A Generic Library for Floating-Point Numbers and Its Application to Exact Computing

International audienceIn this paper we present a general library to reason about floating-point numbers within the Coq system. Most of the results of the library are proved for an arbitrary floating-point format and an arbitrary base. A special emphasis has been put on proving properties for exact computing, i.e. computing without rounding errors

ASHTEX : An interactive previewer for TEX or the marvellous world of ASHTEX

Disponible dans les fichiers attachés à ce documen

Affichage et manipulation interactive de formules mathématiques dans les documents structurés

Afficher des formules mathématiques et interagir avec ces formules sont des atouts primordiaux pour les outils informatiques dédiés aux mathématiques. Dans ce rapport, nous faisons un bilan des outils existants puis nous décrivons FIGUE, moteur d'affichage interactif incrémental et bidimensionnel, développé à l'INRIA, pour obtenir une bibliothèque dédiée au développement d'éditeurs de documents structurés et d'interfaces graphiques. Enfin nous montrons un exemple d'utilisation de FIGUE, dans le cadre du développement de preuves mathématiques sur ordinateur

Coq à la conquête des moulins

Nous presentons la certification formelle en Coq d'un algorithme utilise' dans les compilateurs: l'affectation parallele de registres. Nous proposons deux specifications inductives et une specification fonctionnelle de l'algorithme ainsi que les preuves de correction de ces specifications. Un code fonctionnel ML peut etre extrait de la specification fonctionnelle et integre' au code du compilateur

Formalising Sylow's theorems in Coq

This report presents a formalisation of Sylow's theorems done in Coq. The formalisation has been done in a couple of weeks on top of Georges Gonthier's ssreflect. There were two ideas behind formalising Sylow's theorems. The first one was to get familiar with Georges way of doing proofs. The second one was to contribute to the collective effort to formalise a large subset of group theory in Coq with some non-trivial proofs

A Centaur tutorial

This paper presents the Centaur system through a tutorial describing the creation of an environment for a small language of mathematical expressions called Exp. With Centaur, the user may interactively generate programming language environments, including structured editors, debuggers, interpreters, and other tools. In this tutorial, all phases of language specification are covered : the design of the abstract and concrete syntax of Exp in Metal and Sdf, the pretty printing rules in Ppml, and the semantics of an interpreter in Typol. The tools generated by Centaur based on these specifications are enhanced by user interface built with Centaur graphic primitives

Distributed programming environments: an example of a message protocol

In this paper we present a message protocol used for message passing between external components and a distributed programming environment. These message protocol allows structured data transfer and remote operations as function calls or signal emission. In the distributed programming environment, a new component called a Message Manager handles the incoming messages and management. This message protocol has been implemented and validated in the {\sc centaur} system