x es aduanero
I(x,y) para x impide el paso a y
M(x) para x está motorizada
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_8a:
assumes "∀x. E(x) ∧ ¬P(x) ⟶ (∃y. A(y) ∧ I(y,x))"
"∃x. M(x) ∧ E(x) ∧ (∀y. I(y,x) ⟶ M(y))"
"∀x. M(x) ⟶ ¬P(x)"
shows "∃x. A(x) ∧ M(x)"
using assms
by blast

-- "La demostración estructurada es"
lemma ejercicio_8b:
assumes "∀x. E(x) ∧ ¬P(x) ⟶ (∃y. A(y) ∧ I(y,x))"
"∃x. M(x) ∧ E(x) ∧ (∀y. I(y,x) ⟶ M(y))"
"∀x. M(x) ⟶ ¬P(x)"
shows "∃x. A(x) ∧ M(x)"
proof -
obtain a where a: "M(a) ∧ E(a) ∧ (∀y. I(y,a) ⟶ M(y))" using assms(2) ..
hence "M(a)" ..
have "M(a) ⟶ ¬P(a)" using assms(3) ..
hence "¬P(a)" using `M(a)` ..
have a1: "E(a) ∧ (∀y. I(y,a) ⟶ M(y))" using a ..
hence "E(a)" ..
hence "E(a) ∧ ¬P(a)" using `¬P(a)` ..
have "E(a) ∧ ¬P(a) ⟶ (∃y. A(y) ∧ I(y,a))" using assms(1) ..
hence "∃y. A(y) ∧ I(y,a)" using `E(a) ∧ ¬P(a)`..
then obtain b where b: "A(b) ∧ I(b,a)" ..
have "A(b) ∧ M(b)"
proof
show "A(b)" using b ..
next
have "I(b,a)" using b ..
have "∀y. I(y,a) ⟶ M(y)" using a1 ..
hence "I(b,a) ⟶ M(b)" ..
thus "M(b)" using `I(b,a)` ..
qed
thus "∃x. A(x) ∧ M(x)" ..
qed

-- "La demostración detallada es"
lemma ejercicio_8c:
assumes "∀x. E(x) ∧ ¬P(x) ⟶ (∃y. A(y) ∧ I(y,x))"
"∃x. M(x) ∧ E(x) ∧ (∀y. I(y,x) ⟶ M(y))"
"∀x. M(x) ⟶ ¬P(x)"
shows "∃x. A(x) ∧ M(x)"
proof -
obtain a where a: "M(a) ∧ E(a) ∧ (∀y. I(y,a) ⟶ M(y))"
using assms(2) by (rule exE)
hence "M(a)" by (rule conjunct1)
have "M(a) ⟶ ¬P(a)" using assms(3) by (rule allE)
hence "¬P(a)" using `M(a)` by (rule mp)
have a1: "E(a) ∧ (∀y. I(y,a) ⟶ M(y))" using a by (rule conjunct2)
hence "E(a)" by (rule conjunct1)
hence "E(a) ∧ ¬P(a)" using `¬P(a)` by (rule conjI)
have "E(a) ∧ ¬P(a) ⟶ (∃y. A(y) ∧ I(y,a))"
using assms(1) by (rule allE)
hence "∃y. A(y) ∧ I(y,a)" using `E(a) ∧ ¬P(a)`by (rule mp)
then obtain b where b: "A(b) ∧ I(b,a)" by (rule exE)
have "A(b) ∧ M(b)"
proof (rule conjI)
show "A(b)" using b by (rule conjunct1)
next
have "I(b,a)" using b by (rule conjunct2)
have "∀y. I(y,a) ⟶ M(y)" using a1 by (rule conjunct2)
hence "I(b,a) ⟶ M(b)" by (rule allE)
thus "M(b)" using `I(b,a)`by (rule mp)
qed
thus "∃x. A(x) ∧ M(x)" by (rule exI)
qed

text {* ---------------------------------------------------------------
Ejercicio 9. Formalizar, y decidir la corrección, del siguiente
argumento
Los aficionados al fútbol aplauden a cualquier futbolista
extranjero. Juanito no aplaude a futbolistas extranjeros. Por
tanto, si hay algún futbolista extranjero nacionalizado español,
Juanito no es aficionado al fútbol.
Usar Af(x) para x es aficicionado al fútbol
Ap(x,y) para x aplaude a y
E(x) para x es un futbolista extranjero
N(x) para x es un futbolista nacionalizado español
j para Juanito
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_9a:
assumes "∀x. Af(x) ⟶ (∀y. E(y) ⟶ Ap(x,y))"
"∀x. E(x) ⟶ ¬Ap(j,x)"
shows "(∃x. E(x) ∧ N(x)) ⟶ ¬Af(j)"
using assms
by blast

-- "La demostración estructurada es"
lemma ejercicio_9b:
assumes "∀x. Af(x) ⟶ (∀y. E(y) ⟶ Ap(x,y))"
"∀x. E(x) ⟶ ¬Ap(j,x)"
shows "(∃x. E(x) ∧ N(x)) ⟶ ¬Af(j)"
proof
assume "∃x. E(x) ∧ N(x)"
then obtain a where a: "E(a) ∧ N(a)" ..
show "¬Af(j)"
proof
assume "Af(j)"
have "Af(j) ⟶ (∀y. E(y) ⟶ Ap(j,y))" using assms(1) ..
hence "∀y. E(y) ⟶ Ap(j,y)" using `Af(j)` ..
hence "E(a) ⟶ Ap(j,a)" ..
have "E(a)" using a ..
with `E(a) ⟶ Ap(j,a)` have "Ap(j,a)" ..
have "E(a) ⟶ ¬Ap(j,a)" using assms(2) ..
hence "¬Ap(j,a)" using `E(a)` ..
thus False using `Ap(j,a)` ..
qed
qed

-- "La demostración detallada es"
lemma ejercicio_9c:
assumes "∀x. Af(x) ⟶ (∀y. E(y) ⟶ Ap(x,y))"
"∀x. E(x) ⟶ ¬Ap(j,x)"
shows "(∃x. E(x) ∧ N(x)) ⟶ ¬Af(j)"
proof (rule impI)
assume "∃x. E(x) ∧ N(x)"
then obtain a where a: "E(a) ∧ N(a)" by (rule exE)
show "¬Af(j)"
proof (rule notI)
assume "Af(j)"
have "Af(j) ⟶ (∀y. E(y) ⟶ Ap(j,y))" using assms(1) by (rule allE)
hence "∀y. E(y) ⟶ Ap(j,y)" using `Af(j)` by (rule mp)
hence "E(a) ⟶ Ap(j,a)" by (rule allE)
have "E(a)" using a by (rule conjunct1)
with `E(a) ⟶ Ap(j,a)` have "Ap(j,a)" by (rule mp)
have "E(a) ⟶ ¬Ap(j,a)" using assms(2) by (rule allE)
hence "¬Ap(j,a)" using `E(a)` by (rule mp)
thus False using `Ap(j,a)` by (rule notE)
qed
qed

text {* ---------------------------------------------------------------
Ejercicio 10. Formalizar, y decidir la corrección, del siguiente
argumento
Ningún aristócrata debe ser condenado a galeras a menos que sus
crímenes sean vergonzosos y lleve una vida licenciosa. En la ciudad
hay aristócratas que han cometido crímenes vergonzosos aunque su
forma de vida no sea licenciosa. Por tanto, hay algún aristócrata
que no está condenado a galeras.
Usar A(x) para x es aristócrata
G(x) para x está condenado a galeras
L(x) para x lleva una vida licenciosa
V(x) para x ha cometido crímenes vergonzoso
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_10a:
assumes "∀x. A(x) ∧ G(x) ⟶ L(x) ∧ V(x)"
"∃x. A(x) ∧ V(x) ∧ ¬L(x)"
shows "∃x. A(x) ∧ ¬G(x)"
using assms
by blast

-- "La demostración estructurada es"
lemma ejercicio_10b:
assumes "∀x. A(x) ∧ G(x) ⟶ L(x) ∧ V(x)"
"∃x. A(x) ∧ V(x) ∧ ¬L(x)"
shows "∃x. A(x) ∧ ¬G(x)"
proof -
obtain b where b: "A(b) ∧ V(b) ∧ ¬L(b)" using assms(2) ..
have "A(b) ∧ ¬G(b)"
proof
show "A(b)" using b ..
next
show "¬G(b)"
proof
assume "G(b)"
have "¬L(b)"
proof -
have "V(b) ∧ ¬L(b)" using b ..
thus "¬L(b)" ..
qed
moreover have "L(b)"
proof -
have "A(b) ∧ G(b) ⟶ L(b) ∧ V(b)" using assms(1) ..
have "A(b)" using b ..
hence "A(b) ∧ G(b)" using `G(b)` ..
with `A(b) ∧ G(b) ⟶ L(b) ∧ V(b)` have "L(b) ∧ V(b)" ..
thus "L(b)" ..
qed
ultimately show False ..
qed
qed
thus "∃x. A(x) ∧ ¬G(x)" ..
qed

-- "La demostración detallada es"
lemma ejercicio_10c:
assumes "∀x. A(x) ∧ G(x) ⟶ L(x) ∧ V(x)"
"∃x. A(x) ∧ V(x) ∧ ¬L(x)"
shows "∃x. A(x) ∧ ¬G(x)"
proof -
obtain b where b: "A(b) ∧ V(b) ∧ ¬L(b)" using assms(2) by (rule exE)
have "A(b) ∧ ¬G(b)"
proof (rule conjI)
show "A(b)" using b by (rule conjunct1)
next
show "¬G(b)"
proof (rule notI)
assume "G(b)"
have "¬L(b)"
proof -
have "V(b) ∧ ¬L(b)" using b by (rule conjunct2)
thus "¬L(b)" by (rule conjunct2)
qed
moreover have "L(b)"
proof -
have "A(b) ∧ G(b) ⟶ L(b) ∧ V(b)" using assms(1) by (rule allE)
have "A(b)" using b by (rule conjunct1)
hence "A(b) ∧ G(b)" using `G(b)` by (rule conjI)
with `A(b) ∧ G(b) ⟶ L(b) ∧ V(b)` have "L(b) ∧ V(b)" by (rule mp)
thus "L(b)" by (rule conjunct1)
qed
ultimately show False by (rule notE)
qed
qed
thus "∃x. A(x) ∧ ¬G(x)" by (rule exI)
qed

text {* ---------------------------------------------------------------
Ejercicio 11. Formalizar, y decidir la corrección, del siguiente
argumento
Todo individuo que esté conforme con el contenido de cualquier
acuerdo internacional lo apoya o se inhibe en absoluto de asuntos
políticos. Cualquiera que se inhiba de los asuntos políticos, no
participará en el próximo referéndum. Todo español, está conforme
con el acuerdo internacional de Maastricht, al que sin embargo no
apoya. Por tanto, cualquier individuo o no es español, o en otro
caso, está conforme con el contenido del acuerdo internacional de
Maastricht y no participará en el próximo referéndum.
Usar C(x,y) para la persona x conforme con el contenido del acuerdo y
A(x,y) para la persona x apoya el acuerdo y
I(x) para la persona x se inibe de asuntos políticos
R(x) para la persona x participará en el próximo referéndum
E(x) para la persona x es española
m para el acuerdo de Maastricht
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_11a:
assumes "∀x y. C(x,y) ⟶ A(x,y) ∨ I(x)"
"∀x. I(x) ⟶ ¬R(x)"
"∀x. E(x) ⟶ C(x,m) ∧ ¬A(x,m)"
shows "∀x. ¬E(x) ∨ (C(x,m) ∧ ¬R(x))"
using assms
by blast

-- "La demostración estructurada es"
lemma ejercicio_11b:
assumes "∀x y. C(x,y) ⟶ A(x,y) ∨ I(x)"
"∀x. I(x) ⟶ ¬R(x)"
"∀x. E(x) ⟶ C(x,m) ∧ ¬A(x,m)"
shows "∀x. ¬E(x) ∨ (C(x,m) ∧ ¬R(x))"
proof
fix a
have "¬E(a) ∨ E(a)" ..
thus "¬E(a) ∨ (C(a,m) ∧ ¬R(a))"
proof
assume "¬E(a)"
thus "¬E(a) ∨ (C(a,m) ∧ ¬R(a))" ..
next
assume "E(a)"
have "E(a) ⟶ C(a,m) ∧ ¬A(a,m)" using assms(3) ..
hence "C(a,m) ∧ ¬A(a,m)" using `E(a)` ..
hence "C(a,m)" ..
have "∀y. C(a,y) ⟶ A(a,y) ∨ I(a)" using assms(1) ..
hence "C(a,m) ⟶ A(a,m) ∨ I(a)" ..
hence "A(a,m) ∨ I(a)" using `C(a,m)` ..
hence "¬R(a)"
proof
assume "A(a,m)"
have "¬A(a,m)" using `C(a,m) ∧ ¬A(a,m)`..
thus "¬R(a)" using `A(a,m)` ..
next
assume "I(a)"
have "I(a) ⟶ ¬R(a)" using assms(2) ..
thus "¬R(a)" using `I(a)` ..
qed
with `C(a,m)` have "C(a,m) ∧ ¬R(a)" ..
thus "¬E(a) ∨ (C(a,m) ∧ ¬R(a))" ..
qed
qed

