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Automated Algebraic Reasoning for Collections and Local Variables with Lenses

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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

Lenses are a useful algebraic structure for giving a unifying semantics to program variables in a variety of store models. They support efficient automated proof in the Isabelle/UTP verification framework. In this paper, we expand our lens library with (1) dynamic lenses, that support mutable indexed collections, such as arrays, and (2) symmetric lenses, which allow partitioning of a state space into disjoint local and global regions to support variable scopes. From this basis, we provide an enriched program model in Isabelle/UTP for collection variables and variable blocks. For the latter, we adopt an approach first used by Back and von Wright, and derive weakest precondition and Hoare calculi. We demonstrate several examples, including verification of insertion sort.

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Notes

  1. 1.

    The seL4 microkernel verification project: http://sel4.systems.

  2. 2.

    The similarly named quotient lens of Foster et al. [9] is a rather different concept.

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Acknowledgements

This work is funded by the EPSRC projects CyPhyAssure (CyPhyAssure Project: https://www.cs.york.ac.uk/circus/CyPhyAssure/.) (Grant EP/S001190/1) and RoboTest (Grant EP/R025479/1).

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Authors and Affiliations

  1. University of York, York, UK

    Simon Foster & James Baxter

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  1. Simon Foster
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  2. James Baxter
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Correspondence to Simon Foster .

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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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Foster, S., Baxter, J. (2020). Automated Algebraic Reasoning for Collections and Local Variables with Lenses. 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_7

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  • DOI: https://doi.org/10.1007/978-3-030-43520-2_7

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