On sequentiality and well-bracketing in the $\pi$-calculus

TL;DR

This paper investigates how enforcing sequentiality and well-bracketing disciplines in the $ ext{pi}$-calculus affects behavioral equivalences, using type systems to formalize these constraints and analyzing their impact on bisimilarity.

Contribution

It introduces formal type-based disciplines for sequentiality and well-bracketing in the $ ext{pi}$-calculus and studies their influence on behavioral equivalences, providing new coarser bisimilarity relations.

Findings

Bisimilarities are sound for contextual barbed equivalence.

Bisimilarities are complete under certain conditions.

Techniques are demonstrated on examples involving functions and storage.

Abstract

The $\pi$-calculus is used as a model for programming languages. Its contexts exhibit arbitrary concurrency, making them very discriminating. This may prevent validating desirable behavioural equivalences in cases when more disciplined contexts are expected. In this paper we focus on two such common disciplines: sequentiality, meaning that at any time there is a single thread of computation, and well-bracketing, meaning that calls to external services obey a stack-like discipline. We formalise the disciplines by means of type systems. The main focus of the paper is on studying the consequence of the disciplines on behavioural equivalence. We define and study labelled bisimilarities for sequentiality and well-bracketing. These relations are coarser than ordinary bisimilarity. We prove that they are sound for the respective (contextual) barbed equivalence, and also complete under a certain technical condition. We show the usefulness of our techniques on a number of examples, that have mainly to do with the representation of functions and store.