Termination in a π-calculus with subtyping

Abstract

We present a type system to guarantee termination of π-calculus processes that exploits input/output capabilities and subtyping, as originally introduced by Pierce and Sangiorgi, in order to analyse the usage of channels.Our type system is based on Deng and Sangiorgi's level-based analysis of processes. We show that the addition of i/o-types makes it possible to typecheck processes where a form oflevel polymorphismis at work. We discuss to what extent this programming idiom can be treated by previously existing proposals. We demonstrate how our system can be extended to handle the encoding of the simply-typed λ-calculus, and discuss questions related to type inference.