Static and dynamic typing for the termination of mobile processes

A process terminates if all its reduction sequences are finite. We propose two type systems that ensure termination of π-calculus processes. Our first type system is purely static. It refines previous type systems by Deng and Sangiorgi by taking into account certain partial order information on names so to enhance the techniques from term rewriting (based on lexicographic and multiset orderings) that underpin the proof of termination. The second system is mixed, in that it combines a static and a dynamic analysis. During the static analysis, processes are annotated with assertions. These are then used at run time to monitor the execution of processes. An exception may be raised if certain conditions that may lead to divergence are met. We illustrate the expressiveness of the solutions proposed with a few examples of programming idioms that were beyond reach for previous type systems.