Abstract
Sledgehammer is a component of Isabelle/HOL that employs first-order automatic theorem provers (ATPs) to discharge goals arising in interactive proofs. It heuristically selects relevant facts and, if an ATP is successful, produces a snippet that replays the proof in Isabelle. We extended Sledgehammer to invoke satisfiability modulo theories (SMT) solvers as well, exploiting its relevance filter and parallel architecture. Isabelle users are now pleasantly surprised by SMT proofs for problems beyond the ATPs’ reach. Remarkably, the best SMT solver performs better than the best ATP on most of our benchmarks.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Ahrendt, W., Beckert, B., Hähnle, R., Menzel, W., Reif, W., Schellhorn, G., Schmitt, P.H.: Integrating automated and interactive theorem proving. In: Bibel, W., Schmitt, P.H. (eds.) Automated Deduction—A Basis for Applications. Systems and Implementation Techniques, vol. II, pp. 97–116. Kluwer, Dordrecht (1998)
Andrews, P.B.: An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof, 2nd edn. Applied Logic, vol. 27. Springer, Heidelberg (2002)
Backes, J., Brown, C.E.: Analytic tableaux for higher-order logic with choice. In: Giesl, J., Hähnle, R. (eds.) IJCAR 2010. LNCS (LNAI), vol. 6173, pp. 76–90. Springer, Heidelberg (2010)
Barrett, C., Tinelli, C.: CVC3. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 298–302. Springer, Heidelberg (2007)
Barsotti, D., Nieto, L.P., Tiu, A.: Verification of clock synchronization algorithms: Experiments on a combination of deductive tools. Formal Asp. Comput. 19(3), 321–341 (2007)
Benzmüller, C., Paulson, L.C., Theiss, F., Fietzke, A.: LEO-II—a cooperative automatic theorem prover for higher-order logic. In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 162–170. Springer, Heidelberg (2008)
Bezem, M., Hendriks, D., de Nivelle, H.: Automatic proof construction in type theory using resolution. J. Auto. Reas. 29(3-4), 253–275 (2002)
Böhme, S., Moskal, M., Schulte, W., Wolff, B.: HOL-Boogie—an interactive prover-backend for the Verifying C Compiler. J. Auto. Reas. 44(1-2), 111–144 (2010)
Böhme, S., Nipkow, T.: Sledgehammer: Judgement Day. In: Giesl, J., Hähnle, R. (eds.) IJCAR 2010. LNCS (LNAI), vol. 6173, pp. 107–121. Springer, Heidelberg (2010)
Böhme, S., Weber, T.: Fast LCF-style proof reconstruction for Z3. In: Kaufmann, M., Paulson, L.C. (eds.) ITP 2010. LNCS, vol. 6172, pp. 179–194. Springer, Heidelberg (2010)
Bradley, A.R., Manna, Z.: Property-directed incremental invariant generation. Formal Asp. Comput. 20, 379–405 (2008)
Claessen, K.: Equinox, a new theorem prover for full first-order logic with equality. Presentation at Dagstuhl Seminar on Deduction and Applications (2005)
Cohen, E., Dahlweid, M., Hillebrand, M.A., Leinenbach, D., Moskal, M., Santen, T., Schulte, W., Tobies, S.: VCC: A practical system for verifying concurrent C. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds.) TPHOLs 2009. LNCS, vol. 5674, pp. 23–42. Springer, Heidelberg (2009)
Couchot, J.-F., Lescuyer, S.: Handling polymorphism in automated deduction. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 263–278. Springer, Heidelberg (2007)
de Moura, L.M., 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)
Dutertre, B., de Moura, L.: The Yices SMT solver (2006), http://yices.csl.sri.com/tool-paper.pdf
