Razonamiento automático (2013-14) - Contribuciones del usuario [es]

Documentación

2022-02-08T17:20:37Z

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 [http://www.bcs.org/server.php?show=ConWebDoc.4364 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]. 5 de diciembre de 2013.
# M. Wenzel [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/Isabelle2013-2/doc/isabelle-ref.pdf The Isabelle/Isar Reference Manual]. 5 de diciembre de 2013.
# M. Wenzel [https://www.lri.fr/~wenzel/Isabelle2011-Paris/quickref.pdf The Isabelle/Isar quick reference].
# J. Siek [http://ecee.colorado.edu/~siek/ecen3703/spring10/quick-ref.pdf Quick Reference for Isabelle/Isar Propositional Logic].
# J. Siek [http://ecee.colorado.edu/~siek/ecen3703/spring10/quick-ref2.pdf Quick Reference for Isabelle/Isar More Proof Techniques].
# J. Siek [http://ecee.colorado.edu/~siek/ecen3703/spring10/quick-ref3.pdf Quick Reference for Isabelle/Isar First-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].
# Viorel Preoteasa, Ralph-Johan Back y Charmi Panchal. [http://users.abo.fi/vpreotea/isabelle-2012 Introduction to mechanized reasoning with Isabelle/HOL]. (Åbo Akademi University, 2012).
# 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).
# Adam Chlipala [http://stellar.mit.edu/S/course/6/fa11/6.892/ Interactive computer theorem proving]. (MIT, 2012-13).
# Adam Chlipala y Armando Solar Lezama [https://stellar.mit.edu/S/course/6/fa13/6.820/index.html Foundations of program analysis]. (MIT, 2013-14).
# Robby Findler [http://www.eecs.northwestern.edu/~robby/courses/395-495-2013-fall Certified programming with dependent types]. (Northwestern, 2013-14).
# Nuno Gaspar [http://www-sop.inria.fr/members/Nuno.Gaspar/teaching/coq2012.php Verification with the Coq Proof Assistant] (INRIA Sophia Antipolis, 2012-13).
# Carlos Luna y Gustavo Betarte. [https://eva.fing.edu.uy/course/view.php?id=363 Construcción formal de programas en teoría de tipos]. (Univ. de la República, Uruguay, 2013-14).
# 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).
# Michael Winter [Logic in Computer Science] (Brock University, Ontario, Canada, 2010-11).

== 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]:
# [http://bit.ly/1iZjgqN Proof Pearl: A probabilistic proof for the Girth-Chromatic number theorem]. L. Noschinski
# [http://bit.ly/1iJ8uVz A graph library for Isabelle]. ~ L. Noschinski
# [http://bit.ly/I0CU80 Gödel’s incompleteness theorems]. ~ L.C. Paulson
# [http://bit.ly/I0CPRN The hereditarily finite sets]. ~ L.C. Paulson
# [http://bit.ly/HBiIJI Applications of real number theorem proving in PVS]. ~ H. Gottliebsen, R. Hardy, O. Lightfoot y U. Martin
# [http://bit.ly/1awnMLB A machine-assisted proof of Gödel’s incompleteness theorems for the theory of hereditarily finite sets]. ~ L.C. Paulson
# [http://bit.ly/19lWeYy Verified AIG algorithms in ACL2]. ~ J. Davis y S. Swords
# [http://bit.ly/GAhC00 A formal model and correctness proof for an access control policy framework]. ~ C. Wu, X. Zhang y C. Urban
# [http://bit.ly/16SMvSS The ontological argument in PVS]. ~ J. Rushby
# [http://bit.ly/1dRt9n0 Formalizing Moessner’s theorem and generalizations in Nuprl]. ~ M. Bickford, D. Kozen y A. Silva
# [http://bit.ly/1bSeDNB Formalization in PVS of balancing properties necessary for the security of the Dolev-Yao cascade protocol model]. ~ M. Ayala y Y. Santos
# [http://bit.ly/1feFqWE Proof assistant based on didactic considerations]. ~ J. Pais y A Tasistro
# [http://bit.ly/18tHNBi Theory exploration for interactive theorem proving]. ~ M. Johansson
# [http://bit.ly/1b0242s From Tarski to Hilbert]. ~ G. Braun y J. Narboux
# [http://bit.ly/18HaXaR Formal verification of language-based concurrent noninterference]. ~ A. Popescu, J. Hölzl y T. Nipkow
# [http://bit.ly/1aRTQsU A Traffic Alert and Collision Avoidance System(TCAS-II) Resolution Advisory Algorithm]. ~ C. Muñoz, A. Narkawicz y J. Chamberlain
# [http://bit.ly/1dNwhDI Formal verification of cryptographic security proofs]. ~ M. Berg
# [http://bit.ly/17muAUv Polygonal numbers in Mizar]. ~ A. Grabowski
# [http://bit.ly/1hk5z6L A mechanised proof of Gödel’s incompleteness theorems using Nominal Isabelle]. ~ L.C. Paulson
# [http://bit.ly/1cSL0wE Steps towards verified implementations of HOL Light]. ~ M.O. Myreen, S. Owens y R. Kumar
# [http://bit.ly/16Kbgm0 Generic datatypes à la carte]. ~ S. Keuchel y T. Schrijvers
# [http://bit.ly/1bqJGx4 Proof pearl: A verified bignum implementation in x86-64 machine code]. ~ M.O. Myreen y G. Curello
# [http://bit.ly/142ow2Q Mechanized metatheory for a λ λ-calculus with trust types]. ~ R. Ribeiro, C. Camarão y L. Figueiredo
# [http://bit.ly/15WZBDy Proving soundness of combinatorial Vickrey auctions and generating verified executable code]. ~ M.B. Caminati, M. Kerber, C. Lange y C. Rowat
# [http://bit.ly/198g4n9 A computer-assisted proof of correctness of a marching cubes algorithm]. ~ A.N. Chernikov y J. Xu
# [http://bit.ly/11QA5g7 Verifying the bridge between simplicial topology and algebra: the Eilenberg-Zilber algorithm]. ~ L. Lambán, J. Rubio, F.J. Martín y J.L. Ruiz
# [http://bit.ly/1cJAXYk The Königsberg bridge problem and the friendship theorem]. ~ W. Li
# [http://bit.ly/13DBK9R Formal verification of a proof procedure for the description logic ALC]. ~ M. Chaabani, M. Mezghiche y M. Strecker
# [http://bit.ly/1ep2ex9 Pratt’s primality certificates]. ~ S. Wimmer y L. Noschinski
# [http://bit.ly/13C95Ci Reasoning about higher-order relational specifications]. ~ Y. Wang, K. Chaudhuri, A. Gacek y G. Nadathur
# [http://bit.ly/18QQLcL Proofs you can believe in – Proving equivalences between Prolog semantics in Coq]. ~ J. Kriener, A. King y S. Blazy
# [http://bit.ly/19uc82J Certified, efficient and sharp univariate Taylor models in Coq]. ~ E. Martin-Dorel, L. Rideau, L. Théry, M. Mayero y I. Paşca
# [http://bit.ly/1c4Rzel Ordinals in HOL: Transfinite arithmetic up to (and beyond) ω₁]. ~ M. Norrish y B. Huffman
# [http://bit.ly/14b4Akz Program verification based on Kleene algebra in Isabelle/HOL] ~ A. Armstrong, G. Struth y T. Weber
# [http://bit.ly/1aOgRKx Reading an algebra textbook (by translating it to a formal document in the Isabelle/Isar language)]. ~ C. Ballarin
# [http://bit.ly/11HKixj Computational verification of network programs in Coq]. ~ G. Stewart
# [http://www.glc.us.es/~jalonso/vestigium/resena-certifying-homological-algorithms-to-study-biomedical-images Certifying homological algorithms to study biomedical images]. ~ M. Poza
# [http://bit.ly/16Nks9m Formalizing cut elimination of coalgebraic logics in Coq]. ~ H. Tews
# [http://www.glc.us.es/~jalonso/vestigium/resena-the-formalization-of-syntax-based-mathematical-algorithms-using-quotation-and-evaluation/ The formalization of syntax-based mathematical algorithms using quotation and evaluation]. ~ W.M. Farmer
# [http://www.glc.us.es/~jalonso/vestigium/resena-certified-symbolic-manipulation-bivariate-simplicial-polynomials/ Certified symbolic manipulation: Bivariate simplicial polynomials]. ~ L. Lambán, F.J. Martín, J. Rubio y J.L. Ruiz
# [http://www.glc.us.es/~jalonso/vestigium/resena-solveurs-cpfd-verifies-formellement/ Solveurs CP(FD) vérifiés formellement]. ~ C Dubois y A. Gotlieb
# [http://www.glc.us.es/~jalonso/vestigium/resena-formalizing-bounded-increase/ Formalizing bounded increase]. ~ R. Thiemann
# [http://www.glc.us.es/~jalonso/vestigium/resena-formal-mathematics-on-display-a-wiki-for-flyspeck/ Formal mathematics on display: A wiki for Flyspeck]. ~ C. Tankink, C. Kaliszyk, J. Urban y H. Geuvers
# [http://www.glc.us.es/~jalonso/vestigium/resena-theorem-of-three-circles-in-coq Theorem of three circles in Coq]. ~ J. Zsidó
# [http://bit.ly/19fiWAY Certified HLints with Isabelle/HOLCF-Prelude]. ~ J. Breitner, B. Huffman, N. Mitchell y C. Sternagel
# [http://bit.ly/ZfSQrQ Automatic data refinement]. ~ P. Lammich
# [http://bit.ly/18vyjm7 The rooster and the butterflies (a machine-checked proof of the Jordan-Hölder theorem for finite groups)]. ~ A. Mahboubi
# [http://bit.ly/114oyZV Mechanical verification of SAT refutations with extended resolution]. ~ N. Wetzler, M.J.H. Heule y W.A. Hunt Jr.
# [http://bit.ly/13H0REu Type classes and filters for mathematical analysis in Isabelle/HOL] ~ J. Hölzl, F. Immler y B. Huffman
# [http://bit.ly/10fv8wO Verifying refutations with extended resolution]. ~ M. J. H. Heule, W. A. Hunt, Jr. y N. Wetzler
# [http://bit.ly/10EcFWj A Web interface for Isabelle: The next generation]. ~ C. Lüth y M. Ring
# [http://bit.ly/18P9CSv On the formalization of continuous-time Markov chains in HOL]. ~ L. Liu, O. Hasan y S. Tahar
# [http://bit.ly/17H2mqy Formalizing Turing machines]. ~ A. Asperti y W. Ricciotti
# [http://bit.ly/YwuCeL Light-weight containers for Isabelle: efficient, extensible, nestable]. ~ A. Lochbihler
# [http://bit.ly/10XLrRA Graph theory]. ~ L. Noschinski
# [http://bit.ly/19kPEP4 A machine-checked proof of the odd order theorem]. ~ G. Gonthier et als.
# [http://goo.gl/LdihL A constructive theory of regular languages in Coq]. ~ C. Doczkal, J.O. Kaiser y G. Smolka
# [http://goo.gl/gwcwL A formal proof of Kruskal’s tree theorem in Isabelle/HOL]. ~ C. Sternagel
# [http://goo.gl/CUF3e Formalizing Knuth-Bendix orders and Knuth-Bendix completion]. ~ C. Sternagel y R. Thiemann
# [http://goo.gl/9JAfX Developing an auction theory toolbox]. ~ C. Lange, C. Rowat, W. Windsteiger y M. Kerber
# [http://goo.gl/6OfmQ Formalization of incremental simplex algorithm by stepwise refinement]. ~ M. Spasić y F. Marić
# [http://goo.gl/Guxky Coinductive pearl: Modular first-order logic completeness]. ~ J.C. Blanchette, A. Popescu y D. Traytel
# [http://goo.gl/HUOl8 A fully verified executable LTL model checker]. ~ J. Esparza et als.
# [http://goo.gl/RV54S ForMaRE - formal mathematical reasoning in economics]. ~ M. Kerber, C. Lange y C. Rowat.
# [http://goo.gl/Y7sIq AI over large formal knowledge bases: The first decade]. ~ J. Urban.
# [http://goo.gl/vvqNg Formalization of real analysis: A survey of proof assistants and libraries]. ~ S. Boldo, C. Lelay y G. Melquiond.
# [http://goo.gl/bEFYa Data refinement in Isabelle/HOL]. ~ F. Haftmann, A. Krauss, O. Kunčar y T. Nipkow
# [http://goo.gl/xTyvE Formalizing the confluence of orthogonal rewriting systems]. ~ A.C. Rocha y M. Ayala.
# [http://goo.gl/zCYHj Formalization of the complex number theory in HOL4]. ~ Z. Shi et als.
# [http://goo.gl/kM0dI Programming and reasonning with PowerLists in Coq]. ~ F. Loulergue y V. Niculescu
# [http://goo.gl/KkU6s A hierarchy of mathematical structures in ACL2]. ~ J. Heras, F.J. Martín y V. Pascual.
# [http://www.inf.kcl.ac.uk/staff/urbanc/Publications/tm.pdf Mechanising Turing Machines and Computability Theory in Isabelle/HOL] ~ J. Xu, X. Zhang y C. Urban

Documentación

2022-02-08T17:20:10Z

Jalonso: Revertidos los cambios de Jalonso (disc.) a la última edición de WikiSysop

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 [http://www.bcs.org/server.php?show=ConWebDoc.4364 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]. 5 de diciembre de 2013.
# M. Wenzel [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/Isabelle2013-2/doc/isabelle-ref.pdf The Isabelle/Isar Reference Manual]. 5 de diciembre de 2013.
# M. Wenzel [https://www.lri.fr/~wenzel/Isabelle2011-Paris/quickref.pdf The Isabelle/Isar quick reference].
# J. Siek [http://ecee.colorado.edu/~siek/ecen3703/spring10/quick-ref.pdf Quick Reference for Isabelle/Isar Propositional Logic].
# J. Siek [http://ecee.colorado.edu/~siek/ecen3703/spring10/quick-ref2.pdf Quick Reference for Isabelle/Isar More Proof Techniques].
# J. Siek [http://ecee.colorado.edu/~siek/ecen3703/spring10/quick-ref3.pdf Quick Reference for Isabelle/Isar First-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].
# Viorel Preoteasa, Ralph-Johan Back y Charmi Panchal. [http://users.abo.fi/vpreotea/isabelle-2012 Introduction to mechanized reasoning with Isabelle/HOL]. (Åbo Akademi University, 2012).
# 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).
# Adam Chlipala [http://stellar.mit.edu/S/course/6/fa11/6.892/ Interactive computer theorem proving]. (MIT, 2012-13).
# Adam Chlipala y Armando Solar Lezama [https://stellar.mit.edu/S/course/6/fa13/6.820/index.html Foundations of program analysis]. (MIT, 2013-14).
# Robby Findler [http://www.eecs.northwestern.edu/~robby/courses/395-495-2013-fall Certified programming with dependent types]. (Northwestern, 2013-14).
# Nuno Gaspar [http://www-sop.inria.fr/members/Nuno.Gaspar/teaching/coq2012.php Verification with the Coq Proof Assistant] (INRIA Sophia Antipolis, 2012-13).
# Carlos Luna y Gustavo Betarte. [https://eva.fing.edu.uy/course/view.php?id=363 Construcción formal de programas en teoría de tipos]. (Univ. de la República, Uruguay, 2013-14).
# 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).
# Michael Winter [Logic in Computer Science] (Brock University, Ontario, Canada, 2010-11).

== 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]:
# [http://bit.ly/1iZjgqN Proof Pearl: A probabilistic proof for the Girth-Chromatic number theorem]. L. Noschinski
# [http://bit.ly/1iJ8uVz A graph library for Isabelle]. ~ L. Noschinski
# [http://bit.ly/I0CU80 Gödel’s incompleteness theorems]. ~ L.C. Paulson
# [http://bit.ly/I0CPRN The hereditarily finite sets]. ~ L.C. Paulson
# [http://bit.ly/HBiIJI Applications of real number theorem proving in PVS]. ~ H. Gottliebsen, R. Hardy, O. Lightfoot y U. Martin
# [http://bit.ly/1awnMLB A machine-assisted proof of Gödel’s incompleteness theorems for the theory of hereditarily finite sets]. ~ L.C. Paulson
# [http://bit.ly/19lWeYy Verified AIG algorithms in ACL2]. ~ J. Davis y S. Swords
# [http://bit.ly/GAhC00 A formal model and correctness proof for an access control policy framework]. ~ C. Wu, X. Zhang y C. Urban
# [http://bit.ly/16SMvSS The ontological argument in PVS]. ~ J. Rushby
# [http://bit.ly/1dRt9n0 Formalizing Moessner’s theorem and generalizations in Nuprl]. ~ M. Bickford, D. Kozen y A. Silva
# [http://bit.ly/1bSeDNB Formalization in PVS of balancing properties necessary for the security of the Dolev-Yao cascade protocol model]. ~ M. Ayala y Y. Santos
# [http://bit.ly/1feFqWE Proof assistant based on didactic considerations]. ~ J. Pais y A Tasistro
# [http://bit.ly/18tHNBi Theory exploration for interactive theorem proving]. ~ M. Johansson
# [http://bit.ly/1b0242s From Tarski to Hilbert]. ~ G. Braun y J. Narboux
# [http://bit.ly/18HaXaR Formal verification of language-based concurrent noninterference]. ~ A. Popescu, J. Hölzl y T. Nipkow
# [http://bit.ly/1aRTQsU A Traffic Alert and Collision Avoidance System(TCAS-II) Resolution Advisory Algorithm]. ~ C. Muñoz, A. Narkawicz y J. Chamberlain
# [http://bit.ly/1dNwhDI Formal verification of cryptographic security proofs]. ~ M. Berg
# [http://bit.ly/17muAUv Polygonal numbers in Mizar]. ~ A. Grabowski
# [http://bit.ly/1hk5z6L A mechanised proof of Gödel’s incompleteness theorems using Nominal Isabelle]. ~ L.C. Paulson
# [http://bit.ly/1cSL0wE Steps towards verified implementations of HOL Light]. ~ M.O. Myreen, S. Owens y R. Kumar
# [http://bit.ly/16Kbgm0 Generic datatypes à la carte]. ~ S. Keuchel y T. Schrijvers
# [http://bit.ly/1bqJGx4 Proof pearl: A verified bignum implementation in x86-64 machine code]. ~ M.O. Myreen y G. Curello
# [http://bit.ly/142ow2Q Mechanized metatheory for a λ λ-calculus with trust types]. ~ R. Ribeiro, C. Camarão y L. Figueiredo
# [http://bit.ly/15WZBDy Proving soundness of combinatorial Vickrey auctions and generating verified executable code]. ~ M.B. Caminati, M. Kerber, C. Lange y C. Rowat
# [http://bit.ly/198g4n9 A computer-assisted proof of correctness of a marching cubes algorithm]. ~ A.N. Chernikov y J. Xu
# [http://bit.ly/11QA5g7 Verifying the bridge between simplicial topology and algebra: the Eilenberg-Zilber algorithm]. ~ L. Lambán, J. Rubio, F.J. Martín y J.L. Ruiz
# [http://bit.ly/1cJAXYk The Königsberg bridge problem and the friendship theorem]. ~ W. Li
# [http://bit.ly/13DBK9R Formal verification of a proof procedure for the description logic ALC]. ~ M. Chaabani, M. Mezghiche y M. Strecker
# [http://bit.ly/1ep2ex9 Pratt’s primality certificates]. ~ S. Wimmer y L. Noschinski
# [http://bit.ly/13C95Ci Reasoning about higher-order relational specifications]. ~ Y. Wang, K. Chaudhuri, A. Gacek y G. Nadathur
# [http://bit.ly/18QQLcL Proofs you can believe in – Proving equivalences between Prolog semantics in Coq]. ~ J. Kriener, A. King y S. Blazy
# [http://bit.ly/19uc82J Certified, efficient and sharp univariate Taylor models in Coq]. ~ E. Martin-Dorel, L. Rideau, L. Théry, M. Mayero y I. Paşca
# [http://bit.ly/1c4Rzel Ordinals in HOL: Transfinite arithmetic up to (and beyond) ω₁]. ~ M. Norrish y B. Huffman
# [http://bit.ly/14b4Akz Program verification based on Kleene algebra in Isabelle/HOL] ~ A. Armstrong, G. Struth y T. Weber
# [http://bit.ly/1aOgRKx Reading an algebra textbook (by translating it to a formal document in the Isabelle/Isar language)]. ~ C. Ballarin
# [http://bit.ly/11HKixj Computational verification of network programs in Coq]. ~ G. Stewart
# [http://www.glc.us.es/~jalonso/vestigium/resena-certifying-homological-algorithms-to-study-biomedical-images Certifying homological algorithms to study biomedical images]. ~ M. Poza
# [http://bit.ly/16Nks9m Formalizing cut elimination of coalgebraic logics in Coq]. ~ H. Tews
# [http://www.glc.us.es/~jalonso/vestigium/resena-the-formalization-of-syntax-based-mathematical-algorithms-using-quotation-and-evaluation/ The formalization of syntax-based mathematical algorithms using quotation and evaluation]. ~ W.M. Farmer
# [http://www.glc.us.es/~jalonso/vestigium/resena-certified-symbolic-manipulation-bivariate-simplicial-polynomials/ Certified symbolic manipulation: Bivariate simplicial polynomials]. ~ L. Lambán, F.J. Martín, J. Rubio y J.L. Ruiz
# [http://www.glc.us.es/~jalonso/vestigium/resena-solveurs-cpfd-verifies-formellement/ Solveurs CP(FD) vérifiés formellement]. ~ C Dubois y A. Gotlieb
# [http://www.glc.us.es/~jalonso/vestigium/resena-formalizing-bounded-increase/ Formalizing bounded increase]. ~ R. Thiemann
# [http://www.glc.us.es/~jalonso/vestigium/resena-formal-mathematics-on-display-a-wiki-for-flyspeck/ Formal mathematics on display: A wiki for Flyspeck]. ~ C. Tankink, C. Kaliszyk, J. Urban y H. Geuvers
# [http://www.glc.us.es/~jalonso/vestigium/resena-theorem-of-three-circles-in-coq Theorem of three circles in Coq]. ~ J. Zsidó
# [http://bit.ly/19fiWAY Certified HLints with Isabelle/HOLCF-Prelude]. ~ J. Breitner, B. Huffman, N. Mitchell y C. Sternagel
# [http://bit.ly/ZfSQrQ Automatic data refinement]. ~ P. Lammich
# [http://bit.ly/18vyjm7 The rooster and the butterflies (a machine-checked proof of the Jordan-Hölder theorem for finite groups)]. ~ A. Mahboubi
# [http://bit.ly/114oyZV Mechanical verification of SAT refutations with extended resolution]. ~ N. Wetzler, M.J.H. Heule y W.A. Hunt Jr.
# [http://bit.ly/13H0REu Type classes and filters for mathematical analysis in Isabelle/HOL] ~ J. Hölzl, F. Immler y B. Huffman
# [http://bit.ly/10fv8wO Verifying refutations with extended resolution]. ~ M. J. H. Heule, W. A. Hunt, Jr. y N. Wetzler
# [http://bit.ly/10EcFWj A Web interface for Isabelle: The next generation]. ~ C. Lüth y M. Ring
# [http://bit.ly/18P9CSv On the formalization of continuous-time Markov chains in HOL]. ~ L. Liu, O. Hasan y S. Tahar
# [http://bit.ly/17H2mqy Formalizing Turing machines]. ~ A. Asperti y W. Ricciotti
# [http://bit.ly/YwuCeL Light-weight containers for Isabelle: efficient, extensible, nestable]. ~ A. Lochbihler
# [http://bit.ly/10XLrRA Graph theory]. ~ L. Noschinski
# [http://bit.ly/19kPEP4 A machine-checked proof of the odd order theorem]. ~ G. Gonthier et als.
# [http://goo.gl/LdihL A constructive theory of regular languages in Coq]. ~ C. Doczkal, J.O. Kaiser y G. Smolka
# [http://goo.gl/gwcwL A formal proof of Kruskal’s tree theorem in Isabelle/HOL]. ~ C. Sternagel
# [http://goo.gl/CUF3e Formalizing Knuth-Bendix orders and Knuth-Bendix completion]. ~ C. Sternagel y R. Thiemann
# [http://goo.gl/9JAfX Developing an auction theory toolbox]. ~ C. Lange, C. Rowat, W. Windsteiger y M. Kerber
# [http://goo.gl/6OfmQ Formalization of incremental simplex algorithm by stepwise refinement]. ~ M. Spasić y F. Marić
# [http://goo.gl/Guxky Coinductive pearl: Modular first-order logic completeness]. ~ J.C. Blanchette, A. Popescu y D. Traytel
# [http://goo.gl/HUOl8 A fully verified executable LTL model checker]. ~ J. Esparza et als.
# [http://goo.gl/RV54S ForMaRE - formal mathematical reasoning in economics]. ~ M. Kerber, C. Lange y C. Rowat.
# [http://goo.gl/Y7sIq AI over large formal knowledge bases: The first decade]. ~ J. Urban.
# [http://goo.gl/vvqNg Formalization of real analysis: A survey of proof assistants and libraries]. ~ S. Boldo, C. Lelay y G. Melquiond.
# [http://goo.gl/bEFYa Data refinement in Isabelle/HOL]. ~ F. Haftmann, A. Krauss, O. Kunčar y T. Nipkow
# [http://goo.gl/xTyvE Formalizing the confluence of orthogonal rewriting systems]. ~ A.C. Rocha y M. Ayala.
# [http://goo.gl/zCYHj Formalization of the complex number theory in HOL4]. ~ Z. Shi et als.
# [http://goo.gl/kM0dI Programming and reasonning with PowerLists in Coq]. ~ F. Loulergue y V. Niculescu
# [http://goo.gl/KkU6s A hierarchy of mathematical structures in ACL2]. ~ J. Heras, F.J. Martín y V. Pascual.
# [http://www.inf.kcl.ac.uk/staff/urbanc/Publications/tm.pdf Mechanising Turing Machines and Computability Theory in Isabelle/HOL] ~ J. Xu, X. Zhang y C. Urban

Documentación

2022-02-08T17:19:32Z

Jalonso: Se ha deshecho la revisión 698 de Jalonso (disc.)

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 [https://www.ias.ac.in/article/fulltext/sadh/034/01/0003-0025 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://mizar.org/trybulec65/8.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://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/Isabelle2021-1/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]. Springer-Verlag.
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL/document.pdf Isabelle/HOL — Higher-Order Logic].
# M. Wenzel [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/Isabelle2013-2/doc/isabelle-ref.pdf The Isabelle/Isar Reference Manual].
# M. Wenzel [https://www.lri.fr/~wenzel/Isabelle2011-Paris/quickref.pdf The Isabelle/Isar quick reference].
# J. Siek [http://ecee.colorado.edu/~siek/ecen3703/spring10/quick-ref.pdf Quick Reference for Isabelle/Isar Propositional Logic].
# J. Siek [http://ecee.colorado.edu/~siek/ecen3703/spring10/quick-ref2.pdf Quick Reference for Isabelle/Isar More Proof Techniques].
# J. Siek [http://ecee.colorado.edu/~siek/ecen3703/spring10/quick-ref3.pdf Quick Reference for Isabelle/Isar First-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].
# Viorel Preoteasa, Ralph-Johan Back y Charmi Panchal. [http://users.abo.fi/vpreotea/isabelle-2012 Introduction to mechanized reasoning with Isabelle/HOL]. (Åbo Akademi University, 2012).
# 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).
# Adam Chlipala [http://stellar.mit.edu/S/course/6/fa11/6.892/ Interactive computer theorem proving]. (MIT, 2012-13).
# Adam Chlipala y Armando Solar Lezama [https://stellar.mit.edu/S/course/6/fa13/6.820/index.html Foundations of program analysis]. (MIT, 2013-14).
# Robby Findler [http://www.eecs.northwestern.edu/~robby/courses/395-495-2013-fall Certified programming with dependent types]. (Northwestern, 2013-14).
# Nuno Gaspar [http://www-sop.inria.fr/members/Nuno.Gaspar/teaching/coq2012.php Verification with the Coq Proof Assistant] (INRIA Sophia Antipolis, 2012-13).
# Carlos Luna y Gustavo Betarte. [https://eva.fing.edu.uy/course/view.php?id=363 Construcción formal de programas en teoría de tipos]. (Univ. de la República, Uruguay, 2013-14).
# 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).
# Michael Winter [Logic in Computer Science] (Brock University, Ontario, Canada, 2010-11).

== 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]:
# [http://bit.ly/1iZjgqN Proof Pearl: A probabilistic proof for the Girth-Chromatic number theorem]. L. Noschinski
# [http://bit.ly/1iJ8uVz A graph library for Isabelle]. ~ L. Noschinski
# [http://bit.ly/I0CU80 Gödel’s incompleteness theorems]. ~ L.C. Paulson
# [http://bit.ly/I0CPRN The hereditarily finite sets]. ~ L.C. Paulson
# [http://bit.ly/HBiIJI Applications of real number theorem proving in PVS]. ~ H. Gottliebsen, R. Hardy, O. Lightfoot y U. Martin
# [http://bit.ly/1awnMLB A machine-assisted proof of Gödel’s incompleteness theorems for the theory of hereditarily finite sets]. ~ L.C. Paulson
# [http://bit.ly/19lWeYy Verified AIG algorithms in ACL2]. ~ J. Davis y S. Swords
# [http://bit.ly/GAhC00 A formal model and correctness proof for an access control policy framework]. ~ C. Wu, X. Zhang y C. Urban
# [http://bit.ly/16SMvSS The ontological argument in PVS]. ~ J. Rushby
# [http://bit.ly/1dRt9n0 Formalizing Moessner’s theorem and generalizations in Nuprl]. ~ M. Bickford, D. Kozen y A. Silva
# [http://bit.ly/1bSeDNB Formalization in PVS of balancing properties necessary for the security of the Dolev-Yao cascade protocol model]. ~ M. Ayala y Y. Santos
# [http://bit.ly/1feFqWE Proof assistant based on didactic considerations]. ~ J. Pais y A Tasistro
# [http://bit.ly/18tHNBi Theory exploration for interactive theorem proving]. ~ M. Johansson
# [http://bit.ly/1b0242s From Tarski to Hilbert]. ~ G. Braun y J. Narboux
# [http://bit.ly/18HaXaR Formal verification of language-based concurrent noninterference]. ~ A. Popescu, J. Hölzl y T. Nipkow
# [http://bit.ly/1aRTQsU A Traffic Alert and Collision Avoidance System(TCAS-II) Resolution Advisory Algorithm]. ~ C. Muñoz, A. Narkawicz y J. Chamberlain
# [http://bit.ly/1dNwhDI Formal verification of cryptographic security proofs]. ~ M. Berg
# [http://bit.ly/17muAUv Polygonal numbers in Mizar]. ~ A. Grabowski
# [http://bit.ly/1hk5z6L A mechanised proof of Gödel’s incompleteness theorems using Nominal Isabelle]. ~ L.C. Paulson
# [http://bit.ly/1cSL0wE Steps towards verified implementations of HOL Light]. ~ M.O. Myreen, S. Owens y R. Kumar
# [http://bit.ly/16Kbgm0 Generic datatypes à la carte]. ~ S. Keuchel y T. Schrijvers
# [http://bit.ly/1bqJGx4 Proof pearl: A verified bignum implementation in x86-64 machine code]. ~ M.O. Myreen y G. Curello
# [http://bit.ly/142ow2Q Mechanized metatheory for a λ λ-calculus with trust types]. ~ R. Ribeiro, C. Camarão y L. Figueiredo
# [http://bit.ly/15WZBDy Proving soundness of combinatorial Vickrey auctions and generating verified executable code]. ~ M.B. Caminati, M. Kerber, C. Lange y C. Rowat
# [http://bit.ly/198g4n9 A computer-assisted proof of correctness of a marching cubes algorithm]. ~ A.N. Chernikov y J. Xu
# [http://bit.ly/11QA5g7 Verifying the bridge between simplicial topology and algebra: the Eilenberg-Zilber algorithm]. ~ L. Lambán, J. Rubio, F.J. Martín y J.L. Ruiz
# [http://bit.ly/1cJAXYk The Königsberg bridge problem and the friendship theorem]. ~ W. Li
# [http://bit.ly/13DBK9R Formal verification of a proof procedure for the description logic ALC]. ~ M. Chaabani, M. Mezghiche y M. Strecker
# [http://bit.ly/1ep2ex9 Pratt’s primality certificates]. ~ S. Wimmer y L. Noschinski
# [http://bit.ly/13C95Ci Reasoning about higher-order relational specifications]. ~ Y. Wang, K. Chaudhuri, A. Gacek y G. Nadathur
# [http://bit.ly/18QQLcL Proofs you can believe in – Proving equivalences between Prolog semantics in Coq]. ~ J. Kriener, A. King y S. Blazy
# [http://bit.ly/19uc82J Certified, efficient and sharp univariate Taylor models in Coq]. ~ E. Martin-Dorel, L. Rideau, L. Théry, M. Mayero y I. Paşca
# [http://bit.ly/1c4Rzel Ordinals in HOL: Transfinite arithmetic up to (and beyond) ω₁]. ~ M. Norrish y B. Huffman
# [http://bit.ly/14b4Akz Program verification based on Kleene algebra in Isabelle/HOL] ~ A. Armstrong, G. Struth y T. Weber
# [http://bit.ly/1aOgRKx Reading an algebra textbook (by translating it to a formal document in the Isabelle/Isar language)]. ~ C. Ballarin
# [http://bit.ly/11HKixj Computational verification of network programs in Coq]. ~ G. Stewart
# [http://www.glc.us.es/~jalonso/vestigium/resena-certifying-homological-algorithms-to-study-biomedical-images Certifying homological algorithms to study biomedical images]. ~ M. Poza
# [http://bit.ly/16Nks9m Formalizing cut elimination of coalgebraic logics in Coq]. ~ H. Tews
# [http://www.glc.us.es/~jalonso/vestigium/resena-the-formalization-of-syntax-based-mathematical-algorithms-using-quotation-and-evaluation/ The formalization of syntax-based mathematical algorithms using quotation and evaluation]. ~ W.M. Farmer
# [http://www.glc.us.es/~jalonso/vestigium/resena-certified-symbolic-manipulation-bivariate-simplicial-polynomials/ Certified symbolic manipulation: Bivariate simplicial polynomials]. ~ L. Lambán, F.J. Martín, J. Rubio y J.L. Ruiz
# [http://www.glc.us.es/~jalonso/vestigium/resena-solveurs-cpfd-verifies-formellement/ Solveurs CP(FD) vérifiés formellement]. ~ C Dubois y A. Gotlieb
# [http://www.glc.us.es/~jalonso/vestigium/resena-formalizing-bounded-increase/ Formalizing bounded increase]. ~ R. Thiemann
# [http://www.glc.us.es/~jalonso/vestigium/resena-formal-mathematics-on-display-a-wiki-for-flyspeck/ Formal mathematics on display: A wiki for Flyspeck]. ~ C. Tankink, C. Kaliszyk, J. Urban y H. Geuvers
# [http://www.glc.us.es/~jalonso/vestigium/resena-theorem-of-three-circles-in-coq Theorem of three circles in Coq]. ~ J. Zsidó
# [http://bit.ly/19fiWAY Certified HLints with Isabelle/HOLCF-Prelude]. ~ J. Breitner, B. Huffman, N. Mitchell y C. Sternagel
# [http://bit.ly/ZfSQrQ Automatic data refinement]. ~ P. Lammich
# [http://bit.ly/18vyjm7 The rooster and the butterflies (a machine-checked proof of the Jordan-Hölder theorem for finite groups)]. ~ A. Mahboubi
# [http://bit.ly/114oyZV Mechanical verification of SAT refutations with extended resolution]. ~ N. Wetzler, M.J.H. Heule y W.A. Hunt Jr.
# [http://bit.ly/13H0REu Type classes and filters for mathematical analysis in Isabelle/HOL] ~ J. Hölzl, F. Immler y B. Huffman
# [http://bit.ly/10fv8wO Verifying refutations with extended resolution]. ~ M. J. H. Heule, W. A. Hunt, Jr. y N. Wetzler
# [http://bit.ly/10EcFWj A Web interface for Isabelle: The next generation]. ~ C. Lüth y M. Ring
# [http://bit.ly/18P9CSv On the formalization of continuous-time Markov chains in HOL]. ~ L. Liu, O. Hasan y S. Tahar
# [http://bit.ly/17H2mqy Formalizing Turing machines]. ~ A. Asperti y W. Ricciotti
# [http://bit.ly/YwuCeL Light-weight containers for Isabelle: efficient, extensible, nestable]. ~ A. Lochbihler
# [http://bit.ly/10XLrRA Graph theory]. ~ L. Noschinski
# [http://bit.ly/19kPEP4 A machine-checked proof of the odd order theorem]. ~ G. Gonthier et als.
# [http://goo.gl/LdihL A constructive theory of regular languages in Coq]. ~ C. Doczkal, J.O. Kaiser y G. Smolka
# [http://goo.gl/gwcwL A formal proof of Kruskal’s tree theorem in Isabelle/HOL]. ~ C. Sternagel
# [http://goo.gl/CUF3e Formalizing Knuth-Bendix orders and Knuth-Bendix completion]. ~ C. Sternagel y R. Thiemann
# [http://goo.gl/9JAfX Developing an auction theory toolbox]. ~ C. Lange, C. Rowat, W. Windsteiger y M. Kerber
# [http://goo.gl/6OfmQ Formalization of incremental simplex algorithm by stepwise refinement]. ~ M. Spasić y F. Marić
# [http://goo.gl/Guxky Coinductive pearl: Modular first-order logic completeness]. ~ J.C. Blanchette, A. Popescu y D. Traytel
# [http://goo.gl/HUOl8 A fully verified executable LTL model checker]. ~ J. Esparza et als.
# [http://goo.gl/RV54S ForMaRE - formal mathematical reasoning in economics]. ~ M. Kerber, C. Lange y C. Rowat.
# [http://goo.gl/Y7sIq AI over large formal knowledge bases: The first decade]. ~ J. Urban.
# [http://goo.gl/vvqNg Formalization of real analysis: A survey of proof assistants and libraries]. ~ S. Boldo, C. Lelay y G. Melquiond.
# [http://goo.gl/bEFYa Data refinement in Isabelle/HOL]. ~ F. Haftmann, A. Krauss, O. Kunčar y T. Nipkow
# [http://goo.gl/xTyvE Formalizing the confluence of orthogonal rewriting systems]. ~ A.C. Rocha y M. Ayala.
# [http://goo.gl/zCYHj Formalization of the complex number theory in HOL4]. ~ Z. Shi et als.
# [http://goo.gl/kM0dI Programming and reasonning with PowerLists in Coq]. ~ F. Loulergue y V. Niculescu
# [http://goo.gl/KkU6s A hierarchy of mathematical structures in ACL2]. ~ J. Heras, F.J. Martín y V. Pascual.
# [http://www.inf.kcl.ac.uk/staff/urbanc/Publications/tm.pdf Mechanising Turing Machines and Computability Theory in Isabelle/HOL] ~ J. Xu, X. Zhang y C. Urban

Documentación

2022-02-08T10:57:39Z

Jalonso:

Documentación

2022-01-27T19:19:49Z

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 [https://www.ias.ac.in/article/fulltext/sadh/034/01/0003-0025 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://mizar.org/trybulec65/8.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://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/Isabelle2021-1/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]. Springer-Verlag.
# [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/HOL/HOL/document.pdf Isabelle/HOL — Higher-Order Logic].
# M. Wenzel [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/Isabelle2013-2/doc/isabelle-ref.pdf The Isabelle/Isar Reference Manual].
# M. Wenzel [https://www.lri.fr/~wenzel/Isabelle2011-Paris/quickref.pdf The Isabelle/Isar quick reference].
# J. Siek [http://ecee.colorado.edu/~siek/ecen3703/spring10/quick-ref.pdf Quick Reference for Isabelle/Isar Propositional Logic].
# J. Siek [http://ecee.colorado.edu/~siek/ecen3703/spring10/quick-ref2.pdf Quick Reference for Isabelle/Isar More Proof Techniques].
# J. Siek [http://ecee.colorado.edu/~siek/ecen3703/spring10/quick-ref3.pdf Quick Reference for Isabelle/Isar First-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].
# Viorel Preoteasa, Ralph-Johan Back y Charmi Panchal. [http://users.abo.fi/vpreotea/isabelle-2012 Introduction to mechanized reasoning with Isabelle/HOL]. (Åbo Akademi University, 2012).
# 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).
# Adam Chlipala [http://stellar.mit.edu/S/course/6/fa11/6.892/ Interactive computer theorem proving]. (MIT, 2012-13).
# Adam Chlipala y Armando Solar Lezama [https://stellar.mit.edu/S/course/6/fa13/6.820/index.html Foundations of program analysis]. (MIT, 2013-14).
# Robby Findler [http://www.eecs.northwestern.edu/~robby/courses/395-495-2013-fall Certified programming with dependent types]. (Northwestern, 2013-14).
# Nuno Gaspar [http://www-sop.inria.fr/members/Nuno.Gaspar/teaching/coq2012.php Verification with the Coq Proof Assistant] (INRIA Sophia Antipolis, 2012-13).
# Carlos Luna y Gustavo Betarte. [https://eva.fing.edu.uy/course/view.php?id=363 Construcción formal de programas en teoría de tipos]. (Univ. de la República, Uruguay, 2013-14).
# 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).
# Michael Winter [Logic in Computer Science] (Brock University, Ontario, Canada, 2010-11).

