A Geometric Approach to the Problem of Unique Decomposition of Processes

This paper proposes a geometric solution to the problem of prime decomposability of concurrent processes first explored by R. Milner and F. Moller in [MM93]. Concurrent programs are given a geometric semantics using cubical areas, for which a unique factorization theorem is proved. An effective factorization method which is correct and complete with respect to the geometric semantics is derived from the factorization theorem. This algorithm is implemented in the static analyzer ALCOOL.Comment: 15 page

On the Implementation of Dynamic Patterns

The evaluation mechanism of pattern matching with dynamic patterns is modelled in the Pure Pattern Calculus by one single meta-rule. This contribution presents a refinement which narrows the gap between the abstract calculus and its implementation. A calculus is designed to allow reasoning on matching algorithms. The new calculus is proved to be confluent, and to simulate the original Pure Pattern Calculus. A family of new, matching-driven, reduction strategies is proposed.Comment: In Proceedings HOR 2010, arXiv:1102.346

A Strong Call-By-Need Calculus

We present a call-by-need ?-calculus that enables strong reduction (that is, reduction inside the body of abstractions) and guarantees that arguments are only evaluated if needed and at most once. This calculus uses explicit substitutions and subsumes the existing strong-call-by-need strategy, but allows for more reduction sequences, and often shorter ones, while preserving the neededness. The calculus is shown to be normalizing in a strong sense: Whenever a ?-term t admits a normal form n in the ?-calculus, then any reduction sequence from t in the calculus eventually reaches a representative of the normal form n. We also exhibit a restriction of this calculus that has the diamond property and that only performs reduction sequences of minimal length, which makes it systematically better than the existing strategy. We have used the Abella proof assistant to formalize part of this calculus, and discuss how this experiment affected its design

Comment s'assurer de garder le contact (et nos distances)

International audienceNous étudions le problème du maintien de connexion dans les réseaux de robots mobiles. On considère un robot incontrôlable (la « cible ») et une flotte de robots volumiques autonomes se déplaçant dans le plan réel et munis de capteurs et transmetteurs à portée limitée. Le problème consiste à maintenir à tout moment une connexion entre un point fixe connu au départ et la cible. Cette situation est par exemple instanciée dans le cas d'une équipe de recherche (la cible) en cours d'exploration et qui doit conserver une liaison avec la base des secours (le point fixe). Dans un tel cas où des vies sont en jeu, le problème devient critique : il est impératif d'avoir les plus fortes garanties de correction possibles sur les protocoles candidats. Nous définissons formellement ce problème et proposons une famille de protocoles que nous prouvons correcte grâce à l'assistant de preuve Coq et la bibliothèque PACTOLE. Nous illustrons en particulier l'utilité de cet outil formel ainsi que de la démarche associée, de la réflexion préliminaire sur un problème à la production d'une solution certifiée

A Unified Approach to Fully Lazy Sharing

We give an axiomatic presentation of sharing-via-labelling for weak λ-calculi, that allows to formally compare many different approaches to fully lazy sharing, and obtain two important results. We prove that the known implementations of full laziness are all equivalent in terms of the number of β-reductions performed, although they behave differently regarding the duplication of terms. We establish a link between the optimality theories of weak λ-calculi and first-order rewriting systems by expressing fully lazy λ-lifting in our framework, thus emphasizing the first-order essence of weak reduction. This technical report extends [Bal12] with comprehensive proofs.

Axiomatic sharing-via-labelling

A judicious use of labelled terms makes it possible to bring together the simplicity of term rewriting and the sharing power of graph rewriting: this has been known for twenty years in the particular case of orthogonal first-order systems. The present paper introduces a concise and easily usable axiomatic presentation of sharing-via-labelling techniques that applies to higher-order term rewriting as well as to non-orthogonal term rewriting. This provides a general framework for the sharing of subterms and keeps the formalism as simple as term rewriting

Full laziness: some kind of optimality (sharing of subterms and reduction strategies in higher-order rewriting)

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