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From CSP to Game Semantics

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

Abstract

In this short essay, we describe in informal terms how game semantics can be seen to arise as a perturbation of process calculi such as CSP, by making an explicit distinction between the rôles of the System and the Environment. Drawing out the consequences of this distinction uncovers a wealth of mathematical structure, with Game intuitions entering in a natural and compelling fashion. This leads ultimately to the elaboration of mathematically well-structured and behaviourally expressive semantic universes for computation. These provide a basis for fully abstract models of a wide range of programming languages, and lead on to algorithmic methods, with applications to compositional model-checking and program analysis.

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Notes

  1. 1.

    The input–output distinction does occur in a more fundamental way in the π-calculus [28, 29, 30]. However, even here there are symmetric variants such as the fusion calculus [31], and the π-calculus does not seem to force a fundamental modification of the distinction we are making here.

  2. 2.

    These calculi do have notions of “deterministic” and “confluent” process as part of their theory [27, 32], but these notions refer to the absence of non-observable branching in the system. They do not directly correspond to the sense in which the computation of a standard functional or imperative program is deterministic.

  3. 3.

    It is also easy to show that if Nigel and Gary are both playing winning strategies, meaning that they always have a response to the Environment’s actions, and that the infinite plays which may arise from following these strategies satisfy some given liveness specifications, then the composed strategy will again be a winning strategy, with respect to a liveness specification defined compositionally in a natural fashion from the given ones. See [1] for details and a proof of this.

  4. 4.

    A key quality of this form of game semantics, as compared to earlier work in the logical literature, such as the Game-Theoretical Semantics of Hintikka [17] and the Dialogical game semantics of Lorenzen and his school [26], is its syntax-independence and compositionality. Here compositionality refers, crucially, to the level of strategies as well as merely to the games.

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Acknowledgements

My thanks to Bill Roscoe and Paul Levy for their comments on an earlier version of this paper, which led to several clarifications. The remaining obscurities and inaccuracies are entirely my responsibility.

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  1. Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford, OX1 3QD, UK

    Samson Abramsky

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  1. Samson Abramsky
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  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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Abramsky, S. (2010). From CSP to Game Semantics. 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_2

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  • DOI: https://doi.org/10.1007/978-1-84882-912-1_2

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