== 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]:
# [http://bit.ly/1iZjgqN Proof Pearl: A probabilistic proof for the Girth-Chromatic number theorem]. L. Noschinski
# [http://bit.ly/1iJ8uVz A graph library for Isabelle]. ~ L. Noschinski
# [http://bit.ly/I0CU80 Gödel’s incompleteness theorems]. ~ L.C. Paulson
# [http://bit.ly/I0CPRN The hereditarily finite sets]. ~ L.C. Paulson
# [http://bit.ly/HBiIJI Applications of real number theorem proving in PVS]. ~ H. Gottliebsen, R. Hardy, O. Lightfoot y U. Martin
# [http://bit.ly/1awnMLB A machine-assisted proof of Gödel’s incompleteness theorems for the theory of hereditarily finite sets]. ~ L.C. Paulson
# [http://bit.ly/19lWeYy Verified AIG algorithms in ACL2]. ~ J. Davis y S. Swords
# [http://bit.ly/GAhC00 A formal model and correctness proof for an access control policy framework]. ~ C. Wu, X. Zhang y C. Urban
# [http://bit.ly/16SMvSS The ontological argument in PVS]. ~ J. Rushby
# [http://bit.ly/1dRt9n0 Formalizing Moessner’s theorem and generalizations in Nuprl]. ~ M. Bickford, D. Kozen y A. Silva
# [http://bit.ly/1bSeDNB Formalization in PVS of balancing properties necessary for the security of the Dolev-Yao cascade protocol model]. ~ M. Ayala y Y. Santos
# [http://bit.ly/1feFqWE Proof assistant based on didactic considerations]. ~ J. Pais y A Tasistro
# [http://bit.ly/18tHNBi Theory exploration for interactive theorem proving]. ~ M. Johansson
# [http://bit.ly/1b0242s From Tarski to Hilbert]. ~ G. Braun y J. Narboux
# [http://bit.ly/18HaXaR Formal verification of language-based concurrent noninterference]. ~ A. Popescu, J. Hölzl y T. Nipkow
# [http://bit.ly/1aRTQsU A Traffic Alert and Collision Avoidance System(TCAS-II) Resolution Advisory Algorithm]. ~ C. Muñoz, A. Narkawicz y J. Chamberlain
# [http://bit.ly/1dNwhDI Formal verification of cryptographic security proofs]. ~ M. Berg
# [http://bit.ly/17muAUv Polygonal numbers in Mizar]. ~ A. Grabowski
# [http://bit.ly/1hk5z6L A mechanised proof of Gödel’s incompleteness theorems using Nominal Isabelle]. ~ L.C. Paulson
# [http://bit.ly/1cSL0wE Steps towards verified implementations of HOL Light]. ~ M.O. Myreen, S. Owens y R. Kumar
# [http://bit.ly/16Kbgm0 Generic datatypes à la carte]. ~ S. Keuchel y T. Schrijvers
# [http://bit.ly/1bqJGx4 Proof pearl: A verified bignum implementation in x86-64 machine code]. ~ M.O. Myreen y G. Curello
# [http://bit.ly/142ow2Q Mechanized metatheory for a λ λ-calculus with trust types]. ~ R. Ribeiro, C. Camarão y L. Figueiredo
# [http://bit.ly/15WZBDy Proving soundness of combinatorial Vickrey auctions and generating verified executable code]. ~ M.B. Caminati, M. Kerber, C. Lange y C. Rowat
# [http://bit.ly/198g4n9 A computer-assisted proof of correctness of a marching cubes algorithm]. ~ A.N. Chernikov y J. Xu
# [http://bit.ly/11QA5g7 Verifying the bridge between simplicial topology and algebra: the Eilenberg-Zilber algorithm]. ~ L. Lambán, J. Rubio, F.J. Martín y J.L. Ruiz
# [http://bit.ly/1cJAXYk The Königsberg bridge problem and the friendship theorem]. ~ W. Li
# [http://bit.ly/13DBK9R Formal verification of a proof procedure for the description logic ALC]. ~ M. Chaabani, M. Mezghiche y M. Strecker
# [http://bit.ly/1ep2ex9 Pratt’s primality certificates]. ~ S. Wimmer y L. Noschinski
# [http://bit.ly/13C95Ci Reasoning about higher-order relational specifications]. ~ Y. Wang, K. Chaudhuri, A. Gacek y G. Nadathur
# [http://bit.ly/18QQLcL Proofs you can believe in – Proving equivalences between Prolog semantics in Coq]. ~ J. Kriener, A. King y S. Blazy
# [http://bit.ly/19uc82J Certified, efficient and sharp univariate Taylor models in Coq]. ~ E. Martin-Dorel, L. Rideau, L. Théry, M. Mayero y I. Paşca
# [http://bit.ly/1c4Rzel Ordinals in HOL: Transfinite arithmetic up to (and beyond) ω₁]. ~ M. Norrish y B. Huffman
# [http://bit.ly/14b4Akz Program verification based on Kleene algebra in Isabelle/HOL] ~ A. Armstrong, G. Struth y T. Weber
# [http://bit.ly/1aOgRKx Reading an algebra textbook (by translating it to a formal document in the Isabelle/Isar language)]. ~ C. Ballarin
# [http://bit.ly/11HKixj Computational verification of network programs in Coq]. ~ G. Stewart
# [http://www.glc.us.es/~jalonso/vestigium/resena-certifying-homological-algorithms-to-study-biomedical-images Certifying homological algorithms to study biomedical images]. ~ M. Poza
# [http://bit.ly/16Nks9m Formalizing cut elimination of coalgebraic logics in Coq]. ~ H. Tews
# [http://www.glc.us.es/~jalonso/vestigium/resena-the-formalization-of-syntax-based-mathematical-algorithms-using-quotation-and-evaluation/ The formalization of syntax-based mathematical algorithms using quotation and evaluation]. ~ W.M. Farmer
# [http://www.glc.us.es/~jalonso/vestigium/resena-certified-symbolic-manipulation-bivariate-simplicial-polynomials/ Certified symbolic manipulation: Bivariate simplicial polynomials]. ~ L. Lambán, F.J. Martín, J. Rubio y J.L. Ruiz
# [http://www.glc.us.es/~jalonso/vestigium/resena-solveurs-cpfd-verifies-formellement/ Solveurs CP(FD) vérifiés formellement]. ~ C Dubois y A. Gotlieb
# [http://www.glc.us.es/~jalonso/vestigium/resena-formalizing-bounded-increase/ Formalizing bounded increase]. ~ R. Thiemann
# [http://www.glc.us.es/~jalonso/vestigium/resena-formal-mathematics-on-display-a-wiki-for-flyspeck/ Formal mathematics on display: A wiki for Flyspeck]. ~ C. Tankink, C. Kaliszyk, J. Urban y H. Geuvers
# [http://www.glc.us.es/~jalonso/vestigium/resena-theorem-of-three-circles-in-coq Theorem of three circles in Coq]. ~ J. Zsidó
# [http://bit.ly/19fiWAY Certified HLints with Isabelle/HOLCF-Prelude]. ~ J. Breitner, B. Huffman, N. Mitchell y C. Sternagel
# [http://bit.ly/ZfSQrQ Automatic data refinement]. ~ P. Lammich
# [http://bit.ly/18vyjm7 The rooster and the butterflies (a machine-checked proof of the Jordan-Hölder theorem for finite groups)]. ~ A. Mahboubi
# [http://bit.ly/114oyZV Mechanical verification of SAT refutations with extended resolution]. ~ N. Wetzler, M.J.H. Heule y W.A. Hunt Jr.
# [http://bit.ly/13H0REu Type classes and filters for mathematical analysis in Isabelle/HOL] ~ J. Hölzl, F. Immler y B. Huffman
# [http://bit.ly/10fv8wO Verifying refutations with extended resolution]. ~ M. J. H. Heule, W. A. Hunt, Jr. y N. Wetzler
# [http://bit.ly/10EcFWj A Web interface for Isabelle: The next generation]. ~ C. Lüth y M. Ring
# [http://bit.ly/18P9CSv On the formalization of continuous-time Markov chains in HOL]. ~ L. Liu, O. Hasan y S. Tahar
# [http://bit.ly/17H2mqy Formalizing Turing machines]. ~ A. Asperti y W. Ricciotti
# [http://bit.ly/YwuCeL Light-weight containers for Isabelle: efficient, extensible, nestable]. ~ A. Lochbihler
# [http://bit.ly/10XLrRA Graph theory]. ~ L. Noschinski
# [http://bit.ly/19kPEP4 A machine-checked proof of the odd order theorem]. ~ G. Gonthier et als.
# [http://goo.gl/LdihL A constructive theory of regular languages in Coq]. ~ C. Doczkal, J.O. Kaiser y G. Smolka
# [http://goo.gl/gwcwL A formal proof of Kruskal’s tree theorem in Isabelle/HOL]. ~ C. Sternagel
# [http://goo.gl/CUF3e Formalizing Knuth-Bendix orders and Knuth-Bendix completion]. ~ C. Sternagel y R. Thiemann
# [http://goo.gl/9JAfX Developing an auction theory toolbox]. ~ C. Lange, C. Rowat, W. Windsteiger y M. Kerber
# [http://goo.gl/6OfmQ Formalization of incremental simplex algorithm by stepwise refinement]. ~ M. Spasić y F. Marić
# [http://goo.gl/Guxky Coinductive pearl: Modular first-order logic completeness]. ~ J.C. Blanchette, A. Popescu y D. Traytel
# [http://goo.gl/HUOl8 A fully verified executable LTL model checker]. ~ J. Esparza et als.
# [http://goo.gl/RV54S ForMaRE - formal mathematical reasoning in economics]. ~ M. Kerber, C. Lange y C. Rowat.
# [http://goo.gl/Y7sIq AI over large formal knowledge bases: The first decade]. ~ J. Urban.
# [http://goo.gl/vvqNg Formalization of real analysis: A survey of proof assistants and libraries]. ~ S. Boldo, C. Lelay y G. Melquiond.
# [http://goo.gl/bEFYa Data refinement in Isabelle/HOL]. ~ F. Haftmann, A. Krauss, O. Kunčar y T. Nipkow
# [http://goo.gl/xTyvE Formalizing the confluence of orthogonal rewriting systems]. ~ A.C. Rocha y M. Ayala.
# [http://goo.gl/zCYHj Formalization of the complex number theory in HOL4]. ~ Z. Shi et als.
# [http://goo.gl/kM0dI Programming and reasonning with PowerLists in Coq]. ~ F. Loulergue y V. Niculescu
# [http://goo.gl/KkU6s A hierarchy of mathematical structures in ACL2]. ~ J. Heras, F.J. Martín y V. Pascual.
# [http://www.inf.kcl.ac.uk/staff/urbanc/Publications/tm.pdf Mechanising Turing Machines and Computability Theory in Isabelle/HOL] ~ J. Xu, X. Zhang y C. Urban

Documentación

2022-01-27T19:18:48Z

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 [https://www.ias.ac.in/article/fulltext/sadh/034/01/0003-0025 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://mizar.org/trybulec65/8.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://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/Isabelle2021-1/doc/prog-prove.pdf Programming and proving in Isabelle/HOL]. 5 de diciembre de 2013.
# 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]. 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]. 5 de diciembre de 2013.
# M. Wenzel [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/Isabelle2013-2/doc/isabelle-ref.pdf The Isabelle/Isar Reference Manual]. 5 de diciembre de 2013.
# M. Wenzel [https://www.lri.fr/~wenzel/Isabelle2011-Paris/quickref.pdf The Isabelle/Isar quick reference].
# J. Siek [http://ecee.colorado.edu/~siek/ecen3703/spring10/quick-ref.pdf Quick Reference for Isabelle/Isar Propositional Logic].
# J. Siek [http://ecee.colorado.edu/~siek/ecen3703/spring10/quick-ref2.pdf Quick Reference for Isabelle/Isar More Proof Techniques].
# J. Siek [http://ecee.colorado.edu/~siek/ecen3703/spring10/quick-ref3.pdf Quick Reference for Isabelle/Isar First-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].
# Viorel Preoteasa, Ralph-Johan Back y Charmi Panchal. [http://users.abo.fi/vpreotea/isabelle-2012 Introduction to mechanized reasoning with Isabelle/HOL]. (Åbo Akademi University, 2012).
# 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).
# Adam Chlipala [http://stellar.mit.edu/S/course/6/fa11/6.892/ Interactive computer theorem proving]. (MIT, 2012-13).
# Adam Chlipala y Armando Solar Lezama [https://stellar.mit.edu/S/course/6/fa13/6.820/index.html Foundations of program analysis]. (MIT, 2013-14).
# Robby Findler [http://www.eecs.northwestern.edu/~robby/courses/395-495-2013-fall Certified programming with dependent types]. (Northwestern, 2013-14).
# Nuno Gaspar [http://www-sop.inria.fr/members/Nuno.Gaspar/teaching/coq2012.php Verification with the Coq Proof Assistant] (INRIA Sophia Antipolis, 2012-13).
# Carlos Luna y Gustavo Betarte. [https://eva.fing.edu.uy/course/view.php?id=363 Construcción formal de programas en teoría de tipos]. (Univ. de la República, Uruguay, 2013-14).
# 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).
# Michael Winter [Logic in Computer Science] (Brock University, Ontario, Canada, 2010-11).

== 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]:
# [http://bit.ly/1iZjgqN Proof Pearl: A probabilistic proof for the Girth-Chromatic number theorem]. L. Noschinski
# [http://bit.ly/1iJ8uVz A graph library for Isabelle]. ~ L. Noschinski
# [http://bit.ly/I0CU80 Gödel’s incompleteness theorems]. ~ L.C. Paulson
# [http://bit.ly/I0CPRN The hereditarily finite sets]. ~ L.C. Paulson
# [http://bit.ly/HBiIJI Applications of real number theorem proving in PVS]. ~ H. Gottliebsen, R. Hardy, O. Lightfoot y U. Martin
# [http://bit.ly/1awnMLB A machine-assisted proof of Gödel’s incompleteness theorems for the theory of hereditarily finite sets]. ~ L.C. Paulson
# [http://bit.ly/19lWeYy Verified AIG algorithms in ACL2]. ~ J. Davis y S. Swords
# [http://bit.ly/GAhC00 A formal model and correctness proof for an access control policy framework]. ~ C. Wu, X. Zhang y C. Urban
# [http://bit.ly/16SMvSS The ontological argument in PVS]. ~ J. Rushby
# [http://bit.ly/1dRt9n0 Formalizing Moessner’s theorem and generalizations in Nuprl]. ~ M. Bickford, D. Kozen y A. Silva
# [http://bit.ly/1bSeDNB Formalization in PVS of balancing properties necessary for the security of the Dolev-Yao cascade protocol model]. ~ M. Ayala y Y. Santos
# [http://bit.ly/1feFqWE Proof assistant based on didactic considerations]. ~ J. Pais y A Tasistro
# [http://bit.ly/18tHNBi Theory exploration for interactive theorem proving]. ~ M. Johansson
# [http://bit.ly/1b0242s From Tarski to Hilbert]. ~ G. Braun y J. Narboux
# [http://bit.ly/18HaXaR Formal verification of language-based concurrent noninterference]. ~ A. Popescu, J. Hölzl y T. Nipkow
# [http://bit.ly/1aRTQsU A Traffic Alert and Collision Avoidance System(TCAS-II) Resolution Advisory Algorithm]. ~ C. Muñoz, A. Narkawicz y J. Chamberlain
# [http://bit.ly/1dNwhDI Formal verification of cryptographic security proofs]. ~ M. Berg
# [http://bit.ly/17muAUv Polygonal numbers in Mizar]. ~ A. Grabowski
# [http://bit.ly/1hk5z6L A mechanised proof of Gödel’s incompleteness theorems using Nominal Isabelle]. ~ L.C. Paulson
# [http://bit.ly/1cSL0wE Steps towards verified implementations of HOL Light]. ~ M.O. Myreen, S. Owens y R. Kumar
# [http://bit.ly/16Kbgm0 Generic datatypes à la carte]. ~ S. Keuchel y T. Schrijvers
# [http://bit.ly/1bqJGx4 Proof pearl: A verified bignum implementation in x86-64 machine code]. ~ M.O. Myreen y G. Curello
# [http://bit.ly/142ow2Q Mechanized metatheory for a λ λ-calculus with trust types]. ~ R. Ribeiro, C. Camarão y L. Figueiredo
# [http://bit.ly/15WZBDy Proving soundness of combinatorial Vickrey auctions and generating verified executable code]. ~ M.B. Caminati, M. Kerber, C. Lange y C. Rowat
# [http://bit.ly/198g4n9 A computer-assisted proof of correctness of a marching cubes algorithm]. ~ A.N. Chernikov y J. Xu
# [http://bit.ly/11QA5g7 Verifying the bridge between simplicial topology and algebra: the Eilenberg-Zilber algorithm]. ~ L. Lambán, J. Rubio, F.J. Martín y J.L. Ruiz
# [http://bit.ly/1cJAXYk The Königsberg bridge problem and the friendship theorem]. ~ W. Li
# [http://bit.ly/13DBK9R Formal verification of a proof procedure for the description logic ALC]. ~ M. Chaabani, M. Mezghiche y M. Strecker
# [http://bit.ly/1ep2ex9 Pratt’s primality certificates]. ~ S. Wimmer y L. Noschinski
# [http://bit.ly/13C95Ci Reasoning about higher-order relational specifications]. ~ Y. Wang, K. Chaudhuri, A. Gacek y G. Nadathur
# [http://bit.ly/18QQLcL Proofs you can believe in – Proving equivalences between Prolog semantics in Coq]. ~ J. Kriener, A. King y S. Blazy
# [http://bit.ly/19uc82J Certified, efficient and sharp univariate Taylor models in Coq]. ~ E. Martin-Dorel, L. Rideau, L. Théry, M. Mayero y I. Paşca
# [http://bit.ly/1c4Rzel Ordinals in HOL: Transfinite arithmetic up to (and beyond) ω₁]. ~ M. Norrish y B. Huffman
# [http://bit.ly/14b4Akz Program verification based on Kleene algebra in Isabelle/HOL] ~ A. Armstrong, G. Struth y T. Weber
# [http://bit.ly/1aOgRKx Reading an algebra textbook (by translating it to a formal document in the Isabelle/Isar language)]. ~ C. Ballarin
# [http://bit.ly/11HKixj Computational verification of network programs in Coq]. ~ G. Stewart
# [http://www.glc.us.es/~jalonso/vestigium/resena-certifying-homological-algorithms-to-study-biomedical-images Certifying homological algorithms to study biomedical images]. ~ M. Poza
# [http://bit.ly/16Nks9m Formalizing cut elimination of coalgebraic logics in Coq]. ~ H. Tews
# [http://www.glc.us.es/~jalonso/vestigium/resena-the-formalization-of-syntax-based-mathematical-algorithms-using-quotation-and-evaluation/ The formalization of syntax-based mathematical algorithms using quotation and evaluation]. ~ W.M. Farmer
# [http://www.glc.us.es/~jalonso/vestigium/resena-certified-symbolic-manipulation-bivariate-simplicial-polynomials/ Certified symbolic manipulation: Bivariate simplicial polynomials]. ~ L. Lambán, F.J. Martín, J. Rubio y J.L. Ruiz
# [http://www.glc.us.es/~jalonso/vestigium/resena-solveurs-cpfd-verifies-formellement/ Solveurs CP(FD) vérifiés formellement]. ~ C Dubois y A. Gotlieb
# [http://www.glc.us.es/~jalonso/vestigium/resena-formalizing-bounded-increase/ Formalizing bounded increase]. ~ R. Thiemann
# [http://www.glc.us.es/~jalonso/vestigium/resena-formal-mathematics-on-display-a-wiki-for-flyspeck/ Formal mathematics on display: A wiki for Flyspeck]. ~ C. Tankink, C. Kaliszyk, J. Urban y H. Geuvers
# [http://www.glc.us.es/~jalonso/vestigium/resena-theorem-of-three-circles-in-coq Theorem of three circles in Coq]. ~ J. Zsidó
# [http://bit.ly/19fiWAY Certified HLints with Isabelle/HOLCF-Prelude]. ~ J. Breitner, B. Huffman, N. Mitchell y C. Sternagel
# [http://bit.ly/ZfSQrQ Automatic data refinement]. ~ P. Lammich
# [http://bit.ly/18vyjm7 The rooster and the butterflies (a machine-checked proof of the Jordan-Hölder theorem for finite groups)]. ~ A. Mahboubi
# [http://bit.ly/114oyZV Mechanical verification of SAT refutations with extended resolution]. ~ N. Wetzler, M.J.H. Heule y W.A. Hunt Jr.
# [http://bit.ly/13H0REu Type classes and filters for mathematical analysis in Isabelle/HOL] ~ J. Hölzl, F. Immler y B. Huffman
# [http://bit.ly/10fv8wO Verifying refutations with extended resolution]. ~ M. J. H. Heule, W. A. Hunt, Jr. y N. Wetzler
# [http://bit.ly/10EcFWj A Web interface for Isabelle: The next generation]. ~ C. Lüth y M. Ring
# [http://bit.ly/18P9CSv On the formalization of continuous-time Markov chains in HOL]. ~ L. Liu, O. Hasan y S. Tahar
# [http://bit.ly/17H2mqy Formalizing Turing machines]. ~ A. Asperti y W. Ricciotti
# [http://bit.ly/YwuCeL Light-weight containers for Isabelle: efficient, extensible, nestable]. ~ A. Lochbihler
# [http://bit.ly/10XLrRA Graph theory]. ~ L. Noschinski
# [http://bit.ly/19kPEP4 A machine-checked proof of the odd order theorem]. ~ G. Gonthier et als.
# [http://goo.gl/LdihL A constructive theory of regular languages in Coq]. ~ C. Doczkal, J.O. Kaiser y G. Smolka
# [http://goo.gl/gwcwL A formal proof of Kruskal’s tree theorem in Isabelle/HOL]. ~ C. Sternagel
# [http://goo.gl/CUF3e Formalizing Knuth-Bendix orders and Knuth-Bendix completion]. ~ C. Sternagel y R. Thiemann
# [http://goo.gl/9JAfX Developing an auction theory toolbox]. ~ C. Lange, C. Rowat, W. Windsteiger y M. Kerber
# [http://goo.gl/6OfmQ Formalization of incremental simplex algorithm by stepwise refinement]. ~ M. Spasić y F. Marić
# [http://goo.gl/Guxky Coinductive pearl: Modular first-order logic completeness]. ~ J.C. Blanchette, A. Popescu y D. Traytel
# [http://goo.gl/HUOl8 A fully verified executable LTL model checker]. ~ J. Esparza et als.
# [http://goo.gl/RV54S ForMaRE - formal mathematical reasoning in economics]. ~ M. Kerber, C. Lange y C. Rowat.
# [http://goo.gl/Y7sIq AI over large formal knowledge bases: The first decade]. ~ J. Urban.
# [http://goo.gl/vvqNg Formalization of real analysis: A survey of proof assistants and libraries]. ~ S. Boldo, C. Lelay y G. Melquiond.
# [http://goo.gl/bEFYa Data refinement in Isabelle/HOL]. ~ F. Haftmann, A. Krauss, O. Kunčar y T. Nipkow
# [http://goo.gl/xTyvE Formalizing the confluence of orthogonal rewriting systems]. ~ A.C. Rocha y M. Ayala.
# [http://goo.gl/zCYHj Formalization of the complex number theory in HOL4]. ~ Z. Shi et als.
# [http://goo.gl/kM0dI Programming and reasonning with PowerLists in Coq]. ~ F. Loulergue y V. Niculescu
# [http://goo.gl/KkU6s A hierarchy of mathematical structures in ACL2]. ~ J. Heras, F.J. Martín y V. Pascual.
# [http://www.inf.kcl.ac.uk/staff/urbanc/Publications/tm.pdf Mechanising Turing Machines and Computability Theory in Isabelle/HOL] ~ J. Xu, X. Zhang y C. Urban

Documentación

2022-01-27T19:17:40Z

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 [https://www.ias.ac.in/article/fulltext/sadh/034/01/0003-0025 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://mizar.org/trybulec65/8.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://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/Isabelle2021-1/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]. 5 de diciembre de 2013.
# M. Wenzel [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/Isabelle2013-2/doc/isabelle-ref.pdf The Isabelle/Isar Reference Manual]. 5 de diciembre de 2013.
# M. Wenzel [https://www.lri.fr/~wenzel/Isabelle2011-Paris/quickref.pdf The Isabelle/Isar quick reference].
# J. Siek [http://ecee.colorado.edu/~siek/ecen3703/spring10/quick-ref.pdf Quick Reference for Isabelle/Isar Propositional Logic].
# J. Siek [http://ecee.colorado.edu/~siek/ecen3703/spring10/quick-ref2.pdf Quick Reference for Isabelle/Isar More Proof Techniques].
# J. Siek [http://ecee.colorado.edu/~siek/ecen3703/spring10/quick-ref3.pdf Quick Reference for Isabelle/Isar First-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].
# Viorel Preoteasa, Ralph-Johan Back y Charmi Panchal. [http://users.abo.fi/vpreotea/isabelle-2012 Introduction to mechanized reasoning with Isabelle/HOL]. (Åbo Akademi University, 2012).
# 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).
# Adam Chlipala [http://stellar.mit.edu/S/course/6/fa11/6.892/ Interactive computer theorem proving]. (MIT, 2012-13).
# Adam Chlipala y Armando Solar Lezama [https://stellar.mit.edu/S/course/6/fa13/6.820/index.html Foundations of program analysis]. (MIT, 2013-14).
# Robby Findler [http://www.eecs.northwestern.edu/~robby/courses/395-495-2013-fall Certified programming with dependent types]. (Northwestern, 2013-14).
# Nuno Gaspar [http://www-sop.inria.fr/members/Nuno.Gaspar/teaching/coq2012.php Verification with the Coq Proof Assistant] (INRIA Sophia Antipolis, 2012-13).
# Carlos Luna y Gustavo Betarte. [https://eva.fing.edu.uy/course/view.php?id=363 Construcción formal de programas en teoría de tipos]. (Univ. de la República, Uruguay, 2013-14).
# 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).
# Michael Winter [Logic in Computer Science] (Brock University, Ontario, Canada, 2010-11).

== 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]:
# [http://bit.ly/1iZjgqN Proof Pearl: A probabilistic proof for the Girth-Chromatic number theorem]. L. Noschinski
# [http://bit.ly/1iJ8uVz A graph library for Isabelle]. ~ L. Noschinski
# [http://bit.ly/I0CU80 Gödel’s incompleteness theorems]. ~ L.C. Paulson
# [http://bit.ly/I0CPRN The hereditarily finite sets]. ~ L.C. Paulson
# [http://bit.ly/HBiIJI Applications of real number theorem proving in PVS]. ~ H. Gottliebsen, R. Hardy, O. Lightfoot y U. Martin
# [http://bit.ly/1awnMLB A machine-assisted proof of Gödel’s incompleteness theorems for the theory of hereditarily finite sets]. ~ L.C. Paulson
# [http://bit.ly/19lWeYy Verified AIG algorithms in ACL2]. ~ J. Davis y S. Swords
# [http://bit.ly/GAhC00 A formal model and correctness proof for an access control policy framework]. ~ C. Wu, X. Zhang y C. Urban
# [http://bit.ly/16SMvSS The ontological argument in PVS]. ~ J. Rushby
# [http://bit.ly/1dRt9n0 Formalizing Moessner’s theorem and generalizations in Nuprl]. ~ M. Bickford, D. Kozen y A. Silva
# [http://bit.ly/1bSeDNB Formalization in PVS of balancing properties necessary for the security of the Dolev-Yao cascade protocol model]. ~ M. Ayala y Y. Santos
# [http://bit.ly/1feFqWE Proof assistant based on didactic considerations]. ~ J. Pais y A Tasistro
# [http://bit.ly/18tHNBi Theory exploration for interactive theorem proving]. ~ M. Johansson
# [http://bit.ly/1b0242s From Tarski to Hilbert]. ~ G. Braun y J. Narboux
# [http://bit.ly/18HaXaR Formal verification of language-based concurrent noninterference]. ~ A. Popescu, J. Hölzl y T. Nipkow
# [http://bit.ly/1aRTQsU A Traffic Alert and Collision Avoidance System(TCAS-II) Resolution Advisory Algorithm]. ~ C. Muñoz, A. Narkawicz y J. Chamberlain
# [http://bit.ly/1dNwhDI Formal verification of cryptographic security proofs]. ~ M. Berg
# [http://bit.ly/17muAUv Polygonal numbers in Mizar]. ~ A. Grabowski
# [http://bit.ly/1hk5z6L A mechanised proof of Gödel’s incompleteness theorems using Nominal Isabelle]. ~ L.C. Paulson
# [http://bit.ly/1cSL0wE Steps towards verified implementations of HOL Light]. ~ M.O. Myreen, S. Owens y R. Kumar
# [http://bit.ly/16Kbgm0 Generic datatypes à la carte]. ~ S. Keuchel y T. Schrijvers
# [http://bit.ly/1bqJGx4 Proof pearl: A verified bignum implementation in x86-64 machine code]. ~ M.O. Myreen y G. Curello
# [http://bit.ly/142ow2Q Mechanized metatheory for a λ λ-calculus with trust types]. ~ R. Ribeiro, C. Camarão y L. Figueiredo
# [http://bit.ly/15WZBDy Proving soundness of combinatorial Vickrey auctions and generating verified executable code]. ~ M.B. Caminati, M. Kerber, C. Lange y C. Rowat
# [http://bit.ly/198g4n9 A computer-assisted proof of correctness of a marching cubes algorithm]. ~ A.N. Chernikov y J. Xu
# [http://bit.ly/11QA5g7 Verifying the bridge between simplicial topology and algebra: the Eilenberg-Zilber algorithm]. ~ L. Lambán, J. Rubio, F.J. Martín y J.L. Ruiz
# [http://bit.ly/1cJAXYk The Königsberg bridge problem and the friendship theorem]. ~ W. Li
# [http://bit.ly/13DBK9R Formal verification of a proof procedure for the description logic ALC]. ~ M. Chaabani, M. Mezghiche y M. Strecker
# [http://bit.ly/1ep2ex9 Pratt’s primality certificates]. ~ S. Wimmer y L. Noschinski
# [http://bit.ly/13C95Ci Reasoning about higher-order relational specifications]. ~ Y. Wang, K. Chaudhuri, A. Gacek y G. Nadathur
# [http://bit.ly/18QQLcL Proofs you can believe in – Proving equivalences between Prolog semantics in Coq]. ~ J. Kriener, A. King y S. Blazy
# [http://bit.ly/19uc82J Certified, efficient and sharp univariate Taylor models in Coq]. ~ E. Martin-Dorel, L. Rideau, L. Théry, M. Mayero y I. Paşca
# [http://bit.ly/1c4Rzel Ordinals in HOL: Transfinite arithmetic up to (and beyond) ω₁]. ~ M. Norrish y B. Huffman
# [http://bit.ly/14b4Akz Program verification based on Kleene algebra in Isabelle/HOL] ~ A. Armstrong, G. Struth y T. Weber
# [http://bit.ly/1aOgRKx Reading an algebra textbook (by translating it to a formal document in the Isabelle/Isar language)]. ~ C. Ballarin
# [http://bit.ly/11HKixj Computational verification of network programs in Coq]. ~ G. Stewart
# [http://www.glc.us.es/~jalonso/vestigium/resena-certifying-homological-algorithms-to-study-biomedical-images Certifying homological algorithms to study biomedical images]. ~ M. Poza
# [http://bit.ly/16Nks9m Formalizing cut elimination of coalgebraic logics in Coq]. ~ H. Tews
# [http://www.glc.us.es/~jalonso/vestigium/resena-the-formalization-of-syntax-based-mathematical-algorithms-using-quotation-and-evaluation/ The formalization of syntax-based mathematical algorithms using quotation and evaluation]. ~ W.M. Farmer
# [http://www.glc.us.es/~jalonso/vestigium/resena-certified-symbolic-manipulation-bivariate-simplicial-polynomials/ Certified symbolic manipulation: Bivariate simplicial polynomials]. ~ L. Lambán, F.J. Martín, J. Rubio y J.L. Ruiz
# [http://www.glc.us.es/~jalonso/vestigium/resena-solveurs-cpfd-verifies-formellement/ Solveurs CP(FD) vérifiés formellement]. ~ C Dubois y A. Gotlieb
# [http://www.glc.us.es/~jalonso/vestigium/resena-formalizing-bounded-increase/ Formalizing bounded increase]. ~ R. Thiemann
# [http://www.glc.us.es/~jalonso/vestigium/resena-formal-mathematics-on-display-a-wiki-for-flyspeck/ Formal mathematics on display: A wiki for Flyspeck]. ~ C. Tankink, C. Kaliszyk, J. Urban y H. Geuvers
# [http://www.glc.us.es/~jalonso/vestigium/resena-theorem-of-three-circles-in-coq Theorem of three circles in Coq]. ~ J. Zsidó
# [http://bit.ly/19fiWAY Certified HLints with Isabelle/HOLCF-Prelude]. ~ J. Breitner, B. Huffman, N. Mitchell y C. Sternagel
# [http://bit.ly/ZfSQrQ Automatic data refinement]. ~ P. Lammich
# [http://bit.ly/18vyjm7 The rooster and the butterflies (a machine-checked proof of the Jordan-Hölder theorem for finite groups)]. ~ A. Mahboubi
# [http://bit.ly/114oyZV Mechanical verification of SAT refutations with extended resolution]. ~ N. Wetzler, M.J.H. Heule y W.A. Hunt Jr.
# [http://bit.ly/13H0REu Type classes and filters for mathematical analysis in Isabelle/HOL] ~ J. Hölzl, F. Immler y B. Huffman
# [http://bit.ly/10fv8wO Verifying refutations with extended resolution]. ~ M. J. H. Heule, W. A. Hunt, Jr. y N. Wetzler
# [http://bit.ly/10EcFWj A Web interface for Isabelle: The next generation]. ~ C. Lüth y M. Ring
# [http://bit.ly/18P9CSv On the formalization of continuous-time Markov chains in HOL]. ~ L. Liu, O. Hasan y S. Tahar
# [http://bit.ly/17H2mqy Formalizing Turing machines]. ~ A. Asperti y W. Ricciotti
# [http://bit.ly/YwuCeL Light-weight containers for Isabelle: efficient, extensible, nestable]. ~ A. Lochbihler
# [http://bit.ly/10XLrRA Graph theory]. ~ L. Noschinski
# [http://bit.ly/19kPEP4 A machine-checked proof of the odd order theorem]. ~ G. Gonthier et als.
# [http://goo.gl/LdihL A constructive theory of regular languages in Coq]. ~ C. Doczkal, J.O. Kaiser y G. Smolka
# [http://goo.gl/gwcwL A formal proof of Kruskal’s tree theorem in Isabelle/HOL]. ~ C. Sternagel
# [http://goo.gl/CUF3e Formalizing Knuth-Bendix orders and Knuth-Bendix completion]. ~ C. Sternagel y R. Thiemann
# [http://goo.gl/9JAfX Developing an auction theory toolbox]. ~ C. Lange, C. Rowat, W. Windsteiger y M. Kerber
# [http://goo.gl/6OfmQ Formalization of incremental simplex algorithm by stepwise refinement]. ~ M. Spasić y F. Marić
# [http://goo.gl/Guxky Coinductive pearl: Modular first-order logic completeness]. ~ J.C. Blanchette, A. Popescu y D. Traytel
# [http://goo.gl/HUOl8 A fully verified executable LTL model checker]. ~ J. Esparza et als.
# [http://goo.gl/RV54S ForMaRE - formal mathematical reasoning in economics]. ~ M. Kerber, C. Lange y C. Rowat.
# [http://goo.gl/Y7sIq AI over large formal knowledge bases: The first decade]. ~ J. Urban.
# [http://goo.gl/vvqNg Formalization of real analysis: A survey of proof assistants and libraries]. ~ S. Boldo, C. Lelay y G. Melquiond.
# [http://goo.gl/bEFYa Data refinement in Isabelle/HOL]. ~ F. Haftmann, A. Krauss, O. Kunčar y T. Nipkow
# [http://goo.gl/xTyvE Formalizing the confluence of orthogonal rewriting systems]. ~ A.C. Rocha y M. Ayala.
# [http://goo.gl/zCYHj Formalization of the complex number theory in HOL4]. ~ Z. Shi et als.
# [http://goo.gl/kM0dI Programming and reasonning with PowerLists in Coq]. ~ F. Loulergue y V. Niculescu
# [http://goo.gl/KkU6s A hierarchy of mathematical structures in ACL2]. ~ J. Heras, F.J. Martín y V. Pascual.
# [http://www.inf.kcl.ac.uk/staff/urbanc/Publications/tm.pdf Mechanising Turing Machines and Computability Theory in Isabelle/HOL] ~ J. Xu, X. Zhang y C. Urban

Documentación

2022-01-27T19:16:46Z

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 [https://www.ias.ac.in/article/fulltext/sadh/034/01/0003-0025 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://mizar.org/trybulec65/8.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]. 5 de diciembre de 2013.
# M. Wenzel [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/Isabelle2013-2/doc/isabelle-ref.pdf The Isabelle/Isar Reference Manual]. 5 de diciembre de 2013.
# M. Wenzel [https://www.lri.fr/~wenzel/Isabelle2011-Paris/quickref.pdf The Isabelle/Isar quick reference].
# J. Siek [http://ecee.colorado.edu/~siek/ecen3703/spring10/quick-ref.pdf Quick Reference for Isabelle/Isar Propositional Logic].
# J. Siek [http://ecee.colorado.edu/~siek/ecen3703/spring10/quick-ref2.pdf Quick Reference for Isabelle/Isar More Proof Techniques].
# J. Siek [http://ecee.colorado.edu/~siek/ecen3703/spring10/quick-ref3.pdf Quick Reference for Isabelle/Isar First-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].
# Viorel Preoteasa, Ralph-Johan Back y Charmi Panchal. [http://users.abo.fi/vpreotea/isabelle-2012 Introduction to mechanized reasoning with Isabelle/HOL]. (Åbo Akademi University, 2012).
# 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).
# Adam Chlipala [http://stellar.mit.edu/S/course/6/fa11/6.892/ Interactive computer theorem proving]. (MIT, 2012-13).
# Adam Chlipala y Armando Solar Lezama [https://stellar.mit.edu/S/course/6/fa13/6.820/index.html Foundations of program analysis]. (MIT, 2013-14).
# Robby Findler [http://www.eecs.northwestern.edu/~robby/courses/395-495-2013-fall Certified programming with dependent types]. (Northwestern, 2013-14).
# Nuno Gaspar [http://www-sop.inria.fr/members/Nuno.Gaspar/teaching/coq2012.php Verification with the Coq Proof Assistant] (INRIA Sophia Antipolis, 2012-13).
# Carlos Luna y Gustavo Betarte. [https://eva.fing.edu.uy/course/view.php?id=363 Construcción formal de programas en teoría de tipos]. (Univ. de la República, Uruguay, 2013-14).
# 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).
# Michael Winter [Logic in Computer Science] (Brock University, Ontario, Canada, 2010-11).

