Sort inference algorithm for the polyadic π-calculus

Abstract

In Milner's polyadic π-calculus there is a notion of sorts which is analogous to the notion of types in functional programming. As a well-typed program applies functions to arguments in a consistent way, a well-sorted process uses communication channels in a consistent way. An open problem is whether there is an algorithm to infer sorts in the π-calculus in the same way that types can be inferred in functional programming. Here we solve the problem by presenting an algorithm which infers the most general sorting for a process in the first-order calculus, and proving its correctness. The algorithm is similar in style to those used for Hindley-Milner type inference in functional languages.