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Automated Reasoning Service for HOL Light

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Intelligent Computer Mathematics (CICM 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7961))

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Abstract

HOL(y)Hammer is an AI/ATP service for formal (computer-understandable) mathematics encoded in the HOL Light system, in particular for the users of the large Flyspeck library. The service uses several automated reasoning systems combined with several premise selection methods trained on previous Flyspeck proofs, to attack a new conjecture that uses the concepts defined in the Flyspeck library. The public online incarnation of the service runs on a 48-CPU server, currently employing in parallel for each task 25 AI/ATP combinations and 4 decision procedures that contribute to its overall performance. The system is also available for local installation by interested users, who can customize it for their own proof development. An Emacs interface allowing parallel asynchronous queries to the service is also provided. The overall structure of the service is outlined, problems that arise are discussed, and an initial account of using the system is given.

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References

  1. Akbarpour, B., Paulson, L.C.: MetiTarski: An automatic theorem prover for real-valued special functions. J. Autom. Reasoning 44(3), 175–205 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Alama, J., Brink, K., Mamane, L., Urban, J.: Large formal wikis: Issues and solutions. In: Davenport, J.H., Farmer, W.M., Urban, J., Rabe, F. (eds.) Calculemus/MKM 2011. LNCS, vol. 6824, pp. 133–148. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  3. Blanchette, J.C., Böhme, S., Popescu, A., Smallbone, N.: Encoding Monomorphic and Polymorphic Types. In: Piterman, N., Smolka, S.A. (eds.) TACAS 2013. LNCS, vol. 7795, pp. 493–507. Springer, Heidelberg (2013), http://www21.in.tum.de/~blanchet/enc_types_paper.pdf

    Chapter  Google Scholar 

  4. Blanchette, J.C., Paskevich, A.: TFF1: The TPTP typed first-order form with rank-1 polymorphism, http://www21.in.tum.de/~blanchet/tff1spec.pdf

  5. Carlson, A., Cumby, C., Rosen, J., Roth, D.: The SNoW Learning Architecture. Technical Report UIUCDCS-R-99-2101, UIUC Computer Science Department, 5 (1999)

    Google Scholar 

  6. de Moura, L., Bjørner, N.: Z3: An efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

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

    MATH  Google Scholar 

  8. Van Gelder, A., Sutcliffe, G.: Extending the TPTP language to higher-order logic with automated parser generation. In: Furbach, Shankar (eds.) [7], pp. 156–161

    Google Scholar 

  9. Hales, T.C.: Introduction to the Flyspeck project. In: Coquand, T., Lombardi, H., Roy, M.-F. (eds.) Mathematics, Algorithms, Proofs. Dagstuhl Seminar Proceedings, vol. 05021. Internationales Begegnungs- und Forschungszentrum für Informatik (IBFI), Schloss Dagstuhl, Germany (2005)

    Google Scholar 

  10. 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 

  11. Harrison, J.: Optimizing Proof Search in Model Elimination. In: McRobbie, M.A., Slaney, J.K. (eds.) CADE 1996. LNCS, vol. 1104, pp. 313–327. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  12. Hoder, K., Voronkov, A.: Sine qua non for large theory reasoning. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS, vol. 6803, pp. 299–314. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  13. Kaliszyk, C., Krauss, A.: Scalable LCF-style proof translation. Accepted to ITP 2013, http://cl-informatik.uibk.ac.at/~cek/import.pdf

  14. Kaliszyk, C., Urban, J.: PRocH: Proof reconstruction for HOL Light. In: Bonacina, M.P. (ed.) CADE 2013. LNCS, vol. 7898, pp. 267–274. Springer, Heidelberg (2013), http://mws.cs.ru.nl/~urban/proofs.pdf

    Chapter  Google Scholar 

  15. Kaliszyk, C., Urban, J.: Learning-assisted automated reasoning with Flyspeck. CoRR, abs/1211.7012 (2012)

    Google Scholar 

  16. Kühlwein, D., van Laarhoven, T., Tsivtsivadze, E., Urban, J., Heskes, T.: Overview and evaluation of premise selection techniques for large theory mathematics. In: Gramlich, B., Miller, D., Sattler, U. (eds.) IJCAR 2012. LNCS, vol. 7364, pp. 378–392. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  17. Meng, J., Paulson, L.C.: Translating higher-order clauses to first-order clauses. J. Autom. Reasoning 40(1), 35–60 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  18. Paulson, L.C., Blanchette, J.: Three years of experience with Sledgehammer, a practical link between automated and interactive theorem provers. In: 8th IWIL (2010) (Invited talk)

