Skip to main content

Towards Knowledge Management for HOL Light

  • Conference paper

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

Abstract

The libraries of deduction systems are growing constantly, so much that knowledge management concerns are becoming increasingly urgent to address. However, due to time constraints and legacy design choices, there is barely any deduction system that can keep up with the MKM state of the art. HOL Light in particular was designed as a lightweight deduction system that systematically relegates most MKM aspects to external solutions — not even the list of theorems is stored by the HOL Light kernel.

We make the first and hardest step towards knowledge management for HOL Light: We provide a representation of the HOL Light library in a standard MKM format that preserves the logical semantics and notations but is independent of the system itself. This provides an interface layer at which independent MKM applications can be developed. Moreover, we develop two such applications as examples. We employ the MMT system and its interactive web browser to view and navigate the library. And we use the MathWebSearch system to obtain a search engine for it.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adams, M., Aspinall, D.: Recording and refactoring HOL Light tactic proofs. In: Proceedings of the IJCAR Workshop on Automated Theory Exploration (2012), http://homepages.inf.ed.ac.uk/smaill/atxwing/atx2012_submission_9.pdf

  2. Buswell, S., Caprotti, O., Carlisle, D., Dewar, M., Gaetano, M., Kohlhase, M.: The Open Math Standard, Version 2.0. Technical report, The Open Math Society (2004), http://www.openmath.org/standard/om20

  3. Corbineau, P., Kaliszyk, C.: Cooperative repositories for formal proofs. In: Kauers, M., Kerber, M., Miner, R., Windsteiger, W. (eds.) MKM/Calculemus 2007. LNCS (LNAI), vol. 4573, pp. 221–234. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  4. Farmer, W., Guttman, J., Thayer, F.: IMPS: An Interactive Mathematical Proof System. Journal of Automated Reasoning 11(2), 213–248 (1993)

    Article  MATH  Google Scholar 

  5. Gonthier, G., et al.: A Machine-Checked Proof of the Odd Order Theorem. In: Blazy, S., Paulin-Mohring, C., Pichardie, D. (eds.) ITP 2013. LNCS, vol. 7998, pp. 163–179. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  6. Gauthier, T., Kaliszyk, C.: Matching concepts across HOL libraries. In: Watt, S.M., Davenport, J.H., Sexton, A.P., Sojka, P., Urban, J. (eds.) CICM 2014. LNCS (LNAI), vol. 8543, pp. 267–281. Springer, Heidelberg (2014)

    Google Scholar 

  7. Hales, T.: Introduction to the Flyspeck Project. In: Coquand, T., Lombardi, H., Roy, M. (eds.) Mathematics, Algorithms, Proofs. Internationales Begegnungs- und Forschungszentrum für Informatik (IBFI), Schloss Dagstuhl, Germany (2005)

    Google Scholar 

  8. Harrison, J.: HOL Light: A Tutorial Introduction. In: Srivas, M., Camilleri, A. (eds.) FMCAD 1996. LNCS, vol. 1166, pp. 265–269. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  9. Harper, R., Honsell, F., Plotkin, G.: A framework for defining logics. Journal of the Association for Computing Machinery 40(1), 143–184 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  10. Horozal, F., Kohlhase, M., Rabe, F.: Extending MKM Formats at the Statement Level. In: Jeuring, J., Campbell, J.A., Carette, J., Dos Reis, G., Sojka, P., Wenzel, M., Sorge, V. (eds.) CICM 2012. LNCS (LNAI), vol. 7362, pp. 65–80. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  11. Horozal, F., Rabe, F., Kohlhase, M.: Flexary Operators for Formalized Mathematics. In: Watt, S.M., Davenport, J.H., Sexton, A.P., Sojka, P., Urban, J. (eds.) CICM 2014. LNCS (LNAI), vol. 8543, pp. 312–327. Springer, Heidelberg (2014)

    Google Scholar 

  12. Hurd, J.: OpenTheory: Package Management for Higher Order Logic Theories. In: Reis, G.D., Théry, L. (eds.) Programming Languages for Mechanized Mathematics Systems, pp. 31–37. ACM (2009)

