On CSP and the Algebraic Theory of Effects
Rob van Glabbeek, Gordon D. Plotkin, Gordon D. Plotkin, Rob van Glabbeek, Gordon Plotkin · 2010
Abstract We consider CSP from the point of view of the algebraic theory of effects, which classifies operations as effect constructors and effect deconstructors; it also provides a link with functional programming, being a refinement of Moggi’s sem-inal 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 nondeterminism operators as constructors and the rest, such as concealment and concurrency, as deconstructors. Carrying this pro-gramme out results in taking deterministic external choice as constructor rather than general external choice. However, binary deconstructors, such as the CSP concur-rency operator, provide unresolved difficulties. We conclude by presenting a com-bination 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. Rob van Glabbeek