Type assignment and termination of interaction nets

Abstract

Interaction nets have proved to be a useful tool for the study of computational aspects of various formalisms (e.g. λ-calculus, term rewriting systems), but they are also a programming paradigm in themselves, and this is actually how they were introduced by Lafont. In this paper we consider semi-simple interaction nets as a programming language, and present a type assignment system using intersection types. First we show that interactions preserve types (i.e., the system enjoys subject reduction), and we compare this type assignment system with the intersection systems for λ-calculus and term rewriting systems. Then we define a recursion scheme that ensures termination of all interaction sequences. By relaxing the scheme and using the type assignment system, we derive another sufficient condition for termination of interaction nets. Finally, we show that although the type system based on general intersection types is not decidable, its restriction to rank 2 types is, and we give an algorithm that computes principal types for nets.