On CSP and the Algebraic Theory of Effects

Rob van Glabbeek, Gordon Plotkin

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We consider CSP from the point of view of the algebraic theory of effects, which classifies operations as effect constructors or effect deconstructors; it also provides a link with functional programming, being a refinement of Moggi’s seminal monadic point of view. There is a natural algebraic theory of the constructors whose free algebra functor is Moggi’s monad; we illustrate this by characterising free and initial algebras in terms of two versions of the stable failures model of CSP, one more general than the other. Deconstructors are dealt with as homomorphisms to (possibly non-free) algebras. One can view CSP’s action and choice operators as constructors and the rest, such as concealment and concurrency, as deconstructors. Carrying this programme out results in taking deterministic external choice as constructor rather than general external choice. However, binary deconstructors, such as the CSP concurrency operator, provide unresolved difficulties. We conclude by presenting a combination of CSP with Moggi’s computational λ-calculus, in which the operators, including concurrency, are polymorphic. While the paper mainly concerns CSP, it ought to be possible to carry over similar ideas to other process calculi.
Original languageEnglish
Title of host publicationReflections on the Work of C.A.R. Hoare
EditorsA.W. Roscoe, Cliff B. Jones, Kenneth R. Wood
Place of PublicationLondon
PublisherSpringer London
Pages333-369
Number of pages37
ISBN (Electronic)978-1-84882-912-1
ISBN (Print)978-1-84882-911-4
DOIs
Publication statusPublished - 2010

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