    Google Scholar 

  13. Harrison, J., Zumkeller, R.: update_database module. Part of the HOL Light distribution

    Google Scholar 

  14. Iancu, M., Kohlhase, M., Rabe, F., Urban, J.: The Mizar Mathematical Library in OMDoc: Translation and Applications. Journal of Automated Reasoning 50(2), 191–202 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  15. 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)

    Chapter  Google Scholar 

  16. Kohlhase, M.: OMDoc – An Open Markup Format for Mathematical Documents [version 1.2]. LNCS (LNAI), vol. 4180. Springer, Heidelberg (2006)

    Book  Google Scholar 

  17. Kohlhase, M., Sucan, I.: A Search Engine for Mathematical Formulae. In: Calmet, J., Ida, T., Wang, D. (eds.) AISC 2006. LNCS (LNAI), vol. 4120, pp. 241–253. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  18. Kaliszyk, C., Urban, J.: Learning-assisted automated reasoning with Flyspeck. Journal of Automated Reasoning (2014), http://dx.doi.org/10.1007/s10817-014-9303-3

  19. 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)

    Chapter  Google Scholar 

  20. Naumov, P., Stehr, M.-O., Meseguer, J.: The HOL/NuPRL proof translator - A practical approach to formal interoperability. In: Boulton, R.J., Jackson, P.B. (eds.) TPHOLs 2001. LNCS, vol. 2152, pp. 329–345. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  21. Obua, S., Adams, M., Aspinall, D.: Capturing hiproofs in HOL light. In: Carette, J., Aspinall, D., Lange, C., Sojka, P., Windsteiger, W. (eds.) CICM 2013. LNCS (LNAI), vol. 7961, pp. 184–199. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  22. Obua, S., Skalberg, S.: Importing HOL into Isabelle/HOL. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 298–302. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  23. Paulson, L.C.: Isabelle: A Generic Theorem Prover. LNCS, vol. 828. Springer, Heidelberg (1994)

    Google Scholar 

  24. Pitts, A.: The HOL logic. In: Gordon, M.J.C., Melham, T.F. (eds.) Introduction to HOL: A Theorem Proving Environment for Higher Order Logic. Cambridge University Press (1993)

    Google Scholar 

  25. 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)

    Chapter  Google Scholar 

  26. Reynolds, J.: Types, Abstraction, and Parametric Polymorphism. In: Information Processing, pp. 513–523. North-Holland, Amsterdam (1983)

    Google Scholar 

  27. Rabe, F., Kohlhase, M.: A Scalable Module System. Information and Computation 230(1), 1–54 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  28. Rabe, F., Kohlhase, M., Sacerdoti Coen, C.: A Foundational View on Integration Problems. In: Davenport, J.H., Farmer, W.M., Urban, J., Rabe, F. (eds.) Calculemus/MKM 2011. LNCS (LNAI), vol. 6824, pp. 107–122. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  29. Tankink, C., Geuvers, H., McKinna, J., Wiedijk, F.: Proviola: A tool for proof re-animation. In: Autexier, S., Calmet, J., Delahaye, D., Ion, P.D.F., Rideau, L., Rioboo, R., Sexton, A.P. (eds.) AISC/Calculemus/MKM 2010. LNCS (LNAI), vol. 6167, pp. 440–454. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  30. Tankink, C., Kaliszyk, C., Urban, J., Geuvers, H.: Communicating formal proofs: The case of Flyspeck. In: Blazy, S., Paulin-Mohring, C., Pichardie, D. (eds.) ITP 2013. LNCS, vol. 7998, pp. 451–456. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  31. Tankink, C., Kaliszyk, C., Urban, J., Geuvers, H.: Formal mathematics on display: A wiki for Flyspeck. In: Carette, J., Aspinall, D., Lange, C., Sojka, P., Windsteiger, W. (eds.) CICM 2013. LNCS (LNAI), vol. 7961, pp. 152–167. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  32. Wiedijk, F.: Stateless HOL. In: Hirschowitz, T. (ed.) TYPES. EPTCS, vol. 53, pp. 47–61 (2009)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Kaliszyk, C., Rabe, F. (2014). Towards Knowledge Management for HOL Light. 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_26

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-08434-3_26

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08433-6

  • Online ISBN: 978-3-319-08434-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics