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Jean-Yves Girard

Bio: Jean-Yves Girard is an academic researcher from Centre national de la recherche scientifique. The author has contributed to research in topics: Linear logic & Sequent calculus. The author has an hindex of 31, co-authored 59 publications receiving 10720 citations. Previous affiliations of Jean-Yves Girard include University of the Mediterranean & University of Paris.


Papers
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Journal ArticleDOI
TL;DR: All logical rules are now defined only on the main formulas of rules, as operations on P -cliques, with the essential result that all usual constructions remain unchanged: technically speaking cliques are replaced with P-cliques and that is it.

16 citations

Book
15 Nov 2004
TL;DR: This paper presents an introduction to category theory with an emphasis on those aspects relevant to the analysis of the model theory of linear logic, and introduces the necessary aspects of the theory of monads in order to describe the categorical modelling of the exponentials.
Abstract: This paper presents an introduction to category theory with an emphasis on those aspects relevant to the analysis of the model theory of linear logic. With this in mind, we focus on the basic definitions of category theory and categorical logic. An analysis of cartesian and cartesian closed categories and their relation to intuitionistic logic is followed by a consideration of symmetric monoidal closed, linearly distributive and *-autonomous categories and their relation to multiplicative linear logic. We examine nonsymmetric monoidal categories, and consider them as models of noncommutative linear logic. We introduce traced monoidal categories, and discuss their relation to the geometry of interaction. The necessary aspects of the theory of monads is introduced in order to describe the categorical modelling of the exponentials. We conclude by briefly describing the notion of full completeness, a strong form of categorical completeness, which originated in the categorical model theory of linear logic. No knowledge of category theory is assumed, but we do assume knowledge of linear logic sequent calculus and the standard models of linear logic, and modest familiarity with typed lambda calculus. 1.0 Introduction Category theory arose as an organizing framework for expressing the maturality of certain constructions in algebraic topology. Its subsequent applicability, both as a language for simply expressing complex relationships between mathematical structures and as a mathematical theory in its own right, is remarkable. Categorical principles have been put to

15 citations

Book ChapterDOI
01 Jan 1995
TL;DR: The paper expounds geometry of interaction, for the first time in the full case, i.e. for all connectives of linear logic, including additives and constants, with a slight modification of familiar sequent calculus in the case of exponential-free conclusions.
Abstract: The paper expounds geometry of interaction, for the first time in the full case, i.e. for all connectives of linear logic, including additives and constants. The interpretation is done within a C*-algebra which is induced by the rule of resolution of logic programming, and therefore the execution formula can be presented as a simple logic programming loop. Part of the data is public (shared channels) but part of it can be viewed as private dialect (defined up to isomorphism) that cannot be shared during interaction, thus illustrating the theme of communication without understanding. One can prove a nilpotency (i.e. termination) theorem for this semantics, and also its soundness w.r.t. a slight modification of familiar sequent calculus in the case of exponential-free conclusions.

14 citations

Journal ArticleDOI
TL;DR: This paper is the systematic rewriting of usual results of ordinal notations, using Pi-1-2-logic, and presents a functorial construction of the Veblen hierarchy.
Abstract: This paper is the first of several works: the matter is the systematic rewriting of usual results of ordinal notations, using Π½ -logic. The purpose of these articles is already realized in Π½ -logic, in a relatively abstract form; also, they are examples for Π½ -logic. The first and second articles in this series are complete versions of unpublished results that one of authors had announced in 1976. Veblen introduced his hierarchy in 1908. The hierarchy has since been widely used in proof theory; in fact, what is actually needed is the more natural hierarchy: , with (not necessarily a Cantor normal form) and K the Veblen hierarchy. We shall show: i) φ is in fact a two-variables functor (denoted by V in the text) commuting with direct limits and with pull-backs. ii) The property of commutation with pull-backs permits one to give a representation of each ordinal x φ α (0) by means of a finite sequence of ordinals α . This representation is independent of α it is ⊆ x , and can be used in the building up of notations systems. This representation is the “blowing-up” of the Cantor normal form, and it corresponds exactly to the denotation of ordinals φ α (0) by means of the functions ( φ β ) β .

