Equational Axiomization of Bicoercibility for Polymorphic Types

Two polymorphic types σ and τ are said to be bicoercible if there is a coercion from σ to τ and conversely. We give a complete equational axiomatization of bicoercible types and prove that the relation of bicoercibility is decidable.National Science Foundation (CCR-9113196); KBN (2 P301 031 06); ESPRIT BRA7232 GENTZE

A Type System For Call-By-Name Exceptions

We present an extension of System F with call-by-name exceptions. The type system is enriched with two syntactic constructs: a union type for programs whose execution may raise an exception at top level, and a corruption type for programs that may raise an exception in any evaluation context (not necessarily at top level). We present the syntax and reduction rules of the system, as well as its typing and subtyping rules. We then study its properties, such as confluence. Finally, we construct a realizability model using orthogonality techniques, from which we deduce that well-typed programs are weakly normalizing and that the ones who have the type of natural numbers really compute a natural number, without raising exceptions.Comment: 25 page

Complete Types in an Extension of the System AF2

International audienceIn this paper, we extend the system AF2 in order to have the subject reduction for the $\beta\eta$-reduction. We prove that the types with positive quantifiers are complete for models that are stable by weak-head expansion

Preciseness of Subtyping on Intersection and Union Types

Abstract. The notion of subtyping has gained an important role both in theoretical and applicative domains: in lambda and concurrent calculi as well as in programming languages. The soundness and the complete-ness, together referred to as the preciseness of subtyping, can be consid-ered from two different points of view: denotational and operational. The former preciseness is based on the denotation of a type which is a math-ematical object that describes the meaning of the type in accordance with the denotations of other expressions from the language. The latter preciseness has been recently developed with respect to type safety, i.e. the safe replacement of a term of a smaller type when a term of a bigger type is expected. We propose a technique for formalising and proving operational pre-ciseness of the subtyping relation in the setting of a concurrent lambda calculus with intersection and union types. The key feature is the link between typings and the operational semantics. We then prove sound-ness and completeness getting that the subtyping relation of this calculus enjoys both denotational and operational preciseness.

Semantic Predicate Types and Approximation for Class-based Object Oriented Programming

We apply the principles of the intersection type discipline to the study of class-based object oriented programs and; our work follows from a similar approach (in the context of Abadi and Cardelli's Varsigma-object calculus) taken by van Bakel and de'Liguoro. We define an extension of Featherweight Java, FJc and present a predicate system which we show to be sound and expressive. We also show that our system provides a semantic underpinning for the object oriented paradigm by generalising the concept of approximant from the Lambda Calculus and demonstrating an approximation result: all expressions to which we can assign a predicate have an approximant that satisfies the same predicate. Crucial to this result is the notion of predicate language, which associates a family of predicates with a class.Comment: Proceedings of 11th Workshop on Formal Techniques for Java-like Programs (FTfJP'09), Genova, Italy, July 6 200

Denotational and operational preciseness of subtyping: A roadmap

The notion of subtyping has gained an important role both in theoretical and applicative domains: in lambda and concurrent calculi as well as in object-oriented programming languages. The soundness and the completeness, together referred to as the preciseness of subtyping, can be considered from two different points of view: denotational and operational. The former preciseness is based on the denotation of a type, which is a mathematical object describing the meaning of the type in accordance with the denotations of other expressions from the language. The latter preciseness has been recently developed with respect to type safety, i.e. the safe replacement of a term of a smaller type when a term of a bigger type is expected. The present paper shows that standard proofs of operational preciseness imply denotational preciseness and gives an overview on this subject

A type system for context-dependent overloading.

This article presents a type system for context-dependent overloading, based on the notion of constrained types. These are types constrained by the definition of functions or constants of given types. This notion supports both overloading and a form of subtyping, and is related to Haskell type classes [11,2], System O [7] and other systems with constrained types. We study an extension of the Damas-Milner system [4,1] with constrained types. The inference system presented uses a context-dependent overloading policy, which is specified by means of a predicate used in a single inference rule. The idea simplifies the treatment of overloading, enables the simplification of inferred types (by means of class type annotations), and is adequate for use in a type system with higher-order types