Precise Subtyping for Asynchronous Multiparty Sessions

TL;DR

This paper formalizes a precise subtyping relation for asynchronous multiparty sessions, ensuring safe process replacement and capturing complex message permutations, with a novel session decomposition technique.

Contribution

It introduces the first formalization of precise subtyping for asynchronous multiparty sessions, including a novel session decomposition method for complex message permutations.

Findings

Subtyping relation is sound and complete for asynchronous multiparty sessions.

Developed a session decomposition technique transforming full session types into single input/output trees.

Proved the subtyping relation is both operationally and denotationally precise.

Abstract

This paper presents the first formalisation of the precise subtyping relation for asynchronous multiparty sessions. We show that our subtyping relation is sound (i.e., guarantees safe process replacement) and also complete: any extension of the relation is unsound. To achieve our results, we develop a novel session decomposition technique, from full session types (including internal/external choices) into single input/output session trees (without choices). Previous work studies precise subtyping for binary sessions (with just two participants), or multiparty sessions (with any number of participants) and synchronous interaction. Here, we cover multiparty sessions with asynchronous interaction, where messages are transmitted via FIFO queues (as in the TCP/IP protocol), and prove that our subtyping is both operationally and denotationally precise. In the asynchronous multiparty setting, finding the precise subtyping relation is a highly complex task: this is because, under some conditions, participants can permute the order of their inputs and outputs, by sending some messages earlier or receiving some later, without causing errors; the precise subtyping relation must capture all such valid permutations -- and consequently, its formalisation, reasoning and proofs become challenging. Our session decomposition technique overcomes this complexity, expressing the subtyping relation as a composition of refinement relations between single input/output trees, and providing a simple reasoning principle for asynchronous message optimisations.