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Automatic Refinement to Efficient Data Structures: A Comparison of Two Approaches

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Abstract

We consider the problem of formally verifying an algorithm in a proof assistant and generating efficient code. Reasoning about correctness is best done at an abstract level, but efficiency of the generated code often requires complicated data structures. Data refinement has been successfully used to reconcile these conflicting requirements, but usability calls for automatic tool support. In the context of Isabelle/HOL, two frameworks for automating data refinement have been proposed (Lammich, in: Blazy, Paulin-Mohring, Pichardie (eds) ITP 2013, LNCS, vol 7998, Springer, Heidelberg, pp 84–99, 2013; Lochbihler, in: Blazy, Paulin-Mohring, Pichardie (eds) ITP 2013, LNCS, vol 7998, Springer, Heidelberg, pp 116–132, 2013). In this paper, we present and compare the two frameworks and their underlying ideas in depth. Thereby, we identify the challenges of automating data refinement, highlight the similarities and differences of the two approaches, and show their strengths and limitations both from the implementer’s and the user’s perspectives. A case study demonstrates how to combine both frameworks, benefiting from the strengths of each.

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Authors and Affiliations

  1. Institut für Informatik, Technische Universität München, Boltzmannstr. 3, 85748, Garching, Germany

    Peter Lammich

  2. Department of Informatics, Institute of Information Security, ETH Zurich, Universitätstrasse 6, 8092, Zurich, Switzerland

    Andreas Lochbihler

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  1. Peter Lammich
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  2. Andreas Lochbihler
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Correspondence to Peter Lammich.

Additional information

This article builds on the author’s individual presentations of the two approaches at Interactive Theorem Proving 2013 [23, 33].

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Lammich, P., Lochbihler, A. Automatic Refinement to Efficient Data Structures: A Comparison of Two Approaches. J Autom Reasoning 63, 53–94 (2019). https://doi.org/10.1007/s10817-018-9461-9

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