Assuming Just Enough Fairness to make Session Types Complete for Lock-freedom

TL;DR

This paper explores how minimal fairness assumptions, specifically justness, influence lock-freedom in session types, and introduces a type system complete for the strongest fairness notion.

Contribution

It identifies three distinct fairness-based lock-freedom notions and develops a session type system complete for the minimal fairness assumption of justness.

Findings

Three semantically distinct lock-freedom notions identified

A session type system complete for the strongest fairness assumption

Use of a merge operator enables completeness under minimal fairness

Abstract

We investigate how different fairness assumptions affect results concerning lock-freedom, a typical liveness property targeted by session type systems. We fix a minimal session calculus and systematically take into account all known fairness assumptions, thereby identifying precisely three interesting and semantically distinct notions of lock-freedom, all of which having a sound session type system. We then show that, by using a general merge operator in an otherwise standard approach to global session types, we obtain a session type system complete for the strongest amongst those notions of lock-freedom, which assumes only justness of execution paths, a minimal fairness assumption for concurrent systems.