JOIN(X): Constraint-Based Type Inference for the Join-Calculus

We present a generic constraint-based type system for the join-calculus. The key issue is type generalization, which, in the presence of concurrency, must be restricted. We first define a liberal generalization criterion, and prove it correct. Then, we find that it hinders type inference, and propose a cruder one, reminiscent of ML's value restriction. We establish type safety using a semi-syntactic technique, which we believe is of independent interest. It consists in interpreting typing judgements as (sets of) judgements in an underlying system, which itself is given a syntactic soundness proof. This hybrid approach allows giving pleasant logical meaning to high-level notions such as type variables, constraints and generalization, and clearly separating them from low-level aspects (substitution lemmas, etc.), which are dealt with in a simple, standard way