== 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]:
# [http://bit.ly/1iZjgqN Proof Pearl: A probabilistic proof for the Girth-Chromatic number theorem]. L. Noschinski
# [http://bit.ly/1iJ8uVz A graph library for Isabelle]. ~ L. Noschinski
# [http://bit.ly/I0CU80 Gödel’s incompleteness theorems]. ~ L.C. Paulson
# [http://bit.ly/I0CPRN The hereditarily finite sets]. ~ L.C. Paulson
# [http://bit.ly/HBiIJI Applications of real number theorem proving in PVS]. ~ H. Gottliebsen, R. Hardy, O. Lightfoot y U. Martin
# [http://bit.ly/1awnMLB A machine-assisted proof of Gödel’s incompleteness theorems for the theory of hereditarily finite sets]. ~ L.C. Paulson
# [http://bit.ly/19lWeYy Verified AIG algorithms in ACL2]. ~ J. Davis y S. Swords
# [http://bit.ly/GAhC00 A formal model and correctness proof for an access control policy framework]. ~ C. Wu, X. Zhang y C. Urban
# [http://bit.ly/16SMvSS The ontological argument in PVS]. ~ J. Rushby
# [http://bit.ly/1dRt9n0 Formalizing Moessner’s theorem and generalizations in Nuprl]. ~ M. Bickford, D. Kozen y A. Silva
# [http://bit.ly/1bSeDNB Formalization in PVS of balancing properties necessary for the security of the Dolev-Yao cascade protocol model]. ~ M. Ayala y Y. Santos
# [http://bit.ly/1feFqWE Proof assistant based on didactic considerations]. ~ J. Pais y A Tasistro
# [http://bit.ly/18tHNBi Theory exploration for interactive theorem proving]. ~ M. Johansson
# [http://bit.ly/1b0242s From Tarski to Hilbert]. ~ G. Braun y J. Narboux
# [http://bit.ly/18HaXaR Formal verification of language-based concurrent noninterference]. ~ A. Popescu, J. Hölzl y T. Nipkow
# [http://bit.ly/1aRTQsU A Traffic Alert and Collision Avoidance System(TCAS-II) Resolution Advisory Algorithm]. ~ C. Muñoz, A. Narkawicz y J. Chamberlain
# [http://bit.ly/1dNwhDI Formal verification of cryptographic security proofs]. ~ M. Berg
# [http://bit.ly/17muAUv Polygonal numbers in Mizar]. ~ A. Grabowski
# [http://bit.ly/1hk5z6L A mechanised proof of Gödel’s incompleteness theorems using Nominal Isabelle]. ~ L.C. Paulson
# [http://bit.ly/1cSL0wE Steps towards verified implementations of HOL Light]. ~ M.O. Myreen, S. Owens y R. Kumar
# [http://bit.ly/16Kbgm0 Generic datatypes à la carte]. ~ S. Keuchel y T. Schrijvers
# [http://bit.ly/1bqJGx4 Proof pearl: A verified bignum implementation in x86-64 machine code]. ~ M.O. Myreen y G. Curello
# [http://bit.ly/142ow2Q Mechanized metatheory for a λ λ-calculus with trust types]. ~ R. Ribeiro, C. Camarão y L. Figueiredo
# [http://bit.ly/15WZBDy Proving soundness of combinatorial Vickrey auctions and generating verified executable code]. ~ M.B. Caminati, M. Kerber, C. Lange y C. Rowat
# [http://bit.ly/198g4n9 A computer-assisted proof of correctness of a marching cubes algorithm]. ~ A.N. Chernikov y J. Xu
# [http://bit.ly/11QA5g7 Verifying the bridge between simplicial topology and algebra: the Eilenberg-Zilber algorithm]. ~ L. Lambán, J. Rubio, F.J. Martín y J.L. Ruiz
# [http://bit.ly/1cJAXYk The Königsberg bridge problem and the friendship theorem]. ~ W. Li
# [http://bit.ly/13DBK9R Formal verification of a proof procedure for the description logic ALC]. ~ M. Chaabani, M. Mezghiche y M. Strecker
# [http://bit.ly/1ep2ex9 Pratt’s primality certificates]. ~ S. Wimmer y L. Noschinski
# [http://bit.ly/13C95Ci Reasoning about higher-order relational specifications]. ~ Y. Wang, K. Chaudhuri, A. Gacek y G. Nadathur
# [http://bit.ly/18QQLcL Proofs you can believe in – Proving equivalences between Prolog semantics in Coq]. ~ J. Kriener, A. King y S. Blazy
# [http://bit.ly/19uc82J Certified, efficient and sharp univariate Taylor models in Coq]. ~ E. Martin-Dorel, L. Rideau, L. Théry, M. Mayero y I. Paşca
# [http://bit.ly/1c4Rzel Ordinals in HOL: Transfinite arithmetic up to (and beyond) ω₁]. ~ M. Norrish y B. Huffman
# [http://bit.ly/14b4Akz Program verification based on Kleene algebra in Isabelle/HOL] ~ A. Armstrong, G. Struth y T. Weber
# [http://bit.ly/1aOgRKx Reading an algebra textbook (by translating it to a formal document in the Isabelle/Isar language)]. ~ C. Ballarin
# [http://bit.ly/11HKixj Computational verification of network programs in Coq]. ~ G. Stewart
# [http://www.glc.us.es/~jalonso/vestigium/resena-certifying-homological-algorithms-to-study-biomedical-images Certifying homological algorithms to study biomedical images]. ~ M. Poza
# [http://bit.ly/16Nks9m Formalizing cut elimination of coalgebraic logics in Coq]. ~ H. Tews
# [http://www.glc.us.es/~jalonso/vestigium/resena-the-formalization-of-syntax-based-mathematical-algorithms-using-quotation-and-evaluation/ The formalization of syntax-based mathematical algorithms using quotation and evaluation]. ~ W.M. Farmer
# [http://www.glc.us.es/~jalonso/vestigium/resena-certified-symbolic-manipulation-bivariate-simplicial-polynomials/ Certified symbolic manipulation: Bivariate simplicial polynomials]. ~ L. Lambán, F.J. Martín, J. Rubio y J.L. Ruiz
# [http://www.glc.us.es/~jalonso/vestigium/resena-solveurs-cpfd-verifies-formellement/ Solveurs CP(FD) vérifiés formellement]. ~ C Dubois y A. Gotlieb
# [http://www.glc.us.es/~jalonso/vestigium/resena-formalizing-bounded-increase/ Formalizing bounded increase]. ~ R. Thiemann
# [http://www.glc.us.es/~jalonso/vestigium/resena-formal-mathematics-on-display-a-wiki-for-flyspeck/ Formal mathematics on display: A wiki for Flyspeck]. ~ C. Tankink, C. Kaliszyk, J. Urban y H. Geuvers
# [http://www.glc.us.es/~jalonso/vestigium/resena-theorem-of-three-circles-in-coq Theorem of three circles in Coq]. ~ J. Zsidó
# [http://bit.ly/19fiWAY Certified HLints with Isabelle/HOLCF-Prelude]. ~ J. Breitner, B. Huffman, N. Mitchell y C. Sternagel
# [http://bit.ly/ZfSQrQ Automatic data refinement]. ~ P. Lammich
# [http://bit.ly/18vyjm7 The rooster and the butterflies (a machine-checked proof of the Jordan-Hölder theorem for finite groups)]. ~ A. Mahboubi
# [http://bit.ly/114oyZV Mechanical verification of SAT refutations with extended resolution]. ~ N. Wetzler, M.J.H. Heule y W.A. Hunt Jr.
# [http://bit.ly/13H0REu Type classes and filters for mathematical analysis in Isabelle/HOL] ~ J. Hölzl, F. Immler y B. Huffman
# [http://bit.ly/10fv8wO Verifying refutations with extended resolution]. ~ M. J. H. Heule, W. A. Hunt, Jr. y N. Wetzler
# [http://bit.ly/10EcFWj A Web interface for Isabelle: The next generation]. ~ C. Lüth y M. Ring
# [http://bit.ly/18P9CSv On the formalization of continuous-time Markov chains in HOL]. ~ L. Liu, O. Hasan y S. Tahar
# [http://bit.ly/17H2mqy Formalizing Turing machines]. ~ A. Asperti y W. Ricciotti
# [http://bit.ly/YwuCeL Light-weight containers for Isabelle: efficient, extensible, nestable]. ~ A. Lochbihler
# [http://bit.ly/10XLrRA Graph theory]. ~ L. Noschinski
# [http://bit.ly/19kPEP4 A machine-checked proof of the odd order theorem]. ~ G. Gonthier et als.
# [http://goo.gl/LdihL A constructive theory of regular languages in Coq]. ~ C. Doczkal, J.O. Kaiser y G. Smolka
# [http://goo.gl/gwcwL A formal proof of Kruskal’s tree theorem in Isabelle/HOL]. ~ C. Sternagel
# [http://goo.gl/CUF3e Formalizing Knuth-Bendix orders and Knuth-Bendix completion]. ~ C. Sternagel y R. Thiemann
# [http://goo.gl/9JAfX Developing an auction theory toolbox]. ~ C. Lange, C. Rowat, W. Windsteiger y M. Kerber
# [http://goo.gl/6OfmQ Formalization of incremental simplex algorithm by stepwise refinement]. ~ M. Spasić y F. Marić
# [http://goo.gl/Guxky Coinductive pearl: Modular first-order logic completeness]. ~ J.C. Blanchette, A. Popescu y D. Traytel
# [http://goo.gl/HUOl8 A fully verified executable LTL model checker]. ~ J. Esparza et als.
# [http://goo.gl/RV54S ForMaRE - formal mathematical reasoning in economics]. ~ M. Kerber, C. Lange y C. Rowat.
# [http://goo.gl/Y7sIq AI over large formal knowledge bases: The first decade]. ~ J. Urban.
# [http://goo.gl/vvqNg Formalization of real analysis: A survey of proof assistants and libraries]. ~ S. Boldo, C. Lelay y G. Melquiond.
# [http://goo.gl/bEFYa Data refinement in Isabelle/HOL]. ~ F. Haftmann, A. Krauss, O. Kunčar y T. Nipkow
# [http://goo.gl/xTyvE Formalizing the confluence of orthogonal rewriting systems]. ~ A.C. Rocha y M. Ayala.
# [http://goo.gl/zCYHj Formalization of the complex number theory in HOL4]. ~ Z. Shi et als.
# [http://goo.gl/kM0dI Programming and reasonning with PowerLists in Coq]. ~ F. Loulergue y V. Niculescu
# [http://goo.gl/KkU6s A hierarchy of mathematical structures in ACL2]. ~ J. Heras, F.J. Martín y V. Pascual.
# [http://www.inf.kcl.ac.uk/staff/urbanc/Publications/tm.pdf Mechanising Turing Machines and Computability Theory in Isabelle/HOL] ~ J. Xu, X. Zhang y C. Urban

Documentación

2022-01-27T19:15:58Z

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 [https://www.ias.ac.in/article/fulltext/sadh/034/01/0003-0025 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://mizar.org/trybulec65/8.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]. 5 de diciembre de 2013.
# M. Wenzel [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/Isabelle2013-2/doc/isabelle-ref.pdf The Isabelle/Isar Reference Manual]. 5 de diciembre de 2013.
# M. Wenzel [https://www.lri.fr/~wenzel/Isabelle2011-Paris/quickref.pdf The Isabelle/Isar quick reference].
# J. Siek [http://ecee.colorado.edu/~siek/ecen3703/spring10/quick-ref.pdf Quick Reference for Isabelle/Isar Propositional Logic].
# J. Siek [http://ecee.colorado.edu/~siek/ecen3703/spring10/quick-ref2.pdf Quick Reference for Isabelle/Isar More Proof Techniques].
# J. Siek [http://ecee.colorado.edu/~siek/ecen3703/spring10/quick-ref3.pdf Quick Reference for Isabelle/Isar First-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].
# Viorel Preoteasa, Ralph-Johan Back y Charmi Panchal. [http://users.abo.fi/vpreotea/isabelle-2012 Introduction to mechanized reasoning with Isabelle/HOL]. (Åbo Akademi University, 2012).
# 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).
# Adam Chlipala [http://stellar.mit.edu/S/course/6/fa11/6.892/ Interactive computer theorem proving]. (MIT, 2012-13).
# Adam Chlipala y Armando Solar Lezama [https://stellar.mit.edu/S/course/6/fa13/6.820/index.html Foundations of program analysis]. (MIT, 2013-14).
# Robby Findler [http://www.eecs.northwestern.edu/~robby/courses/395-495-2013-fall Certified programming with dependent types]. (Northwestern, 2013-14).
# Nuno Gaspar [http://www-sop.inria.fr/members/Nuno.Gaspar/teaching/coq2012.php Verification with the Coq Proof Assistant] (INRIA Sophia Antipolis, 2012-13).
# Carlos Luna y Gustavo Betarte. [https://eva.fing.edu.uy/course/view.php?id=363 Construcción formal de programas en teoría de tipos]. (Univ. de la República, Uruguay, 2013-14).
# 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).
# Michael Winter [Logic in Computer Science] (Brock University, Ontario, Canada, 2010-11).

== 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]:
# [http://bit.ly/1iZjgqN Proof Pearl: A probabilistic proof for the Girth-Chromatic number theorem]. L. Noschinski
# [http://bit.ly/1iJ8uVz A graph library for Isabelle]. ~ L. Noschinski
# [http://bit.ly/I0CU80 Gödel’s incompleteness theorems]. ~ L.C. Paulson
# [http://bit.ly/I0CPRN The hereditarily finite sets]. ~ L.C. Paulson
# [http://bit.ly/HBiIJI Applications of real number theorem proving in PVS]. ~ H. Gottliebsen, R. Hardy, O. Lightfoot y U. Martin
# [http://bit.ly/1awnMLB A machine-assisted proof of Gödel’s incompleteness theorems for the theory of hereditarily finite sets]. ~ L.C. Paulson
# [http://bit.ly/19lWeYy Verified AIG algorithms in ACL2]. ~ J. Davis y S. Swords
# [http://bit.ly/GAhC00 A formal model and correctness proof for an access control policy framework]. ~ C. Wu, X. Zhang y C. Urban
# [http://bit.ly/16SMvSS The ontological argument in PVS]. ~ J. Rushby
# [http://bit.ly/1dRt9n0 Formalizing Moessner’s theorem and generalizations in Nuprl]. ~ M. Bickford, D. Kozen y A. Silva
# [http://bit.ly/1bSeDNB Formalization in PVS of balancing properties necessary for the security of the Dolev-Yao cascade protocol model]. ~ M. Ayala y Y. Santos
# [http://bit.ly/1feFqWE Proof assistant based on didactic considerations]. ~ J. Pais y A Tasistro
# [http://bit.ly/18tHNBi Theory exploration for interactive theorem proving]. ~ M. Johansson
# [http://bit.ly/1b0242s From Tarski to Hilbert]. ~ G. Braun y J. Narboux
# [http://bit.ly/18HaXaR Formal verification of language-based concurrent noninterference]. ~ A. Popescu, J. Hölzl y T. Nipkow
# [http://bit.ly/1aRTQsU A Traffic Alert and Collision Avoidance System(TCAS-II) Resolution Advisory Algorithm]. ~ C. Muñoz, A. Narkawicz y J. Chamberlain
# [http://bit.ly/1dNwhDI Formal verification of cryptographic security proofs]. ~ M. Berg
# [http://bit.ly/17muAUv Polygonal numbers in Mizar]. ~ A. Grabowski
# [http://bit.ly/1hk5z6L A mechanised proof of Gödel’s incompleteness theorems using Nominal Isabelle]. ~ L.C. Paulson
# [http://bit.ly/1cSL0wE Steps towards verified implementations of HOL Light]. ~ M.O. Myreen, S. Owens y R. Kumar
# [http://bit.ly/16Kbgm0 Generic datatypes à la carte]. ~ S. Keuchel y T. Schrijvers
# [http://bit.ly/1bqJGx4 Proof pearl: A verified bignum implementation in x86-64 machine code]. ~ M.O. Myreen y G. Curello
# [http://bit.ly/142ow2Q Mechanized metatheory for a λ λ-calculus with trust types]. ~ R. Ribeiro, C. Camarão y L. Figueiredo
# [http://bit.ly/15WZBDy Proving soundness of combinatorial Vickrey auctions and generating verified executable code]. ~ M.B. Caminati, M. Kerber, C. Lange y C. Rowat
# [http://bit.ly/198g4n9 A computer-assisted proof of correctness of a marching cubes algorithm]. ~ A.N. Chernikov y J. Xu
# [http://bit.ly/11QA5g7 Verifying the bridge between simplicial topology and algebra: the Eilenberg-Zilber algorithm]. ~ L. Lambán, J. Rubio, F.J. Martín y J.L. Ruiz
# [http://bit.ly/1cJAXYk The Königsberg bridge problem and the friendship theorem]. ~ W. Li
# [http://bit.ly/13DBK9R Formal verification of a proof procedure for the description logic ALC]. ~ M. Chaabani, M. Mezghiche y M. Strecker
# [http://bit.ly/1ep2ex9 Pratt’s primality certificates]. ~ S. Wimmer y L. Noschinski
# [http://bit.ly/13C95Ci Reasoning about higher-order relational specifications]. ~ Y. Wang, K. Chaudhuri, A. Gacek y G. Nadathur
# [http://bit.ly/18QQLcL Proofs you can believe in – Proving equivalences between Prolog semantics in Coq]. ~ J. Kriener, A. King y S. Blazy
# [http://bit.ly/19uc82J Certified, efficient and sharp univariate Taylor models in Coq]. ~ E. Martin-Dorel, L. Rideau, L. Théry, M. Mayero y I. Paşca
# [http://bit.ly/1c4Rzel Ordinals in HOL: Transfinite arithmetic up to (and beyond) ω₁]. ~ M. Norrish y B. Huffman
# [http://bit.ly/14b4Akz Program verification based on Kleene algebra in Isabelle/HOL] ~ A. Armstrong, G. Struth y T. Weber
# [http://bit.ly/1aOgRKx Reading an algebra textbook (by translating it to a formal document in the Isabelle/Isar language)]. ~ C. Ballarin
# [http://bit.ly/11HKixj Computational verification of network programs in Coq]. ~ G. Stewart
# [http://www.glc.us.es/~jalonso/vestigium/resena-certifying-homological-algorithms-to-study-biomedical-images Certifying homological algorithms to study biomedical images]. ~ M. Poza
# [http://bit.ly/16Nks9m Formalizing cut elimination of coalgebraic logics in Coq]. ~ H. Tews
# [http://www.glc.us.es/~jalonso/vestigium/resena-the-formalization-of-syntax-based-mathematical-algorithms-using-quotation-and-evaluation/ The formalization of syntax-based mathematical algorithms using quotation and evaluation]. ~ W.M. Farmer
# [http://www.glc.us.es/~jalonso/vestigium/resena-certified-symbolic-manipulation-bivariate-simplicial-polynomials/ Certified symbolic manipulation: Bivariate simplicial polynomials]. ~ L. Lambán, F.J. Martín, J. Rubio y J.L. Ruiz
# [http://www.glc.us.es/~jalonso/vestigium/resena-solveurs-cpfd-verifies-formellement/ Solveurs CP(FD) vérifiés formellement]. ~ C Dubois y A. Gotlieb
# [http://www.glc.us.es/~jalonso/vestigium/resena-formalizing-bounded-increase/ Formalizing bounded increase]. ~ R. Thiemann
# [http://www.glc.us.es/~jalonso/vestigium/resena-formal-mathematics-on-display-a-wiki-for-flyspeck/ Formal mathematics on display: A wiki for Flyspeck]. ~ C. Tankink, C. Kaliszyk, J. Urban y H. Geuvers
# [http://www.glc.us.es/~jalonso/vestigium/resena-theorem-of-three-circles-in-coq Theorem of three circles in Coq]. ~ J. Zsidó
# [http://bit.ly/19fiWAY Certified HLints with Isabelle/HOLCF-Prelude]. ~ J. Breitner, B. Huffman, N. Mitchell y C. Sternagel
# [http://bit.ly/ZfSQrQ Automatic data refinement]. ~ P. Lammich
# [http://bit.ly/18vyjm7 The rooster and the butterflies (a machine-checked proof of the Jordan-Hölder theorem for finite groups)]. ~ A. Mahboubi
# [http://bit.ly/114oyZV Mechanical verification of SAT refutations with extended resolution]. ~ N. Wetzler, M.J.H. Heule y W.A. Hunt Jr.
# [http://bit.ly/13H0REu Type classes and filters for mathematical analysis in Isabelle/HOL] ~ J. Hölzl, F. Immler y B. Huffman
# [http://bit.ly/10fv8wO Verifying refutations with extended resolution]. ~ M. J. H. Heule, W. A. Hunt, Jr. y N. Wetzler
# [http://bit.ly/10EcFWj A Web interface for Isabelle: The next generation]. ~ C. Lüth y M. Ring
# [http://bit.ly/18P9CSv On the formalization of continuous-time Markov chains in HOL]. ~ L. Liu, O. Hasan y S. Tahar
# [http://bit.ly/17H2mqy Formalizing Turing machines]. ~ A. Asperti y W. Ricciotti
# [http://bit.ly/YwuCeL Light-weight containers for Isabelle: efficient, extensible, nestable]. ~ A. Lochbihler
# [http://bit.ly/10XLrRA Graph theory]. ~ L. Noschinski
# [http://bit.ly/19kPEP4 A machine-checked proof of the odd order theorem]. ~ G. Gonthier et als.
# [http://goo.gl/LdihL A constructive theory of regular languages in Coq]. ~ C. Doczkal, J.O. Kaiser y G. Smolka
# [http://goo.gl/gwcwL A formal proof of Kruskal’s tree theorem in Isabelle/HOL]. ~ C. Sternagel
# [http://goo.gl/CUF3e Formalizing Knuth-Bendix orders and Knuth-Bendix completion]. ~ C. Sternagel y R. Thiemann
# [http://goo.gl/9JAfX Developing an auction theory toolbox]. ~ C. Lange, C. Rowat, W. Windsteiger y M. Kerber
# [http://goo.gl/6OfmQ Formalization of incremental simplex algorithm by stepwise refinement]. ~ M. Spasić y F. Marić
# [http://goo.gl/Guxky Coinductive pearl: Modular first-order logic completeness]. ~ J.C. Blanchette, A. Popescu y D. Traytel
# [http://goo.gl/HUOl8 A fully verified executable LTL model checker]. ~ J. Esparza et als.
# [http://goo.gl/RV54S ForMaRE - formal mathematical reasoning in economics]. ~ M. Kerber, C. Lange y C. Rowat.
# [http://goo.gl/Y7sIq AI over large formal knowledge bases: The first decade]. ~ J. Urban.
# [http://goo.gl/vvqNg Formalization of real analysis: A survey of proof assistants and libraries]. ~ S. Boldo, C. Lelay y G. Melquiond.
# [http://goo.gl/bEFYa Data refinement in Isabelle/HOL]. ~ F. Haftmann, A. Krauss, O. Kunčar y T. Nipkow
# [http://goo.gl/xTyvE Formalizing the confluence of orthogonal rewriting systems]. ~ A.C. Rocha y M. Ayala.
# [http://goo.gl/zCYHj Formalization of the complex number theory in HOL4]. ~ Z. Shi et als.
# [http://goo.gl/kM0dI Programming and reasonning with PowerLists in Coq]. ~ F. Loulergue y V. Niculescu
# [http://goo.gl/KkU6s A hierarchy of mathematical structures in ACL2]. ~ J. Heras, F.J. Martín y V. Pascual.
# [http://www.inf.kcl.ac.uk/staff/urbanc/Publications/tm.pdf Mechanising Turing Machines and Computability Theory in Isabelle/HOL] ~ J. Xu, X. Zhang y C. Urban

Documentación

2022-01-27T19:14:25Z

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 [https://www.ias.ac.in/article/fulltext/sadh/034/01/0003-0025 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]. 5 de diciembre de 2013.
# M. Wenzel [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/Isabelle2013-2/doc/isabelle-ref.pdf The Isabelle/Isar Reference Manual]. 5 de diciembre de 2013.
# M. Wenzel [https://www.lri.fr/~wenzel/Isabelle2011-Paris/quickref.pdf The Isabelle/Isar quick reference].
# J. Siek [http://ecee.colorado.edu/~siek/ecen3703/spring10/quick-ref.pdf Quick Reference for Isabelle/Isar Propositional Logic].
# J. Siek [http://ecee.colorado.edu/~siek/ecen3703/spring10/quick-ref2.pdf Quick Reference for Isabelle/Isar More Proof Techniques].
# J. Siek [http://ecee.colorado.edu/~siek/ecen3703/spring10/quick-ref3.pdf Quick Reference for Isabelle/Isar First-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].
# Viorel Preoteasa, Ralph-Johan Back y Charmi Panchal. [http://users.abo.fi/vpreotea/isabelle-2012 Introduction to mechanized reasoning with Isabelle/HOL]. (Åbo Akademi University, 2012).
# 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).
# Adam Chlipala [http://stellar.mit.edu/S/course/6/fa11/6.892/ Interactive computer theorem proving]. (MIT, 2012-13).
# Adam Chlipala y Armando Solar Lezama [https://stellar.mit.edu/S/course/6/fa13/6.820/index.html Foundations of program analysis]. (MIT, 2013-14).
# Robby Findler [http://www.eecs.northwestern.edu/~robby/courses/395-495-2013-fall Certified programming with dependent types]. (Northwestern, 2013-14).
# Nuno Gaspar [http://www-sop.inria.fr/members/Nuno.Gaspar/teaching/coq2012.php Verification with the Coq Proof Assistant] (INRIA Sophia Antipolis, 2012-13).
# Carlos Luna y Gustavo Betarte. [https://eva.fing.edu.uy/course/view.php?id=363 Construcción formal de programas en teoría de tipos]. (Univ. de la República, Uruguay, 2013-14).
# 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).
# Michael Winter [Logic in Computer Science] (Brock University, Ontario, Canada, 2010-11).

== 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]:
# [http://bit.ly/1iZjgqN Proof Pearl: A probabilistic proof for the Girth-Chromatic number theorem]. L. Noschinski
# [http://bit.ly/1iJ8uVz A graph library for Isabelle]. ~ L. Noschinski
# [http://bit.ly/I0CU80 Gödel’s incompleteness theorems]. ~ L.C. Paulson
# [http://bit.ly/I0CPRN The hereditarily finite sets]. ~ L.C. Paulson
# [http://bit.ly/HBiIJI Applications of real number theorem proving in PVS]. ~ H. Gottliebsen, R. Hardy, O. Lightfoot y U. Martin
# [http://bit.ly/1awnMLB A machine-assisted proof of Gödel’s incompleteness theorems for the theory of hereditarily finite sets]. ~ L.C. Paulson
# [http://bit.ly/19lWeYy Verified AIG algorithms in ACL2]. ~ J. Davis y S. Swords
# [http://bit.ly/GAhC00 A formal model and correctness proof for an access control policy framework]. ~ C. Wu, X. Zhang y C. Urban
# [http://bit.ly/16SMvSS The ontological argument in PVS]. ~ J. Rushby
# [http://bit.ly/1dRt9n0 Formalizing Moessner’s theorem and generalizations in Nuprl]. ~ M. Bickford, D. Kozen y A. Silva
# [http://bit.ly/1bSeDNB Formalization in PVS of balancing properties necessary for the security of the Dolev-Yao cascade protocol model]. ~ M. Ayala y Y. Santos
# [http://bit.ly/1feFqWE Proof assistant based on didactic considerations]. ~ J. Pais y A Tasistro
# [http://bit.ly/18tHNBi Theory exploration for interactive theorem proving]. ~ M. Johansson
# [http://bit.ly/1b0242s From Tarski to Hilbert]. ~ G. Braun y J. Narboux
# [http://bit.ly/18HaXaR Formal verification of language-based concurrent noninterference]. ~ A. Popescu, J. Hölzl y T. Nipkow
# [http://bit.ly/1aRTQsU A Traffic Alert and Collision Avoidance System(TCAS-II) Resolution Advisory Algorithm]. ~ C. Muñoz, A. Narkawicz y J. Chamberlain
# [http://bit.ly/1dNwhDI Formal verification of cryptographic security proofs]. ~ M. Berg
# [http://bit.ly/17muAUv Polygonal numbers in Mizar]. ~ A. Grabowski
# [http://bit.ly/1hk5z6L A mechanised proof of Gödel’s incompleteness theorems using Nominal Isabelle]. ~ L.C. Paulson
# [http://bit.ly/1cSL0wE Steps towards verified implementations of HOL Light]. ~ M.O. Myreen, S. Owens y R. Kumar
# [http://bit.ly/16Kbgm0 Generic datatypes à la carte]. ~ S. Keuchel y T. Schrijvers
# [http://bit.ly/1bqJGx4 Proof pearl: A verified bignum implementation in x86-64 machine code]. ~ M.O. Myreen y G. Curello
# [http://bit.ly/142ow2Q Mechanized metatheory for a λ λ-calculus with trust types]. ~ R. Ribeiro, C. Camarão y L. Figueiredo
# [http://bit.ly/15WZBDy Proving soundness of combinatorial Vickrey auctions and generating verified executable code]. ~ M.B. Caminati, M. Kerber, C. Lange y C. Rowat
# [http://bit.ly/198g4n9 A computer-assisted proof of correctness of a marching cubes algorithm]. ~ A.N. Chernikov y J. Xu
# [http://bit.ly/11QA5g7 Verifying the bridge between simplicial topology and algebra: the Eilenberg-Zilber algorithm]. ~ L. Lambán, J. Rubio, F.J. Martín y J.L. Ruiz
# [http://bit.ly/1cJAXYk The Königsberg bridge problem and the friendship theorem]. ~ W. Li
# [http://bit.ly/13DBK9R Formal verification of a proof procedure for the description logic ALC]. ~ M. Chaabani, M. Mezghiche y M. Strecker
# [http://bit.ly/1ep2ex9 Pratt’s primality certificates]. ~ S. Wimmer y L. Noschinski
# [http://bit.ly/13C95Ci Reasoning about higher-order relational specifications]. ~ Y. Wang, K. Chaudhuri, A. Gacek y G. Nadathur
# [http://bit.ly/18QQLcL Proofs you can believe in – Proving equivalences between Prolog semantics in Coq]. ~ J. Kriener, A. King y S. Blazy
# [http://bit.ly/19uc82J Certified, efficient and sharp univariate Taylor models in Coq]. ~ E. Martin-Dorel, L. Rideau, L. Théry, M. Mayero y I. Paşca
# [http://bit.ly/1c4Rzel Ordinals in HOL: Transfinite arithmetic up to (and beyond) ω₁]. ~ M. Norrish y B. Huffman
# [http://bit.ly/14b4Akz Program verification based on Kleene algebra in Isabelle/HOL] ~ A. Armstrong, G. Struth y T. Weber
# [http://bit.ly/1aOgRKx Reading an algebra textbook (by translating it to a formal document in the Isabelle/Isar language)]. ~ C. Ballarin
# [http://bit.ly/11HKixj Computational verification of network programs in Coq]. ~ G. Stewart
# [http://www.glc.us.es/~jalonso/vestigium/resena-certifying-homological-algorithms-to-study-biomedical-images Certifying homological algorithms to study biomedical images]. ~ M. Poza
# [http://bit.ly/16Nks9m Formalizing cut elimination of coalgebraic logics in Coq]. ~ H. Tews
# [http://www.glc.us.es/~jalonso/vestigium/resena-the-formalization-of-syntax-based-mathematical-algorithms-using-quotation-and-evaluation/ The formalization of syntax-based mathematical algorithms using quotation and evaluation]. ~ W.M. Farmer
# [http://www.glc.us.es/~jalonso/vestigium/resena-certified-symbolic-manipulation-bivariate-simplicial-polynomials/ Certified symbolic manipulation: Bivariate simplicial polynomials]. ~ L. Lambán, F.J. Martín, J. Rubio y J.L. Ruiz
# [http://www.glc.us.es/~jalonso/vestigium/resena-solveurs-cpfd-verifies-formellement/ Solveurs CP(FD) vérifiés formellement]. ~ C Dubois y A. Gotlieb
# [http://www.glc.us.es/~jalonso/vestigium/resena-formalizing-bounded-increase/ Formalizing bounded increase]. ~ R. Thiemann
# [http://www.glc.us.es/~jalonso/vestigium/resena-formal-mathematics-on-display-a-wiki-for-flyspeck/ Formal mathematics on display: A wiki for Flyspeck]. ~ C. Tankink, C. Kaliszyk, J. Urban y H. Geuvers
# [http://www.glc.us.es/~jalonso/vestigium/resena-theorem-of-three-circles-in-coq Theorem of three circles in Coq]. ~ J. Zsidó
# [http://bit.ly/19fiWAY Certified HLints with Isabelle/HOLCF-Prelude]. ~ J. Breitner, B. Huffman, N. Mitchell y C. Sternagel
# [http://bit.ly/ZfSQrQ Automatic data refinement]. ~ P. Lammich
# [http://bit.ly/18vyjm7 The rooster and the butterflies (a machine-checked proof of the Jordan-Hölder theorem for finite groups)]. ~ A. Mahboubi
# [http://bit.ly/114oyZV Mechanical verification of SAT refutations with extended resolution]. ~ N. Wetzler, M.J.H. Heule y W.A. Hunt Jr.
# [http://bit.ly/13H0REu Type classes and filters for mathematical analysis in Isabelle/HOL] ~ J. Hölzl, F. Immler y B. Huffman
# [http://bit.ly/10fv8wO Verifying refutations with extended resolution]. ~ M. J. H. Heule, W. A. Hunt, Jr. y N. Wetzler
# [http://bit.ly/10EcFWj A Web interface for Isabelle: The next generation]. ~ C. Lüth y M. Ring
# [http://bit.ly/18P9CSv On the formalization of continuous-time Markov chains in HOL]. ~ L. Liu, O. Hasan y S. Tahar
# [http://bit.ly/17H2mqy Formalizing Turing machines]. ~ A. Asperti y W. Ricciotti
# [http://bit.ly/YwuCeL Light-weight containers for Isabelle: efficient, extensible, nestable]. ~ A. Lochbihler
# [http://bit.ly/10XLrRA Graph theory]. ~ L. Noschinski
# [http://bit.ly/19kPEP4 A machine-checked proof of the odd order theorem]. ~ G. Gonthier et als.
# [http://goo.gl/LdihL A constructive theory of regular languages in Coq]. ~ C. Doczkal, J.O. Kaiser y G. Smolka
# [http://goo.gl/gwcwL A formal proof of Kruskal’s tree theorem in Isabelle/HOL]. ~ C. Sternagel
# [http://goo.gl/CUF3e Formalizing Knuth-Bendix orders and Knuth-Bendix completion]. ~ C. Sternagel y R. Thiemann
# [http://goo.gl/9JAfX Developing an auction theory toolbox]. ~ C. Lange, C. Rowat, W. Windsteiger y M. Kerber
# [http://goo.gl/6OfmQ Formalization of incremental simplex algorithm by stepwise refinement]. ~ M. Spasić y F. Marić
# [http://goo.gl/Guxky Coinductive pearl: Modular first-order logic completeness]. ~ J.C. Blanchette, A. Popescu y D. Traytel
# [http://goo.gl/HUOl8 A fully verified executable LTL model checker]. ~ J. Esparza et als.
# [http://goo.gl/RV54S ForMaRE - formal mathematical reasoning in economics]. ~ M. Kerber, C. Lange y C. Rowat.
# [http://goo.gl/Y7sIq AI over large formal knowledge bases: The first decade]. ~ J. Urban.
# [http://goo.gl/vvqNg Formalization of real analysis: A survey of proof assistants and libraries]. ~ S. Boldo, C. Lelay y G. Melquiond.
# [http://goo.gl/bEFYa Data refinement in Isabelle/HOL]. ~ F. Haftmann, A. Krauss, O. Kunčar y T. Nipkow
# [http://goo.gl/xTyvE Formalizing the confluence of orthogonal rewriting systems]. ~ A.C. Rocha y M. Ayala.
# [http://goo.gl/zCYHj Formalization of the complex number theory in HOL4]. ~ Z. Shi et als.
# [http://goo.gl/kM0dI Programming and reasonning with PowerLists in Coq]. ~ F. Loulergue y V. Niculescu
# [http://goo.gl/KkU6s A hierarchy of mathematical structures in ACL2]. ~ J. Heras, F.J. Martín y V. Pascual.
# [http://www.inf.kcl.ac.uk/staff/urbanc/Publications/tm.pdf Mechanising Turing Machines and Computability Theory in Isabelle/HOL] ~ J. Xu, X. Zhang y C. Urban

Documentación

2022-01-27T19:03:21Z

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 [https://www.ias.ac.in/article/fulltext/sadh/034/01/0003-0025 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 [http://www.bcs.org/server.php?show=ConWebDoc.4364 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]. 5 de diciembre de 2013.
# M. Wenzel [http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/Isabelle2013-2/doc/isabelle-ref.pdf The Isabelle/Isar Reference Manual]. 5 de diciembre de 2013.
# M. Wenzel [https://www.lri.fr/~wenzel/Isabelle2011-Paris/quickref.pdf The Isabelle/Isar quick reference].
# J. Siek [http://ecee.colorado.edu/~siek/ecen3703/spring10/quick-ref.pdf Quick Reference for Isabelle/Isar Propositional Logic].
# J. Siek [http://ecee.colorado.edu/~siek/ecen3703/spring10/quick-ref2.pdf Quick Reference for Isabelle/Isar More Proof Techniques].
# J. Siek [http://ecee.colorado.edu/~siek/ecen3703/spring10/quick-ref3.pdf Quick Reference for Isabelle/Isar First-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].
# Viorel Preoteasa, Ralph-Johan Back y Charmi Panchal. [http://users.abo.fi/vpreotea/isabelle-2012 Introduction to mechanized reasoning with Isabelle/HOL]. (Åbo Akademi University, 2012).
# 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).
# Adam Chlipala [http://stellar.mit.edu/S/course/6/fa11/6.892/ Interactive computer theorem proving]. (MIT, 2012-13).
# Adam Chlipala y Armando Solar Lezama [https://stellar.mit.edu/S/course/6/fa13/6.820/index.html Foundations of program analysis]. (MIT, 2013-14).
# Robby Findler [http://www.eecs.northwestern.edu/~robby/courses/395-495-2013-fall Certified programming with dependent types]. (Northwestern, 2013-14).
# Nuno Gaspar [http://www-sop.inria.fr/members/Nuno.Gaspar/teaching/coq2012.php Verification with the Coq Proof Assistant] (INRIA Sophia Antipolis, 2012-13).
# Carlos Luna y Gustavo Betarte. [https://eva.fing.edu.uy/course/view.php?id=363 Construcción formal de programas en teoría de tipos]. (Univ. de la República, Uruguay, 2013-14).
# 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).
# Michael Winter [Logic in Computer Science] (Brock University, Ontario, Canada, 2010-11).

