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Matching Concepts across HOL Libraries

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

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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References

  1. Bortin, M., Johnsen, E.B., Lüth, C.: Structured formal development in Isabelle. Nordic Journal of Computing 13, 1–20 (2006)

    MathSciNet  MATH  Google Scholar 

  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. Furbach, U., Shankar, N. (eds.): IJCAR 2006. LNCS (LNAI), vol. 4130. Springer, Heidelberg (2006)

    MATH  Google Scholar 

  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)

    CrossRef  Google Scholar 

  5. Harrison, J.: Towards self-verification of HOL Light. In: Furbach, Shankar (eds.) [3], pp. 177–191

    Google Scholar 

  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)

    CrossRef  Google Scholar 

  7. Harrison, J.: The HOL Light theory of euclidean space. J. Autom. Reasoning 50(2), 173–190 (2013)

    MathSciNet  CrossRef  MATH  Google Scholar 

  8. Heras, J., Komendantskaya, E.: Proof pattern search in Coq/SSReflect. arXiv preprint, CoRR, abs/1402.0081 (2014)

    Google Scholar 

  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)

    CrossRef  Google Scholar 

  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)

    CrossRef  Google Scholar 

  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)

    CrossRef  Google Scholar 

  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. 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. 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)

    CrossRef  Google Scholar 

  15. Mohamed, O.A., Muñoz, C., Tahar, S. (eds.): TPHOLs 2008. LNCS, vol. 5170. Springer, Heidelberg (2008)

    Google Scholar 

  16. Obua, S., Skalberg, S.: Importing HOL into Isabelle/HOL. In: Furbach, Shankar (eds.) [3], pp. 298–302

    Google Scholar 

  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)

    CrossRef  Google Scholar 

  18. Slind, K., Norrish, M.: A brief overview of HOL4. In: Mohamed, et al. (eds.) [15], pp. 28–32

    Google Scholar 

  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. Urban, J.: MoMM - fast interreduction and retrieval in large libraries of formalized mathematics. Int. J. on Artificial Intelligence Tools 15(1), 109–130 (2006)

    CrossRef  Google Scholar 

  21. Wenzel, M., Paulson, L.C., Nipkow, T.: The Isabelle framework. In: Mohamed, et al. (eds.) [15], pp. 33–38

    Google Scholar 

  22. Wiedijk, F. (ed.): The Seventeen Provers of the World. LNCS (LNAI), vol. 3600. Springer, Heidelberg (2006)

    Google Scholar 

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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)