Matching Concepts across HOL Libraries

  • Thibault Gauthier
  • Cezary Kaliszyk
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8543)


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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  1. 1.
    Bortin, M., Johnsen, E.B., Lüth, C.: Structured formal development in Isabelle. Nordic Journal of Computing 13, 1–20 (2006)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Carlisle, D., Davenport, J., Dewar, M., Hur, N., Naylor, W.: Conversion between MathML and OpenMath. Technical Report 24.969. The OpenMath Society (2001)Google Scholar
  3. 3.
    Furbach, U., Shankar, N. (eds.): IJCAR 2006. LNCS (LNAI), vol. 4130. Springer, Heidelberg (2006)zbMATHGoogle Scholar
  4. 4.
    Haftmann, F., Krauss, A., Kunčar, O., Nipkow, T.: Data refinement in isabelle/HOL. In: Blazy, S., Paulin-Mohring, C., Pichardie, D. (eds.) ITP 2013. LNCS, vol. 7998, pp. 100–115. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  5. 5.
    Harrison, J.: Towards self-verification of HOL Light. In: Furbach, Shankar (eds.) [3], pp. 177–191Google Scholar
  6. 6.
    Harrison, J.: HOL Light: An overview. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds.) TPHOLs 2009. LNCS, vol. 5674, pp. 60–66. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  7. 7.
    Harrison, J.: The HOL Light theory of euclidean space. J. Autom. Reasoning 50(2), 173–190 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Heras, J., Komendantskaya, E.: Proof pattern search in Coq/SSReflect. arXiv preprint, CoRR, abs/1402.0081 (2014)Google Scholar
  9. 9.
    Hurd, J.: The OpenTheory standard theory library. In: Bobaru, M., Havelund, K., Holzmann, G.J., Joshi, R. (eds.) NFM 2011. LNCS, vol. 6617, pp. 177–191. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  10. 10.
    Kaliszyk, C., Krauss, A.: Scalable LCF-style proof translation. In: Blazy, S., Paulin-Mohring, C., Pichardie, D. (eds.) ITP 2013. LNCS, vol. 7998, pp. 51–66. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  11. 11.
    Kaliszyk, C., Urban, J.: Lemma mining over HOL Light. In: McMillan, K., Middeldorp, A., Voronkov, A. (eds.) LPAR-19. LNCS, vol. 8312, pp. 503–517. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  12. 12.
    Kaliszyk, C., Urban, J.: HOL(y)Hammer: Online ATP service for HOL Light. arXiv preprint abs/1309.4962, accepted for publication in Mathematics in Computer Science (2014)Google Scholar
  13. 13.
    Kaliszyk, C., Urban, J.: Learning-assisted automated reasoning with Flyspeck. arXiv preprint abs/1211.7012, accepted for publication in Journal of Automated Reasoning (2014)Google Scholar
  14. 14.
    Keller, C., Werner, B.: Importing HOL Light into Coq. In: Kaufmann, M., Paulson, L.C. (eds.) ITP 2010. LNCS, vol. 6172, pp. 307–322. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  15. 15.
    Mohamed, O.A., Muñoz, C., Tahar, S. (eds.): TPHOLs 2008. LNCS, vol. 5170. Springer, Heidelberg (2008)Google Scholar
  16. 16.
    Obua, S., Skalberg, S.: Importing HOL into Isabelle/HOL. In: Furbach, Shankar (eds.) [3], pp. 298–302Google Scholar
  17. 17.
    Rabe, F.: The MMT API: A generic MKM system. In: Carette, J., Aspinall, D., Lange, C., Sojka, P., Windsteiger, W. (eds.) CICM 2013. LNCS (LNAI), vol. 7961, pp. 339–343. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  18. 18.
    Slind, K., Norrish, M.: A brief overview of HOL4. In: Mohamed, et al. (eds.) [15], pp. 28–32Google Scholar
  19. 19.
    So, C.M., Watt, S.M.: On the conversion between content MathML and OpenMath. In: Proc. of the Conference on the Communicating Mathematics in the Digital Era (CMDE 2006), pp. 169–182 (2006)Google Scholar
  20. 20.
    Urban, J.: MoMM - fast interreduction and retrieval in large libraries of formalized mathematics. Int. J. on Artificial Intelligence Tools 15(1), 109–130 (2006)CrossRefGoogle Scholar
  21. 21.
    Wenzel, M., Paulson, L.C., Nipkow, T.: The Isabelle framework. In: Mohamed, et al. (eds.) [15], pp. 33–38Google Scholar
  22. 22.
    Wiedijk, F. (ed.): The Seventeen Provers of the World. LNCS (LNAI), vol. 3600. Springer, Heidelberg (2006)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Thibault Gauthier
    • 1
  • Cezary Kaliszyk
    • 1
  1. 1.University of InnsbruckAustria

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