== 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]:
# [http://bit.ly/1iZjgqN Proof Pearl: A probabilistic proof for the Girth-Chromatic number theorem]. L. Noschinski
# [http://bit.ly/1iJ8uVz A graph library for Isabelle]. ~ L. Noschinski
# [http://bit.ly/I0CU80 Gödel’s incompleteness theorems]. ~ L.C. Paulson
# [http://bit.ly/I0CPRN The hereditarily finite sets]. ~ L.C. Paulson
# [http://bit.ly/HBiIJI Applications of real number theorem proving in PVS]. ~ H. Gottliebsen, R. Hardy, O. Lightfoot y U. Martin
# [http://bit.ly/1awnMLB A machine-assisted proof of Gödel’s incompleteness theorems for the theory of hereditarily finite sets]. ~ L.C. Paulson
# [http://bit.ly/19lWeYy Verified AIG algorithms in ACL2]. ~ J. Davis y S. Swords
# [http://bit.ly/GAhC00 A formal model and correctness proof for an access control policy framework]. ~ C. Wu, X. Zhang y C. Urban
# [http://bit.ly/16SMvSS The ontological argument in PVS]. ~ J. Rushby
# [http://bit.ly/1dRt9n0 Formalizing Moessner’s theorem and generalizations in Nuprl]. ~ M. Bickford, D. Kozen y A. Silva
# [http://bit.ly/1bSeDNB Formalization in PVS of balancing properties necessary for the security of the Dolev-Yao cascade protocol model]. ~ M. Ayala y Y. Santos
# [http://bit.ly/1feFqWE Proof assistant based on didactic considerations]. ~ J. Pais y A Tasistro
# [http://bit.ly/18tHNBi Theory exploration for interactive theorem proving]. ~ M. Johansson
# [http://bit.ly/1b0242s From Tarski to Hilbert]. ~ G. Braun y J. Narboux
# [http://bit.ly/18HaXaR Formal verification of language-based concurrent noninterference]. ~ A. Popescu, J. Hölzl y T. Nipkow
# [http://bit.ly/1aRTQsU A Traffic Alert and Collision Avoidance System(TCAS-II) Resolution Advisory Algorithm]. ~ C. Muñoz, A. Narkawicz y J. Chamberlain
# [http://bit.ly/1dNwhDI Formal verification of cryptographic security proofs]. ~ M. Berg
# [http://bit.ly/17muAUv Polygonal numbers in Mizar]. ~ A. Grabowski
# [http://bit.ly/1hk5z6L A mechanised proof of Gödel’s incompleteness theorems using Nominal Isabelle]. ~ L.C. Paulson
# [http://bit.ly/1cSL0wE Steps towards verified implementations of HOL Light]. ~ M.O. Myreen, S. Owens y R. Kumar
# [http://bit.ly/16Kbgm0 Generic datatypes à la carte]. ~ S. Keuchel y T. Schrijvers
# [http://bit.ly/1bqJGx4 Proof pearl: A verified bignum implementation in x86-64 machine code]. ~ M.O. Myreen y G. Curello
# [http://bit.ly/142ow2Q Mechanized metatheory for a λ λ-calculus with trust types]. ~ R. Ribeiro, C. Camarão y L. Figueiredo
# [http://bit.ly/15WZBDy Proving soundness of combinatorial Vickrey auctions and generating verified executable code]. ~ M.B. Caminati, M. Kerber, C. Lange y C. Rowat
# [http://bit.ly/198g4n9 A computer-assisted proof of correctness of a marching cubes algorithm]. ~ A.N. Chernikov y J. Xu
# [http://bit.ly/11QA5g7 Verifying the bridge between simplicial topology and algebra: the Eilenberg-Zilber algorithm]. ~ L. Lambán, J. Rubio, F.J. Martín y J.L. Ruiz
# [http://bit.ly/1cJAXYk The Königsberg bridge problem and the friendship theorem]. ~ W. Li
# [http://bit.ly/13DBK9R Formal verification of a proof procedure for the description logic ALC]. ~ M. Chaabani, M. Mezghiche y M. Strecker
# [http://bit.ly/1ep2ex9 Pratt’s primality certificates]. ~ S. Wimmer y L. Noschinski
# [http://bit.ly/13C95Ci Reasoning about higher-order relational specifications]. ~ Y. Wang, K. Chaudhuri, A. Gacek y G. Nadathur
# [http://bit.ly/18QQLcL Proofs you can believe in – Proving equivalences between Prolog semantics in Coq]. ~ J. Kriener, A. King y S. Blazy
# [http://bit.ly/19uc82J Certified, efficient and sharp univariate Taylor models in Coq]. ~ E. Martin-Dorel, L. Rideau, L. Théry, M. Mayero y I. Paşca
# [http://bit.ly/1c4Rzel Ordinals in HOL: Transfinite arithmetic up to (and beyond) ω₁]. ~ M. Norrish y B. Huffman
# [http://bit.ly/14b4Akz Program verification based on Kleene algebra in Isabelle/HOL] ~ A. Armstrong, G. Struth y T. Weber
# [http://bit.ly/1aOgRKx Reading an algebra textbook (by translating it to a formal document in the Isabelle/Isar language)]. ~ C. Ballarin
# [http://bit.ly/11HKixj Computational verification of network programs in Coq]. ~ G. Stewart
# [http://www.glc.us.es/~jalonso/vestigium/resena-certifying-homological-algorithms-to-study-biomedical-images Certifying homological algorithms to study biomedical images]. ~ M. Poza
# [http://bit.ly/16Nks9m Formalizing cut elimination of coalgebraic logics in Coq]. ~ H. Tews
# [http://www.glc.us.es/~jalonso/vestigium/resena-the-formalization-of-syntax-based-mathematical-algorithms-using-quotation-and-evaluation/ The formalization of syntax-based mathematical algorithms using quotation and evaluation]. ~ W.M. Farmer
# [http://www.glc.us.es/~jalonso/vestigium/resena-certified-symbolic-manipulation-bivariate-simplicial-polynomials/ Certified symbolic manipulation: Bivariate simplicial polynomials]. ~ L. Lambán, F.J. Martín, J. Rubio y J.L. Ruiz
# [http://www.glc.us.es/~jalonso/vestigium/resena-solveurs-cpfd-verifies-formellement/ Solveurs CP(FD) vérifiés formellement]. ~ C Dubois y A. Gotlieb
# [http://www.glc.us.es/~jalonso/vestigium/resena-formalizing-bounded-increase/ Formalizing bounded increase]. ~ R. Thiemann
# [http://www.glc.us.es/~jalonso/vestigium/resena-formal-mathematics-on-display-a-wiki-for-flyspeck/ Formal mathematics on display: A wiki for Flyspeck]. ~ C. Tankink, C. Kaliszyk, J. Urban y H. Geuvers
# [http://www.glc.us.es/~jalonso/vestigium/resena-theorem-of-three-circles-in-coq Theorem of three circles in Coq]. ~ J. Zsidó
# [http://bit.ly/19fiWAY Certified HLints with Isabelle/HOLCF-Prelude]. ~ J. Breitner, B. Huffman, N. Mitchell y C. Sternagel
# [http://bit.ly/ZfSQrQ Automatic data refinement]. ~ P. Lammich
# [http://bit.ly/18vyjm7 The rooster and the butterflies (a machine-checked proof of the Jordan-Hölder theorem for finite groups)]. ~ A. Mahboubi
# [http://bit.ly/114oyZV Mechanical verification of SAT refutations with extended resolution]. ~ N. Wetzler, M.J.H. Heule y W.A. Hunt Jr.
# [http://bit.ly/13H0REu Type classes and filters for mathematical analysis in Isabelle/HOL] ~ J. Hölzl, F. Immler y B. Huffman
# [http://bit.ly/10fv8wO Verifying refutations with extended resolution]. ~ M. J. H. Heule, W. A. Hunt, Jr. y N. Wetzler
# [http://bit.ly/10EcFWj A Web interface for Isabelle: The next generation]. ~ C. Lüth y M. Ring
# [http://bit.ly/18P9CSv On the formalization of continuous-time Markov chains in HOL]. ~ L. Liu, O. Hasan y S. Tahar
# [http://bit.ly/17H2mqy Formalizing Turing machines]. ~ A. Asperti y W. Ricciotti
# [http://bit.ly/YwuCeL Light-weight containers for Isabelle: efficient, extensible, nestable]. ~ A. Lochbihler
# [http://bit.ly/10XLrRA Graph theory]. ~ L. Noschinski
# [http://bit.ly/19kPEP4 A machine-checked proof of the odd order theorem]. ~ G. Gonthier et als.
# [http://goo.gl/LdihL A constructive theory of regular languages in Coq]. ~ C. Doczkal, J.O. Kaiser y G. Smolka
# [http://goo.gl/gwcwL A formal proof of Kruskal’s tree theorem in Isabelle/HOL]. ~ C. Sternagel
# [http://goo.gl/CUF3e Formalizing Knuth-Bendix orders and Knuth-Bendix completion]. ~ C. Sternagel y R. Thiemann
# [http://goo.gl/9JAfX Developing an auction theory toolbox]. ~ C. Lange, C. Rowat, W. Windsteiger y M. Kerber
# [http://goo.gl/6OfmQ Formalization of incremental simplex algorithm by stepwise refinement]. ~ M. Spasić y F. Marić
# [http://goo.gl/Guxky Coinductive pearl: Modular first-order logic completeness]. ~ J.C. Blanchette, A. Popescu y D. Traytel
# [http://goo.gl/HUOl8 A fully verified executable LTL model checker]. ~ J. Esparza et als.
# [http://goo.gl/RV54S ForMaRE - formal mathematical reasoning in economics]. ~ M. Kerber, C. Lange y C. Rowat.
# [http://goo.gl/Y7sIq AI over large formal knowledge bases: The first decade]. ~ J. Urban.
# [http://goo.gl/vvqNg Formalization of real analysis: A survey of proof assistants and libraries]. ~ S. Boldo, C. Lelay y G. Melquiond.
# [http://goo.gl/bEFYa Data refinement in Isabelle/HOL]. ~ F. Haftmann, A. Krauss, O. Kunčar y T. Nipkow
# [http://goo.gl/xTyvE Formalizing the confluence of orthogonal rewriting systems]. ~ A.C. Rocha y M. Ayala.
# [http://goo.gl/zCYHj Formalization of the complex number theory in HOL4]. ~ Z. Shi et als.
# [http://goo.gl/kM0dI Programming and reasonning with PowerLists in Coq]. ~ F. Loulergue y V. Niculescu
# [http://goo.gl/KkU6s A hierarchy of mathematical structures in ACL2]. ~ J. Heras, F.J. Martín y V. Pascual.
# [http://www.inf.kcl.ac.uk/staff/urbanc/Publications/tm.pdf Mechanising Turing Machines and Computability Theory in Isabelle/HOL] ~ J. Xu, X. Zhang y C. Urban

Temas

2020-03-16T10:53:25Z

Jalonso:

* [[Tema 1: Programación funcional en Isabelle]].
* [http://www.cs.us.es/~jalonso/cursos/i1m/temas/tema-8t.pdf Tema 2a: Razonamiento sobre programas Haskell]
* [[Tema 2b: Razonamiento automático sobre programas en Isabelle/HOL]].
* [[Tema 3: Razonamiento estructurado sobre programas en Isabelle/HOL]].
* [[Tema 4: Razonamiento por casos y por inducción]].
* [[Tema 5a: Verificación de la ordenación por inserción]].
* [[Tema 5b: Verificación de la ordenación por mezcla]].
* [http://www.cs.us.es/~jalonso/cursos/li/temas/tema-2.pdf Tema 6a: Deducción natural proposicional]].
* [[Tema 6b: Deducción natural proposicional con Isabelle/HOL]].
* [http://www.cs.us.es/~jalonso/cursos/li/temas/tema-8.pdf Tema 7a: Deducción natural en lógica de primer orden]].
* [[Tema 7b: Deducción natural en lógica de primer orden con Isabelle/HOL]].
* [[Tema 8: Caso de estudio: Compilación de expresiones]].
* [http://www.cs.us.es/~jalonso/cursos/dao-12/temas/tema-1.pdf Tema 9: Panorama de la demostración asistida por ordenador].

== Listas de vídeos de las clases ==

* [https://www.youtube.com/watch?v=3ypB3TUmSHg 2013-11-27 ]
* [https://www.youtube.com/watch?v=yazrdrjlbEU 2013-12-05a ]
* [https://www.youtube.com/watch?v=jwtk99TIoMo 2013-12-05b ]
* [https://www.youtube.com/watch?v=1GynGGucKRQ 2013-12-12a ]
* [https://www.youtube.com/watch?v=cCqwFkDWkqI 2013-12-19a ]
* [https://www.youtube.com/watch?v=lbhkBjbNh3Y 2013-12-19b ]
* [https://www.youtube.com/watch?v=WakkA2x8Gs8 2014-01-09a ]
* [https://www.youtube.com/watch?v=9RgFTM5s-nE 2014-01-09b ]
* [https://www.youtube.com/watch?v=Xf66W5A7yFw 2014-01-16a ]
* [https://www.youtube.com/watch?v=VlIjp3eyDR4 2014-01-16b ]
* [https://www.youtube.com/watch?v=u7_3tW8p4Us 2014-01-23a ]
* [https://www.youtube.com/watch?v=iu2lRLN_Mo4 2014-01-23b ]
* [https://www.youtube.com/watch?v=Cf3quG6TkXE 2014-01-30a ]
* [https://www.youtube.com/watch?v=578loXA_ImI 2014-01-30b ]
* [https://www.youtube.com/watch?v=fd08GOuiaMM 2014-02-06 ]
* [https://www.youtube.com/watch?v=IFJtN7tlyuc 2014-02-13 ]

Temas

2020-03-16T10:51:18Z

Jalonso:

* [[Tema 1: Programación funcional en Isabelle]].
* [http://www.cs.us.es/~jalonso/cursos/i1m/temas/tema-8t.pdf Tema 2a: Razonamiento sobre programas Haskell]
* [[Tema 2b: Razonamiento automático sobre programas en Isabelle/HOL]].
* [[Tema 3: Razonamiento estructurado sobre programas en Isabelle/HOL]].
* [[Tema 4: Razonamiento por casos y por inducción]].
* [[Tema 5a: Verificación de la ordenación por inserción]].
* [[Tema 5b: Verificación de la ordenación por mezcla]].
* [http://www.cs.us.es/~jalonso/cursos/li/temas/tema-2.pdf Tema 6a: Deducción natural proposicional]].
* [[Tema 6b: Deducción natural proposicional con Isabelle/HOL]].
* [http://www.cs.us.es/~jalonso/cursos/li/temas/tema-8.pdf Tema 7a: Deducción natural en lógica de primer orden]].
* [[Tema 7b: Deducción natural en lógica de primer orden con Isabelle/HOL]].
* [[Tema 8: Caso de estudio: Compilación de expresiones]].
* [http://www.cs.us.es/~jalonso/cursos/dao-12/temas/tema-1.pdf Tema 9: Panorama de la demostración asistida por ordenador].

== Listas de vídeos de las clases ==

* [2013-11-27 https://www.youtube.com/watch?v=3ypB3TUmSHg]
* [2013-12-05a https://www.youtube.com/watch?v=yazrdrjlbEU]
* [2013-12-05b https://www.youtube.com/watch?v=jwtk99TIoMo]
* [2013-12-12a https://www.youtube.com/watch?v=1GynGGucKRQ]
* [2013-12-19a https://www.youtube.com/watch?v=cCqwFkDWkqI]
* [2013-12-19b https://www.youtube.com/watch?v=lbhkBjbNh3Y]
* [2014-01-09a https://www.youtube.com/watch?v=WakkA2x8Gs8]
* [2014-01-09b https://www.youtube.com/watch?v=9RgFTM5s-nE]
* [2014-01-16a https://www.youtube.com/watch?v=Xf66W5A7yFw]
* [2014-01-16b https://www.youtube.com/watch?v=VlIjp3eyDR4]
* [2014-01-23a https://www.youtube.com/watch?v=u7_3tW8p4Us]
* [2014-01-23b https://www.youtube.com/watch?v=iu2lRLN_Mo4]
* [2014-01-30a https://www.youtube.com/watch?v=Cf3quG6TkXE]
* [2014-01-30b https://www.youtube.com/watch?v=578loXA_ImI]
* [2014-02-06 https://www.youtube.com/watch?v=fd08GOuiaMM]
* [2014-02-13 https://www.youtube.com/watch?v=IFJtN7tlyuc]

Temas

2020-03-16T10:50:18Z

Jalonso:

* [[Tema 1: Programación funcional en Isabelle]].
* [http://www.cs.us.es/~jalonso/cursos/i1m/temas/tema-8t.pdf Tema 2a: Razonamiento sobre programas Haskell]
* [[Tema 2b: Razonamiento automático sobre programas en Isabelle/HOL]].
* [[Tema 3: Razonamiento estructurado sobre programas en Isabelle/HOL]].
* [[Tema 4: Razonamiento por casos y por inducción]].
* [[Tema 5a: Verificación de la ordenación por inserción]].
* [[Tema 5b: Verificación de la ordenación por mezcla]].
* [http://www.cs.us.es/~jalonso/cursos/li/temas/tema-2.pdf Tema 6a: Deducción natural proposicional]].
* [[Tema 6b: Deducción natural proposicional con Isabelle/HOL]].
* [http://www.cs.us.es/~jalonso/cursos/li/temas/tema-8.pdf Tema 7a: Deducción natural en lógica de primer orden]].
* [[Tema 7b: Deducción natural en lógica de primer orden con Isabelle/HOL]].
* [[Tema 8: Caso de estudio: Compilación de expresiones]].
* [http://www.cs.us.es/~jalonso/cursos/dao-12/temas/tema-1.pdf Tema 9: Panorama de la demostración asistida por ordenador].

== Listas de vídeos de las clases ==

+ [2013-11-27 https://www.youtube.com/watch?v=3ypB3TUmSHg]
+ [2013-12-05a https://www.youtube.com/watch?v=yazrdrjlbEU]
+ [2013-12-05b https://www.youtube.com/watch?v=jwtk99TIoMo]
+ [2013-12-12a https://www.youtube.com/watch?v=1GynGGucKRQ]
+ [2013-12-19a https://www.youtube.com/watch?v=cCqwFkDWkqI]
+ [2013-12-19b https://www.youtube.com/watch?v=lbhkBjbNh3Y]
+ [2014-01-09a https://www.youtube.com/watch?v=WakkA2x8Gs8]
+ [2014-01-09b https://www.youtube.com/watch?v=9RgFTM5s-nE]
+ [2014-01-16a https://www.youtube.com/watch?v=Xf66W5A7yFw]
+ [2014-01-16b https://www.youtube.com/watch?v=VlIjp3eyDR4]
+ [2014-01-23a https://www.youtube.com/watch?v=u7_3tW8p4Us]
+ [2014-01-23b https://www.youtube.com/watch?v=iu2lRLN_Mo4]
+ [2014-01-30a https://www.youtube.com/watch?v=Cf3quG6TkXE]
+ [2014-01-30b https://www.youtube.com/watch?v=578loXA_ImI]
+ [2014-02-06 https://www.youtube.com/watch?v=fd08GOuiaMM]
+ [2014-02-13 https://www.youtube.com/watch?v=IFJtN7tlyuc]

Temas

2014-02-13T09:27:01Z

Jalonso: /* Temas de Razonamiento automático (2013-14) */

== Temas de ''Razonamiento automático (2013-14)'' ==
* [[Tema 1: Programación funcional en Isabelle]].
* [http://www.cs.us.es/~jalonso/cursos/i1m/temas/tema-8t.pdf Tema 2a: Razonamiento sobre programas Haskell]
* [[Tema 2b: Razonamiento automático sobre programas en Isabelle/HOL]].
* [[Tema 3: Razonamiento estructurado sobre programas en Isabelle/HOL]].
* [[Tema 4: Razonamiento por casos y por inducción]].
* [[Tema 5a: Verificación de la ordenación por inserción]].
* [[Tema 5b: Verificación de la ordenación por mezcla]].
* [http://www.cs.us.es/~jalonso/cursos/li/temas/tema-2.pdf Tema 6a: Deducción natural proposicional]].
* [[Tema 6b: Deducción natural proposicional con Isabelle/HOL]].
* [http://www.cs.us.es/~jalonso/cursos/li/temas/tema-8.pdf Tema 7a: Deducción natural en lógica de primer orden]].
* [[Tema 7b: Deducción natural en lógica de primer orden con Isabelle/HOL]].
* [[Tema 8: Caso de estudio: Compilación de expresiones]].
* [http://www.cs.us.es/~jalonso/cursos/dao-12/temas/tema-1.pdf Tema 9: Panorama de la demostración asistida por ordenador].

R12

2014-02-07T04:51:11Z

Jalonso: Protegió «R12» ([edit=sysop] (indefinido) [move=sysop] (indefinido))

<source lang="isar">
header {* R12: Representación de fórmulas proposicionales mediante
polinomios *}

theory R12
imports Main
begin

text {*
El objetivo de esta relación es definir un procedimiento para
transformar fórmulas proposicionales (construidas con ⊤, ∧ y ⊕) en
polinomios de la forma
(p₁ ∧ … ∧ pₙ) ⊕ … ⊕ (q₁ ∧ … ∧ qₘ)
y demostrar que, para cualquier interpretación I, el valor de las
fórmulas coincide con la de su correspondiente polinomio. *}

text {*
---------------------------------------------------------------------
Ejercicio 1. Las fórmulas proposicionales pueden definirse mediante
las siguientes reglas:
· ⊤ es una fórmula proposicional
· Las variables proposicionales p_1, p_2, … son fórmulas
proposicionales,
· Si F y G son fórmulas proposicionales, entonces (F ∧ G) y (F ⊕ G)
también lo son.
donde ⊤ es una fórmula que siempre es verdadera, ∧ es la conjunción y
⊕ es la disyunción exclusiva.

Definir el tipo de datos form para representar las fórmulas
proposicionales usando
· T en lugar de ⊤,
· (Var i) en lugar de p_i,
· (And F G) en lugar de (F ∧ G) y
· (Xor F G) en lugar de (F ⊕ G).
------------------------------------------------------------------ *}

datatype form = T | Var nat | And form form | Xor form form

text {*
---------------------------------------------------------------------
Ejercicio 2. Los siguientes ejemplos de fórmulas
form1 = p0 ⊕ ⊤
form2 = (p0 ⊕ p1) ⊕ (p0 ∧ p1)
es usará en lo que sigue.
------------------------------------------------------------------ *}

abbreviation form1 :: "form" where
"form1 ≡ Xor (Var 0) T"
abbreviation form2 :: "form" where
"form2 ≡ Xor (Xor (Var 0) (Var 1)) (And (Var 0) (Var 1))"

text {*
---------------------------------------------------------------------
Ejercicio 3. Definir la función
xor :: bool ⇒ bool ⇒ bool
tal que (xor p q) es el valor de la disyunción exclusiva de p y q. Por
ejemplo,
xor False True = True
------------------------------------------------------------------ *}

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

text {*
---------------------------------------------------------------------
Ejercicio 4. Una interpretación es una aplicación de los naturales en
los booleanos. Definir las siguientes interpretaciones
| p0 | p1 | p2 | p3 | ...
int1 | F | F | F | F | ...
int2 | F | V | F | F | ...
int3 | V | F | F | F | ...
int3 | V | V | F | F | ...
------------------------------------------------------------------ *}

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

text {*
---------------------------------------------------------------------
Ejercicio 5. Dada una interpretación I, el valor de de una fórmula F
repecto de I, I(F), se define por
· T, si F es ⊤;
· I(n), si F es p_n;
· I(G) ∧ I(H), si F es (G ∧ H);
· I(G) ⊕ I(H), si F es (G ⊕ H).

Definir la función
valorF :: (nat ⇒ bool) ⇒ form ⇒ bool
tal que (valorF i f) es el valor de la fórmula f respecto de la
interpretación i. Por ejemplo,
valorF int1 form1 = True
valorF int3 form1 = False
valorF int1 form2 = False
valorF int2 form2 = True
valorF int3 form2 = True
valorF int4 form2 = True
--------------------------------------------------------------------- *}

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

text {*
---------------------------------------------------------------------
Ejercicio 6. Un monomio es una lista de números naturales y se puede
interpretar como la conjunción de variables proposionales cuyos
índices son los números de la lista. Por ejemplo, el monomio [0,2,1]
se interpreta como la fórmula (p0 ∧ p2 ∧ p1).

Definir la función
formM :: nat list ⇒ form
tal que (formM m) es la fórmula correspondiente al monomio. Por
ejemplo,
formM [0,2,1] = And (Var 0) (And (Var 2) (And (Var 1) T))
--------------------------------------------------------------------- *}

fun formM :: "nat list ⇒ form" where
"formM ns = undefined"

text {*
---------------------------------------------------------------------
Ejercicio 7. Definir, por recursión, la función
valorM :: (nat ⇒ bool) ⇒ nat list ⇒ bool
tal que (valorM i m) es el valor de la fórmula representada por el
monomio m en la interpretación i. Por ejemplo,
valorM int1 [0,2,1] = False
valorM (int1(0:=True,1:=True,2:=True)) [0,2,1] = True
Demostrar que, para toda interpretación i y todo monomio m, se tiene
que
valorM i m = valorF i (formM m)
--------------------------------------------------------------------- *}

fun valorM :: "(nat ⇒ bool) ⇒ nat list ⇒ bool" where
"valorM i ns = undefined"

lemma correccion_valorM:
"valorM i m = valorF i (formM m)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 8. Un polinomio es una lista de monomios y se puede
interpretar como la disyunción exclusiva de los monomios. Por ejemplo,
el polinomio [[0,2,1],[1,3]] se interpreta como la fórmula
(p0 ∧ p2 ∧ p1) ⊕ (p1 ∧ p3).

Definir la función
formP :: nat list list ⇒ form
tal que (formP p) es la fórmula correspondiente al polinomio p. Por
ejemplo,
formP [[1,2],[3]]
= Xor (And (Var 1) (And (Var 2) T)) (Xor (And (Var 3) T) (Xor T T))
--------------------------------------------------------------------- *}

fun formP :: "nat list list ⇒ form" where
"formP ms = undefined"

text {*
---------------------------------------------------------------------
Ejercicio 9. Definir la función
valorP :: (nat ⇒ bool) ⇒ nat list list ⇒ bool
tal que (valorP i p) es el valor de la fórmula representada por el
polinomio p en la interpretación i. Por ejemplo,
valorP (int1(1:=True,3:=True)) [[0,2,1],[1,3]] = True
Demostrar que, para toda interpretación i y todo polinomio p, se tiene
que
valorM i p = valorF i (formP p)
--------------------------------------------------------------------- *}

fun valorP :: "(nat ⇒ bool) ⇒ nat list list ⇒ bool" where
"valorP i ms = undefined"

lemma correccion_valorP:
"valorP i p = valorF i (formP p)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 10. Definir la función
productoM :: nat list ⇒ nat list list ⇒ nat list list
tal que (productoM m p) es el producto del monomio p por el polinomio
p. Por ejemplo,
productoM [1,3] [[1,2,4],[7],[4,1]]
= [[1,3,1,2,4],[1,3,7],[1,3,4,1]]
--------------------------------------------------------------------- *}

fun productoM :: "nat list ⇒ nat list list ⇒ nat list list" where
"productoM m ns = undefined"

text {*
---------------------------------------------------------------------
Ejercicio 11. Demostrar que, en cualquier interpretación i, el valor
de la concatenación de dos monomios es la conjunción de sus valores.
--------------------------------------------------------------------- *}

lemma valorM_conc:
"valorM i (xs @ ys) = (valorM i xs ∧ valorM i ys)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 12. Demostrar que, en cualquier interpretación i, el valor
del producto de un monomio por un polinomio es la conjunción de sus
valores.
--------------------------------------------------------------------- *}

lemma correccion_productoM:
"valorP i (productoM m p) = (valorM i m ∧ valorP i p)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 13. Definir la función
producto :: nat list list ⇒ nat list list ⇒ nat list list
tal que (producto p q) es el producto de los polinomios p y q. Por
ejemplo,
producto [[1,3],[2]] [[1,2,4],[7],[4,1]]
= [[1,3,1,2,4],[1,3,7],[1,3,4,1],[2,1,2,4],[2,7],[2,4,1]]
--------------------------------------------------------------------- *}

fun producto :: "nat list list ⇒ nat list list ⇒ nat list list" where
"producto p q = undefined"

text {*
---------------------------------------------------------------------
Ejercicio 14. Demostrar que, en cualquier interpretación i, el valor
de la concatenación de dos polinomios es la disyunción exclusiva de
sus valores.
--------------------------------------------------------------------- *}

lemma valorP_conc:
"valorP i (xs @ ys) = (xor (valorP i xs) (valorP i ys))"
oops

text {*
---------------------------------------------------------------------
Ejercicio 15. Demostrar que, en cualquier interpretación i, el valor
del producto de dos polinomios es la conjunción de sus valores.
--------------------------------------------------------------------- *}

lemma correccion_producto:
"valorP i (producto p q) = (valorP i p ∧ valorP i q)"
oops

text {*
---------------------------------------------------------------------
Ejercicio 16. Definir la función
polinomio :: form ⇒ nat list list
tal que (polinomio f) es el polinomio que representa la fórmula f. Por
ejemplo,
polinomio (Xor (Var 1) (Var 2)) = [[1],[2]]
polinomio (And (Var 1) (Var 2)) = [[1,2]]
polinomio (Xor (Var 1) T) = [[1],[]]
polinomio (And (Var 1) T) = [[1]]]
polinomio (And (Xor (Var 1) (Var 2)) (Var 3)) = [[1,3],[2,3]]
polinomio (Xor (And (Var 1) (Var 2)) (Var 3)) = [[1,2],[3]]
--------------------------------------------------------------------- *}

fun polinomio :: "form ⇒ nat list list" where
"polinomio f = undefined"

text {*
---------------------------------------------------------------------
Ejercicio 17. Demostrar que, en cualquier interpretación i, el valor
de f es igual que el de su polinomio.
--------------------------------------------------------------------- *}

theorem correccion_polinomio:
"valorF i f = valorP i (polinomio f)"
oops

end
</source>

Relación 12

2014-02-07T04:50:31Z

Jalonso: Página creada con '<source lang="isar"> header {* R12: Representación de fórmulas proposicionales mediante polinomios *} theory R12 imports Main begin text {* El objetivo de esta relaci...'

R12

2014-02-07T04:49:51Z

Ejercicios

2014-02-07T04:46:48Z

Jalonso: /* Relaciones de ejercicios propuestos */

== Relaciones de ejercicios ==

=== Relaciones de ejercicios corregidos ===

En esta sección se encuentran las relaciones de ejercicios corregidos en las clases.

=== Relaciones de ejercicios propuestos ===

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''': Programación funcional en Isabelle/HOL. ([[R1 |Enunciado]] y [[Relación 1 | Solución colaborativa]]).
* '''Relación 2''': Razonamiento automático sobre programas en Isabelle/HOL. ([[R2 |Enunciado]] y [[Relación 2 | Solución colaborativa]]).
* '''Relación 3''': Razonamiento estructurado sobre programas en Isabelle/HOL. ([[R3 |Enunciado]] y [[Relación 3 | Solución colaborativa]]).
* '''Relación 4''': Cons inverso. ([[R4 |Enunciado]] y [[Relación 4 | Solución colaborativa]]).
* '''Relación 5''': Cuantificadores sobre listas. ([[R5 |Enunciado]] y [[Relación 5 | Solución colaborativa]]).
* '''Relación 6''': Sustitución, inversión y eliminación. ([[R6 |Enunciado]] y [[Relación 6 | Solución colaborativa]]).
* '''Relación 7''': Recorridos de árboles. ([[R7 |Enunciado]] y [[Relación 7 | Solución colaborativa]]).
* '''Relación 8''': Árboles binarios completos. ([[R8 |Enunciado]] y [[Relación 8 | Solución colaborativa]]).
* '''Relación 9''': Deducción natural proposicional (1). ([[R9 |Enunciado]] y [[Relación 9 | Solución colaborativa]]).
* '''Relación 10''': Deducción natural proposicional (2). ([[R10 |Enunciado]] y [[Relación 10 | Solución colaborativa]]).
* '''Relación 11''': Deducción natural proposicional de primer orden. ([[R11 |Enunciado]] y [[Relación 11 | Solución colaborativa]]).
* '''Relación 12''': Representación de fórmulas proposicionales mediante polinomios. ([[R12 |Enunciado]] y [[Relación 12 | Solución colaborativa]]).

Tema 8: Caso de estudio: Compilación de expresiones

2014-02-05T19:30:29Z

Jalonso: Página creada con '<source lang="isar"> header {* Tema 8: Caso de estudio: Compilación de expresiones *} theory T8 imports Main begin text {* El objetivo de este tema es contruir un compilado...'

