Theory and practice of sequential algorithms : the Kernel of the applicative Language CDS

Disponible dans les fichiers attachés à ce documen

Confluence properties of weak and strong calculi of explicit substitutions

Projet CHLOE, Projet PARACategorical combinators and more recently ls-calculus have been introduced to provide an explicit treatments of substitutions in the l-calculus. We reintroduce here the ingredients of these calculi in a self-contained and stepwise way, with a special emphasis on confluence properties. The main new results of the paper w.r.t. are the following : - we present a confluent weak calculus of substitutions, where no variable clashes can be feared - we solve a conjecture : ls-calculus is not confluent (it is confluent on ground terms only). This unfortunate result is "repaired" by presenting a confluent version of ls-calculus, named the lEnv-calculus called here the confluent ls-calculus

Focusing in Asynchronous Games

Game semantics provides an interactive point of view on proofs, which enables one to describe precisely their dynamical behavior during cut elimination, by considering formulas as games on which proofs induce strategies. We are specifically interested here in relating two such semantics of linear logic, of very different flavor, which both take in account concurrent features of the proofs: asynchronous games and concurrent games. Interestingly, we show that associating a concurrent strategy to an asynchronous strategy can be seen as a semantical counterpart of the focusing property of linear logic

Focalisation and Classical Realisability (version with appendices)

The original publication is avalaible at : www.springerlink.comInternational audienceWe develop a polarised variant of Curien and Herbelin's lambda-bar-mu-mu-tilde calculus suitable for sequent calculi that admit a focalising cut elimination (i.e. whose proofs are focalised when cut-free), such as Girard's classical logic LC or linear logic. This gives a setting in which Krivine's classical realisability extends naturally (in particular to call-by-value), with a presentation in terms of orthogonality. We give examples of applications to the theory of programming languages

Models of a Non-Associative Composition

International audienceWe characterise the polarised evaluation order through a categorical structure where the hypothesis that composition is associative is relaxed. Duploid is the name of the structure, as a reference to Jean-Louis Loday's duplicial algebras. The main result is a reflection Adj→Dupl where Dupl is a category of duploids and duploid functors, and Adj is the category of adjunctions and pseudo maps of adjunctions. The result suggests that the various biases in denotational semantics: indirect, call-by-value, call-by-name... are a way of hiding the fact that composition is not always associative.Nous caractérisons l'ordre d'évaluation polarisé à travers une structure catégorielle dont l'hypothèse que la composition est associative est relâchée. Duploïde est le nom de la structure, par référence aux algèbres dupliciales de Loday. Le résultat principal est une réflection Adj→Dupl où Dupl est une catégorie des duploïdes et des foncteurs de duploïdes, et Adj est la catégorie des adjonctions et des pseudo-morphismes d'adjonctions. Le résultat suggère que les biais des sémantiques dénotationnelles: indirectes, en appel par valeur, en appel par nom... sont des façons de cacher le fait que la composition n'est pas toujours associative

An Operational Account of Call-by-Value Minimal and Classical λ-Calculus in “Natural Deduction” Form

International audienceWe give a decomposition of the equational theory of call-by-value lambda-calculus into a confluent rewrite system made of three independent subsystems that refines Moggi's computational calculus: - the purely operational system essentially contains Plotkin's beta-v rule and is necessary and sufficient for the evaluation of closed terms; - the structural system contains commutation rules that are necessary and sufficient for the reduction of all ''computational'' redexes of a term, in a sense that we define; - the observational system contains rules that have no proper computational content but are necessary to characterize the valid observational equations on finite normal forms. We extend this analysis to the case of lambda-calculus with control and provide with the first presentation as a confluent rewrite system of Sabry-Felleisen and Hofmann's equational theory of lambda-calculus with control. Incidentally, we give an alternative definition of standardization in call-by-value lambda-calculus that, unlike Plotkin's original definition, prolongs weak head reduction in an unambiguous way