-- "La demostración detallada es"
lemma ejercicio_11c:
assumes "∀x y. C(x,y) ⟶ A(x,y) ∨ I(x)"
"∀x. I(x) ⟶ ¬R(x)"
"∀x. E(x) ⟶ C(x,m) ∧ ¬A(x,m)"
shows "∀x. ¬E(x) ∨ (C(x,m) ∧ ¬R(x))"
proof (rule allI)
fix a
have "¬E(a) ∨ E(a)" by (rule excluded_middle)
thus "¬E(a) ∨ (C(a,m) ∧ ¬R(a))"
proof (rule disjE)
assume "¬E(a)"
thus "¬E(a) ∨ (C(a,m) ∧ ¬R(a))" by (rule disjI1)
next
assume "E(a)"
have "E(a) ⟶ C(a,m) ∧ ¬A(a,m)" using assms(3) by (rule allE)
hence "C(a,m) ∧ ¬A(a,m)" using `E(a)` by (rule mp)
hence "C(a,m)" by (rule conjunct1)
have "∀y. C(a,y) ⟶ A(a,y) ∨ I(a)" using assms(1) by (rule allE)
hence "C(a,m) ⟶ A(a,m) ∨ I(a)" by (rule allE)
hence "A(a,m) ∨ I(a)" using `C(a,m)` by (rule mp)
hence "¬R(a)"
proof (rule disjE)
assume "A(a,m)"
have "¬A(a,m)" using `C(a,m) ∧ ¬A(a,m)`by (rule conjunct2)
thus "¬R(a)" using `A(a,m)` by (rule notE)
next
assume "I(a)"
have "I(a) ⟶ ¬R(a)" using assms(2) by (rule allE)
thus "¬R(a)" using `I(a)` by (rule mp)
qed
with `C(a,m)` have "C(a,m) ∧ ¬R(a)" by (rule conjI)
thus "¬E(a) ∨ (C(a,m) ∧ ¬R(a))" by (rule disjI2)
qed
qed

text {* ---------------------------------------------------------------
Ejercicio 12. Formalizar, y decidir la corrección, del siguiente
argumento
Toda persona pobre tiene un padre rico. Por tanto, existe una
persona rica que tiene un abuelo rico.
Usar R(x) para x es rico
p(x) para el padre de x
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_12a:
assumes "∀x. ¬R(x) ⟶ R(p(x))"
shows "∃x. R(x) ∧ R(p(p(x)))"
using assms
by blast

-- "La demostración estructurada es"
lemma ejercicio_12b:
assumes "∀x. ¬R(x) ⟶ R(p(x))"
shows "∃x. R(x) ∧ R(p(p(x)))"
proof -
have "∃x. R(x)"
proof (rule ccontr)
assume "¬(∃x. R(x))"
hence "∀x. ¬R(x)" by (rule no_ex)
hence "¬R(a)" ..
have "¬R(a) ⟶ R(p(a))" using assms ..
hence "R(p(a))" using `¬R(a)` ..
hence "∃x. R(x)" ..
with `¬(∃x. R(x))` show False ..
qed
then obtain a where "R(a)" ..
have "¬R(p(p(a))) ∨ R(p(p(a)))" by (rule excluded_middle)
thus "∃x. R(x) ∧ R(p(p(x)))"
proof
assume "¬R(p(p(a)))"
have "R(p(a)) ∧ R(p(p(p(a))))"
proof
show "R(p(a))"
proof (rule ccontr)
assume "¬R(p(a))"
have "¬R(p(a)) ⟶ R(p(p(a)))" using assms ..
hence "R(p(p(a)))" using `¬R(p(a))` ..
with `¬R(p(p(a)))` show False ..
qed
next
show "R(p(p(p(a))))"
proof -
have "¬R(p(p(a))) ⟶ R(p(p(p(a))))" using assms ..
thus "R(p(p(p(a))))" using `¬R(p(p(a)))` ..
qed
qed
thus "∃x. R(x) ∧ R(p(p(x)))" ..
next
assume "R(p(p(a)))"
with `R(a)` have "R(a) ∧ R(p(p(a)))" ..
thus "∃x. R(x) ∧ R(p(p(x)))" ..
qed
qed

-- "La demostración detallada es"
lemma ejercicio_12c:
assumes "∀x. ¬R(x) ⟶ R(p(x))"
shows "∃x. R(x) ∧ R(p(p(x)))"
proof -
have "∃x. R(x)"
proof (rule ccontr)
assume "¬(∃x. R(x))"
hence "∀x. ¬R(x)" by (rule no_ex)
hence "¬R(a)" by (rule allE)
have "¬R(a) ⟶ R(p(a))" using assms by (rule allE)
hence "R(p(a))" using `¬R(a)` by (rule mp)
hence "∃x. R(x)" by (rule exI)
with `¬(∃x. R(x))` show False by (rule notE)
qed
then obtain a where "R(a)" by (rule exE)
have "¬R(p(p(a))) ∨ R(p(p(a)))" by (rule excluded_middle)
thus "∃x. R(x) ∧ R(p(p(x)))"
proof (rule disjE)
assume "¬R(p(p(a)))"
have "R(p(a)) ∧ R(p(p(p(a))))"
proof (rule conjI)
show "R(p(a))"
proof (rule ccontr)
assume "¬R(p(a))"
have "¬R(p(a)) ⟶ R(p(p(a)))" using assms by (rule allE)
hence "R(p(p(a)))" using `¬R(p(a))` by (rule mp)
with `¬R(p(p(a)))` show False by (rule notE)
qed
next
show "R(p(p(p(a))))"
proof -
have "¬R(p(p(a))) ⟶ R(p(p(p(a))))" using assms by (rule allE)
thus "R(p(p(p(a))))" using `¬R(p(p(a)))` by (rule mp)
qed
qed
thus "∃x. R(x) ∧ R(p(p(x)))" by (rule exI)
next
assume "R(p(p(a)))"
with `R(a)` have "R(a) ∧ R(p(p(a)))" by (rule conjI)
thus "∃x. R(x) ∧ R(p(p(x)))" by (rule exI)
qed
qed

text {* ---------------------------------------------------------------
Ejercicio 13. Formalizar, y decidir la corrección, del siguiente
argumento
Todo deprimido que estima a un submarinista es listo. Cualquiera
que se estime a sí mismo es listo. Ningún deprimido se estima a sí
mismo. Por tanto, ningún deprimido estima a un submarinista.
Usar D(x) para x está deprimido
E(x,y) para x estima a y
L(x) para x es listo
S(x) para x es submarinista
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_13a:
assumes "∀x. D(x) ∧ (∃y. S(y) ∧ E(x,y)) ⟶ L(x)"
"∀x. E(x,x) ⟶ L(x)"
"¬(∃x. D(x) ∧ E(x,x))"
shows "¬(∃x. D(x) ∧ (∃y. S(y) ∧ E(x,y)))"
quickcheck
oops

text {*
El argumento es incorrecto como muestra el siguiente contraejemplo:
Quickcheck found a counterexample:
D = {a2}
S = {a1}
E = {(a2, a1)}
L = {a2}
*}

text {* ---------------------------------------------------------------
Ejercicio 14. Formalizar, y decidir la corrección, del siguiente
argumento
Todos los robots obedecen a los amigos del programador jefe.
Alvaro es amigo del programador jefe, pero Benito no le
obedece. Por tanto, Benito no es un robot.
Usar R(x) para x es un robot
Ob(x,y) para x obedece a y
A(x) para x es amigo del programador jefe
b para Benito
a para Alvaro
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_14a:
assumes "∀x y. R(x) ∧ A(y) ⟶ Ob(x,y)"
"A(a)"
"¬Ob(b,a)"
shows "¬R(b)"
using assms
by blast

-- "La demostración estructurada es"
lemma ejercicio_14b:
fixes R A :: "'a ⇒ bool" and
Ob :: "'a × 'a ⇒ bool"
assumes "∀x y. R(x) ∧ A(y) ⟶ Ob(x,y)"
"A(a)"
"¬Ob(b,a)"
shows "¬R(b)"
proof
assume "R(b)"
have "∀y. R(b) ∧ A(y) ⟶ Ob(b,y)" using assms(1) ..
hence "R(b) ∧ A(a) ⟶ Ob(b,a)" ..
have "R(b) ∧ A(a)" using `R(b)` assms(2) ..
with `R(b) ∧ A(a) ⟶ Ob(b,a)` have "Ob(b,a)" ..
with assms(3) show False ..
qed

-- "La demostración detallada es"
lemma ejercicio_14c:
fixes R A :: "'a ⇒ bool" and
Ob :: "'a × 'a ⇒ bool"
assumes "∀x y. R(x) ∧ A(y) ⟶ Ob(x,y)"
"A(a)"
"¬Ob(b,a)"
shows "¬R(b)"
proof (rule notI)
assume "R(b)"
have "∀y. R(b) ∧ A(y) ⟶ Ob(b,y)" using assms(1) by (rule allE)
hence "R(b) ∧ A(a) ⟶ Ob(b,a)" by (rule allE)
have "R(b) ∧ A(a)" using `R(b)` assms(2) by (rule conjI)
with `R(b) ∧ A(a) ⟶ Ob(b,a)` have "Ob(b,a)" by (rule mp)
with assms(3) show False by (rule notE)
qed

text {* ---------------------------------------------------------------
Ejercicio 15. Formalizar, y decidir la corrección, del siguiente
argumento
En una pecera nadan una serie de peces. Se observa que:
* Hay algún pez x que para cualquier pez y, si el pez x no se come
al pez y entonces existe un pez z tal que z es un tiburón o bien
z protege al pez y.
* No hay ningún pez que se coma a todos los demás.
* Ningún pez protege a ningún otro.
Por tanto, existe algún tiburón en la pecera.
Usar C(x,y) para x se come a y
P(x,y) para x protege a y
T(x) para x es un tiburón
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_15a:
assumes "∃x. ∀y. ¬C(x,y) ⟶ (∃z. T(z) ∨ P(z,y))"
"∀x. ∃y. ¬C(x,y)"
"∀x y. ¬P(x,y)"
shows "∃x. T(x)"
using assms
by auto

-- "La demostración estructurada es"
lemma ejercicio_15b:
assumes "∃x. ∀y. ¬C(x,y) ⟶ (∃z. T(z) ∨ P(z,y))"
"∀x. ∃y. ¬C(x,y)"
"∀x y. ¬P(x,y)"
shows "∃x. T(x)"
proof -
obtain a where a: "∀y. ¬C(a,y) ⟶ (∃z. T(z) ∨ P(z,y))"
using assms(1) ..
have "∃y. ¬C(a,y)" using assms(2) ..
then obtain b where "¬C(a,b)" ..
have "¬C(a,b) ⟶ (∃z. T(z) ∨ P(z,b))" using a ..
hence "∃z. T(z) ∨ P(z,b)" using `¬C(a,b)` ..
then obtain c where "T(c) ∨ P(c,b)" ..
thus "∃x. T(x)"
proof
assume "T(c)"
thus "∃x. T(x)" ..
next
assume "P(c,b)"
have "∀y. ¬P(c,y)" using assms(3) ..
hence "¬P(c,b)" ..
thus "∃x. T(x)" using `P(c,b)` ..
qed
qed

-- "La demostración detallada es"
lemma ejercicio_15c:
assumes "∃x. ∀y. ¬C(x,y) ⟶ (∃z. T(z) ∨ P(z,y))"
"∀x. ∃y. ¬C(x,y)"
"∀x y. ¬P(x,y)"
shows "∃x. T(x)"
proof -
obtain a where a: "∀y. ¬C(a,y) ⟶ (∃z. T(z) ∨ P(z,y))"
using assms(1) by (rule exE)
have "∃y. ¬C(a,y)" using assms(2) by (rule allE)
then obtain b where "¬C(a,b)" by (rule exE)
have "¬C(a,b) ⟶ (∃z. T(z) ∨ P(z,b))" using a by (rule allE)
hence "∃z. T(z) ∨ P(z,b)" using `¬C(a,b)` by (rule mp)
then obtain c where "T(c) ∨ P(c,b)" by (rule exE)
thus "∃x. T(x)"
proof (rule disjE)
assume "T(c)"
thus "∃x. T(x)" by (rule exI)
next
assume "P(c,b)"
have "∀y. ¬P(c,y)" using assms(3) by (rule allE)
hence "¬P(c,b)" by (rule allE)
thus "∃x. T(x)" using `P(c,b)` by (rule notE)
qed
qed

end
</source>

RA12 Relación 14

2018-07-15T11:57:32Z

Jalonso: Texto reemplazado: «lang="isar"» por «lang="isabelle"»

