Abstract
HOL(y)Hammer is an online AI/ATP service for formal (computer-understandable) mathematics encoded in the HOL Light system. The service allows its users to upload and automatically process an arbitrary formal development (project) based on HOL Light, and to attack arbitrary conjectures that use the concepts defined in some of the uploaded projects. For that, the service uses several automated reasoning systems combined with several premise selection methods trained on all the project proofs. The projects that are readily available on the server for such query answering include the recent versions of the Flyspeck, Multivariate Analysis and Complex Analysis libraries. The service runs on a 48-CPU server, currently employing in parallel for each task 7 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 and their solutions are discussed, and an initial account of using the system is given.
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References
Akbarpour B., Paulson L.C.: MetiTarski: an automatic theorem prover for real-valued special functions. J. Autom. Reason. 44(3), 175–205 (2010)
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, volume 6824 of LNCS, pp. 133–148. Springer, Berlin (2011)
Alama J., Heskes T., Kühlwein D., Tsivtsivadze E., Urban J.: Premise selection for mathematics by corpus analysis and kernel methods. J. Autom. Reason. 52(2), 191–213 (2014)
Blanchette, J.C., Böhme, S., Popescu, A., Smallbone, N.: Encoding monomorphic and polymorphic types. In: Piterman, N., Smolka, S.A. (eds.) TACAS, volume 7795 of Lecture Notes in Computer Science, pp. 493–507. Springer, Berlin (2013)
Blanchette, J.C., Paskevich, A.: TFF1: the TPTP typed first-order form with rank-1 polymorphism. In: Bonacina, M.P. (ed.) Proceedings of Automated Deduction –CADE-24–24th International Conference on Automated Deduction, Lake Placid, NY, USA, June 9–14. Lecture Notes in Computer Science, vol. 7898, pp. 414–420. Springer (2013)
Carlson, A., Cumby, C., Rosen, J., Roth, D.: The SNoW learning architecture. Technical Report UIUCDCS-R-99-2101, UIUC Computer Science Department, 5 (1999)
de Moura L.M., Bjørner N.: Z3: An Efficient SMT Solver. In: Ramakrishnan, C.R., Rehof, J. (eds) TACAS, volume 4963 of LNCS, pp. 337–340. Springer, Berlin (2008)
Dudani S.A.: The distance-weighted k-nearest-neighbor rule. IEEE Trans. Syst. Man Cybern. SMC-6(4), 325–327 (1976)
Van Gelder, A., Sutcliffe, G.: Extending the TPTP language to higher-order logic with automated parser generation. In: Furbach, U., Shankar, N. (eds.) Proceedings of Third International Joint Conference on Automated Reasoning, IJCAR 2006, Seattle, WA, USA, August 17–20. Lecture Notes in Computer Science, vol. 4130, pp. 156–161. Springer (2006)
Hales, T.C.: Introduction to the Flyspeck project. In: Coquand, T., Lombardi, H., Roy, M.-F. (eds.) Mathematics, Algorithms, Proofs, number 05021 in Dagstuhl Seminar Proceedings, pp. 1–11, Dagstuhl, Germany, 2006. Internationales Begegnungs- und Forschungszentrum für Informatik (IBFI), Schloss Dagstuhl, Germany
John H.: HOL Light: A tutorial introduction. In: Srivas, M.K., Camilleri, A.J. (eds) FMCAD, volume 1166 of LNCS, pp. 265–269. Springer, Berlin (1996)
Harrison, J.: Optimizing proof search in model elimination. In: McRobbie, M., Slaney, J.K. (eds.): Proceedings of the 13th International Conference on Automated Deduction, number 1104 in LNAI, pp. 313–327. Springer (1996)
Hendriks M., Kaliszyk C., van Raamsdonk F., Wiedijk F.: Teaching logic using a state-of-the-art proof assistant. Acta Didact. Napoc. 3(2), 35–48 (2010)
Hoder K., Voronkov A.: Sine qua non for large theory reasoning. In: Bjørner, N., Sofronie-Stokkermans, V. (eds) CADE, volume 6803 of LNCS, pp. 299–314. Springer, Berlin (2011)
Kaliszyk, C.: Web interfaces for proof assistants. In: Autexier, S., Benzmüller, C. (eds.): Proceedings of the Workshop on User Interfaces for Theorem Provers (UITP’06), volume 174[2] of ENTCS, pp. 49–61 (2007)
Kaliszyk, C., Krauss, A.: Scalable LCF-style proof translation. In: Blazy, S., Paulin-Mohring, C., Pichardie, D. (eds.) Proceedings of the 4th International Conference on Interactive Theorem Proving (ITP’13), volume 7998 of LNCS, pp. 51–66. Springer (2013)
