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Matching Concepts across HOL Libraries

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Intelligent Computer Mathematics (CICM 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8543))

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Abstract

Many proof assistant libraries contain formalizations of the same mathematical concepts. The concepts are often introduced (defined) in different ways, but the properties that they have, and are in turn formalized, are the same. For the basic concepts, like natural numbers, matching them between libraries is often straightforward, because of mathematical naming conventions. However, for more advanced concepts, finding similar formalizations in different libraries is a non-trivial task even for an expert.

In this paper we investigate automatic discovery of similar concepts across libraries of proof assistants. We propose an approach for normalizing properties of concepts in formal libraries and a number of similarity measures. We evaluate the approach on HOL based proof assistants HOL4, HOL Light and Isabelle/HOL, discovering 398 pairs of isomorphic constants and types.

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Author information

Authors and Affiliations

  1. University of Innsbruck, Austria

    Thibault Gauthier & Cezary Kaliszyk

Authors
  1. Thibault Gauthier
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  2. Cezary Kaliszyk
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Editor information

Editors and Affiliations

  1. Computer Science Department, The University of Western Ontario, MC 375,, N6A 5B7, London, ON, Canada

    Stephen M. Watt

  2. Departments of Computer Science and Mathematical Sciences, University of Bath, Claverton Down, BA2 7AY, Bath, UK

    James H. Davenport

  3. School of Computer Science, Edgbaston, University of Birmingham, B15 2TT, Birmingham, UK

    Alan P. Sexton

  4. Faculty of Informatics, Masaryk University, Botanicá 6a, 60200, Brno, Czech Republic

    Petr Sojka

  5. Institute for Computing Sciences, Radboud University Nijmegen, Postbus 9010,, 6525, Nijmegen, GL, The Netherlands

    Josef Urban

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© 2014 Springer International Publishing Switzerland

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Gauthier, T., Kaliszyk, C. (2014). Matching Concepts across HOL Libraries. In: Watt, S.M., Davenport, J.H., Sexton, A.P., Sojka, P., Urban, J. (eds) Intelligent Computer Mathematics. CICM 2014. Lecture Notes in Computer Science(), vol 8543. Springer, Cham. https://doi.org/10.1007/978-3-319-08434-3_20

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  • DOI: https://doi.org/10.1007/978-3-319-08434-3_20

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08433-6

  • Online ISBN: 978-3-319-08434-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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