<source lang="isabelle">
header {* R14: Contador de occurrencias *}

theory R14
imports Main
begin

text {*
---------------------------------------------------------------------
Ejercicio 1. Definir la función
veces :: "'a ⇒ 'a list ⇒ nat"
tal que (veces x ys) es el número de occurrencias del elemento x en la
lista ys. Por ejemplo,
veces (2::nat) [2,1,2,5,2] = 3
---------------------------------------------------------------------
*}

fun veces :: "'a ⇒ 'a list ⇒ nat" where
"veces x ys = undefined"

text {*
---------------------------------------------------------------------
Ejercicio 2. Demostrar o refutar:
veces a (xs @ ys) = veces a xs + veces a ys
---------------------------------------------------------------------
*}

lemma veces_append:
"veces a (xs @ ys) = veces a xs + veces a ys"
oops

text {*
---------------------------------------------------------------------
Ejercicio 3. Demostrar o refutar:
veces a xs = veces a (rev xs)
---------------------------------------------------------------------
*}

lemma veces_rev:
"veces a xs = veces a (rev xs)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 4. Demostrar o refutar:
"veces a xs ≤ length xs".
---------------------------------------------------------------------
*}

lemma veces_le_length_auto:
"veces a xs ≤ length xs"
oops

text {*
---------------------------------------------------------------------
Ejercicio 5. Sabiendo que la función map aplica una función a todos
los elementos de una lista:
map f [x\<^isub>1,…,x\<^isub>n] = [f x\<^isub>1,…,f x\<^isub>n],
demostrar o refutar
veces a (map f xs) = veces (f a) xs
---------------------------------------------------------------------
*}

lemma veces_map:
"veces a (map f xs) = veces (f a) xs"
oops

text {*
---------------------------------------------------------------------
Ejercicio 6. La función
filter :: "('a ⇒ bool) ⇒ 'a list ⇒ 'a list"
está definida por
filter P [] = []
filter P (x # xs) = (if P x then x # filter P xs else filter P xs)
Encontrar una expresión e que no contenga filter tal que se verifique
la siguiente propiedad:
veces a (filter P xs) = e
y demostrar la conjetura.
---------------------------------------------------------------------
*}

text {*
---------------------------------------------------------------------
Ejercicio 7. Usando veces, definir la función
borraDups :: "'a list ⇒ bool"
tal que (borraDups xs) es la lista obtenida eliminando los elementos
duplicados de la lista xs. Por ejemplo,
borraDups [1::nat,2,4,2,3] = [1,4,2,3]

Nota: La función borraDups es equivalente a la predefinida remdups.
---------------------------------------------------------------------
*}

fun borraDups :: "'a list ⇒ 'a list" where
"borraDups xs = undefined"

text {*
---------------------------------------------------------------------
Ejercicio 8. Encontrar una expresión e que no contenga la función
borraDups tal que se verifique
veces x (borraDups xs) = e
y demostrar la conjetura.
---------------------------------------------------------------------
*}

text {*
---------------------------------------------------------------------
Ejercicio 9. Usando la función "veces", definir la función
distintos :: "'a list ⇒ bool"
tal que (distintos xs) se verifica si cada elemento de xs aparece tan
solo una vez. Por ejemplo,
distintos [1,4,3]
¬ distintos [1,4,1]

Nota: La función "distintos" es equivalente a la predefinida "distinct".
---------------------------------------------------------------------
*}

fun distintos :: "'a list ⇒ bool" where
"distintos xs = undefined"

text {*
---------------------------------------------------------------------
Ejercicio 10. Demostrar que el valor de "borraDups" verifica
"distintos".
---------------------------------------------------------------------
*}

lemma distintos_borraDups:
"distintos (borraDups xs)"
oops

end
</source>

GLC T2R2b

2018-07-15T11:57:26Z

Jalonso: Texto reemplazado: «lang="isar"» por «lang="isabelle"»

<source lang="isabelle">
header {* T2R2b: Argumentación en lógica de primer orden *}

theory T2R2b
imports Main
begin

text {* ---------------------------------------------------------------
Ejercicio 16. Formalizar, y decidir la corrección, del siguiente
argumento
Supongamos conocidos los siguientes hechos acerca del número de
aprobados de dos asignaturas A y B:
* Si todos los alumnos aprueban la asignatura A, entonces todos
aprueban la asignatura B.
* Si algún delegado de la clase aprueba A y B, entonces todos los
alumnos aprueban A.
* Si nadie aprueba B, entonces ningún delegado aprueba A.
* Si Manuel no aprueba B, entonces nadie aprueba B.
Por tanto, si Manuel es un delegado y aprueba la asignatura A,
entonces todos los alumnos aprueban las asignaturas A y B.
Usar A(x,y) para x aprueba la asignatura y
D(x) para x es delegado
m para Manuel
a para la asignatura A
b para la asignatura B
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_16a:
assumes "(∀x. A(x,a)) ⟶ (∀x. A(x,b))"
"(∃x. D(x) ∧ A(x,a) ∧ A(x,b)) ⟶ (∀x. A(x,a))"
"(∀x. ¬A(x,b)) ⟶ (∀x. D(x) ⟶ ¬A(x,a))"
"¬A(m,b) ⟶ (∀x. ¬A(x,b))"
shows "D(m) ∧ A(m,a) ⟶ (∀x. A(x,a) ∧ A(x,b))"
using assms
by blast

-- "La demostración estructurada es"
lemma ejercicio_16b:
assumes "(∀x. A(x,a)) ⟶ (∀x. A(x,b))"
"(∃x. D(x) ∧ A(x,a) ∧ A(x,b)) ⟶ (∀x. A(x,a))"
"(∀x. ¬A(x,b)) ⟶ (∀x. D(x) ⟶ ¬A(x,a))"
"¬A(m,b) ⟶ (∀x. ¬A(x,b))"
shows "D(m) ∧ A(m,a) ⟶ (∀x. A(x,a) ∧ A(x,b))"
proof
assume "D(m) ∧ A(m,a)"
hence "D(m)" ..
have "A(m,a)" using `D(m) ∧ A(m,a)` ..
have "A(m,b)"
proof (rule ccontr)
assume "¬A(m,b)"
with assms(4) have "∀x. ¬A(x,b)" ..
with assms(3) have "∀x. D(x) ⟶ ¬A(x,a)" ..
hence "D(m) ⟶ ¬A(m,a)" ..
hence "¬A(m,a)" using `D(m)` ..
thus False using `A(m,a)` ..
qed
with `A(m,a)` have "A(m,a) ∧ A(m,b)" ..
with `D(m)` have "D(m) ∧ A(m,a) ∧ A(m,b)" ..
hence "∃x. D(x) ∧ A(x,a) ∧ A(x,b)" ..
with assms(2) have "∀x. A(x,a)" ..
with assms(1) have "∀x. A(x,b)" ..
show "∀x. A(x,a) ∧ A(x,b)"
proof
fix c
show "A(c,a) ∧ A(c,b)"
proof
show "A(c,a)" using `∀x. A(x,a)` ..
next
show "A(c,b)" using `∀x. A(x,b)` ..
qed
qed
qed

-- "La demostración detallada es"
lemma ejercicio_16c:
assumes "(∀x. A(x,a)) ⟶ (∀x. A(x,b))"
"(∃x. D(x) ∧ A(x,a) ∧ A(x,b)) ⟶ (∀x. A(x,a))"
"(∀x. ¬A(x,b)) ⟶ (∀x. D(x) ⟶ ¬A(x,a))"
"¬A(m,b) ⟶ (∀x. ¬A(x,b))"
shows "D(m) ∧ A(m,a) ⟶ (∀x. A(x,a) ∧ A(x,b))"
proof (rule impI)
assume "D(m) ∧ A(m,a)"
hence "D(m)" by (rule conjunct1)
have "A(m,a)" using `D(m) ∧ A(m,a)` by (rule conjunct2)
have "A(m,b)"
proof (rule ccontr)
assume "¬A(m,b)"
with assms(4) have "∀x. ¬A(x,b)" by (rule mp)
with assms(3) have "∀x. D(x) ⟶ ¬A(x,a)" by (rule mp)
hence "D(m) ⟶ ¬A(m,a)" by (rule allE)
hence "¬A(m,a)" using `D(m)` by (rule mp)
thus False using `A(m,a)` by (rule notE)
qed
with `A(m,a)` have "A(m,a) ∧ A(m,b)" by (rule conjI)
with `D(m)` have "D(m) ∧ A(m,a) ∧ A(m,b)" by (rule conjI)
hence "∃x. D(x) ∧ A(x,a) ∧ A(x,b)" by (rule exI)
with assms(2) have "∀x. A(x,a)" by (rule mp)
with assms(1) have "∀x. A(x,b)" by (rule mp)
show "∀x. A(x,a) ∧ A(x,b)"
proof (rule allI)
fix c
show "A(c,a) ∧ A(c,b)"
proof (rule conjI)
show "A(c,a)" using `∀x. A(x,a)` by (rule allE)
next
show "A(c,b)" using `∀x. A(x,b)` by (rule allE)
qed
qed
qed

text {* ---------------------------------------------------------------
Ejercicio 17. Formalizar, y decidir la corrección, del siguiente
argumento
En cierto país oriental se ha celebrado la fase final del
campeonato mundial de fútbol. Cierto diario deportivo ha publicado
las siguientes estadísticas de tan magno acontecimiento:
* A todos los porteros que no vistieron camiseta negra les marcó un
gol algún delantero europeo.
* Algún portero jugó con botas blancas y sólo le marcaron goles
jugadores con botas blancas.
* Ningún portero se marcó un gol a sí mismo.
* Ningún jugador con botas blancas vistió camiseta negra.
Por tanto, algún delantero europeo jugó con botas blancas.
Usar P(x) para x es portero
D(x) para x es delantero europeo
N(x) para x viste camiseta negra
B(x) para x juega con botas blancas
M(x,y) para x marcó un gol a y
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_17a:
assumes "∀x. P(x) ∧ ¬N(x) ⟶ (∃y. D(y) ∧ M(y,x))"
"∃x. P(x) ∧ B(x) ∧ (∀y. M(y,x) ⟶ B(y))"
"¬(∃x. P(x) ∧ M(x,x))"
"¬(∃x. B(x) ∧ N(x))"
shows "∃x. D(x) ∧ B(x)"
using assms
by blast

-- "La demostración estructurada es"
lemma ejercicio_17b:
assumes "∀x. P(x) ∧ ¬N(x) ⟶ (∃y. D(y) ∧ M(y,x))"
"∃x. P(x) ∧ B(x) ∧ (∀y. M(y,x) ⟶ B(y))"
"¬(∃x. P(x) ∧ M(x,x))"
"¬(∃x. B(x) ∧ N(x))"
shows "∃x. D(x) ∧ B(x)"
proof -
obtain a where a: "P(a) ∧ B(a) ∧ (∀y. M(y,a) ⟶ B(y))"
using assms(2) ..
have "P(a) ∧ ¬N(a)"
proof
show "P(a)" using a ..
next
have "B(a) ∧ (∀y. M(y,a) ⟶ B(y))" using a ..
hence "B(a)" ..
have "∀x. ¬(B(x) ∧ N(x))" using assms(4) by (rule no_ex)
hence "¬(B(a) ∧ N(a))" ..
show "¬N(a)"
proof
assume "N(a)"
with `B(a)` have "B(a) ∧ N(a)" ..
with `¬(B(a) ∧ N(a))` show False ..
qed
qed
hence "∃y. D(y) ∧ M(y,a)"
proof -
have "P(a) ∧ ¬N(a) ⟶ (∃y. D(y) ∧ M(y,a))" using assms(1) ..
thus "∃y. D(y) ∧ M(y,a)" using `P(a) ∧ ¬N(a)` ..
qed
then obtain b where "D(b) ∧ M(b,a)" ..
have "D(b) ∧ B(b)"
proof
show "D(b)" using `D(b) ∧ M(b,a)` ..
next
have "M(b,a)" using `D(b) ∧ M(b,a)` ..
have "B(a) ∧ (∀y. M(y,a) ⟶ B(y))" using a ..
hence "∀y. M(y,a) ⟶ B(y)" ..
hence "M(b,a) ⟶ B(b)" ..
thus "B(b)" using `M(b,a)` ..
qed
thus "∃x. D(x) ∧ B(x)" ..
qed

-- "La demostración estructurada es"
lemma ejercicio_17c:
assumes "∀x. P(x) ∧ ¬N(x) ⟶ (∃y. D(y) ∧ M(y,x))"
"∃x. P(x) ∧ B(x) ∧ (∀y. M(y,x) ⟶ B(y))"
"¬(∃x. P(x) ∧ M(x,x))"
"¬(∃x. B(x) ∧ N(x))"
shows "∃x. D(x) ∧ B(x)"
proof -
obtain a where a: "P(a) ∧ B(a) ∧ (∀y. M(y,a) ⟶ B(y))"
using assms(2) by (rule exE)
have "P(a) ∧ ¬N(a)"
proof (rule conjI)
show "P(a)" using a by (rule conjunct1)
next
have "B(a) ∧ (∀y. M(y,a) ⟶ B(y))" using a by (rule conjunct2)
hence "B(a)" by (rule conjunct1)
have "∀x. ¬(B(x) ∧ N(x))" using assms(4) by (rule no_ex)
hence "¬(B(a) ∧ N(a))" by (rule allE)
show "¬N(a)"
proof (rule notI)
assume "N(a)"
with `B(a)` have "B(a) ∧ N(a)" by (rule conjI)
with `¬(B(a) ∧ N(a))` show False by (rule notE)
qed
qed
hence "∃y. D(y) ∧ M(y,a)"
proof -
have "P(a) ∧ ¬N(a) ⟶ (∃y. D(y) ∧ M(y,a))"
using assms(1) by (rule allE)
thus "∃y. D(y) ∧ M(y,a)" using `P(a) ∧ ¬N(a)` by (rule mp)
qed
then obtain b where "D(b) ∧ M(b,a)" by (rule exE)
have "D(b) ∧ B(b)"
proof (rule conjI)
show "D(b)" using `D(b) ∧ M(b,a)` by (rule conjunct1)
next
have "M(b,a)" using `D(b) ∧ M(b,a)` by (rule conjunct2)
have "B(a) ∧ (∀y. M(y,a) ⟶ B(y))" using a by (rule conjunct2)
hence "∀y. M(y,a) ⟶ B(y)" by (rule conjunct2)
hence "M(b,a) ⟶ B(b)" by (rule allE)
thus "B(b)" using `M(b,a)` by (rule mp)
qed
thus "∃x. D(x) ∧ B(x)" by (rule exI)
qed

text {* ---------------------------------------------------------------
Ejercicio 18. Formalizar, y decidir la corrección, del siguiente
argumento
Las relaciones de parentesco verifican la siguientes propiedades
generales:
* Si x es hermano de y, entonces y es hermano de x.
* Todo el mundo es hijo de alguien.
* Nadie es hijo del hermano de su padre.
* Cualquier padre de una persona es también padre de todos los
hermanos de esa persona.
* Nadie es hijo ni hermano de sí mismo.
Tenemos los siguientes miembros de la familia Peláez: Don Antonio,
Don Luis, Antoñito y Manolito y sabemos que Don Antonio y Don Luis
son hermanos, Antoñito y Manolito son hermanos, y Antoñito es hijo
de Don Antonio. Por tanto, Don Luis no es el padre de Manolito.
Usar A para Don Antonio
He(x,y) para x es hermano de y
Hi(x,y) para x es hijo de y
L para Don Luis
a para Antoñito
m para Manolito
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_18a:
assumes "∀x y. He(x,y) ⟶ He(y,x)"
"∀x. ∃y. Hi(x,y)"
"∀x y z. Hi(x,y) ∧ He(z,y) ⟶ ¬Hi(x,z)"
"∀x y. Hi(x,y) ⟶ (∀z. He(z,x) ⟶ Hi(z,y))"
"∀x. ¬Hi(x,x) ∧ ¬He(x,x)"
"He(A,L)"
"He(a,m)"
"Hi(a,A)"
shows "¬Hi(m,L)"
using assms
by blast

