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On CSP and the Algebraic Theory of Effects

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Reflections on the Work of C.A.R. Hoare

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.

This work was done with the support of a Royal Society-Wolfson Award.

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Authors and Affiliations

  1. NICTA, Sydney, Australia

    Rob van Glabbeek

  2. University of New South Wales, Sydney, Australia

    Rob van Glabbeek

  3. Laboratory for the Foundations of Computer Science, School of Informatics, University of Edinburgh, Edinburgh, UK

    Gordon Plotkin

Authors
  1. Rob van Glabbeek
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  2. Gordon Plotkin
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Correspondence to Gordon Plotkin .

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Editors and Affiliations

  1. Oxford University Computing Laboratory, Parks Road, Oxford, OX13QD, United Kingdom

    A.W. Roscoe

  2. Dept. Computing Science, University of Newcastle upon Tyne, Newcastle upon Tyne, NE17RU, United Kingdom

    Cliff B. Jones

  3. Microsoft Research Ltd., J. J. Thomson Avenue 7, Cambridge, CB30FB, United Kingdom

    Kenneth R. Wood

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van Glabbeek, R., Plotkin, G. (2010). On CSP and the Algebraic Theory of Effects. In: Roscoe, A., Jones, C., Wood, K. (eds) Reflections on the Work of C.A.R. Hoare. Springer, London. https://doi.org/10.1007/978-1-84882-912-1_15

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  • DOI: https://doi.org/10.1007/978-1-84882-912-1_15

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