<source lang="isar">
header {* Tema 8: Caso de estudio: Compilación de expresiones *}

theory T8
imports Main
begin

text {*
El objetivo de este tema es contruir un compilador de expresiones
genéricas (construidas con variables, constantes y operaciones
binarias) a una máquina de pila y demostrar su corrección.
*}

section {* Las expresiones y el intérprete *}

text {*
Definición. Las expresiones son las constantes, las variables
(representadas por números naturales) y las aplicaciones de operadores
binarios a dos expresiones.
*}

type_synonym 'v binop = "'v ⇒ 'v ⇒ 'v"

datatype 'v expr =
Const 'v
| Var nat
| App "'v binop" "'v expr" "'v expr"

text {*
Definición. [Intérprete]
La función "valor" toma como argumentos una expresión y un entorno
(i.e. una aplicación de las variables en elementos del lenguaje) y
devuelve el valor de la expresión en el entorno.
*}

fun valor :: "'v expr ⇒ (nat ⇒ 'v) ⇒ 'v" where
"valor (Const b) ent = b"
| "valor (Var x) ent = ent x"
| "valor (App f e1 e2) ent = (f (valor e1 ent) (valor e2 ent))"

text {*
Ejemplo. A continuación mostramos algunos ejemplos de evaluación con
el intérprete.
*}

lemma
"valor (Const 3) id = 3 ∧
valor (Var 2) id = 2 ∧
valor (Var 2) (λx. x+1) = 3 ∧
valor (App (op +) (Const 3) (Var 2)) (λx. x+1) = 6 ∧
valor (App (op +) (Const 3) (Var 2)) (λx. x+4) = 9"
by simp

section {* La máquina de pila *}

text {*
Nota. La máquina de pila tiene tres clases de intrucciones:
· cargar en la pila una constante,
· cargar en la pila el contenido de una dirección y
· aplicar un operador binario a los dos elementos superiores de la pila.
*}

datatype 'v instr =
IConst 'v
| ILoad nat
| IApp "'v binop"

text {*
Definición. [Ejecución]
La ejecución de la máquina de pila se modeliza mediante la función
"ejec" que toma una lista de intrucciones, una memoria (representada
como una función de las direcciones a los valores, análogamente a los
entornos) y una pila (representada como una lista) y devuelve la pila
al final de la ejecución.
*}

fun ejec :: "'v instr list ⇒ (nat ⇒ 'v) ⇒ 'v list ⇒ 'v list" where
"ejec [] ent vs = vs"
| "ejec (i#is) ent vs =
(case i of
IConst v ⇒ ejec is ent (v#vs)
| ILoad x ⇒ ejec is ent ((ent x)#vs)
| IApp f ⇒ ejec is ent ((f (hd vs) (hd (tl vs)))#(tl(tl vs))))"

text {*
A continuación se muestran ejemplos de ejecución.
*}

lemma
"ejec [IConst 3] id [7] = [3,7] ∧
ejec [ILoad 2, IConst 3] id [7] = [3,2,7] ∧
ejec [ILoad 2, IConst 3] (λx. x+4) [7] = [3,6,7] ∧
ejec [ILoad 2, IConst 3, IApp (op +)] (λx. x+4) [7] = [9,7]"
by simp

section {* El compilador *}

text {*
Definición. El compilador "comp" traduce una expresión en una lista de
instrucciones.
*}

fun comp :: "'v expr ⇒ 'v instr list" where
"comp (Const v) = [IConst v]"
| "comp (Var x) = [ILoad x]"
| "comp (App f e1 e2) = (comp e2) @ (comp e1) @ [IApp f]"

text {*
A continuación se muestran ejemplos de compilación.
*}

lemma
"comp (Const 3) = [IConst 3] ∧
comp (Var 2) = [ILoad 2] ∧
comp (App (op +) (Const 3) (Var 2)) = [ILoad 2, IConst 3, IApp (op +)]"
by simp

section {* Corrección del compilador *}

text {*
Para demostrar que el compilador es correcto, probamos que el
resultado de compilar una expresión y a continuación ejecutarla es lo
mismo que interpretarla; es decir,
*}

theorem "ejec (comp e) ent [] = [valor e ent]"
oops

text {*
El teorema anterior no puede demostrarse por inducción en e. Para
demostrarlo, lo generalizamos a
*}

theorem "∀vs. ejec (comp e) ent vs = (valor e ent)#vs"
oops

text {*
En la demostración del teorema anterior usaremos el siguiente lema.
*}

lemma ejec_append:
"∀ vs. ejec (xs@ys) ent vs = ejec ys ent (ejec xs ent vs)" (is "?P xs")
proof (induct xs)
show "?P []" by simp
next
fix a xs
assume "?P xs"
thus "?P (a#xs)" by (cases "a", auto)
qed

-- "La demostración detallada es"
lemma ejec_append_1:
"∀ vs. ejec (xs@ys) ent vs = ejec ys ent (ejec xs ent vs)" (is "?P xs")
proof (induct xs)
show "?P []" by simp
next
fix a xs
assume HI: "?P xs"
thus "?P (a#xs)"
proof (cases "a")
case IConst thus ?thesis using HI by simp
next
case ILoad thus ?thesis using HI by simp
next
case IApp thus ?thesis using HI by simp
qed
qed

text {*
Una demostración más detallada del lema es la siguiente:
*}

lemma ejec_append_2:
"∀vs. ejec (xs@ys) ent vs = ejec ys ent (ejec xs ent vs)" (is "?P xs")
proof (induct xs)
show "?P []" by simp
next
fix a xs
assume HI: "?P xs"
thus "?P (a#xs)"
proof (cases "a")
fix v assume C1: "a=IConst v"
show " ∀vs. ejec ((a#xs)@ys) ent vs = ejec ys ent (ejec (a#xs) ent vs)"
proof
fix vs
have "ejec ((a#xs)@ys) ent vs = ejec (((IConst v)#xs)@ys) ent vs"
using C1 by simp
also have "… = ejec (xs@ys) ent (v#vs)" by simp
also have "… = ejec ys ent (ejec xs ent (v#vs))" using HI by simp
also have "… = ejec ys ent (ejec ((IConst v)#xs) ent vs)" by simp
also have "… = ejec ys ent (ejec (a#xs) ent vs)" using C1 by simp
finally show "ejec ((a#xs)@ys) ent vs =
ejec ys ent (ejec (a#xs) ent vs)" .
qed
next
fix n assume C2: "a=ILoad n"
show " ∀vs. ejec ((a#xs)@ys) ent vs = ejec ys ent (ejec (a#xs) ent vs)"
proof
fix vs
have "ejec ((a#xs)@ys) ent vs = ejec (((ILoad n)#xs)@ys) ent vs"
using C2 by simp
also have "… = ejec (xs@ys) ent ((ent n)#vs)" by simp
also have "… = ejec ys ent (ejec xs ent ((ent n)#vs))" using HI by simp
also have "… = ejec ys ent (ejec ((ILoad n)#xs) ent vs)" by simp
also have "… = ejec ys ent (ejec (a#xs) ent vs)" using C2 by simp
finally show "ejec ((a#xs)@ys) ent vs =
ejec ys ent (ejec (a#xs) ent vs)" .
qed
next
fix f assume C3: "a=IApp f"
show "∀vs. ejec ((a#xs)@ys) ent vs = ejec ys ent (ejec (a#xs) ent vs)"
proof
fix vs
have "ejec ((a#xs)@ys) ent vs = ejec (((IApp f)#xs)@ys) ent vs"
using C3 by simp
also have "… = ejec (xs@ys) ent ((f (hd vs) (hd (tl vs)))#(tl(tl vs)))"
by simp
also have "… = ejec ys
ent
(ejec xs ent ((f (hd vs) (hd (tl vs)))#(tl(tl vs))))"
using HI by simp
also have "… = ejec ys ent (ejec ((IApp f)#xs) ent vs)" by simp
also have "… = ejec ys ent (ejec (a#xs) ent vs)" using C3 by simp
finally show "ejec ((a#xs)@ys) ent vs =
ejec ys ent (ejec (a#xs) ent vs)" .
qed
qed
qed

text {*
La demostración automática del teorema es
*}

theorem "∀vs. ejec (comp e) ent vs = (valor e ent)#vs"
by (induct e) (auto simp add:ejec_append)

text {*
La demostración estructurada del teorema es
*}

theorem "∀vs. ejec (comp e) ent vs = (valor e ent)#vs"
proof (induct e)
fix v
show "∀vs. ejec (comp (Const v)) ent vs = (valor (Const v) ent)#vs" by simp
next
fix x
show "∀vs. ejec (comp (Var x)) ent vs = (valor (Var x) ent) # vs" by simp
next
fix f e1 e2
assume HI1: "∀vs. ejec (comp e1) ent vs = (valor e1 ent) # vs"
and HI2: "∀vs. ejec (comp e2) ent vs = (valor e2 ent) # vs"
show "∀vs. ejec (comp (App f e1 e2)) ent vs = (valor (App f e1 e2) ent) # vs"
proof
fix vs
have "ejec (comp (App f e1 e2)) ent vs
= ejec ((comp e2) @ (comp e1) @ [IApp f]) ent vs" by simp
also have "… = ejec ((comp e1) @ [IApp f]) ent (ejec (comp e2) ent vs)"
using ejec_append by blast
also have "… = ejec [IApp f]
ent
(ejec (comp e1) ent (ejec (comp e2) ent vs))"
using ejec_append by blast
also have "… = ejec [IApp f] ent (ejec (comp e1) ent ((valor e2 ent)#vs))"
using HI2 by simp
also have "… = ejec [IApp f] ent ((valor e1 ent)#((valor e2 ent)#vs))"
using HI1 by simp
also have "… = (f (valor e1 ent) (valor e2 ent))#vs" by simp
also have "… = (valor (App f e1 e2) ent) # vs" by simp
finally
show "ejec (comp (App f e1 e2)) ent vs = (valor (App f e1 e2) ent) # vs"
by blast
qed
qed

end
</source>

Temas

2014-02-05T19:29:02Z

Jalonso:

Relación 11

2014-01-31T17:10:02Z

Jalonso: Página creada con '<source lang="isar"> header {* R11: Deducción natural de primer orden *} theory R11 imports Main begin text {* Demostrar o refutar los siguientes lemas usando sólo las re...'

<source lang="isar">
header {* R11: Deducción natural de primer orden *}

theory R11
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, mt y not_ex 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

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

text {* ---------------------------------------------------------------
Ejercicio 2. 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)
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 3. Demostrar o refutar
(∀x. ∃y. P x y) ⟶ (∃y. ∀x. P x y)
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 4. Demostrar o refutar
(∃y. ∀x. P x y) ⟶ (∀x. ∃y. P x y)
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 5. 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))
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 6. 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))
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 7. (En APLI2 el ejercicio 13 de LP) 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.
Or : Se aceptan órdenes del operador.
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 8. (En APLI2 el ejercicio 5 de LP) 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 9. (En APLI2 el ejercicio 13 de LPO) 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
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 10. (En APLI2 el ejercicio 10 de LPO) 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
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 11. 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
------------------------------------------------------------------ *}

end
</source>

R11

2014-01-31T17:09:40Z

Jalonso: Protegió «R11» ([edit=sysop] (indefinido) [move=sysop] (indefinido))

R11

2014-01-31T17:08:55Z

Ejercicios

2014-01-31T17:07:46Z

Jalonso: /* Relaciones de ejercicios propuestos */

Relación 10

2014-01-24T06:03:48Z

Jalonso: Página creada con '<source lang="isar"> header {* R10: Deducción natural proposicional *} theory R10 imports Main begin text {* --------------------------------------------------------------...'

<source lang="isar">
header {* R10: Deducción natural proposicional *}

theory R10
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

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

text {* ---------------------------------------------------------------
Ejercicio 2. Demostrar
p ∧ q ⊢ ¬(¬p ∨ ¬q)
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 3. Demostrar
¬(p ∨ q) ⊢ ¬p ∧ ¬q
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 4. Demostrar
¬p ∧ ¬q ⊢ ¬(p ∨ q)
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 5. Demostrar
¬p ∨ ¬q ⊢ ¬(p ∧ q)
------------------------------------------------------------------ *}

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

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

text {* ---------------------------------------------------------------
Ejercicio 8. Demostrar
¬(¬p ∧ ¬q) ⊢ p ∨ q
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 9. Demostrar
¬(¬p ∨ ¬q) ⊢ p ∧ q
------------------------------------------------------------------ *}

text {* ---------------------------------------------------------------
Ejercicio 10. Demostrar
¬(p ∧ q) ⊢ ¬p ∨ ¬q
------------------------------------------------------------------ *}

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

end
</source>

R10

2014-01-24T06:03:33Z

Jalonso: Protegió «R10» ([edit=sysop] (indefinido) [move=sysop] (indefinido))

R10

2014-01-24T06:03:15Z

Ejercicios

2014-01-24T06:01:31Z

Jalonso: /* Relaciones de ejercicios propuestos */

Temas

2014-01-24T06:00:26Z

Jalonso:

Tema 7b: Deducción natural en lógica de primer orden con Isabelle/HOL

2014-01-24T06:00:09Z

Jalonso: Tema 6b: Deducción natural en lógica de primer orden con Isabelle/HOL trasladada a Tema 7b: Deducción natural en lógica de primer orden con Isabelle/HOL

<source lang="isar">
header {* Tema 7: Deducción natural en lógica de primer orden *}

theory T7b_Deduccion_natural_en_logica_de_primer_orden
imports Main
begin

text {*
El objetivo de este tema es presentar la deducción natural en
lógica de primer orden con Isabelle/HOL. La presentación se
basa en los ejemplos de tema 8 del curso LMF que se encuentra
en http://goo.gl/uJj8d (que a su vez se basa en el libro de
Huth y Ryan "Logic in Computer Science" http://goo.gl/qsVpY ).

La página al lado de cada ejemplo indica la página de las
transparencias de LMF donde se encuentra la demostración. *}

section {* Reglas del cuantificador universal *}

text {*
Las reglas del cuantificador universal son
· allE: ⟦∀x. P x; P a ⟹ R⟧ ⟹ R
· allI: (⋀x. P x) ⟹ ∀x. P x
*}

text {*
Ejemplo 1 (p. 10). Demostrar que
P(c), ∀x. (P(x) ⟶ ¬Q(x)) ⊢ ¬Q(c)
*}

-- "La demostración detallada es"
lemma ejemplo_1a:
assumes 1: "P(c)" and
2: "∀x. (P(x) ⟶ ¬Q(x))"
shows "¬Q(c)"
proof -
have 3: "P(c) ⟶ ¬Q(c)" using 2 by (rule allE)
show 4: "¬Q(c)" using 3 1 by (rule mp)
qed

-- "La demostración estructurada es"
lemma ejemplo_1b:
assumes "P(c)"
"∀x. (P(x) ⟶ ¬Q(x))"
shows "¬Q(c)"
proof -
have "P(c) ⟶ ¬Q(c)" using assms(2) ..
thus "¬Q(c)" using assms(1) ..
qed

-- "La demostración automática es"
lemma ejemplo_1c:
assumes "P(c)"
"∀x. (P(x) ⟶ ¬Q(x))"
shows "¬Q(c)"
using assms
by auto

text {*
Ejemplo 2 (p. 11). Demostrar que
∀x. (P x ⟶ ¬(Q x)), ∀x. P x ⊢ ∀x. ¬(Q x)
*}

-- "La demostración detallada es"
lemma ejemplo_2a:
assumes 1: "∀x. (P x ⟶ ¬(Q x))" and
2: "∀x. P x"
shows "∀x. ¬(Q x)"
proof -
{ fix a
have 3: "P a ⟶ ¬(Q a)" using 1 by (rule allE)
have 4: "P a" using 2 by (rule allE)
have 5: "¬(Q a)" using 3 4 by (rule mp) }
thus "∀x. ¬(Q x)" by (rule allI)
qed

-- "La demostración detallada hacia atrás es"
lemma ejemplo_2b:
assumes 1: "∀x. (P x ⟶ ¬(Q x))" and
2: "∀x. P x"
shows "∀x. ¬(Q x)"
proof (rule allI)
fix a
have 3: "P a ⟶ ¬(Q a)" using 1 by (rule allE)
have 4: "P a" using 2 by (rule allE)
show 5: "¬(Q a)" using 3 4 by (rule mp)
qed

-- "La demostración estructurada es"
lemma ejemplo_2c:
assumes "∀x. (P x ⟶ ¬(Q x))"
"∀x. P x"
shows "∀x. ¬(Q x)"
proof
fix a
have "P a" using assms(2) ..
have "P a ⟶ ¬(Q a)" using assms(1) ..
thus "¬(Q a)" using `P a` ..
qed

-- "La demostración automática es"
lemma ejemplo_2d:
assumes "∀x. (P x ⟶ ¬(Q x))"
"∀x. P x"
shows "∀x. ¬(Q x)"
using assms
by auto

section {* Reglas del cuantificador existencial *}

text {*
Las reglas del cuantificador existencial son
· exI: P a ⟹ ∃x. P x
· exE: ⟦∃x. P x; ⋀x. P x ⟹ Q⟧ ⟹ Q

En la regla exE la nueva variable se introduce mediante la declaración
"obtain ... where ... by (rule exE)"
*}

text {*
Ejemplo (p. 12). Demostrar que
∀x. P x ⊢ ∃x. P x
*}

-- "La demostración detallada es"
lemma ejemplo_3a:
assumes "∀x. P x"
shows "∃x. P x"
proof -
fix a
have "P a" using assms by (rule allE)
thus "∃x. P x" by (rule exI)
qed

-- "La demostración estructurada es"
lemma ejemplo_3b:
assumes "∀x. P x"
shows "∃x. P x"
proof -
fix a
have "P a" using assms ..
thus "∃x. P x" ..
qed

-- "La demostración estructurada se puede simplificar"
lemma ejemplo_3c:
assumes "∀x. P x"
shows "∃x. P x"
proof (rule exI)
fix a
show "P a" using assms ..
qed

-- "La demostración estructurada se puede simplificar aún más"
lemma ejemplo_3d:
assumes "∀x. P x"
shows "∃x. P x"
proof
fix a
show "P a" using assms ..
qed

-- "La demostración automática es"
lemma ejemplo_3e:
assumes "∀x. P x"
shows "∃x. P x"
using assms
by auto

text {*
Ejemplo 4 (p. 13). Demostrar
∀x. (P x ⟶ Q x), ∃x. P x ⊢ ∃x. Q x
*}

-- "La demostración detallada es"
lemma ejemplo_4a:
assumes 1: "∀x. (P x ⟶ Q x)" and
2: "∃x. P x"
shows "∃x. Q x"
proof -
obtain a where 3: "P a" using 2 by (rule exE)
have 4: "P a ⟶ Q a" using 1 by (rule allE)
have 5: "Q a" using 4 3 by (rule mp)
thus 6: "∃x. Q x" by (rule exI)
qed

-- "La demostración estructurada es"
lemma ejemplo_4b:
assumes "∀x. (P x ⟶ Q x)"
"∃x. P x"
shows "∃x. Q x"
proof -
obtain a where "P a" using assms(2) ..
have "P a ⟶ Q a" using assms(1) ..
hence "Q a" using `P a` ..
thus "∃x. Q x" ..
qed

-- "La demostración automática es"
lemma ejemplo_4c:
assumes "∀x. (P x ⟶ Q x)"
"∃x. P x"
shows "∃x. Q x"
using assms
by auto

section {* Demostración de equivalencias *}

text {*
Ejemplo 5.1 (p. 15). Demostrar
¬∀x. P x ⊢ ∃x. ¬(P x) *}

-- "La demostración detallada es"
lemma ejemplo_5_1a:
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 (rule ccontr)
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

-- "La demostración estructurada es"
lemma ejemplo_5_1b:
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 (rule ccontr)
assume "¬P(a)"
hence "∃x. ¬P(x)" ..
with `¬(∃x. ¬P(x))` show False ..
qed
qed
with assms show False ..
qed

-- "La demostración automática es"
lemma ejemplo_5_1c:
assumes "¬(∀x. P(x))"
shows "∃x. ¬P(x)"
using assms
by auto

text {*
Ejemplo 5.2 (p. 16). Demostrar
∃x. ¬(P x) ⊢ ¬∀x. P x *}

-- "La demostración detallada es"
lemma ejemplo_5_2a:
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)
with `¬P(a)` show False by (rule notE)
qed

-- "La demostración estructurada es"
lemma ejemplo_5_2b:
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)` ..
with `¬P(a)` show False ..
qed

-- "La demostración automática es"
lemma ejemplo_5_2c:
assumes "∃x. ¬P(x)"
shows "¬(∀x. P(x))"
using assms
by auto

text {*
Ejemplo 5.3 (p. 17). Demostrar
⊢ ¬∀x. P x ⟷ ∃x. ¬(P x) *}

-- "La demostración detallada es"
lemma ejemplo_5_3a:
"(¬(∀x. P(x))) ⟷ (∃x. ¬P(x))"
proof (rule iffI)
assume "¬(∀x. P(x))"
thus "∃x. ¬P(x)" by (rule ejemplo_5_1a)
next
assume "∃x. ¬P(x)"
thus "¬(∀x. P(x))" by (rule ejemplo_5_2a)
qed

-- "La demostración automática es"
lemma ejemplo_5_3b:
"(¬(∀x. P(x))) ⟷ (∃x. ¬P(x))"
by auto

text {*
Ejemplo 6.1 (p. 18). Demostrar
∀x. P(x) ∧ Q(x) ⊢ (∀x. P(x)) ∧ (∀x. Q(x)) *}

-- "La demostración detallada es"
lemma ejemplo_6_1a:
assumes "∀x. P(x) ∧ Q(x)"
shows "(∀x. P(x)) ∧ (∀x. Q(x))"
proof (rule conjI)
show "∀x. P(x)"
proof (rule allI)
fix a
have "P(a) ∧ Q(a)" using assms by (rule allE)
thus "P(a)" by (rule conjunct1)
qed
next
show "∀x. Q(x)"
proof (rule allI)
fix a
have "P(a) ∧ Q(a)" using assms by (rule allE)
thus "Q(a)" by (rule conjunct2)
qed
qed

-- "La demostración estructurada es"
lemma ejemplo_6_1b:
assumes "∀x. P(x) ∧ Q(x)"
shows "(∀x. P(x)) ∧ (∀x. Q(x))"
proof
show "∀x. P(x)"
proof
fix a
have "P(a) ∧ Q(a)" using assms ..
thus "P(a)" ..
qed
next
show "∀x. Q(x)"
proof
fix a
have "P(a) ∧ Q(a)" using assms ..
thus "Q(a)" ..
qed
qed

-- "La demostración automática es"
lemma ejemplo_6_1c:
assumes "∀x. P(x) ∧ Q(x)"
shows "(∀x. P(x)) ∧ (∀x. Q(x))"
using assms
by auto

text {*
Ejemplo 6.2 (p. 19). Demostrar
(∀x. P(x)) ∧ (∀x. Q(x)) ⊢ ∀x. P(x) ∧ Q(x) *}

-- "La demostración detallada es"
lemma ejemplo_6_2a:
assumes "(∀x. P(x)) ∧ (∀x. Q(x))"
shows "∀x. P(x) ∧ Q(x)"
proof (rule allI)
fix a
have "∀x. P(x)" using assms by (rule conjunct1)
hence "P(a)" by (rule allE)
have "∀x. Q(x)" using assms by (rule conjunct2)
hence "Q(a)" by (rule allE)
with `P(a)` show "P(a) ∧ Q(a)" by (rule conjI)
qed

-- "La demostración estructurada es"
lemma ejemplo_6_2b:
assumes "(∀x. P(x)) ∧ (∀x. Q(x))"
shows "∀x. P(x) ∧ Q(x)"
proof
fix a
have "∀x. P(x)" using assms ..
hence "P(a)" by (rule allE)
have "∀x. Q(x)" using assms ..
hence "Q(a)" ..
with `P(a)` show "P(a) ∧ Q(a)" ..
qed

-- "La demostración automática es"
lemma ejemplo_6_2c:
assumes "(∀x. P(x)) ∧ (∀x. Q(x))"
shows "∀x. P(x) ∧ Q(x)"
using assms
by auto

text {*
Ejemplo 6.3 (p. 20). Demostrar
⊢ ∀x. P(x) ∧ Q(x) ⟷ (∀x. P(x)) ∧ (∀x. Q(x)) *}

-- "La demostración detallada es"
lemma ejemplo_6_3a:
"(∀x. P(x) ∧ Q(x)) ⟷ ((∀x. P(x)) ∧ (∀x. Q(x)))"
proof (rule iffI)
assume "∀x. P(x) ∧ Q(x)"
thus "(∀x. P(x)) ∧ (∀x. Q(x))" by (rule ejemplo_6_1a)
next
assume "(∀x. P(x)) ∧ (∀x. Q(x))"
thus "∀x. P(x) ∧ Q(x)" by (rule ejemplo_6_2a)
qed

text {*
Ejemplo 7.1 (p. 21). Demostrar
(∃x. P(x)) ∨ (∃x. Q(x)) ⊢ ∃x. P(x) ∨ Q(x) *}

-- "La demostración detallada es"
lemma ejemplo_7_1a:
assumes "(∃x. P(x)) ∨ (∃x. Q(x))"
shows "∃x. P(x) ∨ Q(x)"
using assms
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

-- "La demostración estructurada es"
lemma ejemplo_7_1b:
assumes "(∃x. P(x)) ∨ (∃x. Q(x))"
shows "∃x. P(x) ∨ Q(x)"
using assms
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

-- "La demostración automática es"
lemma ejemplo_7_1c:
assumes "(∃x. P(x)) ∨ (∃x. Q(x))"
shows "∃x. P(x) ∨ Q(x)"
using assms
by auto

text {*
Ejemplo 7.2 (p. 22). Demostrar
∃x. P(x) ∨ Q(x) ⊢ (∃x. P(x)) ∨ (∃x. Q(x)) *}

-- "La demostración detallada es"
lemma ejemplo_7_2a:
assumes "∃x. P(x) ∨ Q(x)"
shows "(∃x. P(x)) ∨ (∃x. Q(x))"
proof -
obtain a where "P(a) ∨ Q(a)" using assms 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

-- "La demostración estructurada es"
lemma ejercicio_7_2b:
assumes "∃x. P(x) ∨ Q(x)"
shows "(∃x. P(x)) ∨ (∃x. Q(x))"
proof -
obtain a where "P(a) ∨ Q(a)" using assms ..
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 automática es"
lemma ejercicio_7_2c:
assumes "∃x. P(x) ∨ Q(x)"
shows "(∃x. P(x)) ∨ (∃x. Q(x))"
using assms
by auto

text {*
Ejemplo 7.3 (p. 23). Demostrar
⊢ ((∃x. P(x)) ∨ (∃x. Q(x))) ⟷ (∃x. P(x) ∨ Q(x)) *}

-- "La demostración detallada es"
lemma ejemplo_7_3a:
"((∃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)" by (rule ejemplo_7_1a)
next
assume "∃x. P(x) ∨ Q(x)"
thus "(∃x. P(x)) ∨ (∃x. Q(x))" by (rule ejemplo_7_2a)
qed

-- "La demostración automática es"
lemma ejemplo_7_3b:
"((∃x. P(x)) ∨ (∃x. Q(x))) ⟷ (∃x. P(x) ∨ Q(x))"
using assms
by auto

text {*
Ejemplo 8.1 (p. 24). Demostrar
∃x y. P(x,y) ⊢ ∃y x. P(x,y) *}

-- "La demostración detallada es"
lemma ejemplo_8_1a:
assumes "∃x y. P(x,y)"
shows "∃y x. P(x,y)"
proof -
obtain a where "∃y. P(a,y)" using assms by (rule exE)
then obtain b where "P(a,b)" by (rule exE)
hence "∃x. P(x,b)" by (rule exI)
thus "∃y x. P(x,y)" by (rule exI)
qed

-- "La demostración estructurada es"
lemma ejemplo_8_1b:
assumes "∃x y. P(x,y)"
shows "∃y x. P(x,y)"
proof -
obtain a where "∃y. P(a,y)" using assms ..
then obtain b where "P(a,b)" ..
hence "∃x. P(x,b)" ..
thus "∃y x. P(x,y)" ..
qed

-- "La demostración automática es"
lemma ejemplo_8_1c:
assumes "∃x y. P(x,y)"
shows "∃y x. P(x,y)"
using assms
by auto

text {*
Ejemplo 8.2. Demostrar
∃y x. P(x,y) ⊢ ∃x y. P(x,y) *}

-- "La demostración detallada es"
lemma ejemplo_8_2a:
assumes "∃y x. P(x,y)"
shows "∃x y. P(x,y)"
proof -
obtain b where "∃x. P(x,b)" using assms by (rule exE)
then obtain a where "P(a,b)" by (rule exE)
hence "∃y. P(a,y)" by (rule exI)
thus "∃x y. P(x,y)" by (rule exI)
qed

-- "La demostración estructurada es"
lemma ejemplo_8_2b:
assumes "∃y x. P(x,y)"
shows "∃x y. P(x,y)"
proof -
obtain b where "∃x. P(x,b)" using assms ..
then obtain a where "P(a,b)" ..
hence "∃y. P(a,y)" ..
thus "∃x y. P(x,y)" ..
qed

-- "La demostración estructurada es"
lemma ejemplo_8_2c:
assumes "∃y x. P(x,y)"
shows "∃x y. P(x,y)"
using assms
by auto

text {*
Ejemplo 8.3 (p. 25). Demostrar
⊢ (∃x y. P(x,y)) ⟷ (∃y x. P(x,y)) *}

-- "La demostración detallada es"
lemma ejemplo_8_3a:
"(∃x y. P(x,y)) ⟷ (∃y x. P(x,y))"
proof (rule iffI)
assume "∃x y. P(x,y)"
thus "∃y x. P(x,y)" by (rule ejemplo_8_1a)
next
assume "∃y x. P(x,y)"
thus "∃x y. P(x,y)" by (rule ejemplo_8_2a)
qed

-- "La demostración automática es"
lemma ejemplo_8_3b:
"(∃x y. P(x,y)) ⟷ (∃y x. P(x,y))"
by auto

section {* Reglas de la igualdad *}

text {*
Las reglas básicas de la igualdad son:
· refl: t = t
· subst: ⟦s = t; P s⟧ ⟹ P t
*}

text {*
Ejemplo 9 (p. 27). Demostrar
x+1 = 1+x, x+1 > 1 ⟶ x+1 > 0 ⊢ 1+x > 1 ⟶ 1+x > 0
*}

-- "La demostración detallada es"
lemma ejemplo_9a:
assumes "x+1 = 1+x"
"x+1 > 1 ⟶ x+1 > 0"
shows "1+x > 1 ⟶ 1+x > 0"
proof -
show "1+x > 1 ⟶ 1+x > 0" using assms by (rule subst)
qed

-- "La demostración estructurada es"
lemma ejemplo_9b:
assumes "x+1 = 1+x"
"x+1 > 1 ⟶ x+1 > 0"
shows "1+x > 1 ⟶ 1+x > 0"
using assms
by (rule subst)

-- "La demostración automática es"
lemma ejemplo_9c:
assumes "x+1 = 1+x"
"x+1 > 1 ⟶ x+1 > 0"
shows "1+x > 1 ⟶ 1+x > 0"
using assms
by auto

text {*
Ejemplo 10 (p. 27). Demostrar
x = y, y = z ⊢ x = z
*}

-- "La demostración detallada es"
lemma ejemplo_10a:
assumes "x = y"
"y = z"
shows "x = z"
proof -
show "x = z" using assms(2,1) by (rule subst)
qed

-- "La demostración estructurada es"
lemma ejemplo_10b:
assumes "x = y"
"y = z"
shows "x = z"
using assms(2,1)
by (rule subst)

-- "La demostración automática es"
lemma ejemplo_10c:
assumes "x = y"
"y = z"
shows "x = z"
using assms
by auto

text {*
Ejemplo 11 (p. 28). Demostrar
s = t ⊢ t = s
*}

-- "La demostración detallada es"
lemma ejemplo_11a:
assumes "s = t"
shows "t = s"
proof -
have "s = s" by (rule refl)
with assms show "t = s" by (rule subst)
qed

-- "La demostración automática es"
lemma ejemplo_11b:
assumes "s = t"
shows "t = s"
using assms
by auto

end
</source>

Relación 5

2014-01-22T18:25:07Z

Jalonso: Desprotegió «Relación 5»

<source lang="isar">
header {* R5: Cuantificadores sobre listas *}

theory R5
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.
---------------------------------------------------------------------
*}
-- "irealetei diecabmen1 pabflomar maresccas4 domlloriv juaruipav marescpla julrobrel"
fun todos :: "('a ⇒ bool) ⇒ 'a list ⇒ bool" where
"todos p [] = True"
|"todos p (x#xs) =(p x ∧ todos p xs)"

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

-- "diecabmen1"
value "algunos (λx. 1<length x) [[2,1,4],[3]]"
value "algunos (λx. 1<length x) [[],[3]]"

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.
---------------------------------------------------------------------
*}

-- "irealetei diecabmen1 pabflomar maresccas4 domlloriv juaruipav marescpla julrobrel"
fun algunos :: "('a ⇒ bool) ⇒ 'a list ⇒ bool" where
"algunos p [] = False"
| "algunos p (x#xs) = (p x ∨ algunos p (xs))" --"(xs)=xs julrobrel"

value "algunos (λx. 1<length x) [[2,1,4],[3]]" -- "TRUE"
value "algunos (λx. 1<length x) [[],[3]]" -- "FALSE"

text {*
---------------------------------------------------------------------
Ejercicio 3.1. Demostrar o refutar automáticamente
todos (λx. P x ∧ Q x) xs = (todos P xs ∧ todos Q xs)
---------------------------------------------------------------------
*}

-- "irealetei diecabmen1 pabflomar domlloriv juaruipav marescpla julrobrel"
lemma "todos (λx. P x ∧ Q x) xs = (todos P xs ∧ todos Q xs)"
by (induct xs) auto

text {*
---------------------------------------------------------------------
Ejercicio 3.2. Demostrar o refutar detalladamente
todos (λx. P x ∧ Q x) xs = (todos P xs ∧ todos Q xs)
---------------------------------------------------------------------
*}

-- "irealetei pabflomar maresccas4 juaruipav domlloriv"
lemma "todos (λx. P x ∧ Q x) xs = (todos P xs ∧ todos Q xs)"
proof (induct xs)
show "todos (λx. P x ∧ Q x)[] = (todos P [] ∧ todos Q [])" by simp
next
fix a xs
assume HI: "todos (λx. P x ∧ Q x) xs = (todos P xs ∧ todos Q xs)"
have "todos (λx. P x ∧ Q x) (a#xs) = ((P a ∧ Q a) ∧ todos (λx. P x ∧ Q x) xs )" by simp
also have "... = (P a ∧ Q a ∧ todos P xs ∧ todos Q xs)" using HI by simp
finally show "todos (λx. P x ∧ Q x) (a#xs) = (todos P (a # xs) ∧ todos Q (a # xs))" by auto
qed

-- "diecabmen1"
lemma "todos (λx. P x ∧ Q x) xs = (todos P xs ∧ todos Q xs)" (is "?P xs")
proof (induct xs)
show "?P []" by simp
next
fix a xs
assume HI: "?P xs"
have "todos (λx. P x ∧ Q x) (a # xs) = (( P a ∧ Q a) ∧ todos (λx. P x ∧ Q x) xs)" by simp
also have "… = (( P a ∧ Q a) ∧ todos P xs ∧ todos Q xs)" using HI by simp
finally show "?P (a#xs)" by auto
qed

--"marescpla"
lemma "todos (λx. P x ∧ Q x) xs = (todos P xs ∧ todos Q xs)" (is "?P Q xs")
proof (induct xs)
show "?P Q []" by simp
next
fix x xs
assume HI: "?P Q xs"
have "todos (λx. P x ∧ Q x) (x#xs) =((λx. P x ∧ Q x) x ∧ todos (λx. P x ∧ Q x) xs)" by (simp only: todos.simps(2))
also have " ... = ((λx. P x ∧ Q x) x ∧ todos P xs ∧ todos Q xs)" using HI by simp
also have " ...= ((P x) ∧ (Q x) ∧ todos P xs ∧ todos Q xs) " by simp
also have "... =((P x) ∧ todos P xs ∧ (Q x)∧ todos Q xs)" by auto
also have " ...= (todos P (x#xs) ∧ todos Q (x#xs))" by simp
finally show "?P Q (x#xs)" by simp
qed

--"julrobrel: sin usar auto"
lemma "todos (λx. P x ∧ Q x) xs = (todos P xs ∧ todos Q xs)"
proof (induct xs)
show "todos (λx. P x ∧ Q x) [] = (todos P [] ∧ todos Q [])" by simp
next
fix a xs
assume HI:"todos (λx. P x ∧ Q x) xs = (todos P xs ∧ todos Q xs)"
have "todos (λx. P x ∧ Q x) (a#xs) = ((P a ∧ Q a) ∧ todos (λx. P x ∧ Q x) xs)" by simp
also have "...=((P a ∧ Q a) ∧ (todos P xs ∧ todos Q xs))" using HI by simp
also have "...=((P a) ∧ ((Q a) ∧ (todos P xs)) ∧ (todos Q xs))" by simp
also have "...=((P a) ∧ ((todos P xs) ∧ (Q a)) ∧ (todos Q xs))" by (simp add:conj_commute)
also have "...=((todos P [a]) ∧ (todos P xs) ∧ (todos Q [a]) ∧ (todos Q xs))" by simp
finally show "todos (λx. P x ∧ Q x) (a#xs) = (todos P (a#xs) ∧ todos Q (a#xs))" by simp
qed

text {*
---------------------------------------------------------------------
Ejercicio 4.1. Demostrar o refutar automáticamente
todos P (x @ y) = (todos P x ∧ todos P y)
---------------------------------------------------------------------
*}

-- "irealetei diecabmen1 pabflomar maresccas4 domlloriv juaruipav marescpla julrobrel"
lemma "todos P (x @ y) = (todos P x ∧ todos P y)"
by (induct x ) auto

text {*
---------------------------------------------------------------------
Ejercicio 4.2. Demostrar o refutar detalladamente
todos P (x @ y) = (todos P x ∧ todos P y)
---------------------------------------------------------------------
*}
-- "irealetei pabflomar maresccas4 domllorv juaruipav julrobrel"
lemma todos_append:
"todos P (x @ y) = (todos P x ∧ todos P y)"
proof (induct x)
show "todos P ([] @ y) = (todos P [] ∧ todos P y)" by simp
next
fix a x
assume HI:"todos P (x @ y) = (todos P x ∧ todos P y)"
have " todos P ((a # x) @ y) = (P a ∧ todos P (x @ y))" by simp
also have "...= (P a ∧ todos P x ∧ todos P y)" using HI by simp
finally show "todos P ((a # x) @ y) = (todos P (a # x) ∧ todos P y)" by simp
qed

-- "diecabmen1 marescpla"
lemma todos_append: "todos P (x @ y) = (todos P x ∧ todos P y)" (is "?P x y")
proof (induct x)
show "?P [] y" by simp
next
fix a x
assume HI: "?P x y"
have "todos P (a#x @ y) = (P a ∧ todos P (x@y))" by simp
also have "… = (P a ∧ todos P x ∧ todos P y)" using HI by simp
finally show "?P (a#x) y" by auto
qed

text {*
---------------------------------------------------------------------
Ejercicio 5.1. Demostrar o refutar automáticamente
todos P (rev xs) = todos P xs
---------------------------------------------------------------------
*}

--"maresccas4 julrobrel"

lemma "todos P (rev xs) = todos P xs"
apply (induct xs)
apply (simp_all add:todos_append)
by auto

-- "diecabmen1 irealetei juaruipav domlloriv marescpla"
lemma "todos P (rev xs) = todos P xs"
by (induct xs) (auto simp add: todos_append)

text {*
---------------------------------------------------------------------
Ejercicio 5.2. Demostrar o refutar detalladamente
todos P (rev xs) = todos P xs
---------------------------------------------------------------------
*}

--"irealetei maresccas4"
lemma "todos P (rev xs) = todos P xs"
proof (induct xs)
show "todos P (rev []) = todos P []" by simp
next
fix xs a
assume HI:"todos P (rev xs) = todos P xs"
have "todos P (rev (a # xs)) = todos P (rev xs @ [a])" by simp
also have "... = ( P a ∧ todos P (rev xs))" by (simp add:todos_append) auto
also have "... = ( P a ∧ todos P xs)" using HI by simp
finally show "todos P (rev (a # xs))= todos P (a#xs)" by simp
qed
(* pabflomar: Irene, la primera línea es prescindible
irealetei: Ya pero lo veo más claro así ^_^O *)

-- "pabflomar domlloriv"
lemma "todos P (rev xs) = todos P xs"
proof (induct xs)
show "todos P (rev []) = todos P []" by simp
next
fix a xs
assume HI: "todos P (rev xs) = todos P xs"
have "todos P (rev (a # xs)) = (P a ∧ todos P (rev xs))" by (simp add:todos_append) auto
also have "... = (P a ∧ todos P xs)" using HI by simp
finally show "todos P (rev (a # xs)) = todos P (a # xs)" by simp
qed

-- "diecabmen1"
lemma "todos P (rev xs) = todos P xs" (is "?P xs")
proof (induct xs)
show "?P []" by simp
next
fix a xs
assume HI: "?P xs"
have "todos P (rev (a#xs)) = todos P (rev xs @ [a])" by simp
also have "… = (todos P (rev xs) ∧ todos P [a])" by (simp add: todos_append)
also have "… = (todos P xs ∧ todos P [a])" using HI by simp
finally show "?P (a#xs)" by auto
qed

-- "juaruipav marescpla"
lemma "todos P (rev xs) = todos P xs"
proof (induct xs)
show " todos P (rev []) = todos P []" by simp
next
fix a xs
assume HI: "todos P (rev xs) = todos P xs"
have " todos P (rev (a # xs))= todos P ((rev xs)@[a])" by simp
also have "...= (todos P (rev xs)∧todos P [a])" by (simp add:todos_append)
also have "...= (todos P xs ∧todos P [a])" using HI by simp
also have "...= (todos P[a]∧todos P xs)" by auto
also have "...= todos P ([a]@xs)" by (simp add:todos_append)
also have "...= todos P (a#xs)" by simp
finally show "todos P (rev (a # xs)) = todos P (a#xs)" by simp
qed

--"ya veo que me he vuelto a complicar la vida (marescpla) jajaja"

--"julrobrel: sin usar auto"
lemma "todos P (rev xs) = todos P xs"
proof (induct xs)
show "todos P (rev []) = todos P []" by simp
next
fix a xs
assume HI: "todos P (rev xs) = todos P xs"
have "todos P (rev (a#xs)) = todos P (rev xs @ rev [a])" by simp
also have "...=(todos P (rev xs) ∧ todos P (rev [a]))" by (simp add: todos_append)
also have "...=(todos P xs ∧ P a)" using HI by simp
also have "...=(P a ∧ todos P xs)" by (simp add: conj_commute)
also have "...=(todos P [a] ∧ todos P xs)" by simp
also have "...=(todos P ([a]@xs))" by simp
finally show "todos P (rev (a#xs)) = (todos P (a#xs))" by simp
qed

text {*
---------------------------------------------------------------------
Ejercicio 6. Demostrar o refutar:
algunos (λx. P x ∧ Q x) xs = (algunos P xs ∧ algunos Q xs)
---------------------------------------------------------------------
*}

--"irealetei"
(*lemma "algunos (λx. P x ∧ Q x) xs = (algunos P xs ∧ algunos Q xs)"
proof (induct xs)
show "algunos (λx. P x ∧ Q x) [] = (algunos P [] ∧ algunos Q [])" by simp
next
fix a xs
assume HI:"algunos (λx. P x ∧ Q x) xs = (algunos P xs ∧ algunos Q xs)"
have " algunos (λx. P x ∧ Q x) (a # xs) =((P a ∧ Q a) ∨ algunos (λx. P x ∧ Q x) xs)" by simp
also have "... = ((P a ∧ Q a) ∨ (algunos P xs ∧ algunos Q xs))" using HI by simp
--"Me da que esto es falso"
qed*)