-- "La demostración estructurada es"
lemma ejercicio_18b:
assumes "∀x y. He(x,y) ⟶ He(y,x)"
"∀x. ∃y. Hi(x,y)"
"∀x y z. Hi(x,y) ∧ He(z,y) ⟶ ¬Hi(x,z)"
"∀x y. Hi(x,y) ⟶ (∀z. He(z,x) ⟶ Hi(z,y))"
"∀x. ¬Hi(x,x) ∧ ¬He(x,x)"
"He(A,L)"
"He(a,m)"
"Hi(a,A)"
shows "¬Hi(m,L)"
proof
assume "Hi(m,L)"
have "He(L,A)"
proof -
have "∀y. He(A,y) ⟶ He(y,A)" using assms(1) ..
hence "He(A,L) ⟶ He(L,A)" ..
thus "He(L,A)" using assms(6) ..
qed
have "Hi(a,L)"
proof -
have "∀y. Hi(m,y) ⟶ (∀z. He(z,m) ⟶ Hi(z,y))" using assms(4) ..
hence "Hi(m,L) ⟶ (∀z. He(z,m) ⟶ Hi(z,L))" ..
hence "∀z. He(z,m) ⟶ Hi(z,L)" using `Hi(m,L)` ..
hence "He(a,m) ⟶ Hi(a,L)" ..
thus "Hi(a,L)" using assms(7) ..
qed
have "¬Hi(a,L)"
proof -
have "Hi(a,A) ∧ He(L,A)" using assms(8) `He(L,A)` ..
have "∀y z. Hi(a,y) ∧ He(z,y) ⟶ ¬Hi(a,z)" using assms(3) ..
hence "∀z. Hi(a,A) ∧ He(z,A) ⟶ ¬Hi(a,z)" ..
hence "Hi(a,A) ∧ He(L,A) ⟶ ¬Hi(a,L)" ..
thus "¬Hi(a,L)" using `Hi(a,A) ∧ He(L,A)` ..
qed
thus False using `Hi(a,L)` ..
qed

-- "La demostración detallada es"
lemma ejercicio_18c:
assumes "∀x y. He(x,y) ⟶ He(y,x)"
"∀x. ∃y. Hi(x,y)"
"∀x y z. Hi(x,y) ∧ He(z,y) ⟶ ¬Hi(x,z)"
"∀x y. Hi(x,y) ⟶ (∀z. He(z,x) ⟶ Hi(z,y))"
"∀x. ¬Hi(x,x) ∧ ¬He(x,x)"
"He(A,L)"
"He(a,m)"
"Hi(a,A)"
shows "¬Hi(m,L)"
proof (rule notI)
assume "Hi(m,L)"
have "He(L,A)"
proof -
have "∀y. He(A,y) ⟶ He(y,A)" using assms(1) by (rule allE)
hence "He(A,L) ⟶ He(L,A)" by (rule allE)
thus "He(L,A)" using assms(6) by (rule mp)
qed
have "Hi(a,L)"
proof -
have "∀y. Hi(m,y) ⟶ (∀z. He(z,m) ⟶ Hi(z,y))"
using assms(4) by (rule allE)
hence "Hi(m,L) ⟶ (∀z. He(z,m) ⟶ Hi(z,L))" by (rule allE)
hence "∀z. He(z,m) ⟶ Hi(z,L)" using `Hi(m,L)` by (rule mp)
hence "He(a,m) ⟶ Hi(a,L)" by (rule allE)
thus "Hi(a,L)" using assms(7) by (rule mp)
qed
have "¬Hi(a,L)"
proof -
have "Hi(a,A) ∧ He(L,A)" using assms(8) `He(L,A)` by (rule conjI)
have "∀y z. Hi(a,y) ∧ He(z,y) ⟶ ¬Hi(a,z)"
using assms(3) by (rule allE)
hence "∀z. Hi(a,A) ∧ He(z,A) ⟶ ¬Hi(a,z)" by (rule allE)
hence "Hi(a,A) ∧ He(L,A) ⟶ ¬Hi(a,L)" by (rule allE)
thus "¬Hi(a,L)" using `Hi(a,A) ∧ He(L,A)` by (rule mp)
qed
thus False using `Hi(a,L)` by (rule notE)
qed

text {* ---------------------------------------------------------------
Ejercicio 19. [Problema del apisonador de Schubert (en inglés,
"Schubert’s steamroller")] Formalizar, y decidir la corrección, del
siguiente argumento
Si uno de los miembros del club afeita a algún otro (incluido a
sí mismo), entonces todos los miembros del club lo han afeitado
a él (aunque no necesariamente al mismo tiempo). Guido, Lorenzo,
Petruccio y Cesare pertenecen al club de barberos. Guido ha
afeitado a Cesare. Por tanto, Petruccio ha afeitado a Lorenzo.
Usar g para Guido
l para Lorenzo
p para Petruccio
c para Cesare
B(x) para x es un miembro del club de barberos
A(x,y) para x ha afeitado a y
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_19a:
assumes "∀x. B(x) ∧ (∃y. B(y) ∧ A(x,y)) ⟶ (∀z. B(z) ⟶ A(z,x))"
"B(g)"
"B(l)"
"B(p)"
"B(c)"
"A(g,c)"
shows "A(p,l)"
using assms
by meson

-- "La demostración estructurada es"
lemma ejercicio_19b:
assumes "∀x. B(x) ∧ (∃y. B(y) ∧ A(x,y)) ⟶ (∀z. B(z) ⟶ A(z,x))"
"B(g)"
"B(l)"
"B(p)"
"B(c)"
"A(g,c)"
shows "A(p,l)"
proof -
have "A(l,g)"
proof -
have "B(g) ∧ (∃y. B(y) ∧ A(g,y)) ⟶ (∀z. B(z) ⟶ A(z,g))"
using assms(1) ..
have "B(c) ∧ A(g,c)" using assms(5,6) ..
hence "(∃y. B(y) ∧ A(g,y))" ..
with assms(2) have "B(g) ∧ (∃y. B(y) ∧ A(g,y))" ..
with `B(g) ∧ (∃y. B(y) ∧ A(g,y)) ⟶ (∀z. B(z) ⟶ A(z,g))`
have "(∀z. B(z) ⟶ A(z,g))" ..
hence "B(l) ⟶ A(l,g)" ..
thus "A(l,g)" using assms(3) ..
qed
have "B(l) ∧ (∃y. B(y) ∧ A(l,y)) ⟶ (∀z. B(z) ⟶ A(z,l))"
using assms(1) ..
have "B(g) ∧ A(l,g)" using assms(2) `A(l,g)` ..
hence "(∃y. B(y) ∧ A(l,y))" ..
with assms(3) have "B(l) ∧ (∃y. B(y) ∧ A(l,y))" ..
with `B(l) ∧ (∃y. B(y) ∧ A(l,y)) ⟶ (∀z. B(z) ⟶ A(z,l))`
have "(∀z. B(z) ⟶ A(z,l))" ..
hence "B(p) ⟶ A(p,l)" ..
thus "A(p,l)" using assms(4) ..
qed

-- "La demostración detallada es"
lemma ejercicio_19c:
assumes "∀x. B(x) ∧ (∃y. B(y) ∧ A(x,y)) ⟶ (∀z. B(z) ⟶ A(z,x))"
"B(g)"
"B(l)"
"B(p)"
"B(c)"
"A(g,c)"
shows "A(p,l)"
proof -
have "A(l,g)"
proof -
have "B(g) ∧ (∃y. B(y) ∧ A(g,y)) ⟶ (∀z. B(z) ⟶ A(z,g))"
using assms(1) by (rule allE)
have "B(c) ∧ A(g,c)" using assms(5,6) by (rule conjI)
hence "(∃y. B(y) ∧ A(g,y))" by (rule exI)
with assms(2) have "B(g) ∧ (∃y. B(y) ∧ A(g,y))" by (rule conjI)
with `B(g) ∧ (∃y. B(y) ∧ A(g,y)) ⟶ (∀z. B(z) ⟶ A(z,g))`
have "(∀z. B(z) ⟶ A(z,g))" by (rule mp)
hence "B(l) ⟶ A(l,g)" by (rule allE)
thus "A(l,g)" using assms(3) by (rule mp)
qed
have "B(l) ∧ (∃y. B(y) ∧ A(l,y)) ⟶ (∀z. B(z) ⟶ A(z,l))"
using assms(1) by (rule allE)
have "B(g) ∧ A(l,g)" using assms(2) `A(l,g)` by (rule conjI)
hence "(∃y. B(y) ∧ A(l,y))" by (rule exI)
with assms(3) have "B(l) ∧ (∃y. B(y) ∧ A(l,y))" by (rule conjI)
with `B(l) ∧ (∃y. B(y) ∧ A(l,y)) ⟶ (∀z. B(z) ⟶ A(z,l))`
have "(∀z. B(z) ⟶ A(z,l))" by (rule mp)
hence "B(p) ⟶ A(p,l)" by (rule allE)
thus "A(p,l)" using assms(4) by (rule mp)
qed

text {* ---------------------------------------------------------------
Ejercicio 20. Formalizar, y decidir la corrección, del siguiente
argumento
Carlos afeita a todos los habitantes de Las Chinas que no se
afeitan a sí mismo y sólo a ellos. Carlos es un habitante de las
Chinas. Por consiguiente, Carlos no afeita a nadie.
Usar A(x,y) para x afeita a y
C(x) para x es un habitante de Las Chinas
c para Carlos
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_20a:
assumes "∀x. A(c,x) ⟷ C(x) ∧ ¬A(x,x)"
"C(c)"
shows "¬(∃x. A(c,x))"
using assms
by blast

-- "La demostración estructurada es"
lemma ejercicio_20b:
assumes "∀x. A(c,x) ⟷ C(x) ∧ ¬A(x,x)"
"C(c)"
shows "¬(∃x. A(c,x))"
proof -
have 1: "A(c,c) ⟷ C(c) ∧ ¬A(c,c)" using assms(1) ..
have "A(c,c)"
proof (rule ccontr)
assume "¬A(c,c)"
with assms(2) have "C(c) ∧ ¬A(c,c)" ..
with 1 have "A(c,c)" ..
with `¬A(c,c)` show False ..
qed
have "¬A(c,c)"
proof -
have "C(c) ∧ ¬A(c,c)" using 1 `A(c,c)` ..
thus "¬A(c,c)" ..
qed
thus "¬(∃x. A(c,x))" using `A(c,c)` ..
qed

-- "La demostración detallada es"
lemma ejercicio_20c:
assumes "∀x. A(c,x) ⟷ C(x) ∧ ¬A(x,x)"
"C(c)"
shows "¬(∃x. A(c,x))"
proof -
have 1: "A(c,c) ⟷ C(c) ∧ ¬A(c,c)" using assms(1) by (rule allE)
have "A(c,c)"
proof (rule ccontr)
assume "¬A(c,c)"
with assms(2) have "C(c) ∧ ¬A(c,c)" by (rule conjI)
with 1 have "A(c,c)" by (rule iffD2)
with `¬A(c,c)` show False by (rule notE)
qed
have "¬A(c,c)"
proof -
have "C(c) ∧ ¬A(c,c)" using 1 `A(c,c)` by (rule iffD1)
thus "¬A(c,c)" by (rule conjunct2)
qed
thus "¬(∃x. A(c,x))" using `A(c,c)` by (rule notE)
qed

text {* ---------------------------------------------------------------
Ejercicio 21. Formalizar, y decidir la corrección, del siguiente
argumento
Quien desprecia a todos los fanáticos desprecia también a todos los
políticos. Alguien no desprecia a un determinado político. Por
consiguiente, hay un fanático al que no todo el mundo desprecia.
Usar D(x,y) para x desprecia a y
F(x) para x es fanático
P(x) para x es político
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_21a:
assumes "∀x. (∀y. F(y) ⟶ D(x,y)) ⟶ (∀y. P(y) ⟶ D(x,y))"
"∃x y. P(y) ∧ ¬D(x,y)"
shows "∃x. F(x) ∧ ¬(∀y. D(y,x))"
using assms
by blast