14 citations


Cited by
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Book
01 Jan 2002
TL;DR: This text provides a comprehensive introduction both to type systems in computer science and to the basic theory of programming languages, with a variety of approaches to modeling the features of object-oriented languages.
Abstract: A type system is a syntactic method for automatically checking the absence of certain erroneous behaviors by classifying program phrases according to the kinds of values they compute. The study of type systems -- and of programming languages from a type-theoretic perspective -- has important applications in software engineering, language design, high-performance compilers, and security.This text provides a comprehensive introduction both to type systems in computer science and to the basic theory of programming languages. The approach is pragmatic and operational; each new concept is motivated by programming examples and the more theoretical sections are driven by the needs of implementations. Each chapter is accompanied by numerous exercises and solutions, as well as a running implementation, available via the Web. Dependencies between chapters are explicitly identified, allowing readers to choose a variety of paths through the material.The core topics include the untyped lambda-calculus, simple type systems, type reconstruction, universal and existential polymorphism, subtyping, bounded quantification, recursive types, kinds, and type operators. Extended case studies develop a variety of approaches to modeling the features of object-oriented languages.

2,391 citations

Journal ArticleDOI
TL;DR: This column presents an intuitive overview of linear logic, some recent theoretical results, and summarizes several applications oflinear logic to computer science.
Abstract: Linear logic was introduced by Girard in 1987 [11] . Since then many results have supported Girard' s statement, \"Linear logic is a resource conscious logic,\" and related slogans . Increasingly, computer scientists have come to recognize linear logic as an expressive and powerful logic with connection s to a variety of topics in computer science . This column presents a.n intuitive overview of linear logic, some recent theoretical results, an d summarizes several applications of linear logic to computer science . Other introductions to linear logic may be found in [12, 361 .

2,304 citations

Journal ArticleDOI
TL;DR: A λ-calculus-based model for type systems that allows us to explore the interaction among the concepts of type, data abstraction, and polymorphism in a simple setting, unencumbered by complexities of production programming languages is developed.
Abstract: Our objective is to understand the notion of type in programming languages, present a model of typed, polymorphic programming languages that reflects recent research in type theory, and examine the relevance of recent research to the design of practical programming languages.Object-oriented languages provide both a framework and a motivation for exploring the interaction among the concepts of type, data abstraction, and polymorphism, since they extend the notion of type to data abstraction and since type inheritance is an important form of polymorphism. We develop a l-calculus-based model for type systems that allows us to explore these interactions in a simple setting, unencumbered by complexities of production programming languages.The evolution of languages from untyped universes to monomorphic and then polymorphic type systems is reviewed. Mechanisms for polymorphism such as overloading, coercion, subtyping, and parameterization are examined. A unifying framework for polymorphic type systems is developed in terms of the typed l-calculus augmented to include binding of types by quantification as well as binding of values by abstraction.The typed l-calculus is augmented by universal quantification to model generic functions with type parameters, existential quantification and packaging (information hiding) to model abstract data types, and bounded quantification to model subtypes and type inheritance. In this way we obtain a simple and precise characterization of a powerful type system that includes abstract data types, parametric polymorphism, and multiple inheritance in a single consistent framework. The mechanisms for type checking for the augmented l-calculus are discussed.The augmented typed l-calculus is used as a programming language for a variety of illustrative examples. We christen this language Fun because fun instead of l is the functional abstraction keyword and because it is pleasant to deal with.Fun is mathematically simple and can serve as a basis for the design and implementation of real programming languages with type facilities that are more powerful and expressive than those of existing programming languages. In particular, it provides a basis for the design of strongly typed object-oriented languages.

1,875 citations

Book
01 Jan 1989
TL;DR: In this paper, the Curry-Howard isomorphism and the normalisation theorem of a natural deduction system T coherence spaces have been studied in the context of linear logic and linear logic semantics.
Abstract: Sense, denotation and semantics natural deduction the Curry-Howard isomorphism the normalisation theorem Godel's system T coherence spaces denotational semantics of T sums in natural deduction system F coherence semantics of the sum cut elimination (Hauptsatz) strong normalisation for F representation theorem semantics of System F what is linear logic?

