Session Coalgebras: A Coalgebraic View on Session Types and Communication Protocols

TL;DR

This paper introduces a coalgebraic framework for session types and communication protocols, providing a unified, syntax-free approach that clarifies type relations and enables decidable subtyping in concurrent systems.

Contribution

It offers a novel coalgebraic perspective on session types, unifying existing concepts and deriving a decidable type system for π-calculus processes.

Findings

Coalgebraic description of session types and protocols

Canonical coinductive presentations of type relations

Decidable subtyping for π-calculus processes

Abstract

Compositional methods are central to the development and verification of software systems. They allow to break down large systems into smaller components, while enabling reasoning about the behaviour of the composed system. For concurrent and communicating systems, compositional techniques based on behavioural type systems have received much attention. By abstracting communication protocols as types, these type systems can statically check that programs interact with channels according to a certain protocol, whether the intended messages are exchanged in a certain order. In this paper, we put on our coalgebraic spectacles to investigate session types, a widely studied class of behavioural type systems. We provide a syntax-free description of session-based concurrency as states of coalgebras. As a result, we rediscover type equivalence, duality, and subtyping relations in terms of canonical coinductive presentations. In turn, this coinductive presentation makes it possible to elegantly derive a decidable type system with subtyping for $\pi$-calculus processes, in which the states of a coalgebra will serve as channel protocols. Going full circle, we exhibit a coalgebra structure on an existing session type system, and show that the relations and type system resulting from our coalgebraic perspective agree with the existing ones.