-- "La demostración semiautomática es"
lemma ejercicio_21b:
assumes "∀x. (∀y. F(y) ⟶ D(x,y)) ⟶ (∀y. P(y) ⟶ D(x,y))"
"∃x y. P(y) ∧ ¬D(x,y)"
shows "∃x. F(x) ∧ ¬(∀y. D(y,x))"
proof -
obtain a where "∃y. P(y) ∧ ¬D(a,y)" using assms(2) ..
then obtain b where "P(b) ∧ ¬D(a,b)" ..
hence "¬(∀y. P(y) ⟶ D(a,y))" by auto
have "(∀y. F(y) ⟶ D(a,y)) ⟶ (∀y. P(y) ⟶ D(a,y))" using assms(1) ..
hence "¬(∀y. F(y) ⟶ D(a,y))" using `¬(∀y. P(y) ⟶ D(a,y))` by (rule mt)
hence "∃y. ¬(F(y) ⟶ D(a,y))" by (rule no_para_todo)
then obtain c where "¬(F(c) ⟶ D(a,c))" ..
hence "F(c) ∧ ¬(∀y. D(y,c))" by auto
thus "∃x. F(x) ∧ ¬(∀y. D(y,x))" ..
qed

-- "En la demostración estructurada usaremos el siguiente lema"
lemma no_implica:
assumes "¬(p ⟶ q)"
shows "p ∧ ¬q"
using assms
by auto

-- "La demostración estructurada del lema es"
lemma no_implica_1:
assumes "¬(p ⟶ q)"
shows "p ∧ ¬q"
proof
show "p"
proof (rule ccontr)
assume "¬p"
have "p ⟶ q"
proof
assume "p"
with `¬p` show "q" ..
qed
with assms show False ..
qed
next
show "¬q"
proof
assume "q"
have "p ⟶ q"
proof
assume "p"
show "q" using `q` .
qed
with assms show False ..
qed
qed

-- "La demostración detallada del lema es"
lemma no_implica_2:
assumes "¬(p ⟶ q)"
shows "p ∧ ¬q"
proof (rule conjI)
show "p"
proof (rule ccontr)
assume "¬p"
have "p ⟶ q"
proof (rule impI)
assume "p"
with `¬p` show "q" by (rule notE)
qed
with assms show False by (rule notE)
qed
next
show "¬q"
proof (rule notI)
assume "q"
have "p ⟶ q"
proof (rule impI)
assume "p"
show "q" using `q` by this
qed
with assms show False by (rule notE)
qed
qed

-- "La demostración estructurada es"
lemma ejercicio_21c:
assumes "∀x. (∀y. F(y) ⟶ D(x,y)) ⟶ (∀y. P(y) ⟶ D(x,y))"
"∃x y. P(y) ∧ ¬D(x,y)"
shows "∃x. F(x) ∧ ¬(∀y. D(y,x))"
proof -
obtain a where "∃y. P(y) ∧ ¬D(a,y)" using assms(2) ..
then obtain b where b: "P(b) ∧ ¬D(a,b)" ..
have "¬(∀y. P(y) ⟶ D(a,y))"
proof
assume "∀y. P(y) ⟶ D(a,y)"
hence "P(b) ⟶ D(a,b)" ..
have "P(b)" using b ..
with `P(b) ⟶ D(a,b)` have "D(a,b)" ..
have "¬D(a,b)" using b ..
thus False using `D(a,b)` ..
qed
have "(∀y. F(y) ⟶ D(a,y)) ⟶ (∀y. P(y) ⟶ D(a,y))" using assms(1) ..
hence "¬(∀y. F(y) ⟶ D(a,y))" using `¬(∀y. P(y) ⟶ D(a,y))` by (rule mt)
hence "∃y. ¬(F(y) ⟶ D(a,y))" by (rule no_para_todo)
then obtain c where c: "¬(F(c) ⟶ D(a,c))" ..
have "F(c) ∧ ¬(∀y. D(y,c))"
proof
have "F(c) ∧ ¬D(a,c)" using c by (rule no_implica)
thus "F(c)" ..
next
show "¬(∀y. D(y,c))"
proof
assume "∀y. D(y,c)"
hence "D(a,c)" ..
have "F(c) ∧ ¬D(a,c)" using c by (rule no_implica)
hence "¬D(a,c)" ..
thus False using `D(a,c)` ..
qed
qed
thus "∃x. F(x) ∧ ¬(∀y. D(y,x))" ..
qed

-- "La demostración detallada es"
lemma ejercicio_21d:
assumes "∀x. (∀y. F(y) ⟶ D(x,y)) ⟶ (∀y. P(y) ⟶ D(x,y))"
"∃x y. P(y) ∧ ¬D(x,y)"
shows "∃x. F(x) ∧ ¬(∀y. D(y,x))"
proof -
obtain a where "∃y. P(y) ∧ ¬D(a,y)" using assms(2) by (rule exE)
then obtain b where b: "P(b) ∧ ¬D(a,b)" by (rule exE)
have "¬(∀y. P(y) ⟶ D(a,y))"
proof (rule notI)
assume "∀y. P(y) ⟶ D(a,y)"
hence "P(b) ⟶ D(a,b)" by (rule allE)
have "P(b)" using b by (rule conjunct1)
with `P(b) ⟶ D(a,b)` have "D(a,b)" by (rule mp)
have "¬D(a,b)" using b by (rule conjunct2)
thus False using `D(a,b)` by (rule notE)
qed
have "(∀y. F(y) ⟶ D(a,y)) ⟶ (∀y. P(y) ⟶ D(a,y))"
using assms(1) by (rule allE)
hence "¬(∀y. F(y) ⟶ D(a,y))" using `¬(∀y. P(y) ⟶ D(a,y))` by (rule mt)
hence "∃y. ¬(F(y) ⟶ D(a,y))" by (rule no_para_todo)
then obtain c where c: "¬(F(c) ⟶ D(a,c))" by (rule exE)
have "F(c) ∧ ¬(∀y. D(y,c))"
proof (rule conjI)
have "F(c) ∧ ¬D(a,c)" using c by (rule no_implica)
thus "F(c)" by (rule conjunct1)
next
show "¬(∀y. D(y,c))"
proof (rule notI)
assume "∀y. D(y,c)"
hence "D(a,c)" by (rule allE)
have "F(c) ∧ ¬D(a,c)" using c by (rule no_implica)
hence "¬D(a,c)" by (rule conjunct2)
thus False using `D(a,c)` by (rule notE)
qed
qed
thus "∃x. F(x) ∧ ¬(∀y. D(y,x))" by (rule exI)
qed

text {* ---------------------------------------------------------------
Ejercicio 22. Formalizar, y decidir la corrección, del siguiente
argumento
El hombre puro ama todo lo que es puro. Por tanto, el hombre puro
se ama a sí mismo.
Usar A(x,y) para x ama a y
H(x) para x es un hombre
P(x) para x es puro
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_22a:
assumes "∀x. H(x) ∧ P(x) ⟶ (∀y. P(y) ⟶ A(x,y))"
shows "∀x. H(x) ∧ P(x) ⟶ A(x,x)"
using assms
by auto

-- "La demostración estructurada es"
lemma ejercicio_22b:
assumes "∀x. H(x) ∧ P(x) ⟶ (∀y. P(y) ⟶ A(x,y))"
shows "∀x. H(x) ∧ P(x) ⟶ A(x,x)"
proof
fix b
show "H(b) ∧ P(b) ⟶ A(b,b)"
proof
assume "H(b) ∧ P(b)"
hence "P(b)" ..
have "H(b) ∧ P(b) ⟶ (∀y. P(y) ⟶ A(b,y))" using assms ..
hence "∀y. P(y) ⟶ A(b,y)" using `H(b) ∧ P(b)` ..
hence "P(b) ⟶ A(b,b)" ..
thus "A(b,b)" using `P(b)` ..
qed
qed

-- "La demostración detallada es"
lemma ejercicio_22c:
assumes "∀x. H(x) ∧ P(x) ⟶ (∀y. P(y) ⟶ A(x,y))"
shows "∀x. H(x) ∧ P(x) ⟶ A(x,x)"
proof (rule allI)
fix b
show "H(b) ∧ P(b) ⟶ A(b,b)"
proof (rule impI)
assume "H(b) ∧ P(b)"
hence "P(b)" by (rule conjunct2)
have "H(b) ∧ P(b) ⟶ (∀y. P(y) ⟶ A(b,y))"
using assms by (rule allE)
hence "∀y. P(y) ⟶ A(b,y)" using `H(b) ∧ P(b)` by (rule mp)
hence "P(b) ⟶ A(b,b)" by (rule allE)
thus "A(b,b)" using `P(b)` by (rule mp)
qed
qed

text {* ---------------------------------------------------------------
Ejercicio 23. Formalizar, y decidir la corrección, del siguiente
argumento
Ningún socio del club está en deuda con el tesorero del club. Si
un socio del club no paga su cuota está en deuda con el tesorero
del club. Por tanto, si el tesorero del club es socio del club,
entonces paga su cuota.
Usar P(x) para x es socio del club
Q(x) para x paga su cuota
R(x) para x está en deuda con el tesorero
a para el tesorero del club
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_23a:
assumes "¬(∃x. P(x) ∧ R(x))"
"∀x. P(x) ∧ ¬Q(x) ⟶ R(x)"
shows "P(a) ⟶ Q(a)"
using assms
by auto

-- "La demostración estructurada es"
lemma ejercicio_23b:
assumes "¬(∃x. P(x) ∧ R(x))"
"∀x. P(x) ∧ ¬Q(x) ⟶ R(x)"
shows "P(a) ⟶ Q(a)"
proof
assume "P(a)"
show "Q(a)"
proof (rule ccontr)
assume "¬Q(a)"
with `P(a)` have "P(a) ∧ ¬Q(a)" ..
have "P(a) ∧ ¬Q(a) ⟶ R(a)" using assms(2) ..
hence "R(a)" using `P(a) ∧ ¬Q(a)` ..
with `P(a)` have "P(a) ∧ R(a)" ..
hence "∃x. P(x) ∧ R(x)" ..
with assms(1) show False ..
qed
qed

-- "La demostración detallada es"
lemma ejercicio_23c:
assumes "¬(∃x. P(x) ∧ R(x))"
"∀x. P(x) ∧ ¬Q(x) ⟶ R(x)"
shows "P(a) ⟶ Q(a)"
proof (rule impI)
assume "P(a)"
show "Q(a)"
proof (rule ccontr)
assume "¬Q(a)"
with `P(a)` have "P(a) ∧ ¬Q(a)" by (rule conjI)
have "P(a) ∧ ¬Q(a) ⟶ R(a)" using assms(2) by (rule allE)
hence "R(a)" using `P(a) ∧ ¬Q(a)` by (rule mp)
with `P(a)` have "P(a) ∧ R(a)" by (rule conjI)
hence "∃x. P(x) ∧ R(x)" by (rule exI)
with assms(1) show False by (rule notE)
qed
qed

text {* ---------------------------------------------------------------
Ejercicio 24. Formalizar, y decidir la corrección, del siguiente
argumento
1. Los lobos, zorros, pájaros, orugas y caracoles son animales y
existen algunos ejemplares de estos animales.
2. También hay algunas semillas y las semillas son plantas.
3. A todo animal le gusta o bien comer todo tipo de plantas o bien
le gusta comerse a todos los animales más pequeños que él mismo
que gustan de comer algunas plantas.
4. Las orugas y los caracoles son mucho más pequeños que los
pájaros, que son mucho más pequeños que los zorros que a su vez
son mucho más pequeños que los lobos.
5. A los lobos no les gusta comer ni zorros ni semillas, mientras
que a los pájaros les gusta comer orugas pero no caracoles.
6. Las orugas y los caracoles gustan de comer algunas plantas.
7. Luego, existe un animal al que le gusta comerse un animal al que
le gusta comer semillas.
Usar A(x) para x es un animal
Ca(x) para x es un caracol
Co(x,y) para x le gusta comerse a y
L(x) para x es un lobo
M(x,y) para x es más pequeño que y
Or(x) para x es una oruga
Pa(x) para x es un pájaro
Pl(x) para x es una planta
S(x) para x es una semilla
Z(x) para x es un zorro
------------------------------------------------------------------ *}