(* irealetei: Me ha gustado la solución de maresccas4 diecabmen1 y me uno *)
(* juaruipav: Antes de empezar la demostración, quickcheck te avisa del contraejemplo*)
-- "maresccas4 diecabmen1 irealetei pabflomar juaruipav domlloriv marescpla julrobrel"
lemma "algunos (λx. P x ∧ Q x) xs = (algunos P xs ∧ algunos Q xs)"
quickcheck
oops
(* Contraejemplo:
P = {a⇣1}
Q = {a⇣2}
xs = {a⇣1, a⇣2}
*)

text {*
---------------------------------------------------------------------
Ejercicio 7.1. Demostrar o refutar automáticamente
algunos P (map f xs) = algunos (P ∘ f) xs
---------------------------------------------------------------------
*}

-- "irealetei maresccas4 pabflomar domlloriv juaruipav marescpla julrobrel"
lemma "algunos P (map f xs) = algunos (P o f) xs"
by (induct xs) auto

text {*
---------------------------------------------------------------------
Ejercicio 7.2. Demostrar o refutar datalladamente
algunos P (map f xs) = algunos (P ∘ f) xs
---------------------------------------------------------------------
*}

-- "irealetei diecabmen1 maresccas4 juaruipav domlloriv marescpla"
lemma "algunos P (map f xs) = algunos (P o f) xs"
proof (induct xs)
show "algunos P (map f []) = algunos (P ∘ f) []" by simp
next
fix a xs
assume HI:"algunos P (map f xs) = algunos (P ∘ f) xs"
have "algunos P (map f (a # xs)) = algunos P (f a # (map f xs))" by simp
also have "... = (P (f a) ∨ algunos P (map f xs))" by simp
also have "... = (P (f a) ∨ algunos (P ∘ f) xs)" using HI by simp
also have "... = ((P ∘ f) a ∨ algunos (P ∘ f) xs)" by simp
finally show " algunos P (map f (a # xs)) = algunos (P ∘ f) (a # xs)" by simp
qed

-- "pabflomar"
(* pabflomar: A mi al menos me resulta más cómoda mi versión, con menos "pasos intermedios" *)

lemma "algunos P (map f xs) = algunos (P o f) xs"
proof (induct xs)
show "algunos P (map f []) = algunos (P ∘ f) []" by simp
next
fix a xs
assume HI: "algunos P (map f xs) = algunos (P ∘ f) xs"
have "algunos P (map f (a # xs)) = (P (f a) ∨ algunos P (map f xs))" by simp
also have "... = (P (f a) ∨ algunos (P ∘ f) xs)" using HI by simp
finally show "algunos P (map f (a # xs)) = algunos (P ∘ f) (a # xs) " by simp
qed

--"julrobrel"
lemma "algunos P (map f xs) = algunos (P ∘ f) xs"
proof (induct xs)
show "algunos P (map f []) = algunos (P ∘ f) []" by simp
next
fix a xs
assume HI: "algunos P (map f xs) = algunos (P ∘ f) xs"
have "algunos P (map f (a#xs)) = algunos P (f a # (map f xs))" by simp
also have "...=((P ∘ f) a ∨ algunos P (map f xs))" by simp
also have "...=((P ∘ f) a ∨ algunos (P ∘ f) xs)" using HI by simp
finally show "algunos P (map f (a#xs)) = algunos (P ∘ f) (a#xs)" by simp
qed

text {*
---------------------------------------------------------------------
Ejercicio 8.1. Demostrar o refutar automáticamente
algunos P (xs @ ys) = (algunos P xs ∨ algunos P ys)
---------------------------------------------------------------------
*}

-- "irealetei diecabmen1 maresccas4 pabflomar domlloriv juaruipav marescpla julrobrel"
lemma "algunos P (xs @ ys) = (algunos P xs ∨ algunos P ys)"
by (induct xs) auto

text {*
---------------------------------------------------------------------
Ejercicio 8.2. Demostrar o refutar detalladamente
algunos P (xs @ ys) = (algunos P xs ∨ algunos P ys)
---------------------------------------------------------------------
*}

-- "irealetei maresccas4 pabflomar juaruipav domlloriv marescpla julrobrel"
lemma algunos_append:
"algunos P (xs @ ys) = (algunos P xs ∨ algunos P ys)"
proof (induct xs)
show "algunos P ([] @ ys) = (algunos P [] ∨ algunos P ys)" by simp
next
fix a xs
assume HI:"algunos P (xs @ ys) = (algunos P xs ∨ algunos P ys)"
have " algunos P ((a # xs) @ ys) = (P a ∨ algunos P (xs @ys))" by simp
also have "... = (P a ∨ algunos P xs ∨ algunos P ys)" using HI by simp
finally show "algunos P ((a # xs) @ ys) = (algunos P (a # xs) ∨ algunos P ys)" by simp
qed

-- "diecabmen1"
lemma algunos_append:
"algunos P (xs @ ys) = (algunos P xs ∨ algunos P ys)" (is "?P xs ys")
proof (induct xs)
show "?P [] ys" by simp
next
fix a xs
assume HI: "?P xs ys"
have "algunos P ((a#xs) @ ys) = algunos P (a # xs @ ys) " by simp
also have "… = (P a ∨ algunos P (xs @ ys))" by simp
also have "… = (P a ∨ algunos P xs ∨ algunos P ys)" using HI by simp
finally show "?P (a#xs) ys" by simp
qed

text {*
---------------------------------------------------------------------
Ejercicio 9.1. Demostrar o refutar automáticamente
algunos P (rev xs) = algunos P xs
---------------------------------------------------------------------
*}

-- "irealetei diecabmen1 pabflomar juaruipav domlloriv marescpla julrobrel"
lemma "algunos P (rev xs) = algunos P xs"
by (induct xs) (auto simp add:algunos_append)

-- "maresccas4"

lemma "algunos P (rev xs) = algunos P xs"
apply (induct xs)
apply (simp_all add:algunos_append)
by auto

text {*
---------------------------------------------------------------------
Ejercicio 9.2. Demostrar o refutar detalladamente
algunos P (rev xs) = algunos P xs
---------------------------------------------------------------------
*}

--"irealetei maresccas4 domlloriv"
lemma "algunos P (rev xs) = algunos P xs"
proof (induct xs)
show "algunos P (rev []) = algunos P []" by simp
next
fix a xs
assume HI:"algunos P (rev xs) = algunos P xs"
have " algunos P (rev (a # xs))= algunos P (rev xs @ [a])" by simp
also have "... = (P a ∨ algunos P (rev xs))" by (simp add:algunos_append) auto
also have "... = (P a ∨ algunos P xs)" using HI by simp
finally show "algunos P (rev (a # xs)) = algunos P (a # xs)" by simp
qed

-- "pabflomar"
(* ṕabflomar: Yo sigo empeñado en lo mismo, la primera linea sobra, ¿qué mas da el orden en el que verifiques el primer elemento de una lista?*)
lemma "algunos P (rev xs) = algunos P xs"
proof (induct xs)
show "algunos P (rev []) = algunos P []" by simp
next
fix a xs
assume HI: "algunos P (rev xs) = algunos P xs"
have "algunos P (rev (a # xs)) = (P a ∨ algunos P (rev xs))" by (simp add:algunos_append) auto
also have "... = (P a ∨ algunos P xs)" using HI by simp
finally show "algunos P (rev (a # xs)) = algunos P (a # xs)" by simp
qed

-- "diecabmen1 marescpla"
lemma "algunos P (rev xs) = algunos P xs" (is "?P xs")
proof (induct xs)
show "?P []" by simp
next
fix a xs
assume HI: "?P xs"
have "algunos P (rev (a#xs)) = algunos P (rev xs @ [a])" by simp
also have "… = (algunos P (rev xs) ∨ algunos P [a])" by (simp add: algunos_append)
also have "… = (algunos P xs ∨ algunos P [a])" using HI by simp
finally show "?P (a#xs)" by auto
qed

-- "juaruipav"
(* juaruipav: Versión con más "pasos intermedios" (eso que no le gusta a pabflomar),
yo lo veo más útil a la hora de interpretar el código. En otro caso utilizariamos la versión automática *)

lemma "algunos P (rev xs) = algunos P xs"
proof (induct xs)
show " algunos P (rev []) = algunos P []" by simp
next
fix a xs
assume HI: "algunos P (rev xs) = algunos P xs"
have " algunos P (rev (a # xs))= algunos P ((rev xs)@[a])" by simp
also have "...= (algunos P (rev xs)∨ algunos P [a])" by (simp add:algunos_append)
also have "...= (algunos P xs ∨ algunos P [a])" using HI by simp
also have "...= (algunos P[a]∨ algunos P xs)" by auto
also have "...= algunos P ([a]@xs)" by (simp add:todos_append)
also have "...= algunos P (a#xs)" by simp
finally show "algunos P (rev (a # xs)) = algunos P (a#xs)" by simp
qed

--"julrobrel: sin auto"
lemma "algunos P (rev xs) = algunos P xs"
proof (induct xs)
show "algunos P (rev []) = algunos P []" by simp
next
fix a xs
assume HI: "algunos P (rev xs) = algunos P xs"
have "algunos P (rev (a#xs)) = algunos P ((rev xs) @ [a])" by simp
also have "...=(algunos P (rev xs) ∨ algunos P [a])" by (simp add:algunos_append)
also have "...=(algunos P xs ∨ algunos P [a])" using HI by simp
also have "...=(algunos P [a] ∨ algunos P xs)" by (simp add:disj_commute)
also have "...=(algunos P (a#xs))" by simp
finally show "algunos P (rev (a#xs)) = algunos P (a#xs)" by simp
qed

text {*
---------------------------------------------------------------------
Ejercicio 10. Encontrar un término no trivial Z tal que sea cierta la
siguiente ecuación:
algunos (λx. P x ∨ Q x) xs = Z
y demostrar la equivalencia de forma automática y detallada.
---------------------------------------------------------------------
*}

--"irealetei diecabmen1 maresccas4 marescpla julrobrel domlloriv"
lemma "algunos (λx. P x ∨ Q x) xs =(algunos P xs ∨ algunos Q xs)"
by (induct xs) auto

lemma "algunos (λx. P x ∨ Q x) xs =(algunos P xs ∨ algunos Q xs)"
proof (induct xs)
show " algunos (λx. P x ∨ Q x) [] = (algunos P [] ∨ algunos Q [])" by simp
next
fix a xs
assume HI:"algunos (λx. P x ∨ Q x) xs = (algunos P xs ∨ algunos Q xs)"
have " algunos (λx. P x ∨ Q x) (a # xs) = ((P a ∨ Q a) ∨ algunos (λx. P x ∨ Q x) xs)" by simp
also have "... = ((P a ∨ Q a) ∨ (algunos P xs ∨ algunos Q xs))" using HI by simp
also have "... = (P a ∨ algunos P xs ∨ Q a ∨ algunos Q xs)" by auto
finally show " algunos (λx. P x ∨ Q x) (a # xs) = (algunos P (a # xs) ∨ algunos Q (a # xs))" by simp
qed

--"marescpla: encima de largo, me da error xD pero bueno"
lemma "algunos (λx. P x ∨ Q x) xs = algunos (λx. P x) xs ∨ algunos (λx. Q x) xs" (is "?P xs")
proof (induct xs)
show "?P []" by simp
next
fix x xs
assume HI: "?P xs"
have "algunos (λx. P x ∨ Q x) (x#xs) = ((λx. P x ∨ Q x) x ∨ algunos (λx. P x ∨ Q x) xs)" by (simp only: algunos.simps(2))
also have "... = ((λx. P x ∨ Q x) x ∨ algunos (λx. P x) xs ∨ algunos (λx. Q x) xs)"using HI by simp
also have "...=((P x) ∨ (Q x) ∨ algunos (λx. P x) xs ∨ algunos (λx. Q x) xs)" by simp
also have "...=((P x) ∨ algunos (λx. P x) xs ∨ (Q x) ∨ algunos (λx. Q x) xs)" by auto
also have "...=(algunos (λx. P x) (x#xs) ∨ algunos (λx. Q x) (x#xs))" by simp
finally show "?P (x#xs)" by auto
qed

--"julrobrel: sin usar auto"
lemma "algunos (λx. P x ∨ Q x) xs =(algunos P xs ∨ algunos Q xs)"
proof (induct xs)
show "algunos (λx. P x ∨ Q x) [] = (algunos P [] ∨ algunos Q [])" by simp
next
fix a xs
assume HI: "algunos (λx. P x ∨ Q x) xs =(algunos P xs ∨ algunos Q xs)"
have "algunos (λx. P x ∨ Q x) (a#xs)=(algunos (λx. P x ∨ Q x) [a] ∨ algunos (λx. P x ∨ Q x) xs)" by simp
also have "...=(P a ∨ Q a ∨ algunos (λx. P x ∨ Q x) xs)" by simp
also have "...=(P a ∨ Q a ∨ (algunos P xs ∨ algunos Q xs))" using HI by simp
also have "...=(P a ∨ (Q a ∨ algunos P xs) ∨ algunos Q xs)" by simp
also have "...=(P a ∨ (algunos P xs ∨ Q a) ∨ algunos Q xs)" by (simp add:disj_commute)
also have "...=(P a ∨ algunos P xs ∨ Q a ∨ algunos Q xs)" by simp
finally show "algunos (λx. P x ∨ Q x) (a#xs)=(algunos P (a#xs) ∨ algunos Q (a#xs))" by simp
qed

text {*
---------------------------------------------------------------------
Ejercicio 11.1. Demostrar o refutar automáticamente
algunos P xs = (¬ todos (λx. (¬ P x)) xs)
---------------------------------------------------------------------
*}

-- "irealetei diecabmen1 maresccas4 juaruipav pabflomar marescpla julrobrel domlloriv"
lemma "algunos P xs = (¬ todos (λx. (¬ P x)) xs)"
by (induct xs) auto

text {*
---------------------------------------------------------------------
Ejercicio 11.2. Demostrar o refutar datalladamente
algunos P xs = (¬ todos (λx. (¬ P x)) xs)
---------------------------------------------------------------------
*}

--"irealetei maresccas4 domlloriv"
lemma "algunos P xs = (¬ todos (λx. (¬ P x)) xs)"
proof (induct xs)
show "algunos P [] = (¬ todos (λx. ¬ P x) [])" by simp
next
fix a xs
assume HI:"algunos P xs = (¬ todos (λx. ¬ P x) xs)"
have "algunos P (a # xs) = (P a ∨ algunos P xs)" by simp
also have "... = (P a ∨ (¬ todos (λx. ¬ P x) xs))" using HI by simp
also have "... = (¬(¬P a ∧ ¬¬ todos (λx. ¬ P x) xs))" by simp
also have "... = (¬(¬P a ∧ todos (λx. ¬ P x) xs))" by simp
finally show "algunos P (a # xs) = (¬ todos (λx. ¬ P x) (a # xs))" by simp
qed

-- "diecabmen1 marescpla"
lemma "algunos P xs = (¬ todos (λx. (¬ P x)) xs)" (is "?P xs")
proof (induct xs)
show "?P []" by simp
next
fix a xs
assume HI: "?P xs"
have "algunos P (a#xs) = (P a ∨ algunos P xs)" by simp
also have "… = (P a ∨ (¬ todos (λx. (¬ P x)) xs))" using HI by simp
finally show "?P (a#xs)" by simp
qed

-- "juaruipav pabflomar"
lemma "algunos P xs = (¬ todos (λx. (¬ P x)) xs)"
proof (induct xs)
show "algunos P [] = (¬ todos (λx. ¬ P x) [])" by simp
next
fix a xs
assume HI: " algunos P xs = (¬ todos (λx. ¬ P x) xs)"
have "algunos P (a # xs) = (P a ∨ algunos P xs)" by simp
also have "...= (P a ∨ (¬ todos (λx. ¬ P x) xs))" using HI by simp
finally show " algunos P (a # xs) = (¬ todos (λx. ¬ P x) (a # xs))" by simp
qed

--"julrobrel"
lemma "algunos P xs = (¬ todos (λx. (¬ P x)) xs)"
proof (induct xs)
show "algunos P [] = (¬ todos (λx. ¬ P x) [])" by simp
next
fix a xs
assume HI: "algunos P xs = (¬ todos (λx. (¬ P x)) xs)"
have "algunos P (a # xs) = (algunos P [a] ∨ algunos P xs)" by simp
also have "...=(P a ∨ (¬ todos (λx. (¬ P x)) xs))" using HI by simp
also have "...=(¬(¬P a ∧ todos (λx. (¬ P x)) xs))" by simp
finally show "algunos P (a # xs) =(¬ (todos (λx. (¬ P x)) (a#xs)))" by simp
qed

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
---------------------------------------------------------------------
*}

--"irealetei diecabmen1 maresccas4 pabflomar marescpla julrobrel domlloriv juaruipav"
fun estaEn :: "'a ⇒ 'a list ⇒ bool" where
"estaEn x [] = False"
|"estaEn x (a # xs) = (a=x ∨ estaEn x xs)"

value "estaEn (2::nat) [3,2,4]" -- "True"
value "estaEn (1::nat) [3,2,4]" -- "False"

text {*
---------------------------------------------------------------------
Ejercicio 13. Expresar la relación existente entre estaEn y algunos.
Demostrar dicha relación de forma automática y detallada.
---------------------------------------------------------------------
*}
-- "irealetei"

fun igual :: "'a ⇒ 'a ⇒ bool" where
"igual x y = (x=y)"

lemma "(algunos (igual x) xs) = (estaEn x xs)"
by (induct xs) auto

lemma "(algunos (igual x) xs) = (estaEn x xs)"
proof (induct xs)
show " algunos (igual x) [] = estaEn x []" by simp
next
fix a xs
assume HI:"algunos (igual x) xs = estaEn x xs"
have "algunos (igual x) (a # xs) = (igual x a ∨ algunos (igual x) xs)" by simp
also have "... = (igual x a ∨ estaEn x xs)" using HI by simp
finally show "algunos (igual x) (a # xs) = (estaEn x (a#xs))" by simp auto
qed

-- "diecabmen1 marescpla julrobrel domlloriv juaruipav"
lemma "estaEn a xs = algunos (λx. (x=a)) xs"
by (induct xs) auto

lemma "estaEn a xs = algunos (λx. (x=a)) xs" (is "?P xs")
proof (induct xs)
show "?P []" by simp
next
fix aa xs
assume HI: "?P xs"
have "estaEn a (aa#xs) = (a=aa ∨ estaEn a xs)" by simp
also have "… = (a=aa ∨ algunos (λx. (x=a)) xs)" using HI by simp
finally show "?P (aa#xs)" by auto
qed

-- "maresccas4"
lemma "algunos (λx. x=a) xs = estaEn a xs"
proof (induct xs)
show "algunos (λx. x=a) [] = estaEn a []" by simp
next
fix y xs
assume HI: "algunos (λx. x=a) xs = estaEn a xs"
have "algunos (λx. x=a) (y#xs) = (y=a ∨ algunos (λx. x=a) xs)" by simp
also have "... = (y=a ∨ estaEn a xs)" using HI by simp
finally show "algunos (λx. x=a) (y#xs) = estaEn a (y#xs)" by simp
qed

-- "pabflomar"
(* Equivalente a la de diecabmen1, sin predicados.*)

lemma "estaEn a xs = algunos (λx. x=a) xs"
by (induct xs) auto

lemma "estaEn a xs = algunos (λx. x=a) xs"
proof (induct xs)
show "estaEn a [] = algunos (λx. x = a) []" by simp
next
fix aa xs
assume HI: "estaEn a xs = algunos (λx. x = a) xs"
have "estaEn a (aa # xs) = ( a=aa ∨ estaEn a xs)" by simp
also have "... = (a=aa ∨ algunos (λx. x = a) xs)" using HI by simp
finally show "estaEn a (aa # xs) = algunos (λx. x = a) (aa # xs)" by auto
qed

--"julrobrel: sin usar auto"
lemma "algunos P xs = (¬ todos (λx. (¬ P x)) xs)"
proof (induct xs)
show "algunos P [] = (¬ todos (λx. ¬ P x) [])" by simp
next
fix a xs
assume HI: "algunos P xs = (¬ todos (λx. (¬ P x)) xs)"
have "algunos P (a # xs) = (algunos P [a] ∨ algunos P xs)" by simp
also have "...=(P a ∨ (¬ todos (λx. (¬ P x)) xs))" using HI by simp
also have "...=(¬(¬P a ∧ todos (λx. (¬ P x)) xs))" by simp
finally show "algunos P (a # xs) =(¬ (todos (λx. (¬ P x)) (a#xs)))" by simp
qed

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
---------------------------------------------------------------------
*}

-- "diecabmen1"
fun sinDuplicados' :: "'a ⇒'a list ⇒ bool" where
"sinDuplicados' a [] = True"
| "sinDuplicados' a (x#xs) = (a≠x ∧ sinDuplicados' a xs)"

fun sinDuplicados :: "'a list ⇒ bool" where
"sinDuplicados [] = True"
| "sinDuplicados (x#xs) = (sinDuplicados' x xs ∧ sinDuplicados xs)"

value "sinDuplicados [1::nat,4,2]"
value "sinDuplicados [1::nat,4,2,4]"

-- "maresccas4 pabflomar marescpla julrobrel domlloriv irealetei juaruipav"
fun sinDuplicados2 :: "'a list ⇒ bool" where
"sinDuplicados [] = True"
| "sinDuplicados (x#xs) = (¬estaEn x xs ∧ sinDuplicados xs)"

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.
---------------------------------------------------------------------
*}

-- "diecabmen1"
fun borraDuplicados :: "'a list ⇒ 'a list" where
"borraDuplicados [] = []"
| "borraDuplicados (x#xs) = (if x ∈ set xs then borraDuplicados xs else x#borraDuplicados xs)"

value " borraDuplicados [1::nat,2,4,2,3]"

-- "maresccas4 irealetei pabflomar marescpla julrobrel domlloriv juaruipav"
fun borraDuplicados2 :: "'a list ⇒ 'a list" where
"borraDuplicados2 [] = []"
| "borraDuplicados2 (x#xs) = (if estaEn x xs then borraDuplicados2 xs else x # borraDuplicados2 xs)"

(* irealetei: así tambien lo hice, pero no me terminaba de gustar y lo cambié usando el "if"*)
fun borraDuplicados3 :: "'a list => 'a list" where
"borraDuplicados3 [] = []"
| "borraDuplicados3 (x#xs) = (case estaEn x xs of True => borraDuplicados3 xs | False => x#borraDuplicados3 xs)"

text {*
---------------------------------------------------------------------
Ejercicio 16.1. Demostrar o refutar automáticamente
length (borraDuplicados xs) ≤ length xs
---------------------------------------------------------------------
*}

-- "diecabmen1 maresccas4 irealetei pabflomar marescpla domlloriv julrobrel juaruipav"

lemma length_borraDuplicados:
"length (borraDuplicados xs) ≤ length xs"
by (induct xs) auto

text {*
---------------------------------------------------------------------
Ejercicio 16.2. Demostrar o refutar detalladamente
length (borraDuplicados xs) ≤ length xs
---------------------------------------------------------------------
*}

-- "diecabmen1"
lemma length_borraDuplicados2:
"length (borraDuplicados xs) ≤ length xs" (is "?P xs")
proof (induct xs)
show "?P []" by simp
next
fix a xs
assume HI: "?P xs"
have "length (a#xs) = Suc 0 + length xs" by simp
also have "length (borraDuplicados (a#xs)) = length (if a ∈ set xs then borraDuplicados xs else a#borraDuplicados xs)" by simp
have "length xs ≤ Suc 0 + length xs" using HI by simp
have "length (a#borraDuplicados xs) ≤ Suc 0 + length xs "using HI by simp
finally show "?P (a#xs)" by simp
qed

-- "maresccas4 irealetei marescpla domlloriv pabflomar juaruipav"
(* pabflomar: A la hora de fijar x y xs no es necesario especificar los tipos.*)
lemma
"length (borraDuplicados xs) ≤ length xs"
proof (induct xs)
show "length (borraDuplicados []) ≤ length []" by simp
next
fix x :: "'a"
fix xs :: "'a list"
assume HI: "length (borraDuplicados xs) ≤ length xs"
have "length (borraDuplicados (x#xs)) ≤ 1 + length (borraDuplicados xs)" by simp
also have "... ≤ 1 + length xs" using HI by simp
finally show "length (borraDuplicados (x#xs)) ≤ length (x#xs)" by simp
qed

--"julrobrel"
lemma "length (borraDuplicados xs) ≤ length xs"
proof (induct xs)
show "length (borraDuplicados []) ≤ length []" by simp
next
fix a xs
assume HI:"length (borraDuplicados xs) ≤ length xs"
have "length (borraDuplicados (a # xs)) ≤ 1 + length (borraDuplicados (xs))" by simp
also have "...≤ 1 + length xs" using HI by simp
finally show "length (borraDuplicados (a # xs)) ≤ length (a#xs)" by simp
qed

text {*
---------------------------------------------------------------------
Ejercicio 17.1. Demostrar o refutar automáticamente
estaEn a (borraDuplicados xs) = estaEn a xs
---------------------------------------------------------------------
*}

-- "maresccas4 irealetei marescpla diecabmen1 julrobrel domlloriv juaruipav"
lemma "estaEn a (borraDuplicados2 xs) = estaEn a xs"
by (induct xs) auto

text {*
---------------------------------------------------------------------
Ejercicio 17.2. Demostrar o refutar detalladamente
estaEn a (borraDuplicados xs) = estaEn a xs
---------------------------------------------------------------------
*}

-- "maresccas4"
lemma estaEn_borraDuplicados:
"estaEn a (borraDuplicados2 xs) = estaEn a xs"
proof (induct xs)
show "estaEn a (borraDuplicados2 []) = estaEn a []" by simp
next
fix x xs
assume HI: "estaEn a (borraDuplicados2 xs) = estaEn a xs"
have "estaEn a (borraDuplicados2 (x#xs)) = estaEn a (if estaEn x xs then borraDuplicados2 xs else x # borraDuplicados2 xs)" by simp
also have "... = (if estaEn x xs then estaEn a (borraDuplicados2 xs) else estaEn a (x#borraDuplicados2 xs))" by simp
also have "... = (if estaEn x xs then estaEn a xs else (x=a ∨ estaEn a xs))" using HI by simp
also have "... = (if estaEn x xs then estaEn a xs else estaEn a (x#xs))" by simp
finally show "estaEn a (borraDuplicados2 (x#xs)) = estaEn a (x#xs)" by auto
qed

-- "maesccas4 irealetei diecabmen1 domlloriv marescpla juaruipav"
lemma estaEn_borraDuplicados_porCasos:
"estaEn a (borraDuplicados2 xs) = estaEn a xs"
proof (induct xs)
show "estaEn a (borraDuplicados2 []) = estaEn a []" by simp
next
fix x xs
assume HI: "estaEn a (borraDuplicados2 xs) = estaEn a xs"
show "estaEn a (borraDuplicados2 (x#xs)) = estaEn a (x#xs)"
proof (cases)
assume "estaEn x xs"
then have "estaEn a (borraDuplicados2 (x#xs)) = estaEn a (borraDuplicados2 xs)" by simp
also have "...= estaEn a xs" using HI by simp
finally show "estaEn a (borraDuplicados2 (x#xs)) = estaEn a (x#xs)" by auto
next
assume "¬estaEn x xs"
then have "estaEn a (borraDuplicados2 (x#xs)) = estaEn a (x#borraDuplicados2 xs)" by simp
also have "...= (x = a ∨ estaEn a (borraDuplicados2 xs))" by simp
finally show "estaEn a (borraDuplicados2 (x#xs)) = estaEn a (x#xs)" using HI by simp
qed
qed

text {*
---------------------------------------------------------------------
Ejercicio 18.1. Demostrar o refutar automáticamente
sinDuplicados (borraDuplicados xs)
---------------------------------------------------------------------
*}

-- "maresccas4 irealetei diecabmen1 julrobrel domlloriv marescpla juaruipav"
lemma "sinDuplicados (borraDuplicados xs)"
by (induct xs) (auto simp add: estaEn_borraDuplicados)

text {*
---------------------------------------------------------------------
Ejercicio 18.2. Demostrar o refutar detalladamente
sinDuplicados (borraDuplicados xs)
---------------------------------------------------------------------
*}

-- "maresccas4"
lemma sinDuplicados_borraDuplicados:
"sinDuplicados (borraDuplicados2 xs)"
proof (induct xs)
show "sinDuplicados (borraDuplicados2 [])" by simp
next
fix x :: "'a"
fix xs :: "'a list"
assume HI: "sinDuplicados (borraDuplicados2 xs)"
have "sinDuplicados (borraDuplicados2 (x#xs)) = sinDuplicados ((if estaEn x xs then borraDuplicados2 xs else x # borraDuplicados2 xs))" by simp
also have "...= (if estaEn x xs then sinDuplicados (borraDuplicados2 xs) else sinDuplicados (x#borraDuplicados2 xs))" by simp
also have "...= (if estaEn x xs then sinDuplicados (borraDuplicados2 xs) else (¬estaEn x (borraDuplicados2 xs) ∧ sinDuplicados (borraDuplicados2 xs)))" by simp
also have "...= (if estaEn x xs then sinDuplicados (borraDuplicados2 xs) else (¬estaEn x xs ∧ sinDuplicados (borraDuplicados2 xs)))" by (simp add: estaEn_borraDuplicados)
then show "sinDuplicados (borraDuplicados2 (x#xs))" using HI by (simp add: estaEn_borraDuplicados)
qed

lemma sinDuplicados_borraDuplicados_porCasos:
"sinDuplicados (borraDuplicados2 xs)"
proof (induct xs)
show "sinDuplicados (borraDuplicados2 [])" by simp
next
fix x :: "'a"
fix xs :: "'a list"
assume HI: "sinDuplicados (borraDuplicados2 xs)"
show "sinDuplicados (borraDuplicados2 (x#xs))"
proof (cases)
assume h1: "estaEn x xs"
have "sinDuplicados (borraDuplicados2 (x#xs)) = sinDuplicados ((if estaEn x xs then borraDuplicados2 xs else x # borraDuplicados2 xs))" by simp
also have "...= sinDuplicados (borraDuplicados2 xs)" using h1 by simp
finally show "sinDuplicados (borraDuplicados2 (x#xs))" using HI by simp
next
assume h2: "¬estaEn x xs"
have "sinDuplicados (borraDuplicados2 (x#xs)) = sinDuplicados ((if estaEn x xs then borraDuplicados2 xs else x # borraDuplicados2 xs))" by simp
also have "...= sinDuplicados (x#borraDuplicados2 xs)" using h2 by simp
also have "...= (¬estaEn x xs ∧ sinDuplicados (borraDuplicados2 xs))" by (simp add: estaEn_borraDuplicados)
also have "...= sinDuplicados (borraDuplicados2 xs)" using h2 by simp
finally show "sinDuplicados (borraDuplicados2 (x#xs))" using HI by simp
qed
qed

--"irealetei diecabmen1 domlloriv marescpla juaruipav"
lemma sinDuplicados_borraDuplicados:
"sinDuplicados (borraDuplicados xs)"
proof (induct xs)
show "sinDuplicados (borraDuplicados [])" by simp
next
fix a::"'a"
fix xs::"'a list"
assume HI:"sinDuplicados (borraDuplicados xs)"
show "sinDuplicados (borraDuplicados (a # xs))"
proof (cases)
assume "estaEn a xs"
then have "sinDuplicados (borraDuplicados (a # xs)) = sinDuplicados (borraDuplicados xs)" by simp
also have "... = True" using HI by simp
finally show "sinDuplicados (borraDuplicados (a # xs))" by simp
next
assume HI2:"¬estaEn a xs"
then have "sinDuplicados (borraDuplicados (a # xs)) = sinDuplicados (a # borraDuplicados xs)" by simp
also have "... = (¬estaEn a (borraDuplicados xs) ∧ sinDuplicados(borraDuplicados xs))" by simp
also have "... = (¬estaEn a (borraDuplicados xs) ∧ True)" using HI by simp
also have "...= (¬estaEn a xs)" by (simp add:estaEn_borraDuplicados)
finally show "sinDuplicados (borraDuplicados (a # xs))" using HI2 by simp
qed
qed

text {*
---------------------------------------------------------------------
Ejercicio 19. Demostrar o refutar:
borraDuplicados (rev xs) = rev (borraDuplicados xs)
---------------------------------------------------------------------
*}

-- "maresccas4 irealetei diecabmen1 julrobrel domlloriv marescpla juaruipav"
lemma "borraDuplicados (rev xs) = rev (borraDuplicados xs)"
quickcheck
oops
(* Contraejemplo:
xs = {a⇣1, a⇣2, a⇣1}
*)

end
</source>

Relación 3

2014-01-22T18:24:21Z

Jalonso: Desprotegió «Relación 3»

<source lang="isar">
header {* R3: Razonamiento sobre programas en Isabelle/HOL *}

theory R3
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
------------------------------------------------------------------ *}

-- "maresccas4 irealetei diecabmen1 domlloriv pabflomar marescpla"

fun sumaImpares :: "nat ⇒ nat" where
"sumaImpares 0 = 0"
| "sumaImpares (Suc n) = 2 * n + 1 + sumaImpares n"

value "sumaImpares 5" -- "= 25"

-- "julrobrel"
fun sumaImpares2 :: "nat ⇒ nat" where
"sumaImpares2 0 = 0"
| "sumaImpares2 (Suc n) = (2 * (Suc n) - 1) + sumaImpares2 n"

value "sumaImpares2 5" -- "= 25"

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

-- "maresccas4 pabflomar juaruipav marescpla"

lemma "sumaImpares n = n*n"
proof (induct n)
show "sumaImpares 0 = 0*0" by simp
next
fix n
assume HI: "sumaImpares n = n*n"
have "sumaImpares (Suc n) = 2 * n + 1 + sumaImpares n" by (simp only: sumaImpares.simps(2))
also have "... = 2 * n + 1 + n * n" using HI by simp
finally show "sumaImpares (Suc n) = (Suc n) * (Suc n)" by simp
qed

-- "irealetei diecabmen1 domlloriv"
lemma "sumaImpares n = n*n"
proof (induct n)
show "sumaImpares (0) = 0 * 0" by simp
next
fix n
assume HI: "sumaImpares n = n * n"
have "sumaImpares (Suc n) = (2*n + 1) + sumaImpares n " by simp
also have "... = 2*n + 1 + (n * n)" using HI by simp
also have "...= (n+1)*(n+1)" by simp
finally show "sumaImpares (Suc n) =Suc n * Suc n" by simp
qed

-- "Sobrarían varios parentesis."

