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Conflation Confers Concurrency
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Conflation Confers Concurrency

Robert Atkey, Sam Lindley and J. Garrett Morris
A List of Successes That Can Change the World, pp.32-55
Lecture Notes in Computer Science, v. 9600, Springer International Publishing
03/25/2016
DOI: 10.1007/978-3-319-30936-1_2

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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 π-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 (⊗ and) allows processes to share multiple channels; conflating the additives (⊕ 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.
Access Point Intuitionistic Logic Linear Logic Proof Rule Reduction Rule

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