On the Expressiveness of Joining

TL;DR

This paper investigates the expressiveness of joining communication primitives, demonstrating that joining languages are inherently more expressive than binary ones and cannot be fully simulated by other features.

Contribution

It introduces coordination as a new dimension in communication expressiveness and proves that joining languages cannot be encoded into binary languages with existing features.

Findings

Joining languages are more expressive than binary languages.

No combination of other features can encode joining languages.

Joining cannot encode other features unless they are encodable otherwise.

Abstract

The expressiveness of communication primitives has been explored in a common framework based on the pi-calculus by considering four features: synchronism (asynchronous vs synchronous), arity (monadic vs polyadic data), communication medium (shared dataspaces vs channel-based), and pattern-matching (binding to a name vs testing name equality vs intensionality). Here another dimension coordination is considered that accounts for the number of processes required for an interaction to occur. Coordination generalises binary languages such as pi-calculus to joining languages that combine inputs such as the Join Calculus and general rendezvous calculus. By means of possibility/impossibility of encodings, this paper shows coordination is unrelated to the other features. That is, joining languages are more expressive than binary languages, and no combination of the other features can encode a joining language into a binary language. Further, joining is not able to encode any of the other features unless they could be encoded otherwise.