-- "La demostración automática es"
lemma ejercicio_24a:
assumes
(* 1 *) "∀x. L(x) ⟶ A(x)"
(* 2 *) "∀x. Z(x) ⟶ A(x)"
(* 3 *) "∀x. Pa(x) ⟶ A(x)"
(* 4 *) "∀x. Or(x) ⟶ A(x)"
(* 5 *) "∀x. Ca(x) ⟶ A(x)"
(* 6 *) "∃x. L(x)"
(* 7 *) "∃x. Z(x)"
(* 8 *) "∃x. Pa(x)"
(* 9 *) "∃x. Or(x)"
(* 10 *) "∃x. Ca(x)"
(* 11 *) "∃x. S(x)"
(* 12 *) "∀x. S(x) ⟶ Pl(x)"
(* 13 *) "∀x. A(x) ⟶
(∀y. Pl(y) ⟶ Co(x,y)) ∨
(∀y. A(y) ∧ M(y,x) ∧ (∃z. Pl(z) ∧ Co(y,z)) ⟶ Co(x,y))"
(* 14 *) "∀x y. Pa(y) ∧ (Ca(x) ∨ Or(x)) ⟶ M(x,y)"
(* 15 *) "∀x y. Pa(x) ∧ Z(y) ⟶ M(x,y)"
(* 16 *) "∀x y. Z(x) ∧ L(y) ⟶ M(x,y)"
(* 17 *) "∀x y. L(x) ∧ (Z(y)∨ S(y)) ⟶ ¬Co(x,y)"
(* 18 *) "∀x y. Pa(x) ∧ Or(y) ⟶ Co(x,y)"
(* 19 *) "∀x y. Pa(x) ∧ Ca(y) ⟶ ¬Co(x,y)"
(* 20 *) "∀x. Or(x) ∨ Ca(x) ⟶ (∃y. Pl(y) ∧ Co(x,y))"
shows
"∃x y. A(x) ∧ A(y) ∧ (∃z. S(z) ∧ Co(y,z) ∧ Co(x,y))"
using assms
by meson

-- "La demostración semiautomática es"
lemma ejercicio_24b:
assumes
(* 1 *) "∀x. L(x) ⟶ A(x)"
(* 2 *) "∀x. Z(x) ⟶ A(x)"
(* 3 *) "∀x. Pa(x) ⟶ A(x)"
(* 4 *) "∀x. Or(x) ⟶ A(x)"
(* 5 *) "∀x. Ca(x) ⟶ A(x)"
(* 6 *) "∃x. L(x)"
(* 7 *) "∃x. Z(x)"
(* 8 *) "∃x. Pa(x)"
(* 9 *) "∃x. Or(x)"
(* 10 *) "∃x. Ca(x)"
(* 11 *) "∃x. S(x)"
(* 12 *) "∀x. S(x) ⟶ Pl(x)"
(* 13 *) "∀x. A(x) ⟶
(∀y. Pl(y) ⟶ Co(x,y)) ∨
(∀y. A(y) ∧ M(y,x) ∧ (∃z. Pl(z) ∧ Co(y,z)) ⟶ Co(x,y))"
(* 14 *) "∀x y. Pa(y) ∧ (Ca(x) ∨ Or(x)) ⟶ M(x,y)"
(* 15 *) "∀x y. Pa(x) ∧ Z(y) ⟶ M(x,y)"
(* 16 *) "∀x y. Z(x) ∧ L(y) ⟶ M(x,y)"
(* 17 *) "∀x y. L(x) ∧ (Z(y)∨ S(y)) ⟶ ¬Co(x,y)"
(* 18 *) "∀x y. Pa(x) ∧ Or(y) ⟶ Co(x,y)"
(* 19 *) "∀x y. Pa(x) ∧ Ca(y) ⟶ ¬Co(x,y)"
(* 20 *) "∀x. Or(x) ∨ Ca(x) ⟶ (∃y. Pl(y) ∧ Co(x,y))"
shows
"∃x y. A(x) ∧ A(y) ∧ (∃z. S(z) ∧ Co(y,z) ∧ Co(x,y))"
proof -
obtain l where l: "L(l)" using assms(6) ..
obtain z where z: "Z(z)" using assms(7) ..
obtain p where p: "Pa(p)" using assms(8) ..
obtain c where c: "Ca(c)" using assms(10) ..
obtain s where s: "S(s)" using assms(11) ..
have 1: "Co(p,s)" using p c s assms(3,5,12,13,14,19,20) by meson
have 2: "¬Co(z,s)" using z l s assms(1,2,12,16,17,13) by meson
have 3: "M(p,z)" using p z assms(15) by auto
have 4: "Co(z,p)" using z p s 1 2 3 assms(2,3,12,13) by meson
hence "Co(z,p) ∧ Co(p,s)" using 1 ..
thus "∃x y. A(x) ∧ A(y) ∧ (∃z. S(z) ∧ Co(y,z) ∧ Co(x,y))"
using z p s assms(2,3) by meson
qed

lemma instancia:
assumes "∀x. P(x) ⟶ Q(x)"
"P(a)"
shows "Q(a)"
proof -
have "P(a) ⟶ Q(a)" using assms(1) ..
thus "Q(a)" using assms(2) ..
qed

lemma mt2:
assumes "p ∧ q ∧ r ⟶ s"
"p"
"q"
"¬s"
shows "¬r"
proof
assume "r"
with `q` have "q ∧ r" ..
with `p` have "p ∧ q ∧ r" ..
with assms(1) have "s" ..
with `¬s` show False ..
qed

lemma mp3:
assumes "p ∧ q ∧ r ⟶ s"
"p"
"q"
"r"
shows "s"
proof -
have "q ∧ r" using assms(3,4) ..
with `p` have "p ∧ q ∧ r" ..
with assms(1) show "s" ..
qed

lemma conjI3:
assumes "p"
"q"
"r"
shows "p ∧ q ∧ r"
proof -
have "q ∧ r" using assms(2,3) ..
with `p` show "p ∧ q ∧ r" ..
qed

-- "La demostración estructurada es"
lemma ejercicio_24c:
assumes
(* 1 *) "∀x. L(x) ⟶ A(x)"
(* 2 *) "∀x. Z(x) ⟶ A(x)"
(* 3 *) "∀x. Pa(x) ⟶ A(x)"
(* 4 *) "∀x. Or(x) ⟶ A(x)"
(* 5 *) "∀x. Ca(x) ⟶ A(x)"
(* 6 *) "∃x. L(x)"
(* 7 *) "∃x. Z(x)"
(* 8 *) "∃x. Pa(x)"
(* 9 *) "∃x. Or(x)"
(* 10 *) "∃x. Ca(x)"
(* 11 *) "∃x. S(x)"
(* 12 *) "∀x. S(x) ⟶ Pl(x)"
(* 13 *) "∀x. A(x) ⟶
(∀y. Pl(y) ⟶ Co(x,y)) ∨
(∀y. A(y) ∧ M(y,x) ∧ (∃z. Pl(z) ∧ Co(y,z)) ⟶ Co(x,y))"
(* 14 *) "∀x y. Pa(y) ∧ (Ca(x) ∨ Or(x)) ⟶ M(x,y)"
(* 15 *) "∀x y. Pa(x) ∧ Z(y) ⟶ M(x,y)"
(* 16 *) "∀x y. Z(x) ∧ L(y) ⟶ M(x,y)"
(* 17 *) "∀x y. L(x) ∧ (Z(y)∨ S(y)) ⟶ ¬Co(x,y)"
(* 18 *) "∀x y. Pa(x) ∧ Or(y) ⟶ Co(x,y)"
(* 19 *) "∀x y. Pa(x) ∧ Ca(y) ⟶ ¬Co(x,y)"
(* 20 *) "∀x. Or(x) ∨ Ca(x) ⟶ (∃y. Pl(y) ∧ Co(x,y))"
shows
"∃x y. A(x) ∧ A(y) ∧ (∃z. S(z) ∧ Co(y,z) ∧ Co(x,y))"
proof -
obtain l where l: "L(l)" using assms(6) ..
obtain z where z: "Z(z)" using assms(7) ..
obtain p where p: "Pa(p)" using assms(8) ..
obtain c where c: "Ca(c)" using assms(10) ..
obtain s where s: "S(s)" using assms(11) ..
have 1: "Co(p,s)"
proof -
have "¬Co(p,c)"
proof -
have "Pa(p) ∧ Ca(c)" using p c ..
have "∀y. Pa(p) ∧ Ca(y) ⟶ ¬Co(p,y)" using assms(19) ..
hence "Pa(p) ∧ Ca(c) ⟶ ¬Co(p,c)" ..
thus "¬Co(p,c)" using `Pa(p) ∧ Ca(c)` ..
qed
have "∃y. Pl(y) ∧ Co(c,y)"
proof -
have "Or(c) ∨ Ca(c)" using c ..
have "Or(c) ∨ Ca(c) ⟶ (∃y. Pl(y) ∧ Co(c,y))" using assms(20) ..
thus "∃y. Pl(y) ∧ Co(c,y)" using `Or(c) ∨ Ca(c)` ..
qed
have "M(c,p)"
proof -
have "∀y. Pa(y) ∧ (Ca(c) ∨ Or(c)) ⟶ M(c,y)" using assms(14) ..
hence "Pa(p) ∧ (Ca(c) ∨ Or(c)) ⟶ M(c,p)" ..
have "Ca(c) ∨ Or(c)" using c ..
with p have "Pa(p) ∧ (Ca(c) ∨ Or(c))" ..
with `Pa(p) ∧ (Ca(c) ∨ Or(c)) ⟶ M(c,p)` show "M(c,p)" ..
qed
show "Co(p,s)"
proof -
have "A(p)" using assms(3) p by (rule instancia)
have "A(p) ⟶ (∀y. Pl(y) ⟶ Co(p,y)) ∨
(∀y. A(y) ∧ M(y,p) ∧ (∃z. Pl(z) ∧ Co(y,z)) ⟶ Co(p,y))"
using assms(13) ..
hence "(∀y. Pl(y) ⟶ Co(p,y)) ∨
(∀y. A(y) ∧ M(y,p) ∧ (∃z. Pl(z) ∧ Co(y,z)) ⟶ Co(p,y))"
using `A(p)` ..
thus "Co(p,s)"
proof
assume "∀y. Pl(y) ⟶ Co(p,y)"
hence "Pl(s) ⟶ Co(p,s)" ..
have "Pl(s)" using assms(12) s by (rule instancia)
with `Pl(s) ⟶ Co(p,s)` show "Co(p,s)" ..
next
assume "∀y. A(y) ∧ M(y,p) ∧ (∃z. Pl(z) ∧ Co(y,z)) ⟶ Co(p,y)"
hence "A(c) ∧ M(c,p) ∧ (∃z. Pl(z) ∧ Co(c,z)) ⟶ Co(p,c)" ..
have "Co(p,c)"
proof -
have "A(c)" using assms(5) c by (rule instancia)
have "M(c,p) ∧ (∃z. Pl(z) ∧ Co(c,z))"
using `M(c,p)` `∃z. Pl(z) ∧ Co(c,z)` ..
with `A(c)` have "A(c) ∧ M(c,p) ∧ (∃z. Pl(z) ∧ Co(c,z))" ..
with `A(c) ∧ M(c,p) ∧ (∃z. Pl(z) ∧ Co(c,z)) ⟶ Co(p,c)`
show "Co(p,c)" ..
qed
with `¬Co(p,c)` show "Co(p,s)" ..
qed
qed
qed
have 2: "¬Co(z,s)"
proof -
have "M(z,l)"
proof -
have "Z(z) ∧ L(l)" using z l ..
have "∀y. Z(z) ∧ L(y) ⟶ M(z,y)" using assms(16) ..
hence "Z(z) ∧ L(l) ⟶ M(z,l)" ..
thus "M(z,l)" using `Z(z) ∧ L(l)` ..
qed
have "¬Co(l,z)"
proof -
have "∀y. L(l) ∧ (Z(y)∨ S(y)) ⟶ ¬Co(l,y)" using assms(17) ..
hence "L(l) ∧ (Z(z)∨ S(z)) ⟶ ¬Co(l,z)" ..
have "Z(z)∨ S(z)" using z ..
with l have "L(l) ∧ (Z(z)∨ S(z))" ..
with `L(l) ∧ (Z(z)∨ S(z)) ⟶ ¬Co(l,z)` show "¬Co(l,z)" ..
qed
have "¬Co(l,s)"
proof -
have "∀y. L(l) ∧ (Z(y)∨ S(y)) ⟶ ¬Co(l,y)" using assms(17) ..
hence "L(l) ∧ (Z(s)∨ S(s)) ⟶ ¬Co(l,s)" ..
have "Z(s)∨ S(s)" using s ..
with l have "L(l) ∧ (Z(s)∨ S(s))" ..
with `L(l) ∧ (Z(s)∨ S(s)) ⟶ ¬Co(l,s)` show "¬Co(l,s)" ..
qed
show "¬Co(z,s)"
proof -
have "A(l)" using assms(1) l by (rule instancia)
have "A(l) ⟶ (∀y. Pl(y) ⟶ Co(l,y)) ∨
(∀y. A(y) ∧ M(y,l) ∧ (∃z. Pl(z) ∧ Co(y,z)) ⟶ Co(l,y))"
using assms(13) ..
hence "(∀y. Pl(y) ⟶ Co(l,y)) ∨
(∀y. A(y) ∧ M(y,l) ∧ (∃z. Pl(z) ∧ Co(y,z)) ⟶ Co(l,y))"
using `A(l)` ..
thus "¬Co(z,s)"
proof
assume "∀y. Pl(y) ⟶ Co(l,y)"
hence "Pl(s) ⟶ Co(l,s)" ..
have "Pl(s)" using assms(12) s by (rule instancia)
with `Pl(s) ⟶ Co(l,s)` have "Co(l,s)" ..
with `¬Co(l,s)` show "¬Co(z,s)" ..
next
assume "∀y. A(y) ∧ M(y,l) ∧ (∃u. Pl(u) ∧ Co(y,u)) ⟶ Co(l,y)"
hence zl: "A(z) ∧ M(z,l) ∧ (∃u. Pl(u) ∧ Co(z,u)) ⟶ Co(l,z)" ..
have "A(z)" using assms(2) z by (rule instancia)
have "¬(∃u. Pl(u) ∧ Co(z,u))"
using zl `A(z)` `M(z,l)` `¬Co(l,z)` by (rule mt2)
show "¬Co(z,s)"
proof
assume "Co(z,s)"
have "Pl(s)" using assms(12) s by (rule instancia)
hence "Pl(s) ∧ Co(z,s)" using `Co(z,s)` ..
hence "∃u. Pl(u) ∧ Co(z,u)" ..
with `¬(∃u. Pl(u) ∧ Co(z,u))` show False ..
qed
qed
qed
qed
have 3: "M(p,z)"
proof -
have "Pa(p) ∧ Z(z)" using p z ..
have "∀y. Pa(p) ∧ Z(y) ⟶ M(p,y)" using assms(15) ..
hence "Pa(p) ∧ Z(z) ⟶ M(p,z)" ..
thus "M(p,z)" using `Pa(p) ∧ Z(z)` ..
qed
have 4: "Co(z,p)"
proof -
have "A(z)" using assms(2) z by (rule instancia)
have "A(z) ⟶ (∀y. Pl(y) ⟶ Co(z,y)) ∨
(∀y. A(y) ∧ M(y,z) ∧ (∃u. Pl(u) ∧ Co(y,u)) ⟶ Co(z,y))"
using assms(13) ..
hence "(∀y. Pl(y) ⟶ Co(z,y)) ∨
(∀y. A(y) ∧ M(y,z) ∧ (∃u. Pl(u) ∧ Co(y,u)) ⟶ Co(z,y))"
using `A(z)` ..
thus "Co(z,p)"
proof
assume "∀y. Pl(y) ⟶ Co(z,y)"
hence "Pl(s) ⟶ Co(z,s)" ..
have "Pl(s)" using assms(12) s by (rule instancia)
with `Pl(s) ⟶ Co(z,s)` have "Co(z,s)" ..
with `¬Co(z,s)` show "Co(z,p)" ..
next
assume "∀y. A(y) ∧ M(y,z) ∧ (∃u. Pl(u) ∧ Co(y,u)) ⟶ Co(z,y)"
hence pz: "A(p) ∧ M(p,z) ∧ (∃u. Pl(u) ∧ Co(p,u)) ⟶ Co(z,p)" ..
have "A(p)" using assms(3) p by (rule instancia)
have "∃u. Pl(u) ∧ Co(p,u)"
proof -
have "Pl(s)" using assms(12) s by (rule instancia)
hence "Pl(s) ∧ Co(p,s)" using `Co(p,s)` ..
thus "∃u. Pl(u) ∧ Co(p,u)" ..
qed
show "Co(z,p)" using pz `A(p)` `M(p,z)` `∃u. Pl(u) ∧ Co(p,u)`
by (rule mp3)
qed
qed
hence "Co(z,p) ∧ Co(p,s)" using 1 ..
show "∃x y. A(x) ∧ A(y) ∧ (∃u. S(u) ∧ Co(y,u) ∧ Co(x,y))"
proof -
have "A(z)" using assms(2) z by (rule instancia)
have "A(p)" using assms(3) p by (rule instancia)
have "S(s) ∧ Co(p,s) ∧ Co(z,p)" using s `Co(p,s)` `Co(z,p)`
by (rule conjI3)
hence "∃u. S(u) ∧ Co(p,u) ∧ Co(z,p)" ..
have "A(z) ∧ A(p) ∧ (∃u. S(u) ∧ Co(p,u) ∧ Co(z,p))"
using `A(z)` `A(p)` `∃u. S(u) ∧ Co(p,u) ∧ Co(z,p)`
by (rule conjI3)
hence "∃y. A(z) ∧ A(y) ∧ (∃u. S(u) ∧ Co(y,u) ∧ Co(z,y))" ..
thus "∃x y. A(x) ∧ A(y) ∧ (∃u. S(u) ∧ Co(y,u) ∧ Co(x,y))" ..
qed
qed

