On the Expressiveness of Mixed Choice Sessions

TL;DR

This paper investigates the expressiveness of mixed choice session types, revealing limitations in their ability to encode pi-calculus behaviors and establishing a formal separation from the full pi-calculus.

Contribution

It proves that CMV+ session types cannot fully encode pi-calculus mixed choices, and provides a sound encoding from CMV+ to CMV without mixed choices.

Findings

CMV+ mixed choices are not fully expressive of pi-calculus.

No good encoding exists from pi-calculus to CMV+ preserving distribution.

A sound encoding from CMV+ to CMV is established.

Abstract

Session types provide a flexible programming style for structuring interaction, and are used to guarantee a safe and consistent composition of distributed processes. Traditional session types include only one-directional input (external) and output (internal) guarded choices. This prevents the session-processes to explore the full expressive power of the pi-calculus where the mixed choices are proved more expressive than the (non-mixed) guarded choices. To account this issue, recently Casal, Mordido, and Vasconcelos proposed the binary session types with mixed choices (CMV+). This paper carries a surprising, unfortunate result on CMV+: in spite of an inclusion of unrestricted channels with mixed choice, CMV+'s mixed choice is rather separate and not mixed. We prove this negative result using two methodologies (using either the leader election problem or a synchronisation pattern as distinguishing feature), showing that there exists no good encoding from the pi-calculus into CMV+, preserving distribution. We then close their open problem on the encoding from CMV+ into CMV (without mixed choice), proving its soundness and thereby that the encoding is good up to coupled similarity.