Investigations in intersection types : confluence, and semantics of expansion in the -calculus, and a type error slicing method

Type systems were invented in the early 1900s to provide foundations for Mathematics where types were used to avoid paradoxes. Type systems have then been developed and extended throughout the years to serve different purposes such as efficiency or expressiveness. The λ-calculus is used in programming languages, logic, mathematics, and linguistics. Intersection types are a kind of types used for building semantic models of the λ-calculus and for static analysis of computer programs. The confluence property was used to prove the λ-calculus’ consistency and the uniqueness of normal forms. Confluence is useful to show that logics are sensibly designed, and to make equality decision procedures for use in theorem provers. Some proofs of the λ-calculus’ confluence are based on syntactic concepts (reduction relations and λ-term sets) and some on semantic concepts (type interpretations). Part I of this thesis presents an original syntactic proof that is a simplification of a semantic proof based on a sound type interpretation w.r.t. an intersection type system. Our proof can be seen as bridging some semantic and syntactic proofs. Expansion is an operation on typings (pairs of type environments and result types) in type systems for the λ-calculus. It was introduced to prove that the principal typing property (i.e., that every typable term has a strongest typing) holds in intersection type systems. Expansion variables were introduced to simplify the expansion mechanism. Part II of this thesis presents a complete realisability semantics w.r.t. an intersection type system with infinitely many expansion variables. This represents the first study on semantics of expansion. Providing sound (and complete) realisability semantics allows one to study the algorithmic behaviour of typed λ-terms through their types w.r.t. a type system. We believe such semantics will cast some light on the not yet well understood expansion operation. Intersection types were used in a type error slicer for the SML programming language. Existing compilers for many languages have confusing type error messages. Type error slicing (TES) helps the programmer by isolating the part of a program contributing to a type error (a slice). TES was initially done for a tiny toy language (the λ-calculus with polymorphic let-expressions). Extending TES to a full language is extremely challenging, and for SML we needed a number of innovations. Some issues would be faced for any language, and some are SML-specific but representative of the complexity of language-specific issues likely to be faced for other languages. Part III of this thesis solves both kinds of issues and presents an original, simple, and general constraint system for providing type error slices for ill-typed programs. We believe TES helps demystify language features known to confuse users

Actes de la conférence JFLA 2009 (Vingtièmes Journées Francophones des Langages Applicatifs)

Ce fichier regroupe en un seul document l'ensemble des articles acceptés pour la conférence JFLA 2009.Pour la vingtième année consécutive, les Journées Francophones des Langages Applications sont l'occasion de se retrouver dans un cadre agréable et propice aux échanges conviviaux. Cette année, c'est à Saint-Quentin sur Isère, près de Grenoble, que nous nous réunissons, maintenant la tradition de l'alternance mer-montagne. Les neuf articles choisis par le comité de programme reflètent bien la diversité de notre communauté et les avancés tant du point de vue de l'application de langages fonctionnels que de la conception et de l'utilisation d'assistants à la preuve. Nous avons souhaité également inclure des articles plus proches de tutoriels ou de retours d'expérience, ceux-ci étant particulièrement adaptés au cadre pédagogique des Journées. Deux orateurs nous ont fait l'honneur d'accepter notre invitation. L'exposé de Vincent Balat, de l'université Paris 7, intitulé ≪ Ocsigen : approche fonctionnelle typée de la programmation Web ≫ illustre l'utilisation croissante de langages applicatifs dans des milieux inattendus. L'exposé de Bruno Barras, de Trusted Labs, intitulé ≪ Faut-il avoir peur de sa carte SIM ? ≫ présente l'application d'assistants à la preuve dans la modélisation de cartes à puces. Pour la quatrième année consécutive, deux sessions d'une demi-journée chacune sont consacrées à des cours. Le premier porte sur la modélisation de la linguistique (par Gérard Huet, de l'INRIA Paris - Rocquencourt) et le deuxième sur les bibliothèques Coq utilisées dans la preuve récente du théorème des quatre couleurs (par Assia Mahboubi, de l'INRIA Saclay - Île-de-France)

Progressive program reasoning

Ph.DDOCTOR OF PHILOSOPH

Dependency Analysis for Standard ML

Automatic dependency analysis is a useful addition to a system like CM, our compilation manager for Standard ML of New Jersey. It relieves the programmer from the tedious and error-prone task of having to specify compilation dependencies by hand and thereby makes its usage more user-friendly. But dependency analysis is not easy as the general problem for Standard ML is NP-complete. Therefore, CM has to impose certain restrictions on the programming language to recover tractability. We prove the NP-completeness result, discuss the restrictions on ML that are used by CM, and provide the resulting analysis algorithms. 1 Introduction For programs written in Standard ML [MTH90, MTHM97], the order of compilation matters. But the task of maintaining order within collections of sources can be tedious. Therefore, CM [Blu95], the compilation manager for Standard ML of New Jersey [AM91], o#ers automatic dependency analysis. CM provides a language for specifying the semantic structure of large pr..