On the Expressiveness of Mixed Choice Sessions (Technical Report)

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 π-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 π-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. This technical report extends a paper presented at the workshop EXPRESS/SOS'22.

On the Expressiveness of Mixed Choice Sessions

“…We omit these qualifiers to simplify the presentation. However, the proofs are carried out on the languages CMV + and CMV as given by [6] (see [34]). A branch l * v.P specifies a label l, a polarity * (!…”

“…Indeed, our separation result (in both ways to prove it) is carried out on the untyped version of CMV + . See [6] or [34] for the full typing systems.…”

“…However, the proofs are carried out on the original definitions of the languages from [6]. We include complete proofs of all the statements in this paper and the technical details of the notions from the literature that we use in [34].…”