Type-checking Liveness for Collaborative Processes with Bounded and Unbounded Recursion

TL;DR

This paper introduces a novel session typing system that guarantees request-response liveness in non-terminating communicating processes, extending standard session types with response sets, and proves its expressiveness and soundness.

Contribution

It presents the first session typing system ensuring request-response liveness for non-terminating processes, extending standard session types with response sets and proving its soundness.

Findings

Extended types are more expressive than standard session types.

The type system guarantees request-response liveness in deadlock-free processes.

The system is applicable to infinite state systems.

Abstract

We present the first session typing system guaranteeing request-response liveness properties for possibly non-terminating communicating processes. The types augment the branch and select types of the standard binary session types with a set of required responses, indicating that whenever a particular label is selected, a set of other labels, its responses, must eventually also be selected. We prove that these extended types are strictly more expressive than standard session types. We provide a type system for a process calculus similar to a subset of collaborative BPMN processes with internal (data-based) and external (event-based) branching, message passing, bounded and unbounded looping. We prove that this type system is sound, i.e., it guarantees request-response liveness for dead-lock free processes. We exemplify the use of the calculus and type system on a concrete example of an infinite state system.