Contextual equivalence for higher-order pi-calculus revisited

TL;DR

This paper revisits the higher-order pi-calculus, providing a new proof technique that achieves a fully abstract characterization of contextual equivalence, including recursive types, overcoming previous limitations.

Contribution

It introduces an alternative labelled transition system and a novel proof method for higher-order pi-calculus with recursive types, ensuring full abstraction.

Findings

Provides a fully abstract characterization of contextual equivalence

Extends the calculus to include recursive types

Introduces a new proof technique for bisimulation

Abstract

The higher-order pi-calculus is an extension of the pi-calculus to allow communication of abstractions of processes rather than names alone. It has been studied intensively by Sangiorgi in his thesis where a characterisation of a contextual equivalence for higher-order pi-calculus is provided using labelled transition systems and normal bisimulations. Unfortunately the proof technique used there requires a restriction of the language to only allow finite types. We revisit this calculus and offer an alternative presentation of the labelled transition system and a novel proof technique which allows us to provide a fully abstract characterisation of contextual equivalence using labelled transitions and bisimulations for higher-order pi-calculus with recursive types also.