1,771 citations

Book
01 Jan 2006
TL;DR: Researchers from other fields should find in this handbook an effective way to learn about constraint programming and to possibly use some of the constraint programming concepts and techniques in their work, thus providing a means for a fruitful cross-fertilization among different research areas.
Abstract: Constraint programming is a powerful paradigm for solving combinatorial search problems that draws on a wide range of techniques from artificial intelligence, computer science, databases, programming languages, and operations research. Constraint programming is currently applied with success to many domains, such as scheduling, planning, vehicle routing, configuration, networks, and bioinformatics. The aim of this handbook is to capture the full breadth and depth of the constraint programming field and to be encyclopedic in its scope and coverage. While there are several excellent books on constraint programming, such books necessarily focus on the main notions and techniques and cannot cover also extensions, applications, and languages. The handbook gives a reasonably complete coverage of all these lines of work, based on constraint programming, so that a reader can have a rather precise idea of the whole field and its potential. Of course each line of work is dealt with in a survey-like style, where some details may be neglected in favor of coverage. However, the extensive bibliography of each chapter will help the interested readers to find suitable sources for the missing details. Each chapter of the handbook is intended to be a self-contained survey of a topic, and is written by one or more authors who are leading researchers in the area. The intended audience of the handbook is researchers, graduate students, higher-year undergraduates and practitioners who wish to learn about the state-of-the-art in constraint programming. No prior knowledge about the field is necessary to be able to read the chapters and gather useful knowledge. Researchers from other fields should find in this handbook an effective way to learn about constraint programming and to possibly use some of the constraint programming concepts and techniques in their work, thus providing a means for a fruitful cross-fertilization among different research areas. The handbook is organized in two parts. The first part covers the basic foundations of constraint programming, including the history, the notion of constraint propagation, basic search methods, global constraints, tractability and computational complexity, and important issues in modeling a problem as a constraint problem. The second part covers constraint languages and solver, several useful extensions to the basic framework (such as interval constraints, structured domains, and distributed CSPs), and successful application areas for constraint programming. - Covers the whole field of constraint programming - Survey-style chapters - Five chapters on applications Table of Contents Foreword (Ugo Montanari) Part I : Foundations Chapter 1. Introduction (Francesca Rossi, Peter van Beek, Toby Walsh) Chapter 2. Constraint Satisfaction: An Emerging Paradigm (Eugene C. Freuder, Alan K. Mackworth) Chapter 3. Constraint Propagation (Christian Bessiere) Chapter 4. Backtracking Search Algorithms (Peter van Beek) Chapter 5. Local Search Methods (Holger H. Hoos, Edward Tsang) Chapter 6. Global Constraints (Willem-Jan van Hoeve, Irit Katriel) Chapter 7. Tractable Structures for CSPs (Rina Dechter) Chapter 8. The Complexity of Constraint Languages (David Cohen, Peter Jeavons) Chapter 9. Soft Constraints (Pedro Meseguer, Francesca Rossi, Thomas Schiex) Chapter 10. Symmetry in Constraint Programming (Ian P. Gent, Karen E. Petrie, Jean-Francois Puget) Chapter 11. Modelling (Barbara M. Smith) Part II : Extensions, Languages, and Applications Chapter 12. Constraint Logic Programming (Kim Marriott, Peter J. Stuckey, Mark Wallace) Chapter 13. Constraints in Procedural and Concurrent Languages (Thom Fruehwirth, Laurent Michel, Christian Schulte) Chapter 14. Finite Domain Constraint Programming Systems (Christian Schulte, Mats Carlsson) Chapter 15. Operations Research Methods in Constraint Programming (John Hooker) Chapter 16. Continuous and Interval Constraints(Frederic Benhamou, Laurent Granvilliers) Chapter 17. Constraints over Structured Domains (Carmen Gervet) Chapter 18. Randomness and Structure (Carla Gomes, Toby Walsh) Chapter 19. Temporal CSPs (Manolis Koubarakis) Chapter 20. Distributed Constraint Programming (Boi Faltings) Chapter 21. Uncertainty and Change (Kenneth N. Brown, Ian Miguel) Chapter 22. Constraint-Based Scheduling and Planning (Philippe Baptiste, Philippe Laborie, Claude Le Pape, Wim Nuijten) Chapter 23. Vehicle Routing (Philip Kilby, Paul Shaw) Chapter 24. Configuration (Ulrich Junker) Chapter 25. Constraint Applications in Networks (Helmut Simonis) Chapter 26. Bioinformatics and Constraints (Rolf Backofen, David Gilbert)

1,527 citations