end
</source>

RA12 Relación 13

2018-07-15T11:55:27Z

Jalonso: Texto reemplazado: «"isar"» por «"isabelle"»

<source lang="isabelle">
header {* R13: Número de elementos válidos *}

theory R13
imports Main
begin

text {*
---------------------------------------------------------------------
Ejercicio 1. Definir la función
cuentaP :: "('a ⇒ bool) ⇒ 'a list ⇒ nat"
tal que (cuentaP Q xs) es el número de elementos de la lista xs que
satisfacen el predicado Q. Por ejemplo,
cuentaP (λx. 2<x) [1,3,4,0,5] = 3
---------------------------------------------------------------------
*}

fun cuentaP :: "('a ⇒ bool) ⇒ 'a list ⇒ nat" where
"cuentaP Q xs = undefined"

text {*
---------------------------------------------------------------------
Ejercicio 2. Demostrar o refutar:
cuentaP P (xs @ ys) = cuentaP P xs + cuentaP P ys*
---------------------------------------------------------------------
*}

lemma cuentaP_append_auto:
"cuentaP P (xs @ ys) = cuentaP P xs + cuentaP P ys"
oops

text {*
---------------------------------------------------------------------
Ejercicio 3. Demostrar que el número de elementos de una lista que
cumplen una determinada propiedad es el mismo que el de esa lista
invertida.
---------------------------------------------------------------------
*}

lemma cuentaP_rev:
"cuentaP P xs = cuentaP P (rev xs)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 4. Encontrar y demostrar una relación entre las funciones
filter y cuentaP.
---------------------------------------------------------------------
*}

end
</source>

RA12 Relación 11

2018-07-15T11:55:20Z

Jalonso: Texto reemplazado: «"isar"» por «"isabelle"»

<source lang="isabelle">
header {* R11: Sustitución, inversión y eliminación *}

theory R11
imports Main
begin

section {* Sustitución, inversión y eliminación *}

text {*
---------------------------------------------------------------------
Ejercicio 1. Definir la función
sust :: "'a ⇒ 'a ⇒ 'a list ⇒ 'a list"
tal que (sust x y zs) es la lista obtenida sustituyendo cada
occurrencia de x por y en la lista zs. Por ejemplo,
sust (1::nat) 2 [1,2,3,4,1,2,3,4] = [2,2,3,4,2,2,3,4]
---------------------------------------------------------------------
*}

fun sust :: "'a ⇒ 'a ⇒ 'a list ⇒ 'a list" where
"sust x y zs = undefined"

text {*
---------------------------------------------------------------------
Ejercicio 2. Demostrar o refutar:
sust x y (xs@ys) = (sust x y xs)@(sust x y ys)"
---------------------------------------------------------------------
*}

lemma sust_append:
"sust x y (xs@ys) = (sust x y xs)@(sust x y ys)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 3. Demostrar o refutar:
rev (sust x y zs) = sust x y (rev zs)
---------------------------------------------------------------------
*}

lemma rev_sust:
"rev(sust x y zs) = sust x y (rev zs)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 4. Demostrar o refutar:
sust x y (sust u v zs) = sust u v (sust x y zs)
---------------------------------------------------------------------
*}

lemma
"sust x y (sust u v zs) = sust u v (sust x y zs)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 5. Demostrar o refutar:
sust y z (sust x y zs) = sust x z zs
---------------------------------------------------------------------
*}

lemma
"sust y z (sust x y zs) = sust x z zs"
oops

text {*
---------------------------------------------------------------------
Ejercicio 6. Definir la función
borra :: "'a ⇒ 'a list ⇒ 'a list"
tal que (borra x ys) es la lista obtenida borrando la primera
ocurrencia del elemento x en la lista ys. Por ejemplo,
borra (2::nat) [1,2,3,2] = [1,3,2]

Nota: La función borra es equivalente a la predefinida remove1.
---------------------------------------------------------------------
*}

fun borra :: "'a ⇒ 'a list ⇒ 'a list" where
"borra x ys = undefined"

text {*
---------------------------------------------------------------------
Ejercicio 7. Definir la función
borraTodas :: "'a ⇒ 'a list ⇒ 'a list"
tal que (borraTodas x ys) es la lista obtenida borrando todas las
ocurrencias del elemento x en la lista ys. Por ejemplo,
borraTodas (2::nat) [1,2,3,2] = [1,3]
---------------------------------------------------------------------
*}

fun borraTodas :: "'a ⇒ 'a list ⇒ 'a list" where
"borraTodas x ys = undefined"

text {*
---------------------------------------------------------------------
Ejercicio 8. Demostrar o refutar:
borra x (borraTodas x xs) = borraTodas x xs
---------------------------------------------------------------------
*}

lemma
"borra x (borraTodas x xs) = borraTodas x xs"
oops

text {*
---------------------------------------------------------------------
Ejercicio 9. Demostrar o refutar:
borraTodas x (borraTodas x xs) = borraTodas x xs
---------------------------------------------------------------------
*}

lemma
"borraTodas x (borraTodas x xs) = borraTodas x xs"
oops

text {*
---------------------------------------------------------------------
Ejercicio 10. Demostrar o refutar:
borraTodas x (borra x xs) = borraTodas x xs
---------------------------------------------------------------------
*}

lemma
"borraTodas x (borra x xs) = borraTodas x xs"
oops

text {*
---------------------------------------------------------------------
Ejercicio 11. Demostrar o refutar:
borra x (borra y xs) = borra y (borra x xs)
---------------------------------------------------------------------
*}

lemma
"borra x (borra y xs) = borra y (borra x xs)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 12. Demostrar o refutar el teorema:
borraTodas x (borra y xs) = borra y (borraTodas x xs)
---------------------------------------------------------------------
*}

lemma
"borraTodas x (borra y xs) = borra y (borraTodas x xs)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 13. Demostrar o refutar:
borra y (sust x y xs) = borra x xs
---------------------------------------------------------------------
*}

lemma
"borra y (sust x y xs) = borra x xs"
oops

text {*
---------------------------------------------------------------------
Ejercicio 14. Demostrar o refutar:
borraTodas y (sust x y xs) = borraTodas x xs"
---------------------------------------------------------------------
*}

lemma
"borraTodas y (sust x y xs) = borraTodas x xs"
oops

text {*
---------------------------------------------------------------------
Ejercicio 15. Demostrar o refutar:
sust x y (borraTodas x zs) = borraTodas x zs
---------------------------------------------------------------------
*}

lemma
"sust x y (borraTodas x zs) = borraTodas x zs"
oops

text {*
---------------------------------------------------------------------
Ejercicio 16. Demostrar o refutar:
sust x y (borraTodas z zs) = borraTodas z (sust x y zs)
---------------------------------------------------------------------
*}

lemma
"sust x y (borraTodas z zs) = borraTodas z (sust x y zs)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 17. Demostrar o refutar:
rev (borra x xs) = borra x (rev xs)
---------------------------------------------------------------------
*}

lemma
"rev (borra x xs) = borra x (rev xs)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 18. Demostrar o refutar el teorema:
borraTodas x (xs@ys) = (borraTodas x xs)@(borraTodas x ys)
---------------------------------------------------------------------
*}

lemma
"borraTodas x (xs@ys) = (borraTodas x xs)@(borraTodas x ys)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 19. Demostrar o refutar el teorema:
rev (borraTodas x xs) = borraTodas x (rev xs)
---------------------------------------------------------------------
*}

lemma
"rev (borraTodas x xs) = borraTodas x (rev xs)"
oops

end
</source>

RA12 Relación 10

2018-07-15T11:52:14Z

Jalonso: Texto reemplazado: «"isar"» por «"isabelle"»

<source lang="isabelle">
header {* R10: Cuantificadores sobre listas *}

theory R10
imports Main
begin

text {*
---------------------------------------------------------------------
Ejercicio 1. Definir la función
todos :: ('a ⇒ bool) ⇒ 'a list ⇒ bool
tal que (todos p xs) se verifica si todos los elementos de la lista
xs cumplen la propiedad p. Por ejemplo, se verifica
todos (λx. 1<length x) [[2,1,4],[1,3]]
¬todos (λx. 1<length x) [[2,1,4],[3]]

Nota: La función todos es equivalente a la predefinida list_all.
---------------------------------------------------------------------
*}

fun todos :: "('a ⇒ bool) ⇒ 'a list ⇒ bool" where
"todos p xs = undefined"

text {*
---------------------------------------------------------------------
Ejercicio 2. Definir la función
algunos :: ('a ⇒ bool) ⇒ 'a list ⇒ bool
tal que (algunos p xs) se verifica si algunos elementos de la lista
xs cumplen la propiedad p. Por ejemplo, se verifica
algunos (λx. 1<length x) [[2,1,4],[3]]
¬algunos (λx. 1<length x) [[],[3]]"