Kaliszyk, C., Urban, J.: Automated reasoning service for HOL light. In: Carette, J., Aspinall, D., Lange, C., Sojka, P., Windsteiger, W. (eds.) Proceedings of Intelligent Computer Mathematics–MKM, Calculemus, DML, and Systems and Projects 2013, Held as Part of CICM 2013, Bath, UK, July 8–12. Lecture Notes in Computer Science, vol. 7961, pp. 120–135. Springer (2013)
Kaliszyk, C., Urban, J.: Lemma mining over HOL light. In: McMillan, K.L., Middeldorp, A., Voronkov, A. (eds.), LPAR, volume 8312 of Lecture Notes in Computer Science, pp. 503–517. Springer (2013)
Kaliszyk, C., Urban, J.: MizAR 40 for Mizar 40. CoRR, arXiv:1310.2805 (2013)
Kaliszyk, C., Urban, J.: PRocH: Proof reconstruction for HOL Light. In: Bonacina [6], pp. 267–274
Kaliszyk, C., Urban, J.: Stronger automation for Flyspeck by feature weighting and strategy evolution. In: Blanchette, J.C., Urban, J. (eds.) PxTP 2013, volume 14 of EPiC Series, pp. 87–95. EasyChair (2013)
Kaliszyk, C., Urban, J.: Learning-assisted automated reasoning with Flyspeck. J. Autom. Reason. (2014). doi:10.1007/s10817-014-9303-3
Kovács, L., Voronkov, A.: First-order theorem proving and Vampire. In: Sharygina, N., Veith, H. (eds.) CAV, volume 8044 of Lecture Notes in Computer Science, pp. 1–35. Springer (2013)
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, volume 7364 of LNCS, pp. 378–392. Springer, Berlin (2012)
Meng J., Paulson L.C.: Translating higher-order clauses to first-order clauses. J. Autom. Reason. 40(1), 35–60 (2008)
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
Paulson L.C., Susanto K.W.: Source-level proof reconstruction for interactive theorem proving. In: Schneider, K., Brandt, J. (eds) TPHOLs, volume 4732 of LNCS, pp. 232–245. Springer, Berlin (2007)
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, Cambridge (1993)
Schulz S.: E - A Brainiac Theorem Prover. AI Commun. 15(2–3), 111–126 (2002)
Sutcliffe, G., Schulz, S., Claessen, K., Van Gelder, A.: Using the TPTP language for writing derivations and finite interpretations. In: Furbach, U., Shankar, N. (eds.) Proceedings of Third International Joint Conference on Automated Reasoning, IJCAR 2006, Seattle, WA, USA, August 17–20. Lecture Notes in Computer Science, vol. 4130, pp. 67–81. Springer (2006)
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.) Proceedings of Intelligent Computer Mathematics–MKM, Calculemus, DML, and Systems and Projects 2013, Held as Part of CICM 2013, Bath, UK, July 8–12. Lecture Notes in Computer Science, vol. 7961, pp. 152–167. Springer (2013)
Urban J.: MoMM—fast interreduction and retrieval in large libraries of formalized mathematics. Int. J. Artif. Intell. Tools 15(1), 109–130 (2006)
Urban, J.: An overview of methods for large-theory automated theorem proving (Invited Paper). In: Höfner, P., McIver, A., Struth, G. (eds.) ATE Workshop, volume 760 of CEUR Workshop Proceedings, pp. 3–8. CEUR-WS.org (2011)
Urban, J.: Content-based encoding of mathematical and code libraries. In: Lange, C. Urban, J. (eds.) Proceedings of the ITP 2011 Workshop on Mathematical Wikis (MathWikis), number 767 in CEUR Workshop Proceedings, pp. 49–53, Aachen (2011)
Urban, J.: Parallelizing Mizar. CoRR,arXiv:1206.0141 (2012)
Urban, J.: BliStr: The Blind Strategymaker. CoRR, arXiv:1301.2683 (2013)
Urban J., Rudnicki P., Sutcliffe G.: ATP and presentation service for Mizar formalizations. J. Autom. Reason. 50, 229–241 (2013)
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/MKM/Calculemus, volume 6167 of LNCS, pp. 132–146. Springer (2010)
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, volume 5195 of LNCS, pp. 441–456. Springer (2008)
Urban, J., Vyskočil, J., Štěpánek, P.: MaLeCoP: machine learning connection prover. In Brünnler, K., Metcalfe, G. (eds.) TABLEAUX, volume 6793 of LNCS, pp. 263–277. Springer (2011)
Vinge, V.: A Fire Upon the Deep. Tor Books, New York City (1992)
Worden, L., WorkingWiki: a MediaWiki-based platform for collaborative research. In: Lange, C. Urban, J. (eds.) ITP Workshop on Mathematical Wikis (MathWikis), number 767 in CEUR Workshop Proceedings, pp. 63–73, Aachen (2011)
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Kaliszyk, C., Urban, J. HOL(y)Hammer: Online ATP Service for HOL Light . Math.Comput.Sci. 9, 5–22 (2015). https://doi.org/10.1007/s11786-014-0182-0
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DOI: https://doi.org/10.1007/s11786-014-0182-0
Keywords
- Automated theorem proving
- Interactive theorem proving
- Machine learning
- Formal proof assistants
- Large-theory automated reasoning
- HOL light