-- "julrobrel"
lemma "sumaImpares n = n*n"
proof (induct n)
show "sumaImpares 0 = 0 * 0" by simp
next
fix n
assume HI: "sumaImpares n = n * n"
have "sumaImpares (Suc n) = (2 * (Suc n) - 1) + sumaImpares n" by simp
also have "...= (n+1)*(n+1)" using HI by simp
finally show "sumaImpares (Suc n) = (Suc n) * (Suc n)" by simp
qed

-- "ElyIvan"

lemma "sumaImpares n = n*n"
proof -
by (induc n)
show "sumaImpares 0 = 0*0" by simp
next
assume HI: "sumaImpares n = n * n"
have "sumaImpares n = 2 * n - 1) + sumaImpares ( n- 1 )" by sumanImpares2
also have "...= 2 * n - 1 + (n - 1) * ( n - 1)" using HI by simp
also have "...= 2 * n -1 + n * n - 2 * n + 1" by simp
also have "...= n * n" by simp
finally show "sumaImpares n = n * n" by simp
qed

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
------------------------------------------------------------------ *}

-- "maresccas4 irealetei diecabmen1 domlloriv pabflomar julrobrel"

fun sumaPotenciasDeDosMasUno :: "nat ⇒ nat" where
"sumaPotenciasDeDosMasUno 0 = 2"
| "sumaPotenciasDeDosMasUno (Suc n) = 2^(Suc n) + sumaPotenciasDeDosMasUno n"

value "sumaPotenciasDeDosMasUno 3" -- "= 16"

-- "ElyIvan"

fun sumaPotenciasDeDosMasUno2 :: "nat ⇒ nat" where
"sumaPotenciasDeDosMasUno2 0 = 2"
| "sumaPotenciasDeDosMasUno2 n = 2^n + sumaPotenciasDeDosMasUno2 (n-1)"

value "sumaPotenciasDeDosMasUno2 1" -- "= 16"

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

-- "maresccas4 pabflomar juaruipav"

lemma "sumaPotenciasDeDosMasUno n = 2^(n+1)"
proof (induct n)
show "sumaPotenciasDeDosMasUno 0 = 2^(0+1)" by simp
next
fix n
assume HI: "sumaPotenciasDeDosMasUno n = 2^(n+1)"
have "sumaPotenciasDeDosMasUno (Suc n) = 2^(Suc n) + sumaPotenciasDeDosMasUno n" by (simp only: sumaPotenciasDeDosMasUno.simps(2))
also have "... = 2^(Suc n) + 2^(n+1)" using HI by simp
also have "... = 2^(n+1) + 2^(n+1)" by simp
also have "... = 2 * 2^(n+1)" by simp
also have "... = 2 * 2^(Suc n)" by simp
finally show "sumaPotenciasDeDosMasUno (Suc n) = 2^((Suc n)+1)" by simp
qed

--"irealetei"
lemma "sumaPotenciasDeDosMasUno n = 2^(n + 1)"
proof (induct n)
show "sumaPotenciasDeDosMasUno (0) = 2^(0 + 1)" by simp
next
fix n
assume HI: "sumaPotenciasDeDosMasUno n = 2^(n + 1)"
have "sumaPotenciasDeDosMasUno (n+1) = 2^(n+1) + sumaPotenciasDeDosMasUno(n)" by simp
also have "... = 2^(n+1) + 2^(n+1)" using HI by simp
also have "...=2*2^(n+1)" by simp
also have "...=2^(n+2)" by simp
finally show "sumaPotenciasDeDosMasUno (Suc n) = 2^(Suc n +1)" by simp
qed

--"diecabmen1, marescpla"
lemma "sumaPotenciasDeDosMasUno n = 2^(n+1)"
proof (induct n)
show "sumaPotenciasDeDosMasUno 0 = 2^(0+1)" by simp
next
fix n
assume HI: "sumaPotenciasDeDosMasUno n = 2^(n+1)"
have "sumaPotenciasDeDosMasUno (Suc n) = 2^(Suc n)+sumaPotenciasDeDosMasUno n" by simp
also have "… = (2^(Suc n)) + (2^(n+1))" using HI by simp
also have "… = 2^(n+1) + 2^(n+1)" by simp
also have "… = 2 * 2^(Suc n)" by simp
finally show "sumaPotenciasDeDosMasUno (Suc n) = 2^(Suc n +1)" by simp
qed

--"en el primer have yo especifiqué la regla usada: by (simp only: sumaPotenciasDeDosMasUno.simps(2)) marescpla"

--"domlloriv"
lemma "sumaPotenciasDeDosMasUno n = 2^(n+1)"
proof (induct n)
show "sumaPotenciasDeDosMasUno 0 = 2^(0+1)" by simp
next
fix n
assume HI: "sumaPotenciasDeDosMasUno n = 2^(n+1)"
have "sumaPotenciasDeDosMasUno (Suc n) = 2^(Suc n) + sumaPotenciasDeDosMasUno n" by simp
also have "... = 2^(Suc n) + 2^(n+1)" using HI by simp
finally show "sumaPotenciasDeDosMasUno (Suc n) = 2^((Suc n)+1)" by simp
qed

-- "julrobrel"
lemma "sumaPotenciasDeDosMasUno n = 2^(n+1)"
proof (induct n)
show "sumaPotenciasDeDosMasUno 0 = 2^(0+1)" by simp
next
fix n
assume HI: "sumaPotenciasDeDosMasUno n = 2^(n+1)"
have "sumaPotenciasDeDosMasUno (Suc n) = 2^(Suc n) + sumaPotenciasDeDosMasUno n" by simp
also have "...= 2^((n+1)+1)" using HI by simp
finally show "sumaPotenciasDeDosMasUno (Suc n) = 2^((Suc n)+1)" by simp
qed

-- "ElyIvan"

lemma "sumaPotenciasDeDosMasUno2 n = 2^(n+1)"
proof (induct n)
show "sumaPotenciasDeDosMasUno2 0 = 2^(0+1)" by simp
next
fix n
assume HI "sumaPotenciasDeDosMasUno2 n = 2^(n+1)"
have "sumaPotenciasDeDosMasUno2 n = 2^n + sumaPotenciasDeDosMasUno2 (n-1)" by sumaPotenciasDeDosMasUno2 2
also have "...= 2^n + 2 ^((n-1)+1)" by HI
also have "...= 2^n + 2^n" by simp
finally show "sumaPotenciasDeDosMasUno2 n = 2^(n+1)" by simp
qed

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]
------------------------------------------------------------------ *}

-- "maresccas4 irealetei diecabmen1 domlloriv pabflomar julrobrel marescpla"

fun copia :: "nat ⇒ 'a ⇒ 'a list" where
"copia 0 x = []"
| "copia (Suc n) x = x # copia n x"

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

-- "ElyIvan"

fun copia2 :: "nat ⇒ 'a ⇒ 'a list" where
"copia2 0 x = []"
| "copia2 n x = x # copia2 ( n - 1 ) x"

value "copia2 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 ∧
----------------------------------------------------------------- *}

-- "maresccas4 irealetei diecabmen1 domlloriv pabflomar julrobrel marescpla"

fun todos :: "('a ⇒ bool) ⇒ 'a list ⇒ bool" where
"todos p [] = True"
| "todos p (x#xs) = (p x ∧ todos p xs)"

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.
------------------------------------------------------------------- *}

-- "maresccas4"

lemma "todos (λy. y=x) (copia n x)"
proof (induct n)
show "todos (λy. y=x) (copia 0 x)" by simp
next
fix n
assume HI: "todos (λy. y=x) (copia n x)"
have "todos (λy. y=x) (copia (Suc n) x) = todos (λy. y=x) (x # copia n x)" by (simp only: copia.simps(2))
also have "... = todos (λy. y=x) (copia n x)" by simp
finally show "todos (λy. y=x) (copia (Suc n) x)" using HI by simp
qed

-- "irealetei diecabmen1 pabflomar"
lemma "todos (λy. y=x) (copia n x)"
proof (induct n)
show "todos (λy. y = x) (copia 0 x)" by simp
next
fix n
assume HI: " todos (λy. y = x) (copia n x)"
have " todos (λy. y = x) (copia (Suc n) x)= todos (λy. y = x) (x#copia n x)" by simp
also have "... = todos (λy. y = x) (copia n x)" by simp
also have "... = True" using HI by simp
finally show "todos (λy. y = x) (copia (Suc n) x)" by simp
qed

-- "domlloriv"
lemma "todos (λy. y=x) (copia n x)"
proof (induct n)
show "todos (λy. y=x) (copia 0 x)" by simp
next
fix n
assume HI:"todos (λy. y=x) (copia n x)"
have "todos (λy. y=x) (copia (Suc n) x) = ((λy. y=x) x ∧ todos (λy. y=x) (copia n x))" using HI by simp
also have "... = True" using HI by simp
finally show "todos (λy. y=x) (copia (Suc n) x)" by simp
qed

-- "julrobrel"
lemma "todos (λy. y=x) (copia n x)"
proof (induct n)
show "todos (λy. y=x) (copia 0 x)" by simp
next
fix n
assume HI: "todos (λy. y = x) (copia n x)"
have "todos (λy. y = x) (copia (Suc n) x)=todos (λy. y = x) (x # copia n x)" by simp
also have "...=(λy. y = x) x ∧ todos (λy. y = x) (copia n x)" using HI by simp
finally show "todos (λy. y = x) (copia (Suc n) x)" by simp
qed

-- "juaruipav"
lemma "todos (λy. y=x) (copia n x)"
proof (induct n)
show "todos (λy. y=x) (copia 0 x)" by simp
next
fix n
assume HI: "todos (λy. y=x) (copia n x)"
have "todos (λy. y=x) (copia (Suc n) x)= todos (λy. y=x)(x# (copia n x))" by simp
also have "...=todos (λy. y=x)[x]" using HI by simp
finally show "todos (λy. y=x) (copia (Suc n) x)" by simp
qed

--"marescpla"

lemma "todos (λy. y=x) (copia n x)"
proof(induct n)
show "todos (λy. y=x) (copia 0 x)" by (simp only: copia.simps(1) todos.simps(1))
next
fix n
assume HI : "todos (λy. y=x) (copia n x)"
have "todos (λy. y=x) (copia (Suc n) x) = ((λy. y=x) (hd (copia (Suc n) x)) ∧ todos (λy. y=x) (tl(copia (Suc n) x)))" by simp
also have "...= ((λy. y=x) (hd (x # copia n x))∧ todos (λy. y=x) (tl(copia (Suc n) x)))" by (simp only: copia.simps(2))
also have " ...= ((λy. y=x) x ∧ todos (λy. y=x) (tl(copia (Suc n) x)))" by (simp only: hd.simps)
also have "...=(todos (λy. y=x) (tl(copia (Suc n) x)))" by simp
also have "...=(todos (λy. y=x) (tl(x # copia n x)))" by (simp only: copia.simps(2))
also have "...=(todos (λy. y=x) (copia n x))" by (simp only: tl.simps)
also have "...= True" using HI by simp
finally show "todos (λy. y=x) (copia (Suc n) x)" by simp
qed

--"jajaja ya he visto que me he complicado demasiado. Es mejor resolverlo en el otro orden"

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

-- "maresccas4 irealetei diecabmen1 domlloriv pabflomar julrobrel marescpla"

fun factR :: "nat ⇒ nat" where
"factR 0 = 1"
| "factR (Suc n) = Suc n * factR n"

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"

-- "maresccas4"

lemma fact: "factI' n x = x * factR n"
proof (induct n arbitrary: x)
show "⋀x. factI' 0 x = x * factR 0" by simp
next
fix n
assume HI: "⋀x. factI' n x = x * factR n"
show "⋀x. factI' (Suc n) x = x * factR (Suc n)"
proof -
fix x
have "factI' (Suc n) x = factI' n (Suc n)*x" by (simp only: factI'.simps(2))
also have "... = x * factI' n (Suc n)" by simp
also have "... = x * ((Suc n) * factR n)" using HI by simp
finally show "factI' (Suc n) x = x * factR (Suc n)" by simp
qed
qed

-- "irealetei" (*Éste ha sido la muerte a pellizcos, aún leyéndome todo el tema.*)
lemma fact2: "factI' n x = x * factR n"
proof (induct n arbitrary: x)
show "⋀x. factI' 0 x = x * factR 0" by simp
next
fix n x
assume HI: "⋀x. factI' n x = x * factR n"
have "factI' (Suc n) x = factI' n (Suc n)*x" by simp
also have "... = x * factI' n (Suc n)" by simp
also have "... = x * (Suc n * factR n)" using HI by simp
also have "... = x * factR (Suc n)" by simp
finally show "factI' (Suc n) x = x * factR (Suc n)" by simp
qed

-- "diecabmen1" (*Es el mismo que de irealetei solo que me parece que se puede eliminar el último also have y ponerlo directo en el finally.*)
lemma fact3: "factI' n x = x * factR n"
proof (induct n arbitrary: x)
show "⋀x. factI' 0 x = x * factR 0" by simp
next
fix n x
assume HI: "⋀x. factI' n x = x * factR n"
have "factI' (Suc n) x = factI' n (Suc n)*x" by simp
also have "… = x * ((Suc n) * factR n)" using HI by simp
finally show "factI' (Suc n) x = x * factR (Suc n)" by simp
qed

-- "domlloriv"
lemma fact4: "factI' n x = x * factR n"
proof (induct n arbitrary: x)
show "⋀x. factI' 0 x = x * factR 0" by simp (*Para todo x se cumple*)
next
fix n
assume HI: "⋀x. factI' n x = x * factR n"
have "factI' (Suc n) x = factI' n (Suc n)*x" using HI by simp
also have "... = x * (Suc n * factR n)" using HI by simp
finally show "⋀x. factI' (Suc n) x = x * factR (Suc n)" using HI by simp
qed

(* Comentario: "using HI" se necesita sólo una vez. *)

-- "julrobrel"
lemma fact5: "factI' n x = x * factR n"
proof (induct n arbitrary: x)
show "⋀x. factI' 0 x = x * factR 0" by simp
next
fix n x
assume HI: "⋀x. factI' n x = x * factR n"
have "factI' (Suc n) x = factI' n (Suc n)*x" by simp
also have "...=x * ((Suc n) * factR n)" using HI by simp
finally show "factI' (Suc n) x = x* factR (Suc n)" by simp
qed

-- "juaruipav"

lemma fact6: "factI' n x = x * factR n"
proof (induct n arbitrary: x)
show "⋀x. factI' 0 x= x*factR 0" by simp
next
fix n
assume HI: "⋀x. factI' n x = x * factR n"
have "factI'(Suc n) x= factI' n (Suc n)*x" by simp
also have "...=x*((Suc n)*factR n)" using HI by simp
finally show "⋀x. factI' (Suc n) x = x*factR (Suc n)" by simp
qed

-- " juaruipav: No me termina de funcionar"

-- "pabflomar los entiendo casi todos pero yo no habría sacado ni uno de ellos"

--"marescpla (no me resuelve el paso de inducción"
lemma fact: "factI' n x = x * factR n"
proof (induct n)
show "factI' 0 x = x* factR 0" by (simp only: factI'.simps(1) factR.simps(1))
next
fix n
assume HI : "factI' n x = x * factR n"
have " factI' (Suc n) x= factI' n (Suc n)*x" by (simp only: factI'.simps(2))
also have "...= (Suc n)*x * factR n" using HI by simp
also have " ... = x * (Suc n)*factR n" by simp
also have " ... = x * factR (Suc n)" by (simp only: factR.simps(2))
finally show " factI' (Suc n) x = x * factR (Suc n)" by simp
qed

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

-- "maresccas4 julrobrel"

corollary "factI n = factR n"
proof -
show "factI n = factR n" by (simp add:fact)
qed

-- "irealetei diecabmen1 domlloriv pabflomar juaruipav"
corollary "factI n = factR n"
by (simp add: fact)

--"marescpla"
corollary "factI n = factR n"
proof-
have "factI n = factI' n 1" by (simp only: factI.simps(1))
also have " ...= 1*factR n" by (simp add: fact)
finally show "factI n = factR n" by simp
qed

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]
------------------------------------------------------------------ *}

-- "maresccas4 irealetei diecabmen1 domlloriv julrobrel marescpla"

fun amplia :: "'a list ⇒ 'a ⇒ 'a list" where
"amplia [] y = [y]"
| "amplia (x#xs) y = x # (amplia xs y)"

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

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

-- "maresccas4 marescpla"

lemma "amplia xs y = xs @ [y]"
proof (induct xs)
show "amplia [] y = [] @ [y]" by simp
next
fix x xs
assume HI: "amplia xs y = xs @ [y]"
have "amplia (x#xs) y = x # (amplia xs y)" by (simp only: amplia.simps(2))
also have "... = x # xs @ [y]" using HI by simp
finally show "amplia (x#xs) y = (x#xs) @ [y]" by simp
qed

--"irealetei diecabmen1 domlloriv pabflomar juaruipav"
lemma "amplia xs y = xs @ [y]"
proof (induct xs)
show "amplia [] y = [] @ [y]" by simp
next
fix a xs
assume HI: "amplia xs y = xs @ [y]"
have "amplia (a#xs) y = a # (amplia xs y)" by simp
also have "... = (a # xs) @ [y]" using HI by simp
finally show "amplia (a#xs) y = (a # xs) @ [y]" by simp
qed

-- "julrobrel"
lemma "amplia xs y = xs @ [y]"
proof (induct xs)
show "amplia [] y = [] @ [y]" by simp
next
fix x xs
assume HI:"amplia xs y = xs @ [y]"
have "amplia (x#xs) y = x # (amplia xs y)" by simp
also have "...= x # (xs @ [y])" using HI by simp
finally show "amplia (x#xs) y = (x#xs) @ [y]" by simp
qed

end
</source>

Relación 2

2014-01-22T18:23:54Z

Jalonso: Desprotegió «Relación 2»

<source lang="isar">
header {* R2: Razonamiento sobre programas en Isabelle/HOL *}

theory R2
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
------------------------------------------------------------------ *}

-- "maresccas4 pabflomar"

fun sumaImpares :: "nat ⇒ nat" where
"sumaImpares 0 = 0"
|"sumaImpares (Suc n) = (2 * (Suc n) - 1) + sumaImpares n"

value "sumaImpares 5" -- "= 25"

-- "diecabmen1 irealetei juaruipav domlloriv, marescpla"
thm nat.induct
fun sumaImpares2 :: "nat ⇒ nat" where
"sumaImpares2 0 = 0"
| "sumaImpares2 (Suc n) = (2*n + 1) + sumaImpares2 n" <-- "yo he puesto el +1 con un Suc (marescpla)"

value "sumaImpares2 5" -- "= 25"

-- "jaisalmen zoiruicha"
fun sumaImpares3 :: "nat ⇒ nat" where
"sumaImpares3 0 = 0"
| "sumaImpares3 (n) = (2 * n) - 1 + sumaImpares3 (n - 1)"

value "sumaImpares 5" -- "= 25"

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

-- "maresccas4,juaruipav domlloriv pabflomar, marescpla"

lemma "sumaImpares n = n*n"
by (induct n) auto

-- "diecabmen1 irealetei"

lemma "sumaImpares2 n = n*n"
by (induct n) auto

-- "jaisalmen zoiruicha"
lemma "sumaImpares3 n = n*n"
by (induct n) auto

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
------------------------------------------------------------------ *}

-- "maresccas4 diecabmen1 irealetei domlloriv pabflomar, marescpla"

fun sumaPotenciasDeDosMasUno :: "nat ⇒ nat" where
"sumaPotenciasDeDosMasUno 0 = 2"
|"sumaPotenciasDeDosMasUno (Suc n) = 2^(Suc n) + sumaPotenciasDeDosMasUno n"

value "sumaPotenciasDeDosMasUno 3" -- "= 16"

-- "juaruipav"
fun sumaPotenciasDeDosMasUno2 :: "nat ⇒ nat" where
"sumaPotenciasDeDosMasUno2 0 = 2"
| "sumaPotenciasDeDosMasUno2 (Suc n) = 2*sumaPotenciasDeDosMasUno2 n"

value "sumaPotenciasDeDosMasUno2 3" -- "= 16"

-- "jaisalmen zoiruicha"
fun sumaPotenciasDeDosMasUno3 :: "nat ⇒ nat" where
"sumaPotenciasDeDosMasUno3 0 = 2"
| "sumaPotenciasDeDosMasUno3 (n) = 2^n + sumaPotenciasDeDosMasUno3(n - 1)"

value "sumaPotenciasDeDosMasUno3 3" -- "= 16"

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

-- "maresccas4 diecabmen1 irealetei juaruipav domlloriv pabflomar jaisalmen, marescpla zoiruicha"

lemma "sumaPotenciasDeDosMasUno n = 2^(n+1)"
by (induct n) auto

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]
------------------------------------------------------------------ *}

-- "maresccas4 irealetei domlloriv juaruipav pabflomar, marescpla"

fun copia :: "nat ⇒ 'a ⇒ 'a list" where
"copia 0 x = []"
|"copia (Suc n) x = x # copia n x"

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

-- "diecabmen1"

fun copia2 :: "nat ⇒ 'a ⇒ 'a list" where
"copia2 0 x = []"
| "copia2 (Suc n) x = x#[]@copia2 n x"

value "copia2 3 x" -- "= [x,x,x]"

-- "jaisalmen zoiruicha"
fun copia3 :: "nat ⇒ 'a ⇒ 'a list" where
"copia3 0 x = []"
| "copia3 n x = x # (copia3 (n- 1) x)"

value "copia3 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 ∧
----------------------------------------------------------------- *}

-- "maresccas4 irealetei diecabmen1 juaruipav pabflomar jaisalmen, marescpla zoiruicha"

fun todos :: "('a ⇒ bool) ⇒ 'a list ⇒ bool" where
"todos p [] = True"
|"todos p (x#xs) = (p x ∧ todos p xs)"

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

-- "domlloriv"
fun todos2 :: "('a \<Rightarrow> bool) \<Rightarrow> 'a list \<Rightarrow> bool" where
"todos2 p [] = True"
| "todos2 p (x#xs) = ((p x) \<and> todos2 p xs)"

value "todos2 (λx. x>(1::nat)) [2,6,4]" -- "= True"
value "todos2 (λx. x>(2::nat)) [2,6,4]" -- "= False""

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

-- "maresccas4,juaruipav domlloriv pabflomar jaisalmen, marescpla zoiruicha"

lemma "todos (λy. y=x) (copia n x)"
by (induct n) auto

-- "diecabmen1"
lemma "todos (λy. y=x) (copia2 n x)"
by (induct n) auto

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

-- "maresccas4 irealetei diecabmen1 juaruipav domlloriv pabflomar, marescpla"

fun factR :: "nat ⇒ nat" where
"factR 0 = 1"
|"factR (Suc n) = (Suc n) * factR n" <--"creo que no hacen falta los paréntesis del 2º suc (marescpla)"

value "factR 4" -- "= 24"

-- "jaisalmen zoiruicha"
fun factR2 :: "nat ⇒ nat" where
"factR2 0 = 1"
| "factR2 (n) = n * factR2 (n - 1)"

value "factR2 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"

-- "maresccas4 irealetei diecabmen1 juaruipav domlloriv pabflomar jaisalmen, marescpla zoiruicha"

lemma fact: "factI' n x = x * factR n"
by (induct n arbitrary: x) auto

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

-- "maresccas4 diecabmen1 juaruipav pabflomar jaisalmen zoiruicha" "no lo entiendo (marescpla)"

corollary "factI n = factR n"
by (simp add: fact)

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]
------------------------------------------------------------------ *}

-- "maresccas4,juaruipav domlloriv jaisalmen zoiruicha"

fun amplia :: "'a list ⇒ 'a ⇒ 'a list" where
"amplia [] y = [y]"
|"amplia (x#xs) y = x # (amplia xs y)"

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

-- "irealetei diecabmen1"

fun amplia2 :: "'a list ⇒ 'a ⇒ 'a list" where
"amplia2 [] y = y#[]"
|"amplia2 (x#xs) y = x#(amplia2 xs y)"

value "amplia2 [d,a] t" -- "= [d,a,t]"

-- "pabflomar, marescpla" ¿Sería mejor poner los paréntesis en la llamada a amplia como hace maresccas4?
fun amplia3 :: "'a list ⇒ 'a ⇒ 'a list" where
"amplia3 [] y = [y]"
| "amplia3 (x#xs) y = x # amplia3 xs y"

value "amplia3 [d,a] t" -- "= [d,a,t]"

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

-- "maresccas4, juaruipav domlloriv pabflomar jaisalmen zoiruicha"

lemma "amplia xs y = xs @ [y]"
by (induct xs) auto

-- "irealetei diecabmen1" (* Es igual que la de maresccas4, pero lo pego para que compile*)

lemma "amplia2 xs y = xs @ [y]"
by (induct xs) auto

end

</source>

Relación 1

2014-01-22T18:23:27Z

Jalonso: Desprotegió «Relación 1»

<source lang="isar">

header {* R1: Programación funcional en Isabelle *}

theory R1
imports Main
begin

text {* ----------------------------------------------------------------
Ejercicio 0. Definir, por recursión, la función
factorial :: nat ⇒ nat
tal que (factorial n) es el factorial de n. Por ejemplo,
factorial 4 = 24
------------------------------------------------------------------- *}

-- "antmacrui maresccas4 diecabmen1 juaruipav marescpla"
fun factorial :: "nat ⇒ nat" where
"factorial 0 = 1"
| "factorial (Suc n) = Suc n * factorial n"

value "factorial 4" -- "24"

-- "irealetei domlloriv"
fun factorial2 :: "nat ⇒ nat" where
"factorial2 (0::nat)= (1::nat)"
| "factorial2 n = n * factorial2 (n - 1)"

value "factorial2 4" -- "24"

-- "julrobrel"
fun factorial3 :: "nat ⇒ nat" where
"factorial3 0 = 1"
| "factorial3 n = factorial3 (n - 1) * n"

value "factorial3 4" -- "24"

-- "jaisalmen zoiruicha"
fun factorial4 :: "nat ⇒ nat" where
"factorial4 0 = 1"
| "factorial4 (n) = n * factorial4 (n- 1)"

value "factorial4 4" -- "24

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
------------------------------------------------------------------- *}

-- "maresccas4 domlloriv"
fun longitud :: "'a list ⇒ nat" where
"longitud [] = 0"
| "longitud (x # xs) = Suc (longitud xs)"

value "longitud [4,2,5]" -- "= 3"

-- "irealetei pabflomar julrobrel juaruipav"
fun longitud2 :: "'a list ⇒ nat" where
"longitud2 [] = (0::nat)"
| "longitud2 xs = 1 + longitud2 (tl xs) "

value "longitud2 [4,2,5]" -- "= 3"

-- "diecabmen1"
fun longitud3 :: "'a list ⇒ nat" where
"longitud3 [] = 0"
| "longitud3 (head#tail) = 1 + longitud3 tail"

value "longitud3 [4,2,5]" -- "= 3"

-- "marescpla"
fun longitud4 :: "'a list ⇒ nat" where
"longitud4 [] = 0"|
"longitud4 xs = 1 + longitud4 (tl xs) "

value "longitud4 [4,2,5]" -- "= 3"

-- ""jaisalmen zoiruicha"
fun longitud5 :: "'a list ⇒ nat" where
"longitud5 [] = 0"
| "longitud5 (x#a) = 1 + longitud5 a"

value "longitud5 [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)
------------------------------------------------------------------ *}

-- "maresccas4 pabflomar"
fun intercambia :: "'a × 'b ⇒ 'b × 'a" where
"intercambia p = (snd p, fst p)"

value "intercambia (u,v)" -- "= (v,u)"

-- "irealetei diecabmen1 domlloriv julrobrel juaruipav marescpla jaisalmen"
fun intercambia2 :: "'a × 'b ⇒ 'b × 'a" where
"intercambia2 (x,y) = (y,x)"

value "intercambia2 (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]
------------------------------------------------------------------ *}

-- "maresccas4 diecabmen1 domlloriv julrobrel juaruipav"
fun inversa :: "'a list ⇒ 'a list" where
"inversa [] = []"
| "inversa (x#xs) = inversa xs @ (x#[])"

value "inversa [a,d,c]" -- "= [c,d,a]"

-- "irealetei pabflomar"
fun inversa2 :: "'a list ⇒ 'a list" where
"inversa2 [] = [] "
| "inversa2 xs = inversa2 (tl xs) @ (hd xs#[])"

value "inversa2 [a,d,c]" -- "= [c,d,a]"

-- "jaisalmen zoiruicha"
fun inversa3 :: "'a list ⇒ 'a list" where
"inversa3 [] = []"
| "inversa3 (x#a) = inversa3 a @ [x]"

value "inversa3 [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]
------------------------------------------------------------------ *}

-- "maresccas4 julrobrel juaruipav marescpla"
fun repite :: "nat ⇒ 'a ⇒ 'a list" where
"repite 0 x = []"|
"repite (Suc n) x = x # repite n x"

value "repite 3 a" -- "= [a,a,a]"

-- "irealetei"
fun repite2 :: "nat ⇒ 'a ⇒ 'a list" where
"repite2 (0::nat) x = []"
| "repite2 n x = x#(repite2 (n - 1) x) "

value "repite2 3 a" -- "= [a,a,a]"

-- "diecabmen1"
fun repite3 :: "nat ⇒ 'a ⇒ 'a list" where
"repite3 0 x = []"
| "repite3 (Suc n) x = (x#[]) @ (repite3 n x)"

value "repite3 3 a" -- "= [a,a,a]"

-- "domlloriv pabflomar jaisalmen zoiruicha"
fun repite4 :: "nat ⇒ 'a ⇒ 'a list" where
"repite4 0 x = []"
| "repite4 n x = x# repite4 (n - 1) x"

value "repite4 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]
------------------------------------------------------------------ *}

-- "maresccas4 julrobrel"
fun conc :: "'a list ⇒ 'a list ⇒ 'a list" where
"conc [] ys = ys"
| "conc (x#xs) ys = x # conc xs ys"

value "conc [a,d] [b,d,a,c]" -- "= [a,d,b,d,a,c]"

-- irealetei
fun conc2 :: "'a list ⇒ 'a list ⇒ 'a list" where
"conc2 xs [] = xs"
| "conc2 xs ys = hd ys # conc2 xs (tl ys)"

value "conc2 [a,d] [b,d,a,c]" -- "= [a,d,b,d,a,c]"

-- "diecabmen1 domlloriv pabflomar juaruipav"
fun conc3 :: "'a list ⇒ 'a list ⇒ 'a list" where
"conc3 xs ys = xs@ys"

value "conc3 [a,d] [b,d,a,c]" -- "= [a,d,b,d,a,c]"

-- "marescpla"
fun conc4 :: "'a list ⇒ 'a list ⇒ 'a list" where
"conc4 [] [] = []"|
"conc4 [] ys = (hd ys) # conc4 [] (tl ys)"|
"conc4 xs ys = (hd xs) # conc4 (tl xs) ys"

value "conc4 [a,d] [b,d,a,c]" -- "= [a,d,b,d,a,c]"

-- "jaisalmen zoiruicha"
fun conc5 :: "'a list ⇒ 'a list ⇒ 'a list" where
"conc5 [] ys = ys"
| "conc5 xs [] = xs"
| "conc5 (x#xs) ys = x # conc5 xs ys"

value "conc5 [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]
------------------------------------------------------------------ *}

-- "maresccas4 diecabmen1 domlloriv"
fun coge :: "nat ⇒ 'a list ⇒ 'a list" where
"coge 0 xs = []"
| "coge n [] = []"
| "coge (Suc n) (x#xs) = x # (coge n xs)"

-- "irealetei"
fun coge2 :: "nat ⇒ 'a list ⇒ 'a list" where
"coge2 0 xs = []"
| "coge2 n xs = (hd xs) # (coge2 (n - 1) (tl xs))"

-- "pabflomar"
fun coge3 :: "nat ⇒ 'a list ⇒ 'a list" where
"coge3 0 xs = []"
| "coge3 n xs = (hd xs) # (coge3 (n - 1) (tl xs))"

value "coge 2 [a,c,d,b,e]" -- "= [a,c]"

-- "julrobrel,juaruipav"
fun coge4 :: "nat ⇒ 'a list ⇒ 'a list" where
"coge4 0 xs = []"
|"coge4 (Suc n) [] = []"
|"coge4 (Suc n) (x#xs) = x # (coge4 n xs)"

value "coge4 2 [a,c,d,b,e]" -- "= [a,c]"

-- "marescpla"
fun coge5 :: "nat ⇒ 'a list ⇒ 'a list" where
"coge5 0 xs = []"|
"coge5 (Suc n) xs = hd xs # coge5 n (tl xs)"

value "coge5 2 [a,c,d,b,e]" -- "= [a,c]"

-- "jaisalmen zoiruicha"
fun coge6 :: "nat ⇒ 'a list ⇒ 'a list" where
"coge6 0 xs = []"
| "coge6 n [] = []"
| "coge6 n (x#xs) = x # (coge6 (n-(1::nat)) xs)"

value "coge6 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]
------------------------------------------------------------------ *}

-- "maresccas4 domlloriv"
fun elimina :: "nat ⇒ 'a list ⇒ 'a list" where
"elimina 0 xs = xs"
| "elimina n [] = []"
| "elimina (Suc n) (x#xs) = elimina n xs"

value "elimina 2 [a,c,d,b,e]" -- "= [d,b,e]"

-- "irealetei pabflomar"
fun elimina2 :: "nat ⇒ 'a list ⇒ 'a list" where
" elimina2 0 xs = xs "
| "elimina2 n xs = elimina2 (n - 1) (tl xs)"

value "elimina2 2 [a,c,d,b,e]" -- "= [d,b,e]"

-- "diecabmen1"
fun elimina3 :: "nat ⇒ 'a list ⇒ 'a list" where
"elimina3 0 xs = xs"
| "elimina3 n [] = []"
| "elimina3 n (x#xs) = elimina3 (n - 1) xs"

value "elimina3 2 [a,c,d,b,e]" -- "= [d,b,e]"

-- "julrobrel, juaruipav"
fun elimina4 :: "nat ⇒ 'a list ⇒ 'a list" where
"elimina4 0 xs = xs"
|"elimina4 (Suc n) [] = []"
|"elimina4 (Suc n) (x#xs) = (elimina4 n xs)"

value "elimina4 2 [a,c,d,b,e]" -- "= [d,b,e]"

-- "marescpla"
fun elimina5 :: "nat ⇒ 'a list ⇒ 'a list" where
"elimina5 0 xs = xs"|
"elimina5 (Suc n) xs = elimina5 n (tl xs)"

value "elimina5 2 [a,c,d,b,e]"

-- "jaisalmen zoiruicha"
fun elimina6 :: "nat ⇒ 'a list ⇒ 'a list" where
"elimina6 0 xs = xs"
| "elimina6 n [] = []"
| "elimina6 n (x#xs) = elimina6 (n-(1::nat)) xs"

value "elimina6 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
------------------------------------------------------------------ *}

-- "maresccas4"
fun esVacia :: "'a list ⇒ bool" where
"esVacia [] = True"
| "esVacia (x#xs) = False"

value "esVacia []" -- "= True"
value "esVacia [1]" -- "= False"

-- "irealetei domlloriv pabflomar julrobrel juaruipav marescpla"
fun esVacia2 :: "'a list ⇒ bool" where
"esVacia2 [] = True"|
"esVacia2 xs = False"

value "esVacia2 []" -- "= True"
value "esVacia2 [1]" -- "= False"

-- "diecabmen1"
fun esVacia3 :: "'a list ⇒ bool" where
"esVacia3 xs = (if xs = [] then True else False)"

value "esVacia3 []" -- "= True"
value "esVacia3 [1]" -- "= False"

-- "jaisalmen zoiruicha"
fun esVacia4 :: "'a list ⇒ bool" where
"esVacia4 x = (if longitud(x)=0 then True else False)"

value "esVacia4 []" -- "= True"
value "esVacia4 [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]
------------------------------------------------------------------ *}

-- "maresccas4 domlloriv"
fun inversaAcAux :: "'a list ⇒ 'a list ⇒ 'a list" where
"inversaAcAux [] ys = ys"
| "inversaAcAux (x#xs) ys = inversaAcAux xs (x#ys)"

fun inversaAc :: "'a list ⇒ 'a list" where
"inversaAc xs = inversaAcAux xs []"

value "inversaAc2 [a,c,b,e]" -- "= [e,b,c,a]"

-- "irealetei"
fun inversaAc2Aux :: "'a list ⇒ 'a list ⇒ 'a list" where
"inversaAc2Aux xs [] = xs"
| "inversaAc2Aux xs ys = inversaAc2Aux ((hd ys) # xs) (tl ys)"

fun inversaAc2 :: "'a list ⇒ 'a list" where
"inversaAc2 xs = inversaAc2Aux [] xs"

value "inversaAc2 [a,c,b,e]" -- "= [e,b,c,a]"

-- "diecabmen1 julrobrel,juaruipav"
fun inversaAc3Aux :: "'a list ⇒ 'a list ⇒ 'a list" where
"inversaAc3Aux xs ys = xs@ys"

fun inversaAc3 :: "'a list ⇒ 'a list" where
"inversaAc3 [] = []"
| "inversaAc3 (x#xs) = inversaAc3Aux (inversaAc3 xs) (x#[])"

value "inversaAc3 [a,c,b,e]" -- "= [e,b,c,a]"
-- "pabflomar"
fun inversaAcAux4 :: "'a list ⇒ 'a list ⇒ 'a list" where
"inversaAcAux4 [] ys = ys"
| "inversaAcAux4 xs ys = inversaAcAux4 (tl xs) ((hd xs) # ys)"

fun inversaAc4 :: "'a list ⇒ 'a list" where
"inversaAc4 xs = inversaAcAux4 xs []"

value "inversaAc4 [a,c,b,e]" -- "= [e,b,c,a]"

-- "marescpla"
fun inversaAcAux5 :: "'a list ⇒ 'a list ⇒ 'a list" where
"inversaAcAux5 [] ys = ys"|
"inversaAcAux5 xs ys = inversaAcAux5 (elimina 1 xs) (conc (coge 1 xs) ys)"

fun inversaAc5 :: "'a list ⇒ 'a list" where
"inversaAc5 xs = inversaAcAux5 xs []"

value "inversaAc5 [a,c,b,e]" -- "= [e,b,c,a]"

-- "jaisalmen"
fun inverseAcAux6 :: "'a list ⇒ 'a list ⇒ 'a list" where
"inverseAcAux6 xs ys = xs@ys"

fun inversaAc6 :: "'a list ⇒ 'a list" where
"inversaAc6 [] = []"
| "inversaAc6 (x#xs) = inverseAcAux6 (inversaAc6 xs) [x]"

value "inversaAc6 [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
------------------------------------------------------------------ *}

-- "maresccas4 diecabmen1 domlloriv julrobrel juaruipav jaisalmen zoiruicha"
fun sum :: "nat list ⇒ nat" where
"sum [] = 0"
| "sum (x#xs) = x + sum xs"

value "sum [3,2,5]" -- "= 10"

-- "irealetei pabflomar marescpla"
fun sum2 :: "nat list ⇒ nat" where
"sum2 [] = 0"
|"sum2 xs = hd xs + sum2 (tl xs)"

value "sum2 [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]
------------------------------------------------------------------ *}

-- "maresccas4 domlloriv julrobrel juaruipav"
fun map :: "('a ⇒ 'b) ⇒ 'a list ⇒ 'b list" where
"map f [] = []"
| "map f (x#xs) = (f x) # map f xs"

value "map (λx. 2*x) [3::nat,2,5]" -- "= [6,4,10]"

-- "irealetei pabflomar"
fun map2 :: "('a ⇒ 'b) ⇒ 'a list ⇒ 'b list" where
"map2 f [] = []"
|"map2 f xs = f(hd xs) # map2 f (tl xs)"

value "map2 (λx. 2*x) [3::nat,2,5]" -- "= [6,4,10]"

-- "diecabmen1"
fun map3 :: "('a ⇒ 'b) ⇒ 'a list ⇒ 'b list" where
"map3 f [] = []"
| "map3 f (x#xs) = ((f x)#[]) @ (map3 f xs)"

value "map3 (λx. 2*x) [3::nat,2,5]" -- "= [6,4,10]"

-- "marescpla"
fun map4 :: "('a ⇒ 'b) ⇒ 'a list ⇒ 'b list" where
"map4 f [] = []"|
"map4 f xs = value f (coge 1 xs) # map4 f (elimina 1 xs)"

value "map4 (λx. 2*x) [3::nat,2,5]" -- "= [6,4,10]"

-- "jaisalmen zoiruicha"
fun map :: "('a ⇒ 'b) ⇒ 'a list ⇒ 'b list" where
"map5 f [] = []"
| "map5 f (x#xs) = f(x) # map5 f xs "

value "map5 (λx. 2*x) [3::nat,2,5]" -- "= [6,4,10]"

end
</source>

Tema 7b: Deducción natural en lógica de primer orden con Isabelle/HOL

2014-01-22T15:33:51Z

Jalonso: Protegió «Tema 6b: Deducción natural en lógica de primer orden con Isabelle/HOL» ([edit=sysop] (indefinido) [move=sysop] (indefinido))

Tema 7b: Deducción natural en lógica de primer orden con Isabelle/HOL

2014-01-22T15:33:30Z

Jalonso: Página creada con '<source lang="isar"> header {* Tema 7: Deducción natural en lógica de primer orden *} theory T7b_Deduccion_natural_en_logica_de_primer_orden imports Main begin text {* El...'

Temas

2014-01-22T15:27:39Z

Jalonso: /* Temas de Razonamiento automático (2013-14) */

== Temas de ''Razonamiento automático (2013-14)'' ==
* [[Tema 1: Programación funcional en Isabelle]].
* [http://www.cs.us.es/~jalonso/cursos/i1m/temas/tema-8t.pdf Tema 2a: Razonamiento sobre programas Haskell]
* [[Tema 2b: Razonamiento automático sobre programas en Isabelle/HOL]].
* [[Tema 3: Razonamiento estructurado sobre programas en Isabelle/HOL]].
* [[Tema 4: Razonamiento por casos y por inducción]].
* [[Tema 5a: Verificación de la ordenación por inserción]].
* [[Tema 5b: Verificación de la ordenación por mezcla]].
* [http://www.cs.us.es/~jalonso/cursos/li/temas/tema-2.pdf Tema 6a: Deducción natural proposicional]].
* [[Tema 6b: Deducción natural proposicional con Isabelle/HOL]].
* [http://www.cs.us.es/~jalonso/cursos/li/temas/tema-8.pdf Tema 7a: Deducción natural en lógica de primer orden]].
* [[Tema 6b: Deducción natural en lógica de primer orden con Isabelle/HOL]].

Temas

2014-01-22T15:27:26Z

Jalonso: /* Temas de Razonamiento automático (2013-14) */

== Temas de ''Razonamiento automático (2013-14)'' ==
* [[Tema 1: Programación funcional en Isabelle]].
* [http://www.cs.us.es/~jalonso/cursos/i1m/temas/tema-8t.pdf Tema 2a: Razonamiento sobre programas Haskell]
* [[Tema 2b: Razonamiento automático sobre programas en Isabelle/HOL]].
* [[Tema 3: Razonamiento estructurado sobre programas en Isabelle/HOL]].
* [[Tema 4: Razonamiento por casos y por inducción]].
* [[Tema 5a: Verificación de la ordenación por inserción]].
* [[Tema 5b: Verificación de la ordenación por mezcla]].
* [http://www.cs.us.es/~jalonso/cursos/li/temas/tema-2.pdf Tema 6a: Deducción natural proposicional]].
* [[Tema 6b: Deducción natural proposicional con Isabelle/HOL]].
* [http://www.cs.us.es/~jalonso/cursos/li/temas/tema-8.pdf Tema 7a: Deducción
natural en lógica de primer orden]].
* [[Tema 6b: Deducción natural en lógica de primer orden con Isabelle/HOL]].

