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International Conference on Formal Engineering Methods

ICFEM 2018: Formal Methods and Software Engineering pp 3–18Cite as

Engineering a Theory of Concurrent Programming

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11232))

Abstract

Our original goal was to develop a refinement calculus for shared-memory concurrent programs to support Jones-style rely/guarantee developments. Our semantics was based on Aczel traces, which explicitly include environment steps as well as program steps, and were originally proposed as a basis for showing the rely/guarantee rules are sound. Where we have ended up is with a hierarchy of algebraic theories that provide a foundation for concurrent program refinement, which allows us to prove Jones-style rely/guarantee laws, as well as new laws. Our algebraic theory is based on a lattice of commands that includes a sub-lattice of test commands (similar to Kozen’s Kleene Algebra with Tests) and a sub-algebra of atomic step commands (similar to Milner’s SCCS) but with a structure that supports Aczel’s program and environment steps as atomic step commands. The latter allows us to directly encode rely and guarantee commands to represent rely/guarantee specifications, and to encode fair execution of a command.

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Notes

  1. 1.

    Note that some authors, e.g. Kozen [24], make use of the dual lattice with a reversed ordering \(d \le c\) that mean d refines c, and hence their nondeterministic choice operator is the lattice join (rather than meet).

  2. 2.

    Authors using the dual lattice make use of the dual of greatest fixed point, i.e. least fixed point.

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Acknowledgements

This research was supported Australian Research Council Discovery Grant DP130102901. Thanks are due to Joakim von Wright for introducing us to program algebra and Robert Colvin, Cliff Jones, Larissa Meinicke, Patrick Meiring, Kim Solin, Andrius Velykis, and Kirsten Winter, for their input on ideas presented here.

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  1. The University of Queensland, Brisbane, QLD, Australia

    Ian J. Hayes

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  1. Ian J. Hayes
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Correspondence to Ian J. Hayes .

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Editors and Affiliations

  1. University of Auckland, Auckland, New Zealand

    Jing Sun

  2. Peking University, Beijing, China

    Meng Sun

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Hayes, I.J. (2018). Engineering a Theory of Concurrent Programming. In: Sun, J., Sun, M. (eds) Formal Methods and Software Engineering. ICFEM 2018. Lecture Notes in Computer Science(), vol 11232. Springer, Cham. https://doi.org/10.1007/978-3-030-02450-5_1

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  • DOI: https://doi.org/10.1007/978-3-030-02450-5_1

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