Nota: La función algunos es equivalente a la predefinida list_ex.
---------------------------------------------------------------------
*}

fun algunos :: "('a ⇒ bool) ⇒ 'a list ⇒ bool" where
"algunos p xs = undefined"

text {*
---------------------------------------------------------------------
Ejercicio 3. Demostrar o refutar:
todos (λx. P x ∧ Q x) xs = (todos P xs ∧ todos Q xs)
---------------------------------------------------------------------
*}

lemma "todos (λx. P x ∧ Q x) xs = (todos P xs ∧ todos Q xs)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 4. Demostrar o refutar:
todos P (x @ y) = (todos P x ∧ todos P y)
---------------------------------------------------------------------
*}

lemma todos_append:
"todos P (x @ y) = (todos P x ∧ todos P y)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 5. Demostrar o refutar:
todos P (rev xs) = todos P xs
---------------------------------------------------------------------
*}

lemma "todos P (rev xs) = todos P xs"
oops

text {*
---------------------------------------------------------------------
Ejercicio 6. Demostrar o refutar:
algunos (λx. P x ∧ Q x) xs = (algunos P xs ∧ algunos Q xs)
---------------------------------------------------------------------
*}

lemma "algunos (λx. P x ∧ Q x) xs = (algunos P xs ∧ algunos Q xs)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 7. Demostrar o refutar:
algunos P (map f xs) = algunos (P ∘ f) xs
---------------------------------------------------------------------
*}

lemma "algunos P (map f xs) = algunos (P o f) xs"
oops

text {*
---------------------------------------------------------------------
Ejercicio 8. Demostrar o refutar:
algunos P (xs @ ys) = (algunos P xs ∨ algunos P ys)
---------------------------------------------------------------------
*}

lemma algunos_append:
"algunos P (xs @ ys) = (algunos P xs ∨ algunos P ys)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 9. Demostrar o refutar:
algunos P (rev xs) = algunos P xs
---------------------------------------------------------------------
*}

lemma "algunos P (rev xs) = algunos P xs"
oops

text {*
---------------------------------------------------------------------
Ejercicio 10. Encontrar un término no trivial Z tal que sea cierta la
siguiente ecuación:
algunos (λx. P x ∨ Q x) xs = Z
---------------------------------------------------------------------
*}

text {*
---------------------------------------------------------------------
Ejercicio 11. Demostrar o refutar:
algunos P xs = (¬ todos (λx. (¬ P x)) xs)
---------------------------------------------------------------------
*}

lemma "algunos P xs = (¬ todos (λx. (¬ P x)) xs)"
by (induct xs) simp_all

text {*
---------------------------------------------------------------------
Ejercicio 12. Definir la funcion primitiva recursiva
estaEn :: 'a ⇒ 'a list ⇒ bool
tal que (estaEn x xs) se verifica si el elemento x está en la lista
xs. Por ejemplo,
estaEn (2::nat) [3,2,4] = True
estaEn (1::nat) [3,2,4] = False
---------------------------------------------------------------------
*}

fun estaEn :: "'a ⇒ 'a list ⇒ bool" where
"estaEn x xs = undefined"

text {*
---------------------------------------------------------------------
Ejercicio 13. Expresar la relación existente entre estaEn y algunos.
---------------------------------------------------------------------
*}

text {*
---------------------------------------------------------------------
Ejercicio 14. Definir la función primitiva recursiva
sinDuplicados :: 'a list ⇒ bool
tal que (sinDuplicados xs) se verifica si la lista xs no contiene
duplicados. Por ejemplo,
sinDuplicados [1::nat,4,2] = True
sinDuplicados [1::nat,4,2,4] = False
---------------------------------------------------------------------
*}

fun sinDuplicados :: "'a list ⇒ bool" where
"sinDuplicados xs = undefined"

text {*
---------------------------------------------------------------------
Ejercicio 15. Definir la función primitiva recursiva
borraDuplicados :: 'a list ⇒ bool
tal que (borraDuplicados xs) es la lista obtenida eliminando los
elementos duplicados de la lista xs. Por ejemplo,
borraDuplicados [1::nat,2,4,2,3] = [1,4,2,3]

Nota: La función borraDuplicados es equivalente a la predefinida
remdups.
---------------------------------------------------------------------
*}

fun borraDuplicados :: "'a list ⇒ 'a list" where
"borraDuplicados xs = undefined"

text {*
---------------------------------------------------------------------
Ejercicio 16. Demostrar o refutar:
length (borraDuplicados xs) ≤ length xs
---------------------------------------------------------------------
*}

lemma length_borraDuplicados:
"length (borraDuplicados xs) ≤ length xs"
oops

text {*
---------------------------------------------------------------------
Ejercicio 17. Demostrar o refutar:
estaEn a (borraDuplicados xs) = estaEn a xs
---------------------------------------------------------------------
*}

lemma estaEn_borraDuplicados:
"estaEn a (borraDuplicados xs) = estaEn a xs"
oops

text {*
---------------------------------------------------------------------
Ejercicio 18. Demostrar o refutar:
sinDuplicados (borraDuplicados xs)
---------------------------------------------------------------------
*}

lemma sinDuplicados_borraDuplicados:
"sinDuplicados (borraDuplicados xs)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 19. Demostrar o refutar:
borraDuplicados (rev xs) = rev (borraDuplicados xs)
---------------------------------------------------------------------
*}

lemma "borraDuplicados (rev xs) = rev (borraDuplicados xs)"
oops

end
</source>

RA12 Relación 15

2018-07-15T11:52:06Z

Jalonso: Texto reemplazado: «"isar"» por «"isabelle"»

<source lang="isabelle">
header {* R15: Suma y aplanamiento de listas *}

theory R15
imports Main R10
begin

section {* Suma y aplanamiento de listas *}

text {*
---------------------------------------------------------------------
Ejercicio 1. Definir la función
suma :: "nat list ⇒ nat"
tal que (suma xs) es la suma de los elementos de la lista de números
naturales xs. Por ejemplo,
suma [3::nat,2,4] = 9
---------------------------------------------------------------------
*}

fun suma :: "nat list ⇒ nat" where
"suma xs = undefined"

value "suma [3::nat,2,4]" -- "= 9"

text {*
---------------------------------------------------------------------
Ejercicio 2. Definir la función
aplana :: "'a list list ⇒ 'a list"
tal que (aplana xss) es la obtenida concatenando los miembros de la
lista de listas "xss". Por ejemplo,
aplana [[2,3], [4,5], [7,9]] = [2,3,4,5,7,9]
---------------------------------------------------------------------
*}

fun aplana :: "'a list list ⇒ 'a list" where
"aplana xs = undefined"

value "aplana [[2::nat,3], [4,5], [7,9]]" -- "= [2,3,4,5,7,9]"

text {*
---------------------------------------------------------------------
Ejercicio 3. Demostrar o refutar
length (aplana xs) = suma (map length xs)
---------------------------------------------------------------------
*}

lemma length_aplana:
"length (aplana xs) = suma (map length xs)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 4. Demostrar o refutar
suma (xs @ ys) = suma xs + suma ys
---------------------------------------------------------------------
*}

lemma suma_append:
"suma (xs @ ys) = suma xs + suma ys"
oops

text {*
---------------------------------------------------------------------
Ejercicio 5. Demostrar o refutar
aplana (xs @ ys) = (aplana xs) @ (aplana ys)
---------------------------------------------------------------------
*}

lemma aplana_append:
"aplana (xs @ ys) = (aplana xs) @ (aplana ys)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 6. Demostrar o refutar
aplana (map rev (rev xs)) = rev (aplana xs)
---------------------------------------------------------------------
*}

lemma aplana_map_rev_rev:
"aplana (map rev (rev xs)) = rev (aplana xs)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 7. Demostrar o refutar
aplana (rev (map rev xs)) = rev (aplana xs)
---------------------------------------------------------------------
*}

lemma aplana_rev_map_rev:
"aplana (rev (map rev xs)) = rev (aplana xs)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 8. Demostrar o refutar
list_all (list_all P) xs = list_all P (aplana xs)
---------------------------------------------------------------------
*}

lemma list_all_list_all:
"list_all (list_all P) xs = list_all P (aplana xs)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 9. Demostrar o refutar
aplana (rev xs) = aplana xs
---------------------------------------------------------------------
*}

lemma aplana_rev:
"aplana (rev xs) = aplana xs"
oops

text {*
---------------------------------------------------------------------
Ejercicio 10. Demostrar o refutar
suma (rev xs) = suma xs
---------------------------------------------------------------------
*}

lemma suma_rev:
"suma (rev xs) = suma xs"
oops

text {*
---------------------------------------------------------------------
Ejercicio 11. Buscar un predicado P para que se verifique la siguiente
propiedad
list_all P xs ⟶ length xs ≤ suma xs
---------------------------------------------------------------------
*}

text {*
---------------------------------------------------------------------
Ejercicio 12. Demostrar o refutar
algunos (algunos P) xs = algunos P (aplana xs)
---------------------------------------------------------------------
*}

lemma algunos_algunos:
"algunos (algunos P) xs = algunos P (aplana xs)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 13. Redefinir, usando la función list_all, la función
algunos. Llamar la nueva función algunos2 y demostrar que es
equivalente a algunos.
---------------------------------------------------------------------
*}

fun algunos2 :: "('a ⇒ bool) ⇒ ('a list ⇒ bool)" where
"algunos2 P xs = undefined"

lemma algunos2_algunos:
"algunos2 P xs = algunos P xs"
oops

end
</source>

RA12 Relación 21

2018-07-15T11:51:59Z

Jalonso: Texto reemplazado: «lang="isar"» por «lang="isabelle"»

<source lang="isabelle">
header {* R21: Árboles binarios completos *}

theory R21
imports Main
begin

text {*
---------------------------------------------------------------------
Ejercicio 1. Definir el tipo de datos arbol para representar los
árboles binarios que no tienen información ni en los nodos y ni en las
hojas. Por ejemplo, el árbol
·
/ \
/ \
· ·
/ \ / \
· · · ·
se representa por "N (N H H) (N H H)".
---------------------------------------------------------------------
*}

datatype arbol = H | N arbol arbol

value "N (N H H) (N H H)"

text {*
---------------------------------------------------------------------
Ejercicio 2. Definir la función
hojas :: "arbol => nat"
tal que (hojas a) es el número de hojas del árbol a. Por ejemplo,
hojas (N (N H H) (N H H)) = 4
---------------------------------------------------------------------
*}

fun hojas :: "arbol => nat" where
"hojas t = undefined"

value "hojas (N (N H H) (N H H))" -- "= 4"

text {*
---------------------------------------------------------------------
Ejercicio 4. Definir la función
profundidad :: "arbol => nat"
tal que (profundidad a) es la profundidad del árbol a. Por ejemplo,
profundidad (N (N H H) (N H H)) = 2
---------------------------------------------------------------------
*}

fun profundidad :: "arbol => nat" where
"profundidad t = undefined"

value "profundidad (N (N H H) (N H H))" -- "= 2"

text {*
---------------------------------------------------------------------
Ejercicio 5. Definir la función
abc :: "nat ⇒ arbol"
tal que (abc n) es el árbol binario completo de profundidad n. Por
ejemplo,
abc 3 = N (N (N H H) (N H H)) (N (N H H) (N H H))
---------------------------------------------------------------------
*}

fun abc :: "nat ⇒ arbol" where
"abc 0 = undefined"

value "abc 3" -- "= N (N (N H H) (N H H)) (N (N H H) (N H H))"

text {*
---------------------------------------------------------------------
Ejercicio 6. Un árbol binario a es completo respecto de la medida f si
a es una hoja o bien a es de la forma (N i d) y se cumple que tanto i
como d son árboles binarios completos respecto de f y, además,
f(i) = f(r).

Definir la función
es_abc :: "(arbol => 'a) => arbol => bool
tal que (es_abc f a) se verifica si a es un árbol binario completo
respecto de f.
---------------------------------------------------------------------
*}

fun es_abc :: "(arbol => 'a) => arbol => bool" where
"es_abc f t = undefined"

text {*
---------------------------------------------------------------------
Nota. (size a) es el número de nodos del árbol a. Por ejemplo,
size (N (N H H) (N H H)) = 3
---------------------------------------------------------------------
*}

value "size (N (N H H) (N H H))"
value "size (N (N (N H H) (N H H)) (N (N H H) (N H H)))"

text {*
---------------------------------------------------------------------
Nota. Tenemos 3 funciones de medida sobre los árboles: número de
hojas, número de nodos y profundidad. A cada una le corresponde un
concepto de completitud. En los siguientes ejercicios demostraremos
que los tres conceptos de completitud son iguales.
---------------------------------------------------------------------
*}

text {*
---------------------------------------------------------------------
Ejercicio 7. Demostrar que un árbol binario a es completo respecto de
la profundidad syss es completo respecto del número de hojas.
---------------------------------------------------------------------
*}

text {*
---------------------------------------------------------------------
Ejercicio 8. Demostrar que un árbol binario a es completo respecto del
número de hojas syss es completo respecto del número de nodos
---------------------------------------------------------------------
*}

text {*
---------------------------------------------------------------------
Ejercicio 9. Demostrar que un árbol binario a es completo respecto de
la profundidad syss es completo respecto del número de nodos
---------------------------------------------------------------------
*}

text {*
---------------------------------------------------------------------
Ejercicio 10. Demostrar que (abc n) es un árbol binario completo.
---------------------------------------------------------------------
*}

text {*
---------------------------------------------------------------------
Ejercicio 11. Demostrar que si a es un árbolo binario completo
respecto de la profundidad, entonces a es (abc (profundidad a)).
---------------------------------------------------------------------
*}

text {*
---------------------------------------------------------------------
Ejercicio 12. Encontrar una medida f tal que (es_abc f) es distinto de
(es_abc size).
---------------------------------------------------------------------
*}

end
</source>