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Reflections on the Work of C.A.R. Hoare pp 333–369Cite as

On CSP and the Algebraic Theory of Effects

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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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References

  1. Abadi, M., Plotkin, G.D.: A model of cooperative threads. In: Shao, Z., Pierce, B.C. (eds.), Proc. POPL 2009. ACM Press, pp. 29 40 (2009)

    Google Scholar 

  2. Abramsky, S., Gabbay, D.M., Maibaum, T.S.E. (eds.), Handbook of Logic in Computer Science (Vol. 1), Background: Mathematical Structures, Oxford University Press (1995)

    MATH  Google Scholar 

  3. Benton, N., Hughes, J., Moggi, E.: Monads and effects. Proc. APPSEM 2000, LNCS 2395, pp. 42 122, Springer (2002)

    Google Scholar 

  4. Bergstra, J.A., Klop, J.W.: Algebra of communicating processes with abstraction. Theor. Comput. Sci. 37, pp. 77 121 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  5. Bergstra, J.A., Klop, J.W.: Algebra of communicating processes. In: de Bakker, J.W., Hazewinkel, M., Lenstra, J.K. (eds.), Proc. of the CWI Symp. Math. and Comp. Sci. pp. 89 138, North-Holland (1986)

    Google Scholar 

  6. Bergstra, J.A., Klop, J.W., Olderog, E.-R.: Failures without chaos: a new process semantics for fair abstraction. In: Wirsing, M. (ed.), Proc. of the 3rd IFIP WG 2.2 working conference on Formal Description of Programming Concepts. pp. 77 103, North-Holland (1987)

    Google Scholar 

  7. Bloom, S.L.: Varieties of ordered algebras. J. Comput. Syst. Sci., 13(2):200 212 (1976)

    Article  MATH  Google Scholar 

  8. Borceux, F.: Handbook of Categorical Algebra 2, Encyclopedia of Mathematics and Its Applications 51. Cambridge University Press (1994)

    Google Scholar 

  9. Brookes, S.D., Hoare, C.A.R., Roscoe, A.W.: A theory of communicating sequential processes. J. ACM 31(3):560 599 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  10. De Nicola, R.: Two complete axiom systems for a theory of communicating sequential processes. Inform. Control 64, pp. 136 172 (1985)

    Article  MATH  Google Scholar 

  11. Ebrahimi-Fard, K., Guo, L.: Rota-Baxter algebras and dendriform algebras. J. Pure Appl. Algebra 212(2):320 33 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  12. Gierz, G., Hofmann, K.H., Keimel, K., Lawson, J.D., Mislove, M., Scott, D.S.: Continuous Lattices and Domains, Encyclopedia of Mathematics and its Applications 93. Cambridge University Press (2003)

    Google Scholar 

  13. Hoare, C.A.R.: Communicating Sequential Processes. Prentice-Hall (1985)

    Google Scholar 

  14. Hyland, J.M.E., Plotkin, G.D., Power, A.J.: Combining effects: sum and tensor. In: Artemov, S., Mislove, M. (eds.), Clifford Lectures and the Mathematical Foundations of Programming Semantics. Theor. Comput. Sci. 357(1 3):70 99 (2006)

    Google Scholar 

  15. Keimel, K., Plotkin, G.D.: Predicate transformers for extended probability and non-determinism. Math. Struct. Comput. Sci. 19(3):501 539. Cambridge University Press (2009)

    Google Scholar 

  16. Klin, B., Sassone, V.: Structural operational semantics for stochastic process calculi. In: Amadio, R.M. (ed.), Proc. 11th. FoSSaCS. LNCS 4962, pp. 428 442, Springer (2008)

    Google Scholar 

  17. Milner, A.J.R.G.: A Calculus of Communicating Systems. Springer (1980)

    Google Scholar 

  18. Moggi, E.: Computational lambda-calculus and monads. Proc. 3rd. LICS, pp. 14 23, IEEE Press (1989)

    Google Scholar 

  19. Moggi, E.: Notions of computation and monads. Inf. Comp. 93(1):55 92 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  20. Ouaknine, J., Schneider, S.: Timed CSP: a retrospective, Proceedings of the Workshop “Essays on Algebraic Process Calculi” (APC 25), Electr. Notes Theor. Comput. Sci., 162, pp. 273 276 (2006)

    Article  Google Scholar 

  21. Plotkin, G.D.: Some varieties of equational logic. Essays Dedicated to Joseph A. Goguen. In: Futatsugi, K., Jouannaud, J.-P., Meseguer, J. (eds.), LNCS 4060, pp. 150 156, Springer (2006)

    Google Scholar 

  22. Plotkin, G.D., Power, A.J.: Notions of computation determine monads, Proc. 5th. FoSSaCS. LNCS 2303, pp. 342 356, Springer (2002)

    Google Scholar 

  23. Plotkin, G.D., Power, A.J.: Computational effects and operations: an overview. In: Escardó, M., Jung, A. (eds.), Proc. Workshop on Domains VI. Electr. Notes Theor. Comput. Sci. 73, pp. 149 163, Elsevier (2004)

    Google Scholar 

  24. Plotkin, G.D., Pretnar, M.: A logic for algebraic effects. Proc. 23rd. LICS, pp. 118 129, IEEE Press (2008)

    Google Scholar 

  25. Plotkin, G.D., Pretnar, M.: Handlers of algebraic effects. Proc. 18th. ESOP, pp. 80 94 (2009)

    Google Scholar 

  26. Priami, C.: Stochastic pi-calculus. Comput. J. 38 (7):578 589 (1995)

    Article  Google Scholar 

  27. Reed, G.M., Roscoe, A.W.: The timed failures-stability model for CSP. Theor. Comput. Sci. 211(1 2):85 127 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  28. Roscoe, A.W.: Model-checking CSP. In: Roscoe, A.W. (ed.), A Classical Mind: Essays in Honour of Hoare, C.A.R., pp. 353 337, Prentice-Hall (1994)

    Google Scholar 

  29. Roscoe, A.W.: The Theory and Practice of Concurrency. Prentice Hall (1998)

    Google Scholar 

  30. Sangiorgi, D., Walker, D.: The π-Calculus: A Theory of Mobile Processes. Cambridge University Press (2003)

    Google Scholar 

  31. Scattergood, B.: The Semantics and Implementation of Machine-Readable CSP. D.Phil Thesis, Oxford University (1998)

    Google Scholar 

  32. Schröder, M., Simpson, A.: Probabilistic observations and valuations (extended abstract). Electr. Notes Theor. Comput. Sci. 155, pp. 605 615 (2006)

    Article  Google Scholar 

  33. Stark, I.: Free-algebra models for the pi-calculus. Theor. Comput. Sci. 390(2 3):248 270 (2008)

    Article  MATH  Google Scholar 

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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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