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Séance de cours

Atelier Coq: Types de données inductives et preuves

Dans cours

CS-452: Foundations of software

The course introduces the foundations on which programs and programming languages are built. It introduces syntax, types and semantics as building blocks that together define the properties of a program part or a language. Students will learn how to apply ...

Description

Cette séance de cours présente l'assistant de preuve Coq et couvre la définition d'un type de données inductives dans Coq, en se concentrant spécifiquement sur la langue NB. La séance de cours explique comment définir des termes dans Coq, créer des valeurs correspondant aux termes dans la langue NB et définir des relations d'évaluation en plusieurs étapes. Il se penche également sur le concept de valeurs dans la langue NB et comment construire des preuves interactivement en utilisant la tactique dans Coq.

Enseignant·e·s (2)

Martin Odersky

Martin Odersky heads the programming research group at EPFL. His research interests cover fundamental as well as applied aspects of programming languages. They include semantics, type systems, programming language design, and compiler construction. The main focus if his work lies in the integration of object-oriented and functional programming. His research thesis is that the two paradigms are just two sides of the same coin and should be unified as much as possible. To prove this he has experimented a number of language designs, from Pizza to GJ to Functional Nets. He has also influenced the development of Java as a co-designer of Java generics and as the original author of the current javac reference compiler. His current work concentrates on the Scala programming language, which unifies FP and OOP, while staying completely interoperable with Java and .NET. Martin Odersky got his doctorate from ETHZ, in 1989. He held research positions at the IBM T.J. Watson Research Center from 1989 and at Yale University from 1991. He was then a professor at the University of Karlsruhe from 1993 and at the University of South Australia from 1997. He joined EPFL as full professor in 1999. He is associate editor of the Journal of Functional Programming and member of IFIP WG 2.8. He was conference chair for ICFP 2000, and program chair for ECOOP 2004 as well as ETAPS/CC 2007.

Sébastien Jean Robert Doeraene

Source officielle

Concepts associés (32)

Assistant de preuve

En informatique (ou en mathématiques assistées par informatique), un assistant de preuve est un logiciel permettant la vérification de preuves mathématiques, soit sur des théorèmes au sens usuel des mathématiques, soit sur des assertions relatives à l'exécution de programmes informatiques. Beaucoup de projets ont été lancés pour formaliser les mathématiques, en 1966, Nicolaas de Bruijn lance le projet Automath, suivi par d'autres projets.

Isabelle (logiciel)

The Isabelle automated theorem prover is a higher-order logic (HOL) theorem prover, written in Standard ML and Scala. As an LCF-style theorem prover, it is based on a small logical core (kernel) to increase the trustworthiness of proofs without requiring yet supporting explicit proof objects. Isabelle is available inside a flexible system framework allowing for logically safe extensions, which comprise both theories as well as implementations for code-generation, documentation, and specific support for a variety of formal methods.

Read–eval–print loop

A read–eval–print loop (REPL), also termed an interactive toplevel or language shell, is a simple interactive computer programming environment that takes single user inputs, executes them, and returns the result to the user; a program written in a REPL environment is executed piecewise. The term usually refers to programming interfaces similar to the classic Lisp machine interactive environment. Common examples include command-line shells and similar environments for programming languages, and the technique is very characteristic of scripting languages.

Coq (logiciel)

Coq est un assistant de preuve utilisant le langage Gallina, développé par l'équipe PI.R2 de l’Inria au sein du laboratoire PPS du CNRS et en partenariat avec l'École polytechnique, le CNAM, l'Université Paris Diderot et l'Université Paris-Sud (et antérieurement l'École normale supérieure de Lyon). Le nom du logiciel (initialement CoC) est particulièrement adéquat car : il est français ; il est fondé sur le calcul des constructions (CoC abrégé en anglais) introduit par Thierry Coquand.

Hybrid kernel

A hybrid kernel is an operating system kernel architecture that attempts to combine aspects and benefits of microkernel and monolithic kernel architectures used in operating systems. The traditional kernel categories are monolithic kernels and microkernels (with nanokernels and exokernels seen as more extreme versions of microkernels). The "hybrid" category is controversial, due to the similarity of hybrid kernels and ordinary monolithic kernels; the term has been dismissed by Linus Torvalds as simple marketing.

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Concepts associés (32)