An introduction to small scale reflection in Coq

International audienceThis tutorial presents the Ssreflect extension to the Coq system. This extension consists of an extension to the Coq language of script, and of a set of libraries, originating from the formal proof of the Four Color theorem. This tutorial proposes a guided tour in some of the basic libraries distributed in the Ssreflect package. It focuses on the application of the small scale reflection methodology to the formalization of finite objects in intuitionistic type theory

Algebraic calculi of processes and net expressions

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Définitions récursives d’opérateurs

TLA+ originally allowed recursive function definitions, but not recursive operator definitions, because it was not known how how to define their semantics. They were added to the language in 2006 after we discovered a semantics for them. We describe that semantics here.Initialement, TLA+ autorisait les définitions récursives de fonctions, mais pas d’opérateurs, car la sémantique à donner à de telles définitions n’était pas claire. Elles furent finalement ajoutées au langage de spécification en 2006, lorsque nous avons découvert un moyen de leur donner une sémantique satisfaisante. Ce rapport décrit cette sémantique

Incremental development of an HDLC protocol in Esterel

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The ESTEREL synchronous programming language : design, semantics, implementation

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An Ssreflect Tutorial

This document is a tutorial for ssreflect which is a proof language based on Coq. This tutorial is mostly dedicated to people who already know the basics of logic

A Small Scale Reflection Extension for the Coq system

This is the user manual of Ssreflect, a set of extensions to the proof scripting language of the Coq proof assistant. While these extensions were developed to support a particular proof methodology - small-scale reflection - most of them actually are of a quite general nature, improving the functionality of Coq in basic areas such as script layout and structuring, proof context management, and rewriting. Consequently, and in spite of the title of this document, most of the extensions described here should be of interest for all Coq users, whether they embrace small-scale reflection or not

Synchronous programming of reactive systems: an introduction to ESTEREL

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Canonical Big Operators

The original publication is available at http://www.springerlink.com/content/16v67m7248714568/International audienceIn this paper, we present an approach to describe uniformly iterated “big” operations and to provide lemmas that encapsulate all the commonly used reasoning steps on these constructs. We show that these iterated operations can be handled generically using the syntactic notation and canonical structure facilities provided by the Coq system. We then show how these canonical big operations played a crucial enabling role in the study of various parts of linear algebra and multi-dimensional real analysis, as illustrated by the formal proofs of the properties of determinants, of the Cayley-Hamilton theorem and of Kantorovitch's theorem