Arnaud Spiwack

FeatherTrait: A modest extension of Featherweight Java

In the context of statically typed, class-based languages, we investigate classes that can be extended with trait composition. A trait is a collection of methods without state; it can be viewed as an incomplete stateless class. Traits can be composed in any order, but only make sense when imported by a class that provides state variables and additional methods to disambiguate conflicting names arising between the imported traits. We introduce FeatherTrait Java (FTJ), a conservative extension of the simple lightweight class-based calculus Featherweight Java (FJ) with statically typed traits. In FTJ, classes can be built using traits as basic behavioral bricks; method conflicts between imported traits must be resolved explicitly by the user either by (i) aliasing or excluding method names in traits, or by (ii) overriding explicitly the conflicting methods in the class or in the trait itself. We present an operational semantics with a lookup algorithm, and a sound type system that guarantees that evaluating a well-typed expression never yields a message-not-understood run-time error nor gets the interpreter stuck. We give examples of the increased expressive power of the trait-based inheritance model. The resulting calculus appears to be a good starting point for a rigorous mathematical analysis of typed class-based languages featuring trait-based inheritance.

A Proof of Strong Normalisation using Domain Theory

U. Bergel; [ I I ] signijicantly simplijied Taits normalisation proof for bar recursion [27], see also [9], replacing Taits introduction of injinite terms by the construction of a domain having the property that a term is strongly normalizing if its semantics is \ne. The goal of this paper is to show that, using ideas from the theory of intersection types [2, 6, 7, 211 and Martin-Liifs domain interpretation of type theory [18], we can in turn simplify U. Bergers argument in the construction of such a domain model. We think that our domain model can be used to give modular proofs of strong normalization for various type theory. As an example, we show in some details how it can be used to prove strong normalization for Martin-Liif dependent type theory extended with bar recursion, and with some form ofproof-irrelevance.

Towards Constructive Homological Algebra in Type Theory

This paper reports on ongoing work on the project of representing the Kenzo system [15] in type theory [11].

A Proof of Strong Normalisation Using Domain Theory

U. Berger, (2005) significantly simplified Taits normalisation proof for bar recursion, replacing Taits introduction of infinite terms by the construction of a domain having the property that a term, is strongly normalizing if its semantics is neperp. The goal of this paper is to show that, using ideas from the theory of intersection types and Martin-Lofs domain interpretation of type theory, we can in turn simplify U, Bergers argument in the construction of such a domain model. We think that our domain model can be used to give modular proofs of strong normalization for various type theory. As an example, we show in some details how it can be used to prove strong normalization for Martin-Lof dependent type theory extended with bar recursion, and with some form of proof-irrelevance