Yves Lafont

Bio: Yves Lafont is an academic researcher from École Normale Supérieure. The author has contributed to research in topics: Linear logic & Interaction nets. The author has an hindex of 4, co-authored 4 publications receiving 2300 citations.

Proofs and types

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?

Interaction nets

Abstract: We propose a new kind of programming language, with the following features:a simple graph rewriting semantics,a complete symmetry between constructors and destructors,a type discipline for deterministic and deadlock-free (microscopic) parallelism.Interaction nets generalize Girard's proof nets of linear logic and illustrate the advantage of an integrated logic approach, as opposed to the external one. In other words, we did not try to design a logic describing the behaviour of some given computational system, but a programming language for which the type discipline is already (almost) a logic.In fact, we shall scarcely refer to logic, because we adopt a naive and pragmatic style. A typical application we have in mind for this language is the design of interactive softwares such as editors or window managers.

Advances in Linear Logic

Abstract: Linear logic: its syntax and semantics J. Y. Girard Part I. Categories and Semantics: 1. Bilinear logic in algebra and linguistics J. Lambek 2. A category arising in linear logic, complexity theory and set theory A. Blass 3. Hypercoherences: a strongly stable model of linear logic T. Erhard Part II. Complexity and Expressivity: 4. Deciding provability of linear logic formulas P. D. Lincoln 5. The direct simulation of Minsky machines in linear logic M. I. Kanovich 6. Stochastic interaction and linear logic P. D. Lincoln, J. Mitchell and A. Scedrov 7. Inheritance with exceptions C. Fouquere and J. Vauzeilles Part III. Proof Theory: 8. On the fine structure of the exponential rule S. Martini and A. Masini 9. Sequent calculi for second order logic V. Danos, J. B. Joinet and H. Schellinx Part IV. Proff Nets: 10. From proof nets to interaction nets Y. Lafont 11. Empires and kingdoms in MLL G. Bellin and J. Van De Wiele 12. Noncommutative proof nets V. M. Abrusci 13. Volume of multiplicative formulas and provability F. Metayer Part V. Geometry of Interaction: 14. Proof nets and Hilbert space V. Danos and L. Regnier 15. Geometry of interacion III: accomodating the additives J. Y. Girard.

Orientals as free algebras

Abstract: The aim of this paper is to give an alternative construction of Street's cosimplicial object of orientals, based on an idea of Burroni that orientals are free algebras for some algebraic structure on strict $\omega$-categories. More precisely, following Burroni, we define the notion of an expansion on an $\omega$-category and we show that the forgetful functor from strict $\omega$-categories endowed with an expansion to strict $\omega$-categories is monadic. By iterating this monad starting from the empty $\omega$-category, we get a cosimplicial object in strict $\omega$-categories. Our main contribution is to show that this cosimplicial object is the cosimplicial objects of orientals. To do so, we prove, using Steiner's theory of augmented directed chain complexes, a general result for comparing polygraphs having same generators and same linearized sources and targets.

Types and Programming 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.

Linear logic

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 .

A Theory of Objects

Abstract: From the Publisher: Procedural languages are generally well understood. Their foundations have been cast in calculi that prove useful in matters of implementation and semantics. So far, an analogous understanding has not emerged for object-oriented languages. In this book the authors take a novel approach to the understanding of object-oriented languages by introducing object calculi and developing a theory of objects around them. The book covers both the semantics of objects and their typing rules, and explains a range of object-oriented concepts, such as self, dynamic dispatch, classes, inheritance, prototyping, subtyping, covariance and contravariance, and method specialization. Researchers and graduate students will find this an important development of the underpinnings of object-oriented programming.

The Coq proof assistant : reference manual, version 6.1

Abstract: Coq is a proof assistant based on a higher-order logic allowing powerful definitions of functions. Coq V6.1 is available by anonymous ftp at ftp.inria.fr:/INRIA/Projects/coq/V6.1 and ftp.ens-lyon.fr:/pub/LIP/COQ/V6.1

A computational logic

Abstract: • Constraint domains in which the possible values that a variable can take are restricted to a finite set. • Examples: Boolean constraints, or integer constraints in which each variable is constrained to lie in within a finite range of integers. • Widely used in constraint programming. • Many real problems can be easily represented using constraint domains, e.g.: scheduling, routing and timetabling. • They involve choosing amongst a finite number of possibilities. • Commercial importance to many businesses: e.g. deciding how air crews should be allocated to aircraft flights. • Developed methods by different research communities: Arc and node consistency techniques (artificial intelligence). Bounds propagation techniques (constraint programming). Integer programming (operations research).