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Mechanizing the Metatheory of Sledgehammer

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Frontiers of Combining Systems (FroCoS 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8152))

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Abstract

This paper presents an Isabelle/HOL formalization of recent research in automated reasoning: efficient encodings of sorts in unsorted first-order logic, as implemented in Isabelle’s Sledgehammer proof tool. The formalization provides the general-purpose machinery to reason about formulas and models, emulating the theory of institutions. Quantifiers are represented using a nominal-like approach designed for interpreting syntax in semantic domains.

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References

  1. Ballarin, C.: Locales: A module system for mathematical theories. J. Autom. Reasoning (to appear)

    Google Scholar 

  2. Berghofer, S.: First-order logic according to Fitting. In: Klein, G., Nipkow, T., Paulson, L. (eds.) Archive of Formal Proofs (2007), http://afp.sf.net/entries/FOL-Fitting.shtml

  3. Blanchette, J.C., Böhme, S., Popescu, A., Smallbone, N.: Encoding monomorphic and polymorphic types. In: Piterman, N., Smolka, S. (eds.) TACAS 2013. LNCS, vol. 7795, pp. 493–507. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  4. Blanchette, J.C., Böhme, S., Popescu, A., Smallbone, N.: Encoding monomorphic and polymorphic types. Tech. report associated with TACAS 2013 paper [3] (2013), http://www21.in.tum.de/~blanchet/enc_types_report.pdf

  5. Blanchette, J.C., Krauss, A.: Monotonicity inference for higher-order formulas. J. Autom. Reasoning 47(4), 369–398 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  6. Blanchette, J.C., Popescu, A.: Formal development associated with this paper (2013), http://www21.in.tum.de/~popescua/fol_devel.zip

  7. Blanchette, J.C., Popescu, A.: Sound and complete sort encodings for first-order logic. In: Klein, G., Nipkow, T., Paulson, L. (eds.) Archive of Formal Proofs (2013), http://afp.sourceforge.net/entries/Sort_Encodings.shtml

  8. Blanchette, J.C., Popescu, A., Traytel, D.: Coinductive pearl: Modular first-order logic completeness (submitted), http://www21.in.tum.de/~blanchet/compl.pdf

  9. Bouillaguet, C., Kuncak, V., Wies, T., Zee, K., Rinard, M.: Using first-order theorem provers in the Jahob data structure verification system. In: Cook, B., Podelski, A. (eds.) VMCAI 2007. LNCS, vol. 4349, pp. 74–88. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  10. Claessen, K., Lillieström, A., Smallbone, N.: Sort it out with monotonicity—Translating between many-sorted and unsorted first-order logic. In: Bjørner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS (LNAI), vol. 6803, pp. 207–221. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  11. Goguen, J.A., Burstall, R.M.: Institutions: Abstract model theory for specification and programming. J. ACM 39(1), 95–146 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  12. Harrison, J.: Formalizing basic first order model theory. In: Grundy, J., Newey, M. (eds.) TPHOLs 1998. LNCS, vol. 1479, pp. 153–170. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  13. Harrison, J.: Towards self-verification of HOL Light. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 177–191. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  14. Huffman, B., Urban, C.: A new foundation for Nominal Isabelle. In: Kaufmann, M., Paulson, L.C. (eds.) ITP 2010. LNCS, vol. 6172, pp. 35–50. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  15. Kammüller, F., Wenzel, M.T., Paulson, L.C.: Locales - A sectioning concept for Isabelle. In: Bertot, Y., Dowek, G., Hirschowitz, A., Paulin, C., Théry, L. (eds.) TPHOLs 1999. LNCS, vol. 1690, pp. 149–166. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  16. Monk, J.D.: Mathematical Logic. Springer (1976)

    Google Scholar 

  17. Myreen, M.O., Davis, J.: A verified runtime for a verified theorem prover. In: van Eekelen, M., Geuvers, H., Schmaltz, J., Wiedijk, F. (eds.) ITP 2011. LNCS, vol. 6898, pp. 265–280. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  18. Nipkow, T., Paulson, L.C., Wenzel, M.: Isabelle/HOL: A Proof Assistant for Higher-Order Logic. LNCS, vol. 2283. Springer, Heidelberg (2002)

    Book  Google Scholar 

  19. Paulson, L.C., Blanchette, J.C.: Three years of experience with Sledgehammer, a practical link between automatic and interactive theorem provers. In: Sutcliffe, G., Ternovska, E., Schulz, S. (eds.) IWIL 2010 (2010)

    Google Scholar 

  20. Pfenning, F., Elliott, C.: Higher-order abstract syntax. In: Wexelblat, R.L. (ed.) PLDI 1988, pp. 199–208. ACM (1988)

    Google Scholar 

  21. Pitts, A.M.: Nominal logic, a first order theory of names and binding. Inf. Comput. 186(2), 165–193 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  22. Pitts, A.M.: Alpha-structural recursion and induction. J. ACM 53(3), 459–506 (2006)

    Article  MathSciNet  Google Scholar 

  23. Popescu, A., Gunter, E.L.: Recursion principles for syntax with bindings and substitution. In: Chakravarty, M.M.T., Hu, Z., Danvy, O. (eds.) ICFP 2011, pp. 346–358. ACM (2011)

    Google Scholar 

  24. Popescu, A., Gunter, E.L., Osborn, C.J.: Strong normalization of System F by HOAS on top of FOAS. In: LICS 2010, pp. 31–40. IEEE (2010)

    Google Scholar 

  25. Ridge, T., Margetson, J.: A mechanically verified, sound and complete theorem prover for first order logic. In: Hurd, J., Melham, T. (eds.) TPHOLs 2005. LNCS, vol. 3603, pp. 294–309. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  26. Shankar, N.: Metamathematics, Machines, and Gödel’s Proof. Cambridge Tracts in Theoretical Computer Science, vol. 38. Cambridge University Press (1994)

    Google Scholar 

  27. Sutcliffe, G.: The 6th IJCAR automated theorem proving system competition—CASC-J6. AI Comm. 26(2), 211–223 (2013)

    MathSciNet  Google Scholar 

  28. Tinelli, C., Zarba, C.G.: Combining decision procedures for sorted theories. In: Alferes, J.J., Leite, J. (eds.) JELIA 2004. LNCS (LNAI), vol. 3229, pp. 641–653. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

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Authors and Affiliations

  1. Fakultät für Informatik, Technische Universität München, Germany

    Jasmin Christian Blanchette & Andrei Popescu

Authors
  1. Jasmin Christian Blanchette
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  2. Andrei Popescu
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Editor information

Editors and Affiliations

  1. LORIA, Inria Nancy Grand Est, Université de Lorraine, 615 rue du Jardin Botanique, 54602, Villers-les-Nancy, France

    Pascal Fontaine

  2. LORIA, Inria Nancy Grand Est, 615 rue du Jardin Botanique, 54602, Villers-lès-Nancy, France

    Christophe Ringeissen

  3. School of Computer Science, The University of Manchester, Oxford Rd, Kilburn Building, M13 9PL, Manchester, UK

    Renate A. Schmidt

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Blanchette, J.C., Popescu, A. (2013). Mechanizing the Metatheory of Sledgehammer. In: Fontaine, P., Ringeissen, C., Schmidt, R.A. (eds) Frontiers of Combining Systems. FroCoS 2013. Lecture Notes in Computer Science(), vol 8152. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40885-4_17

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  • DOI: https://doi.org/10.1007/978-3-642-40885-4_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40884-7

  • Online ISBN: 978-3-642-40885-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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