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

arXiv (Cornell University)

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 $π$-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.

Authors 3

1. Alex C. Keizer

   University of Amsterdam

   Affiliation as printed

   Master of Logic , ILLC , University of Amsterdam , The Netherlands

2. Henning Basold Aachen

   Leiden University

   Affiliation as printed

   LIACS -Leiden University , The Netherlands

3. Jorge A. Pérez

   University of Groningen

   Affiliation as printed

   University of Groningen , The Netherlands