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A Unary Semigroup Trace Algebra

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Relational and Algebraic Methods in Computer Science (RAMiCS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12062))

Abstract

The Unifying Theories of Programming (UTP) of Hoare and He promote the unification of semantics catering for different concerns, such as, termination, data modelling, concurrency and time. Process calculi like  and CSP can be given semantics in the UTP using reactive designs whose traces can be abstractly specified using a monoid trace algebra. The prefix order over traces is defined in terms of the monoid operator. This order, however, is inadequate to characterise a broader family of timed process algebras whose traces are preordered instead. To accommodate these, we propose a unary semigroup trace algebra that is weaker than the monoid algebra. This structure satisfies some of the axioms of restriction semigroups and is a right P-Ehresmann semigroup. Reactive designs specified using it satisfy core laws that have been mechanised so far in Isabelle/UTP. More importantly, our results improve the support for unifying trace models in the UTP.

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Notes

  1. 1.

    https://github.com/isabelle-utp (definitions and lemmas hyper-linked using ).

  2. 2.

    https://github.com/isabelle-utp/utp-main/tree/ramics2020s.

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Acknowledgements

This work is funded by the EPSRC grant EP/M025756/1. No new primary data was created as part of the study reported here. We are grateful to Ana Cavalcanti for comments on an earlier draft of this paper, and to the anonymous reviewers for their helpful and constructive feedback.

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Authors and Affiliations

  1. Department of Computer Science, University of York, York, YO10 5GH, UK

    Pedro Ribeiro

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  1. Pedro Ribeiro
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Correspondence to Pedro Ribeiro .

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Editors and Affiliations

  1. Laboratoire d’informatique (LIX), École Polytechnique, Palaiseau, France

    Uli Fahrenberg

  2. Faculty of Mathematics, Chapman University, Orange, CA, USA

    Peter Jipsen

  3. Department of Computer Science, Brock University, St. Catharines, ON, Canada

    Michael Winter

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Ribeiro, P. (2020). A Unary Semigroup Trace Algebra. In: Fahrenberg, U., Jipsen, P., Winter, M. (eds) Relational and Algebraic Methods in Computer Science. RAMiCS 2020. Lecture Notes in Computer Science(), vol 12062. Springer, Cham. https://doi.org/10.1007/978-3-030-43520-2_17

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  • DOI: https://doi.org/10.1007/978-3-030-43520-2_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-43519-6

  • Online ISBN: 978-3-030-43520-2

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