En la clase de hoy, se ha presentado el curso Lógica Informática siguiendo el plan de la asignatura. Se ha comentado el contenido de la asignatura, el sistema de evaluación y los materiales de la asignatura en la Red:
Se ha publicado un artículo sobre razonamiento formalizado titulado A survey of interactive theorem proving.
Su autor es Filip Marić (del Automated Reasoning GrOup (ARGO) en la Universidad de Belgrado, Serbia).
Su resumen es
Fully formally verified mathematics and software are long-standing aims that became practically realizable with modern computer tools. Reasoning can be reduced to several basic logical principles, and performed using specialized software, with significant automation. Although full automation is not possible, three main paradigms are represented in formal reasoning tools: (i) decision procedures for special classes of problems, (ii) complete, but potentially unterminating proof search, (iii) checking of proof-sketches given by a human user while automatically constructing simpler proof steps. In this paper, we present a survey of the third approach, embodied in modern interactive theorem provers (ITP), also called proof-assistants. These tools have been successfully developed for more than 40 years, and the current state-of-the-art tools have reached maturity needed to perform real-world large-scale formalizations of mathematics (e.g., Four-Color Theorem, Prime Number Theorem, and Feith-Thompson’s Odd Order theorem) and software correctness (e.g., substantial portions of operating systems and compilers have been verified). We discuss history of ITP, its logical foundations, main features of state-of-the-art systems, and give some details about the most prominent results in the field. We also summarize main results of the researchers from Serbia and personal results of the author.
Este artículo puede servir de lectura complementaria en los cursos de Razonamiento automático, Razonamiento asistido por ordenador y Lógica computacional y teoría de modelos.
Se ha publicado un artículo de razonamiento formalizado en Agda sobre metalógica titulado Formalisation in constructive type theory of Stoughton’s substitution for the lambda calculus.
Sus autores son Álvaro Tasistro, Ernesto Copello y Nora Szasz (del Grupo de Computación Teórica (Compute) en la Universidad ORT, Uruguay).
Su resumen es
In Substitution revisited, Alley Stoughton proposed a notion of (simultaneous) substitution for the Lambda calculus as formulated in its original syntax – i.e. with only one sort of symbols (names) for variables – and without identifying α-convertible terms. According to such formulation, the action of substitution on terms is defined by simple structural recursion and an interesting theory arises concerning the connection to α-conversion.
In this paper we present a formalisation of Stoughton’s work in Constructive Type Theory using the language Agda, which reaches up to the Substitution Lemma for α-conversion. The development has been quite inexpensive e.g. in labour cost, and we are able to formulate some improvements over the original presentation. For instance, our definition of α-conversion is just syntax directed and we prove it to be an equivalence relation in an easy way, whereas in Substitution revisited the latter was included as part of the definition and then proven to be equivalent to an only nearly structural definition as corollary of a lengthier development. As a result of this work we are inclined to assert that Stoughton’s is the right way to formulate the Lambda calculus in its original, conventional syntax and that it is a formulation amenable to fully formal treatment.
El trabajo se ha publicado en Electronic Notes in Theoretical Computer Science.
El código de las correspondientes teorías en Agda literario se encuentra aquí.
He actualizado el libro Exámenes de programación funcional con Haskell. El libro es una recopilación de los exámenes de la asignatura de Informática (de primero del Grado en Matemáticas) desde el curso 30 de noviembre de 2009 al 15 de septiembre de 2014.
Tras la ampliación, el libro contiene 129 exámenes y 833 ejercicios.
Este libro es el complemento de los anteriores:
Se ha publicado un artículo de razonamiento formalizado en Coq titulado Hofstadter’s problem for curious readers.
Su autor es Pierre Letouzey (del grupo PPS (Preuves, Programmes et Systèmes) de la Universidad de París VII Denis Diderot, Francia).
Su resumen es
This document summarizes the proofs made during a Coq development in Summer 2015. This development investigates the function G introduced by Hofstadter in his famous “Gödel, Escher, Bach” book as well as a related infinite tree. The left/right flipped variant of this G tree has also been studied here, following Hofstadter’s “problem for the curious reader”. The initial G function is refered as sequence A005206 in OEIS, while the flipped version is the sequence A123070.
The detailed and machine-checked proofs can be found in the files of
this development and can be re-checked by running Coq version 8.4 on it. No prior knowledge of Coq is assumed here, on the contrary this document has rather been a “Coq-to-English” translation exercise for the author. Nonetheless, some proofs given in this document are still quite sketchy: in this case, the interested reader is encouraged to consult the Coq files given as references.
El código de las correspondientes teorías en Coq se encuentra aquí.
Este artículo puede servir de lectura complementaria en los cursos de Razonamiento automático, Razonamiento asistido por ordenador y Lógica computacional y teoría de modelos.