Showing papers on "Linear logic published in 1986"

Categorical Combinators, Sequential Algorithms and Functional Programming

Abstract: This book is a thoroughly revised edition of a monograph that presents an approach to the design and implementation of sequential programming languages based on the relationship between lambda-calculus and category theory The foundations of a new "categorical" combinatory logic are laid down Compilation and evaluation techniques are investigated A simple abstract machine, called the Categorical Abstract Machine, is presented: it has served as the core of the implementation of the language CAML, of the ML family, developed at INRIA-Roquencourt and Ecole Normale Superieure, and first released in 1987 The main characteristics of this approach are conceptual simplicity and compactness, with bearings on portability, efficiency, and correctness proofs A mathematical semantics of sequentiality is proposed, in which "sequential algorithms" rather than functions are used to interpret procedures The theoretical investigation has led to the development of a programming language, CDSO, in which basic and functional types are not differentiated The evaluation framework is a demand-driven data flow network The model of sequential algorithms is fully abstract with respect to this language: two procedures have the same denotation if and only if they have the same behaviour Background on full abstraction is given The new edition covers new results, and introduces new connections, as suggested by the following non-exhaustive fist of keywords: confluence properties of categorical combinators, explicit substitutions, control operations, linear logic, geometry of interaction, strong stability

Linear logic and lazy computation

Abstract: Recently, J.Y. Girard discovered that usual logical connectors such as ⇒ (implication) could be broken up into more elementary linear connectors. This provided a new linear logic [Girard86] where hypothesis are (in some sense) used once and only once. The most surprising is that all the power of the usual logic can be recovered by means of recursive logical operators (connector “of course”).

The logic of distributed protocols: preliminary report

Abstract: A propositional logic of distributed protocols is introduced which includes both the logic of knowledge and temporal logic. Phenomena in distributed computing systems such as asynchronous time, incomplete knowledge by the computing agents in the system, and game-like behavior among the computing agents are all modeled in the logic. Two versions of the logic, the linear logic of protocols (LLP) and the tree logic of protocols (TLP) are investigated. The main result is that the set of valid formulas in LLP is undecidable.

Linear Logic and Parallelism

Abstract: the paper discusses the relevance of a new logic called linear logic (Girard 1986) to computer science, and in particular to parallel computations. These general remarks will be detailed in a paper in preparation with Gianfranco Mascari.