R9

2014-01-16T19:03:41Z

Jalonso: Protegió «R9» ([edit=sysop] (indefinido) [move=sysop] (indefinido))

<source lang="isar">
header {* R9: Deducción natural proposicional (1) *}

theory R9
imports Main
begin

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

Las reglas básicas de la deducción natural necesarias 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
---------------------------------------------------------------------
*}

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 ⟶ r) ⊢ q ⟶ (p ⟶ r)
------------------------------------------------------------------ *}

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

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

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

section {* Conjunciones *}

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

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

text {* ---------------------------------------------------------------
Ejercicio 7. Demostrar
p ∧ (q ⟶ r) ⊢ (p ⟶ q) ⟶ r
------------------------------------------------------------------ *}

section {* Disyunciones *}

text {* ---------------------------------------------------------------
Ejercicio 8. Demostrar
q ⟶ r ⊢ p ∨ q ⟶ p ∨ r
------------------------------------------------------------------ *}

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

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

end
</source>

Relación 9

2014-01-16T19:03:16Z

Jalonso: Página creada con '<source lang="isar"> header {* R9: Deducción natural proposicional (1) *} theory R9 imports Main begin text {* ------------------------------------------------------------...'

R9

2014-01-16T19:02:24Z

Ejercicios

2014-01-16T19:01:27Z

Jalonso: /* Relaciones de ejercicios propuestos */

Tema 6b: Deducción natural proposicional con Isabelle/HOL

2014-01-16T08:00:03Z

Jalonso: Página creada con '<source lang="isar"> header {* Tema 6b: Deducción natural proposicional con Isabelle/HOL *} theory T6b imports Main begin text {* En este tema se presentan los ejemplos de...'

<source lang="isar">
header {* Tema 6b: Deducción natural proposicional con Isabelle/HOL *}

theory T6b
imports Main
begin

text {*
En este tema se presentan los ejemplos del tema de deducción natural
proposicional siguiendo la presentación de Huth y Ryan en su libro
"Logic in Computer Science" http://goo.gl/qsVpY y, más concretamente,
a la forma como se explica en la asignatura de "Lógica informática" (LI)
http://goo.gl/AwDiv

La página al lado de cada ejemplo indica la página de las transparencias
de LI donde se encuentra la demostración. *}

subsection {* Reglas de la conjunción *}

text {*
Ejemplo 1 (p. 4). Demostrar que
p ∧ q, r ⊢ q ∧ r.
*}

-- "La demostración detallada es"
lemma ejemplo_1_1:
assumes 1: "p ∧ q" and
2: "r"
shows "q ∧ r"
proof -
have 3: "q" using 1 by (rule conjunct2)
show 4: "q ∧ r" using 3 2 by (rule conjI)
qed
thm ejemplo_1_1
text {*
Notas sobre el lenguaje: En la demostración anterior se ha usado
· "assumes" para indicar las hipótesis,
· "and" para separar las hipótesis,
· "shows" para indicar la conclusión,
· "proof" para iniciar la prueba,
· "qed" para terminar la pruebas,
· "-" (después de "proof") para no usar el método por defecto,
· "have" para establecer un paso,
· "using" para usar hechos en un paso,
· "by (rule ..)" para indicar la regla con la que se peueba un hecho,
· "show" para establecer la conclusión.

Notas sobre la lógica: Las reglas de la conjunción son
· conjI: ⟦P; Q⟧ ⟹ P ∧ Q
· conjunct1: P ∧ Q ⟹ P
· conjunct2: P ∧ Q ⟹ Q
*}

text {* Se pueden dejar implícitas las reglas como sigue *}

lemma ejemplo_1_2:
assumes 1: "p ∧ q" and
2: "r"
shows "q ∧ r"
proof -
have 3: "q" using 1 ..
show 4: "q ∧ r" using 3 2 ..
qed

text {*
Nota sobre el lenguaje: En la demostración anterior se ha usado
· ".." para indicar que se prueba por la regla correspondiente. *}

text {* Se pueden eliminar las etiquetas como sigue *}

lemma ejemplo_1_3:
assumes "p ∧ q"
"r"
shows "q ∧ r"
proof -
have "q" using assms(1) ..
thus "q ∧ r" using assms(2) ..
qed

text {*
Nota sobre el lenguaje: En la demostración anterior se ha usado
· "assms(n)" para indicar la hipótesis n y
· "thus" para demostrar la conclusión usando el hecho anterior.
Además, no es necesario usar and entre las hipótesis. *}

text {* Se puede automatizar la demostración como sigue *}

lemma ejemplo_1_4:
assumes "p ∧ q"
"r"
shows "q ∧ r"
using assms
by auto

text {*
Nota sobre el lenguaje: En la demostración anterior se ha usado
· "assms" para indicar las hipótesis y
· "by auto" para demostrar la conclusión automáticamente. *}

text {* Se puede automatizar totalmente la demostración como sigue *}

lemma ejemplo_1_5:
"⟦p ∧ q; r⟧ ⟹ q ∧ r"
by auto

text {*
Nota sobre el lenguaje: En la demostración anterior se ha usado
· "⟦ ... ⟧" para representar las hipótesis,
· ";" para separar las hipótesis y
· "⟹" para separar las hipótesis de la conclusión. *}

text {* Se puede hacer la demostración por razonamiento hacia atrás,
como sigue *}

lemma ejemplo_1_6:
assumes "p ∧ q"
and "r"
shows "q ∧ r"
proof (rule conjI)
show "q" using assms(1) by (rule conjunct2)
next
show "r" using assms(2) by this
qed

text {*
Nota sobre el lenguaje: En la demostración anterior se ha usado
· "proof (rule r)" para indicar que se hará la demostración con la
regla r,
· "next" para indicar el comienzo de la prueba del siguiente
subobjetivo,
· "this" para indicar el hecho actual. *}

text {* Se pueden dejar implícitas las reglas como sigue *}

lemma ejemplo_1_7:
assumes "p ∧ q"
"r"
shows "q ∧ r"
proof
show "q" using assms(1) ..
next
show "r" using assms(2) .
qed

text {*
Nota sobre el lenguaje: En la demostración anterior se ha usado
· "." para indicar por el hecho actual. *}

subsection {* Reglas de la doble negación *}

text {*
La regla de eliminación de la doble negación es
· notnotD: ¬¬ P ⟹ P

Para ajustarnos al tema de LI vamos a introducir la siguiente regla de
introducción de la doble negación
· notnotI: P ⟹ ¬¬ P
aunque, de momento, no detallamos su demostración.
*}

lemma notnotI [intro!]: "P ⟹ ¬¬ P"
by auto

text {*
Ejemplo 2. (p. 5)
p, ¬¬(q ∧ r) ⊢ ¬¬p ∧ r
*}

-- "La demostración detallada es"
lemma ejemplo_2_1:
assumes 1: "p" and
2: "¬¬(q ∧ r)"
shows "¬¬p ∧ r"
proof -
have 3: "¬¬p" using 1 by (rule notnotI)
have 4: "q ∧ r" using 2 by (rule notnotD)
have 5: "r" using 4 by (rule conjunct2)
show 6: "¬¬p ∧ r" using 3 5 by (rule conjI)
qed

-- "La demostración estructurada es"
lemma ejemplo_2_2:
assumes "p"
"¬¬(q ∧ r)"
shows "¬¬p ∧ r"
proof -
have "¬¬p" using assms(1) ..
have "q ∧ r" using assms(2) by (rule notnotD)
hence "r" ..
with `¬¬p` show "¬¬p ∧ r" ..
qed

text {*
Nota sobre el lenguaje: En la demostración anterior se ha usado
· "hence" para indicar que se tiene por el hecho anterior,
· `...` para referenciar un hecho y
· "with P show Q" para indicar que con el hecho anterior junto con el
hecho P se demuestra Q. *}

-- "La demostración automática es"
lemma ejemplo_2_3:
assumes "p"
"¬¬(q ∧ r)"
shows "¬¬p ∧ r"
using assms
by auto

text {* Se puede demostrar hacia atrás *}

lemma ejemplo_2_4:
assumes "p"
"¬¬(q ∧ r)"
shows "¬¬p ∧ r"
proof (rule conjI)
show "¬¬p" using assms(1) by (rule notnotI)
next
have "q ∧ r" using assms(2) by (rule notnotD)
thus "r" by (rule conjunct2)
qed

text {* Se puede eliminar las reglas en la demostración anterior, como
sigue: *}

lemma ejemplo_2_5:
assumes "p"
"¬¬(q ∧ r)"
shows "¬¬p ∧ r"
proof
show "¬¬p" using assms(1) ..
next
have "q ∧ r" using assms(2) by (rule notnotD)
thus "r" ..
qed

subsection {* Regla de eliminación del condicional *}

text {*
La regla de eliminación del condicional es la regla del modus ponens
· mp: ⟦P ⟶ Q; P⟧ ⟹ Q
*}

text {*
Ejemplo 3. (p. 6) Demostrar que
¬p ∧ q, ¬p ∧ q ⟶ r ∨ ¬p ⊢ r ∨ ¬p
*}

-- "La demostración detallada es"
lemma ejemplo_3_1:
assumes 1: "¬p ∧ q" and
2: "¬p ∧ q ⟶ r ∨ ¬p"
shows "r ∨ ¬p"
proof -
show "r ∨ ¬p" using 2 1 by (rule mp)
qed

-- "La demostración estructurada es"
lemma ejemplo_3_2:
assumes "¬p ∧ q"
"¬p ∧ q ⟶ r ∨ ¬p"
shows "r ∨ ¬p"
proof -
show "r ∨ ¬p" using assms(2,1) ..
qed

-- "La demostración automática es"
lemma ejemplo_3_3:
assumes "¬p ∧ q"
"¬p ∧ q ⟶ r ∨ ¬p"
shows "r ∨ ¬p"
using assms
by auto

text {*
Ejemplo 4 (p. 6) Demostrar que
p, p ⟶ q, p ⟶ (q ⟶ r) ⊢ r
*}

-- "La demostración detallada es"
lemma ejemplo_4_1:
assumes 1: "p" and
2: "p ⟶ q" and
3: "p ⟶ (q ⟶ r)"
shows "r"
proof -
have 4: "q" using 2 1 by (rule mp)
have 5: "q ⟶ r" using 3 1 by (rule mp)
show 6: "r" using 5 4 by (rule mp)
qed

-- "La demostración estructurada es"
lemma ejemplo_4_2:
assumes "p"
"p ⟶ q"
"p ⟶ (q ⟶ r)"
shows "r"
proof -
have "q" using assms(2,1) ..
have "q ⟶ r" using assms(3,1) ..
thus "r" using `q` ..
qed

-- "La demostración automática es"
lemma ejemplo_4_3:
"⟦p; p ⟶ q; p ⟶ (q ⟶ r)⟧ ⟹ r"
by auto

subsection {* Regla derivada del modus tollens *}

text {*
Para ajustarnos al tema de LI vamos a introducir la regla del modus
tollens
· mt: ⟦F ⟶ G; ¬G⟧ ⟹ ¬F
aunque, de momento, sin detallar su demostración.
*}

lemma mt: "⟦F ⟶ G; ¬G⟧ ⟹ ¬F"
by auto

text {*
Ejemplo 5 (p. 7). Demostrar
p ⟶ (q ⟶ r), p, ¬r ⊢ ¬q
*}

-- "La demostración detallada es"
lemma ejemplo_5_1:
assumes 1: "p ⟶ (q ⟶ r)" and
2: "p" and
3: "¬r"
shows "¬q"
proof -
have 4: "q ⟶ r" using 1 2 by (rule mp)
show "¬q" using 4 3 by (rule mt)
qed

-- "La demostración estructurada es"
lemma ejemplo_5_2:
assumes "p ⟶ (q ⟶ r)"
"p"
"¬r"
shows "¬q"
proof -
have "q ⟶ r" using assms(1,2) ..
thus "¬q" using assms(3) by (rule mt)
qed

-- "La demostración automática es"
lemma ejemplo_5_3:
assumes "p ⟶ (q ⟶ r)"
"p"
"¬r"
shows "¬q"
using assms
by auto

text {*
Ejemplo 6. (p. 7) Demostrar
¬p ⟶ q, ¬q ⊢ p
*}

-- "La demostración detallada es"
lemma ejemplo_6_1:
assumes 1: "¬p ⟶ q" and
2: "¬q"
shows "p"
proof -
have 3: "¬¬p" using 1 2 by (rule mt)
show "p" using 3 by (rule notnotD)
qed

-- "La demostración estructurada es"
lemma ejemplo_6_2:
assumes "¬p ⟶ q"
"¬q"
shows "p"
proof -
have "¬¬p" using assms(1,2) by (rule mt)
thus "p" by (rule notnotD)
qed

-- "La demostración automática es"
lemma ejemplo_6_3:
"⟦¬p ⟶ q; ¬q⟧ ⟹ p"
by auto

text {*
Ejemplo 7. (p. 7) Demostrar
p ⟶ ¬q, q ⊢ ¬p
*}

-- "La demostración detallada es"
lemma ejemplo_7_1:
assumes 1: "p ⟶ ¬q" and
2: "q"
shows "¬p"
proof -
have 3: "¬¬q" using 2 by (rule notnotI)
show "¬p" using 1 3 by (rule mt)
qed

-- "La demostración detallada es"
lemma ejemplo_7_2:
assumes "p ⟶ ¬q"
"q"
shows "¬p"
proof -
have "¬¬q" using assms(2) by (rule notnotI)
with assms(1) show "¬p" by (rule mt)
qed

-- "La demostración estructurada es"
lemma ejemplo_7_3:
"⟦p ⟶ ¬q; q⟧ ⟹ ¬p"
by auto

subsection {* Regla de introducción del condicional *}

text {*
La regla de introducción del condicional es
· impI: (P ⟹ Q) ⟹ P ⟶ Q
*}

text {*
Ejemplo 8. (p. 8) Demostrar
p ⟶ q ⊢ ¬q ⟶ ¬p
*}

-- "La demostración detallada es"
lemma ejemplo_8_1:
assumes 1: "p ⟶ q"
shows "¬q ⟶ ¬p"
proof -
{ assume 2: "¬q"
have "¬p" using 1 2 by (rule mt) }
thus "¬q ⟶ ¬p" by (rule impI)
qed

text {*
Nota sobre el lenguaje: En la demostración anterior se ha usado
· "{ ... }" para representar una caja. *}

-- "La demostración estructurada es"
lemma ejemplo_8_2:
assumes "p ⟶ q"
shows "¬q ⟶ ¬p"
proof
assume "¬q"
with assms show "¬p" by (rule mt)
qed

-- "La demostración automática es"
lemma ejemplo_8_3:
assumes "p ⟶ q"
shows "¬q ⟶ ¬p"
using assms
by auto

text {*
Ejemplo 9. (p. 9) Demostrar
¬q ⟶ ¬p ⊢ p ⟶ ¬¬q
*}

-- "La demostración detallada es"
lemma ejemplo_9_1:
assumes 1: "¬q ⟶ ¬p"
shows "p ⟶ ¬¬q"
proof -
{ assume 2: "p"
have 3: "¬¬p" using 2 by (rule notnotI)
have "¬¬q" using 1 3 by (rule mt) }
thus "p ⟶ ¬¬q" by (rule impI)
qed

-- "La demostración estructurada es"
lemma ejemplo_9_2:
assumes "¬q ⟶ ¬p"
shows "p ⟶ ¬¬q"
proof
assume "p"
hence "¬¬p" by (rule notnotI)
with assms show "¬¬q" by (rule mt)
qed

-- "La demostración automática es"
lemma ejemplo_9_3:
assumes "¬q ⟶ ¬p"
shows "p ⟶ ¬¬q"
using assms
by auto

text {*
Ejemplo 10 (p. 9). Demostrar
⊢ p ⟶ p
*}

-- "La demostración detallada es"
lemma ejemplo_10_1:
"p ⟶ p"
proof -
{ assume 1: "p"
have "p" using 1 by this }
thus "p ⟶ p" by (rule impI)
qed

-- "La demostración estructurada es"
lemma ejemplo_10_2:
"p ⟶ p"
proof (rule impI)
qed

-- "La demostración automática es"
lemma ejemplo_10_3:
"p ⟶ p"
by auto

text {*
Ejemplo 11 (p. 10) Demostrar
⊢ (q ⟶ r) ⟶ ((¬q ⟶ ¬p) ⟶ (p ⟶ r))
*}

-- "La demostración detallada es"
lemma ejemplo_11_1:
"(q ⟶ r) ⟶ ((¬q ⟶ ¬p) ⟶ (p ⟶ r))"
proof -
{ assume 1: "q ⟶ r"
{ assume 2: "¬q ⟶ ¬p"
{ assume 3: "p"
have 4: "¬¬p" using 3 by (rule notnotI)
have 5: "¬¬q" using 2 4 by (rule mt)
have 6: "q" using 5 by (rule notnotD)
have "r" using 1 6 by (rule mp) }
hence "p ⟶ r" by (rule impI) }
hence "(¬q ⟶ ¬p) ⟶ p ⟶ r" by (rule impI) }
thus "(q ⟶ r) ⟶ ((¬q ⟶ ¬p) ⟶ p ⟶ r)" by (rule impI)
qed

-- "La demostración hacia atrás es"
lemma ejemplo_11_2:
"(q ⟶ r) ⟶ ((¬q ⟶ ¬p) ⟶ (p ⟶ r))"
proof (rule impI)
assume 1: "q ⟶ r"
show "(¬q ⟶ ¬p) ⟶ (p ⟶ r)"
proof (rule impI)
assume 2: "¬q ⟶ ¬p"
show "p ⟶ r"
proof (rule impI)
assume 3: "p"
have 4: "¬¬p" using 3 by (rule notnotI)
have 5: "¬¬q" using 2 4 by (rule mt)
have 6: "q" using 5 by (rule notnotD)
show "r" using 1 6 by (rule mp)
qed
qed
qed

-- "La demostración hacia atrás con reglas implícitas es"
lemma ejemplo_11_3:
"(q ⟶ r) ⟶ ((¬q ⟶ ¬p) ⟶ (p ⟶ r))"
proof
assume 1: "q ⟶ r"
show "(¬q ⟶ ¬p) ⟶ (p ⟶ r)"
proof
assume 2: "¬q ⟶ ¬p"
show "p ⟶ r"
proof
assume 3: "p"
have 4: "¬¬p" using 3 ..
have 5: "¬¬q" using 2 4 by (rule mt)
have 6: "q" using 5 by (rule notnotD)
show "r" using 1 6 ..
qed
qed
qed

-- "La demostración sin etiquetas es"
lemma ejemplo_11_4:
"(q ⟶ r) ⟶ ((¬q ⟶ ¬p) ⟶ (p ⟶ r))"
proof
assume "q ⟶ r"
show "(¬q ⟶ ¬p) ⟶ (p ⟶ r)"
proof
assume "¬q ⟶ ¬p"
show "p ⟶ r"
proof
assume "p"
hence "¬¬p" ..
with `¬q ⟶ ¬p` have "¬¬q" by (rule mt)
hence "q" by (rule notnotD)
with `q ⟶ r` show "r" ..
qed
qed
qed

-- "La demostración automática es"
lemma ejemplo_11_5:
"(q ⟶ r) ⟶ ((¬q ⟶ ¬p) ⟶ (p ⟶ r))"
by auto

subsection {* Reglas de la disyunción *}

text {*
Las reglas de la introducción de la disyunción son
· disjI1: P ⟹ P ∨ Q
· disjI2: Q ⟹ P ∨ Q
La regla de elimación de la disyunción es
· disjE: ⟦P ∨ Q; P ⟹ R; Q ⟹ R⟧ ⟹ R
*}

text {*
Ejemplo 12 (p. 11). Demostrar
p ∨ q ⊢ q ∨ p
*}

-- "La demostración detallada es"
lemma ejemplo_12_1:
assumes "p ∨ q"
shows "q ∨ p"
proof -
have "p ∨ q" using assms by this
moreover
{ assume 2: "p"
have "q ∨ p" using 2 by (rule disjI2) }
moreover
{ assume 3: "q"
have "q ∨ p" using 3 by (rule disjI1) }
ultimately show "q ∨ p" by (rule disjE)
qed

text {*
Nota sobre el lenguaje: En la demostración anterior se ha usado
· "moreover" para separar los bloques y
· "ultimately" para unir los resultados de los bloques. *}

-- "La demostración detallada con reglas implícitas es"
lemma ejemplo_12_2:
assumes "p ∨ q"
shows "q ∨ p"
proof -
note `p ∨ q`
moreover
{ assume "p"
hence "q ∨ p" .. }
moreover
{ assume "q"
hence "q ∨ p" .. }
ultimately show "q ∨ p" ..
qed

text {*
Nota sobre el lenguaje: En la demostración anterior se ha usado
· "note" para copiar un hecho. *}

-- "La demostración hacia atrás es"
lemma ejemplo_12_3:
assumes 1: "p ∨ q"
shows "q ∨ p"
using 1
proof (rule disjE)
{ assume 2: "p"
show "q ∨ p" using 2 by (rule disjI2) }
next
{ assume 3: "q"
show "q ∨ p" using 3 by (rule disjI1) }
qed

-- "La demostración hacia atrás con reglas implícitas es"
lemma ejemplo_12_4:
assumes "p ∨ q"
shows "q ∨ p"
using assms
proof
{ assume "p"
thus "q ∨ p" .. }
next
{ assume "q"
thus "q ∨ p" .. }
qed

-- "La demostración automática es"
lemma ejemplo_12_5:
assumes "p ∨ q"
shows "q ∨ p"
using assms
by auto

text {*
Ejemplo 13. (p. 12) Demostrar
q ⟶ r ⊢ p ∨ q ⟶ p ∨ r
*}

-- "La demostración detallada es"
lemma ejemplo_13_1:
assumes 1: "q ⟶ r"
shows "p ∨ q ⟶ p ∨ r"
proof (rule impI)
assume 2: "p ∨ q"
thus "p ∨ r"
proof (rule disjE)
{ assume 3: "p"
show "p ∨ r" using 3 by (rule disjI1) }
next
{ assume 4: "q"
have 5: "r" using 1 4 by (rule mp)
show "p ∨ r" using 5 by (rule disjI2) }
qed
qed

-- "La demostración estructurada es"
lemma ejemplo_13_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 ejemplo_13_3:
assumes "q ⟶ r"
shows "p ∨ q ⟶ p ∨ r"
using assms
by auto

subsection {* Regla de copia *}

text {*
Ejemplo 14 (p. 13). Demostrar
⊢ p ⟶ (q ⟶ p)
*}

-- "La demostración detallada es"
lemma ejemplo_14_1:
"p ⟶ (q ⟶ p)"
proof (rule impI)
assume 1: "p"
show "q ⟶ p"
proof (rule impI)
assume "q"
show "p" using 1 by this
qed
qed

-- "La demostración estructurada es"
lemma ejemplo_14_2:
"p ⟶ (q ⟶ p)"
proof
assume "p"
thus "q ⟶ p" ..
qed

-- "La demostración automática es"
lemma ejemplo_14_3:
"p ⟶ (q ⟶ p)"
by auto

subsection {* Reglas de la negación *}

text {*
La regla de eliminación de lo falso es
· FalseE: False ⟹ P
La regla de eliminación de la negación es
· notE: ⟦¬P; P⟧ ⟹ R
La regla de introducción de la negación es
· notI: (P ⟹ False) ⟹ ¬P
*}

text {*
Ejemplo 15 (p. 15). Demostrar
¬p ∨ q ⊢ p ⟶ q
*}

-- "La demostración detallada es"
lemma ejemplo_15_1:
assumes 1: "¬p ∨ q"
shows "p ⟶ q"
proof (rule impI)
assume 2: "p"
note 1
thus "q"
proof (rule disjE)
{ assume 3: "¬p"
show "q" using 3 2 by (rule notE) }
next
{ assume 4: "q"
show "q" using 4 by this}
qed
qed

-- "La demostración estructurada es"
lemma ejemplo_15_2:
assumes "¬p ∨ q"
shows "p ⟶ q"
proof
assume "p"
note `¬p ∨ q`
thus "q"
proof
{ assume "¬p"
thus "q" using `p` .. }
next
{ assume "q"
thus "q" . }
qed
qed

-- "La demostración automática es"
lemma ejemplo_15_3:
assumes "¬p ∨ q"
shows "p ⟶ q"
using assms
by auto

text {*
Ejemplo 16 (p. 16). Demostrar
p ⟶ q, p ⟶ ¬q ⊢ ¬p
*}

-- "La demostración detallada es"
lemma ejemplo_16_1:
assumes 1: "p ⟶ q" and
2: "p ⟶ ¬q"
shows "¬p"
proof (rule notI)
assume 3: "p"
have 4: "q" using 1 3 by (rule mp)
have 5: "¬q" using 2 3 by (rule mp)
show False using 5 4 by (rule notE)
qed

-- "La demostración estructurada es"
lemma ejemplo_16_2:
assumes "p ⟶ q"
"p ⟶ ¬q"
shows "¬p"
proof
assume "p"
have "q" using assms(1) `p` ..
have "¬q" using assms(2) `p` ..
thus False using `q` ..
qed

-- "La demostración automática es"
lemma ejemplo_16_3:
assumes "p ⟶ q"
"p ⟶ ¬q"
shows "¬p"
using assms
by auto

subsection {* Reglas del bicondicional *}

text {*
La regla de introducción del bicondicional es
· iffI: ⟦P ⟹ Q; Q ⟹ P⟧ ⟹ P ⟷ Q
Las reglas de eliminación del bicondicional son
· iffD1: ⟦Q ⟷ P; Q⟧ ⟹ P
· iffD2: ⟦P ⟷ Q; Q⟧ ⟹ P
*}

text {*
Ejemplo 17 (p. 17) Demostrar
*}

-- "La demostración detallada es"
lemma ejemplo_17_1:
"(p ∧ q) ⟷ (q ∧ p)"
proof (rule iffI)
{ assume 1: "p ∧ q"
have 2: "p" using 1 by (rule conjunct1)
have 3: "q" using 1 by (rule conjunct2)
show "q ∧ p" using 3 2 by (rule conjI) }
next
{ assume 4: "q ∧ p"
have 5: "q" using 4 by (rule conjunct1)
have 6: "p" using 4 by (rule conjunct2)
show "p ∧ q" using 6 5 by (rule conjI) }
qed

-- "La demostración estructurada es"
lemma ejemplo_17_2:
"(p ∧ q) ⟷ (q ∧ p)"
proof
{ assume 1: "p ∧ q"
have "p" using 1 ..
have "q" using 1 ..
show "q ∧ p" using `q` `p` .. }
next
{ assume 2: "q ∧ p"
have "q" using 2 ..
have "p" using 2 ..
show "p ∧ q" using `p` `q` .. }
qed

-- "La demostración automática es"
lemma ejemplo_17_3:
"(p ∧ q) ⟷ (q ∧ p)"
by auto

text {*
Ejemplo 18 (p. 18). Demostrar
p ⟷ q, p ∨ q ⊢ p ∧ q
*}

-- "La demostración detallada es"
lemma ejemplo_18_1:
assumes 1: "p ⟷ q" and
2: "p ∨ q"
shows "p ∧ q"
using 2
proof (rule disjE)
{ assume 3: "p"
have 4: "q" using 1 3 by (rule iffD1)
show "p ∧ q" using 3 4 by (rule conjI) }
next
{ assume 5: "q"
have 6: "p" using 1 5 by (rule iffD2)
show "p ∧ q" using 6 5 by (rule conjI) }
qed

-- "La demostración estructurada es"
lemma ejemplo_18_2:
assumes "p ⟷ q"
"p ∨ q"
shows "p ∧ q"
using assms(2)
proof
{ assume "p"
with assms(1) have "q" ..
with `p` show "p ∧ q" .. }
next
{ assume "q"
with assms(1) have "p" ..
thus "p ∧ q" using `q` .. }
qed

-- "La demostración automática es"
lemma ejemplo_18_3:
assumes "p ⟷ q"
"p ∨ q"
shows "p ∧ q"
using assms
by auto

subsection {* Reglas derivadas *}

subsubsection {* Regla del modus tollens *}

text {*
Ejemplo 19 (p. 20) Demostrar la regla del modus tollens a partir de
las reglas básicas.
*}

-- "La demostración detallada es"
lemma ejemplo_20_1:
assumes 1: "F ⟶ G" and
2: "¬G"
shows "¬F"
proof (rule notI)
assume 3: "F"
have 4: "G" using 1 3 by (rule mp)
show False using 2 4 by (rule notE)
qed

-- "La demostración estructurada es"
lemma ejemplo_20_2:
assumes "F ⟶ G"
"¬G"
shows "¬F"
proof
assume "F"
with assms(1) have "G" ..
with assms(2) show False ..
qed

-- "La demostración automática es"
lemma ejemplo_20_3:
assumes "F ⟶ G"
"¬G"
shows "¬F"
using assms
by auto

subsubsection {* Regla de la introducción de la doble negación *}

text {*
Ejemplo 21 (p. 21) Demostrar la regla de introducción de la doble
negación a partir de las reglas básicas.
*}

-- "La demostración detallada es"
lemma ejemplo_21_1:
assumes 1: "F"
shows "¬¬F"
proof (rule notI)
assume 2: "¬F"
show False using 2 1 by (rule notE)
qed

-- "La demostración estructurada es"
lemma ejemplo_21_2:
assumes "F"
shows "¬¬F"
proof
assume "¬F"
thus False using assms ..
qed

-- "La demostración automática es"
lemma ejemplo_21_3:
assumes "F"
shows "¬¬F"
using assms
by auto

subsubsection {* Regla de reducción al absurdo *}

text {*
La regla de reducción al absurdo en Isabelle se correponde con la
regla clásica de contradicción
· ccontr: (¬P ⟹ False) ⟹ P
*}

subsubsection {* Ley del tercio excluso *}

text {*
La ley del tercio excluso es
· excluded_middle: ¬P ∨ P
*}

text {*
Ejemplo 22 (p. 23). Demostrar la ley del tercio excluso a partir de
las reglas básicas.
*}

-- "La demostración detallada es"
lemma ejemplo_22_1:
"F ∨ ¬F"
proof (rule ccontr)
assume 1: "¬(F ∨ ¬F)"
thus False
proof (rule notE)
show "F ∨ ¬F"
proof (rule disjI2)
show "¬F"
proof (rule notI)
assume 2: "F"
hence 3: "F ∨ ¬F" by (rule disjI1)
show False using 1 3 by (rule notE)
qed
qed
qed
qed

-- "La demostración estructurada es"
lemma ejemplo_22_2:
"F ∨ ¬F"
proof (rule ccontr)
assume "¬(F ∨ ¬F)"
thus False
proof (rule notE)
show "F ∨ ¬F"
proof (rule disjI2)
show "¬F"
proof (rule notI)
assume "F"
hence "F ∨ ¬F" ..
with `¬(F ∨ ¬F)`show False ..
qed
qed
qed
qed

-- "La demostración automática es"
lemma ejemplo_22_3:
"F ∨ ¬F"
using assms
by auto

text {*
Ejemplo 23 (p. 24). Demostrar
p ⟶ q ⊢ ¬p ∨ q
*}

-- "La demostración detallada es"
lemma ejemplo_23_1:
assumes 1: "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 2: "p"
have "q" using 1 2 by (rule mp)
thus "¬p ∨ q" by (rule disjI2) }
qed
qed

-- "La demostración estructurada es"
lemma ejemplo_23_2:
assumes "p ⟶ q"
shows "¬p ∨ q"
proof -
have "¬p ∨ p" ..
thus "¬p ∨ q"
proof
{ assume "¬p"
thus "¬p ∨ q" .. }
next
{ assume "p"
with assms have "q" ..
thus "¬p ∨ q" .. }
qed
qed

-- "La demostración automática es"
lemma ejemplo_23_3:
assumes "p ⟶ q"
shows "¬p ∨ q"
using assms
by auto

subsection {* Demostraciones por contradicción *}

text {*
Ejemplo 24. Demostrar que
¬p, p ∨ q ⊢ q
*}

-- "La demostración detallada es"
lemma ejemplo_24_1:
assumes "¬p"
"p ∨ q"
shows "q"
using `p ∨ q`
proof (rule disjE)
assume "p"
with assms(1) show "q" by contradiction
next
assume "q"
thus "q" by assumption
qed

-- "La demostración estructurada es"
lemma ejemplo_24_2:
assumes "¬p"
"p ∨ q"
shows "q"
using `p ∨ q`
proof
assume "p"
with assms(1) show "q" ..
next
assume "q"
thus "q" .
qed

-- "La demostración automática es"
lemma ejemplo_24_3:
assumes "¬p"
"p ∨ q"
shows "q"
using assms
by auto

end
</source>

Temas

2014-01-16T07:59:10Z

Jalonso: /* Temas de Razonamiento automático (2013-14) */

Relación 8

2014-01-09T11:55:58Z

Jalonso: Página creada con '<source lang="isar"> header {* R8: Árboles binarios completos *} theory R8_Arboles_binarios_completos imports Main begin text {* ---------------------------------------...'

<source lang="isar">
header {* R8: Árboles binarios completos *}

theory R8_Arboles_binarios_completos
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>

R8

2014-01-09T11:55:42Z

Jalonso: Protegió «R8» ([edit=sysop] (indefinido) [move=sysop] (indefinido))

R8

2014-01-09T11:55:32Z

Ejercicios

2014-01-09T11:53:54Z

Jalonso: /* Relaciones de ejercicios propuestos */

Tema 5b: Verificación de la ordenación por mezcla

2014-01-09T11:52:37Z

Jalonso: Página creada con '<source lang="isar"> header {* T5b: Verificación de la ordenación por mezcla *} theory T5b_Verificacion_de_la_ordenacion_por_mezcla_sol imports Main begin text {* En esta ...'

<source lang="isar">
header {* T5b: Verificación de la ordenación por mezcla *}

theory T5b_Verificacion_de_la_ordenacion_por_mezcla_sol
imports Main
begin

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

text {*
---------------------------------------------------------------------
Ejercicio 1. Definir la función
menor :: int ⇒ int 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 :: "int ⇒ int list ⇒ bool" where
"menor a [] = True"
| "menor a (x#xs) = (a ≤ x ∧ menor a xs)"

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

text {*
---------------------------------------------------------------------
Ejercicio 2. Definir la función
ordenada :: int 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 :: "int list ⇒ bool" where
"ordenada [] = True"
| "ordenada (x#xs) = (menor x xs & ordenada xs)"

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

text {*
---------------------------------------------------------------------
Ejercicio 3. Definir la función
cuenta :: int list => int => 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 :: "int list => int => nat" where
"cuenta [] y = 0"
| "cuenta (x#xs) y = (if x=y then Suc(cuenta xs y) else cuenta xs y)"

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

section {* Ordenación por mezcla *}

text {*
---------------------------------------------------------------------
Ejercicio 4. Definir la función
mezcla :: int list ⇒ int list ⇒ int list
tal que (mezcla xs ys) es la lista obtenida mezclando las listas
ordenadas xs e ys. Por ejemplo,
mezcla [1,2,5] [3,5,7] = [1,2,3,5,5,7]
------------------------------------------------------------------ *}

fun mezcla :: "int list ⇒ int list ⇒ int list" where
"mezcla [] ys = ys"
| "mezcla xs [] = xs"
| "mezcla (x # xs) (y # ys) = (if x ≤ y
then x # mezcla xs (y # ys)
else y # mezcla (x # xs) ys)"

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

text {*
---------------------------------------------------------------------
Ejercicio 5. Definir la función
ordenaM :: int list ⇒ int list
tal que (ordenaM xs) es la lista obtenida ordenando la lista xs
mediante mezclas; es decir, la divide en dos mitades, las ordena y las
mezcla. Por ejemplo,
ordenaM [3,2,5,2] = [2,2,3,5]
------------------------------------------------------------------ *}

fun ordenaM :: "int list ⇒ int list" where
"ordenaM [] = []"
| "ordenaM [x] = [x]"
| "ordenaM xs =
(let mitad = length xs div 2 in
mezcla (ordenaM (take mitad xs))
(ordenaM (drop mitad xs)))"

value "ordenaM [3,2,5,2]" -- "= [2,2,3,5]"

text {*
---------------------------------------------------------------------
Ejercicio 6. Sea x ≤ y. Si y es menor o igual que todos los elementos
de xs, entonces x es menor o igual que todos los elementos de xs
------------------------------------------------------------------ *}

lemma menor_menor:
"x ≤ y ⟹ menor y xs ⟶ menor x xs"
by (induct xs) auto

text {*
---------------------------------------------------------------------
Ejercicio 7. Demostrar que el número de veces que aparece n en la
mezcla de dos listas es igual a la suma del número de apariciones en
cada una de las listas
------------------------------------------------------------------ *}

lemma cuenta_mezcla:
"cuenta (mezcla xs ys) n = cuenta xs n + cuenta ys n"
by (induct xs ys rule: mezcla.induct) auto

text {*
---------------------------------------------------------------------
Ejercicio 8. Demostrar que si x es menor que todos los elementos de
ys y de zs, entonces también lo es de su mezcla.
------------------------------------------------------------------ *}

lemma menor_mezcla:
assumes "menor x ys"
"menor x zs"
shows "menor x (mezcla ys zs)"
using assms
by (induct ys zs rule: mezcla.induct) simp_all

text {*
---------------------------------------------------------------------
Ejercicio 9. Demostrar que la mezcla de dos listas ordenadas es una
lista ordenada.
Indicación: Usar los siguientes lemas
· linorder_not_le: (¬ x ≤ y) = (y < x)
· order_less_le: (x < y) = (x ≤ y ∧ x ≠ y)
------------------------------------------------------------------ *}

lemma ordenada_mezcla:
assumes "ordenada xs"
"ordenada ys"
shows "ordenada (mezcla xs ys)"
using assms
by (induct xs ys rule: mezcla.induct)
(auto simp add: menor_mezcla
menor_menor
linorder_not_le
order_less_le)

text {*
---------------------------------------------------------------------
Ejercicio 10. Demostrar que si x es mayor que 1, entonces el mínimo de
x y su mitad es menor que x.
Indicación: Usar los siguientes lemas
· min_def: min a b = (if a ≤ b then a else b)
· linorder_not_le: (¬ x ≤ y) = (y < x)
------------------------------------------------------------------ *}

lemma min_mitad:
"1 < x ⟹ min x (x div 2::int) < x"
by (simp add: min_def linorder_not_le)

text {*
---------------------------------------------------------------------
Ejercicio 11. Demostrar que si x es mayor que 1, entonces x menos su
mitad es menor que x.
------------------------------------------------------------------ *}

lemma menos_mitad:
"1 < x ⟹ x - x div (2::int) < x"
by arith

text {*
---------------------------------------------------------------------
Ejercicio 11. Demostrar que (ordenaM xs) está ordenada.
------------------------------------------------------------------ *}

theorem ordenada_ordenaM:
"ordenada (ordenaM xs)"
by (induct xs rule: ordenaM.induct)
(auto simp add: ordenada_mezcla)

text {*
---------------------------------------------------------------------
Ejercicio 12. Demostrar que el número de apariciones de un elemento en
la concatenación de dos listas es la suma del número de apariciones en
cada una.
------------------------------------------------------------------ *}

lemma cuenta_conc:
"cuenta (xs @ ys) x = cuenta xs x + cuenta ys x"
by (induct xs) auto

text {*
---------------------------------------------------------------------
Ejercicio 13. Demostrar que las listas xs y (ordenaM xs) tienen los
mismos elementos.
------------------------------------------------------------------ *}

theorem cuenta_ordenaM:
"cuenta (ordenaM xs) x = cuenta xs x"
by (induct xs rule: ordenaM.induct)
(auto simp add: cuenta_mezcla
cuenta_conc [symmetric])

end
</source>