Fair Asynchronous Session Subtyping

TL;DR

This paper introduces a novel fair refinement-based session subtyping for asynchronous session types, enabling anticipation of message emissions with unbounded consumptions, supported by a sound algorithm and empirical evaluation.

Contribution

It proposes a new variant of session subtyping based on fair refinement, leveraging controllability, and provides a sound algorithm with implementation and benchmarks.

Findings

Fair refinement and the new subtyping are undecidable.

The algorithm handles unbounded buffering scenarios.

Empirical evaluation demonstrates practical effectiveness.

Abstract

Session types are widely used as abstractions of asynchronous message passing systems. Refinement for such abstractions is crucial as it allows improvements of a given component without compromising its compatibility with the rest of the system. In the context of session types, the most general notion of refinement is asynchronous session subtyping, which allows message emissions to be anticipated w.r.t. a bounded amount of message consumptions. In this paper we investigate the possibility to anticipate emissions w.r.t. an unbounded amount of consumptions: to this aim we propose to consider fair compliance over asynchronous session types and fair refinement as the relation that preserves it. This allows us to propose a novel variant of session subtyping that leverages the notion of controllability from service contract theory and that is a sound characterisation of fair refinement. In addition, we show that both fair refinement and our novel subtyping are undecidable. We also present a sound algorithm which deals with examples that feature potentially unbounded buffering. Finally, we present an implementation of our algorithm and an empirical evaluation of it on synthetic benchmarks.