On CSP and the Algebraic Theory of Effects

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 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 nondeterminism 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 conc...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Rob J. van Glabbeek, Gordon D. Plotkin
• Keywords: Algebraic Theory, CORR 2010, CSP Concurrency Operator, Education, Free Algebra Functor