Conflation Confers Concurrency

Abstract

Session types provide a static guarantee that concurrent programs respect communication protocols. Recent work has explored a correspondence between proof rules and cut reduction in linear logic and typing and evaluation of process calculi. This paper considers two approaches to extend logically-founded process calculi. First, we consider extensions of the process calculus to more closely resemble $\pi$-calculus. Second, inspired by denotational models of process calculi, we consider conflating dual types. Most interestingly, we observe that these approaches coincide: conflating the multiplicatives ($\otimes$ and $\invamp$) allows processes to share multiple channels; conflating the additives ($\oplus$ and ${\, \& \,}$) provides nondeterminism; and conflating the exponentials (${!}$ and ${?}$) yields access points, a rendezvous mechanism for initiating session typed communication. Access points are particularly expressive: for example, they are sufficient to encode concurrent state and general recursion.