Comparing Type Systems for Deadlock Freedom

TL;DR

This paper compares two type systems for message-passing processes that guarantee deadlock freedom, analyzing their relationships, differences, and translations between them to deepen understanding of their expressive power.

Contribution

It provides the first comparative analysis of type systems for deadlock-free message-passing processes, clarifying their relationships and translating between them.

Findings

Class L is canonical and based on linear logic interpretations.

Class K includes processes not typable in other systems.

L is strictly included in K, with conditions for their equivalence.

Abstract

Message-passing software systems exhibit non-trivial forms of concurrency and distribution; they are expected to follow intended protocols among communicating services, but also to never "get stuck". This intuitive requirement has been expressed by liveness properties such as progress or (dead)lock freedom and various type systems ensure these properties for concurrent processes. Unfortunately, very little is known about the precise relationship between these type systems and the classes of typed processes they induce. This paper puts forward the first comparative study of different type systems for message-passing processes that guarantee deadlock freedom. We compare two classes of deadlock-free typed processes, here denoted L and K. The class L stands out for its canonicity: it results from Curry-Howard interpretations of linear logic propositions as session types. The class K, obtained by encoding session types into Kobayashi's linear types with usages, includes processes not typable in other type systems. We show that L is strictly included in K, and identify the precise conditions under which they coincide. We also provide two type-preserving translations of processes in K into processes in L.