    Google Scholar 

  19. Paulson, L.C., Susanto, K.W.: Source-level proof reconstruction for interactive theorem proving. In: Schneider, K., Brandt, J. (eds.) TPHOLs 2007. LNCS, vol. 4732, pp. 232–245. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  20. 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 

  21. Riazanov, A., Voronkov, A.: The design and implementation of VAMPIRE. AI Commun. 15(2-3), 91–110 (2002)

    MATH  Google Scholar 

  22. Schulz, S.: E - A Brainiac Theorem Prover. AI Commun. 15(2-3), 111–126 (2002)

    MATH  Google Scholar 

  23. Sutcliffe, G., Schulz, S., Claessen, K., Van Gelder, A.: Using the TPTP language for writing derivations and finite interpretations. In: Furbach, Shankar (eds.) [7], pp. 67–81

    Google Scholar 

  24. 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)

    Google Scholar 

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

    Article  Google Scholar 

  26. Urban, J.: An Overview of Methods for Large-Theory Automated Theorem Proving (Invited Paper). In: Höfner, P., McIver, A., Struth, G. (eds.) ATE Workshop. CEUR Workshop Proceedings, vol. 760, pp. 3–8. CEUR-WS.org (2011)

    Google Scholar 

  27. Urban, J.: Parallelizing Mizar. CoRR, abs/1206.0141 (2012)

    Google Scholar 

  28. Urban, J.: BliStr: The Blind Strategymaker. CoRR, abs/1301.2683 (2013)

    Google Scholar 

  29. Urban, J., Rudnicki, P., Sutcliffe, G.: ATP and presentation service for Mizar formalizations. J. Autom. Reasoning 50, 229–241 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  30. Urban, J., Sutcliffe, G.: Automated reasoning and presentation support for formalizing mathematics in Mizar. In: Autexier, S., Calmet, J., Delahaye, D., Ion, P.D.F., Rideau, L., Rioboo, R., Sexton, A.P. (eds.) AISC/Calculemus/MKM 2010. LNCS, vol. 6167, pp. 132–146. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  31. Urban, J., Sutcliffe, G., Pudlák, P., Vyskočil, J.: MaLARea SG1 - Machine Learner for Automated Reasoning with Semantic Guidance. In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 441–456. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  32. Urban, J., Vyskočil, J., Štěpánek, P.: MaLeCoP Machine learning connection prover. In: Brünnler, K., Metcalfe, G. (eds.) TABLEAUX 2011. LNCS, vol. 6793, pp. 263–277. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  33. Vinge, V.: A Fire Upon the Deep. Tor Books (1992)

    Google Scholar 

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Author information

Authors and Affiliations

  1. University of Innsbruck, Austria

    Cezary Kaliszyk

  2. Radboud University, Nijmegen, The Netherlands

    Josef Urban

Authors
  1. Cezary Kaliszyk
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  2. Josef Urban
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Editor information

Editors and Affiliations

  1. Computing and Software, McMaster University, 1280 Main Street West, L8S 4K1, Hamilton, ON, Canada

    Jacques Carette

  2. School of Informatics, University of Edinburgh, 10 Crichton Street, EH8 9AB, Edinburgh, Scotland, UK

    David Aspinall

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

    Christoph Lange

  4. Faculty of Informatics, Department of Computer Graphics and Design, Masaryk University, Botanická 68a, 60200, Brno, Czech Republic

    Petr Sojka

  5. Johannes Kepler University Linz (JKU), RISC, Altenberger Strasse 69, 4040, Linz, Austria

    Wolfgang Windsteiger

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Kaliszyk, C., Urban, J. (2013). Automated Reasoning Service for HOL Light . In: Carette, J., Aspinall, D., Lange, C., Sojka, P., Windsteiger, W. (eds) Intelligent Computer Mathematics. CICM 2013. Lecture Notes in Computer Science(), vol 7961. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39320-4_8

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  • DOI: https://doi.org/10.1007/978-3-642-39320-4_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39319-8

  • Online ISBN: 978-3-642-39320-4

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