Erkök, L., Matthews, J.: Using Yices as an automated solver in Isabelle/HOL. In: Rushby, J., Shankar, N. (eds.) Automated Formal Methods, pp. 3–13 (2008)
Fontaine, P., Marion, J.-Y., Merz, S., Nieto, L.P., Tiu, A.: Expressiveness + automation + soundness: Towards combining SMT solvers and interactive proof assistants. In: Hermanns, H., Palsberg, J. (ed.) TACAS 2006. LNCS, vol. 3920, pp. 167–181. Springer, Heidelberg (2006)
Hoder, K., Voronkov, A.: Sine qua non for large theory reasoning. In: These proceedings (2011)
Hurd, J.: Integrating Gandalf and HOL. In: Bertot, Y., Dowek, G., Hirschowitz, A., Paulin, C., Théry, L. (eds.) TPHOLs 1999. LNCS, vol. 1690, pp. 311–321. Springer, Heidelberg (1999)
Hurd, J.: First-order proof tactics in higher-order logic theorem provers. In: Archer, M., Di Vito, B., Muñoz, C. (eds.) Design and Application of Strategies/Tactics in Higher Order Logics, number CP-2003-212448 in NASA Technical Reports, pp. 56–68 (2003)
Keller, C.: Cooperation between SAT, SMT provers and Coq. Presentation at the Synthesis. Verification and Analysis of Rich Models workshop (2011)
Klein, G., Nipkow, T., Paulson, L. (eds.): The Archive of Formal Proofs, http://afp.sf.net/
Korovin, K.: Instantiation-based automated reasoning: From theory to practice. In: Schmidt, R.A. (ed.) CADE-22. LNCS (LNAI), vol. 5663, pp. 163–166. Springer, Heidelberg (2009)
Leino, K.R.M., Rümmer, P.: A polymorphic intermediate verification language: Design and logical encoding. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 312–327. Springer, Heidelberg (2010)
McLaughlin, S., Barrett, C., Ge, Y.: Cooperating theorem provers: A case study combining HOL-Light and CVC Lite. Electr. Notes Theor. Comput. Sci. 144(2), 43–51 (2006)
Meng, J., Paulson, L.C.: Translating higher-order clauses to first-order clauses. J. Auto. Reas. 40(1), 35–60 (2008)
Meng, J., Paulson, L.C.: Lightweight relevance filtering for machine-generated resolution problems. J. Applied Logic 7(1), 41–57 (2009)
Moskal, M.: Programming with triggers. In: Dutertre, B., Strichman, O. (eds.) Satisfiability Modulo Theories (2009)
Nipkow, T.: Re: [isabelle] A beginner’s questionu [sic], (November 26, 2010), https://lists.cam.ac.uk/pipermail/cl-isabelle-users/2010-November/msg00097.html
Nipkow, T., Paulson, L.C., Wenzel, M.T. (eds.): Isabelle/HOL: A Proof Assistant for Higher-Order Logic, LNCS, vol. 2283. Springer, Heidelberg (2002)
Nonnengart, A., Weidenbach, C.: Computing small clause normal forms. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, pp. 335–367. Elsevier, Amsterdam (2001)
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.) International Workshop on the Implementation of Logics (2010)
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)
Ranise, S., Tinelli, C.: The SMT-LIB standard: Version 1.2 (2006), http://goedel.cs.uiowa.edu/smtlib/papers/format-v1.2-r06.08.30.pdf
Riazanov, A., Voronkov, A.: The design and implementation of Vampire. AI Comm. 15(2-3), 91–110 (2002)
Rushby, J.M.: Tutorial: Automated formal methods with PVS, SAL, and Yices. In: Hung, D.V., Pandya, P. (eds.) Software Engineering and Formal Methods, p. 262. IEEE, New York (2006)
Schulz, S.: System description: E 0.81. In: Basin, D., Rusinowitch, M. (eds.) IJCAR 2004. LNCS (LNAI), vol. 3097, pp. 223–228. Springer, Heidelberg (2004)
Siekmann, J., Benzmüller, C., Fiedler, A., Meier, A., Normann, I., Pollet, M.: Proof development with Ωmega: The irrationality of \(\sqrt2\). In: Kamareddine, F. (ed.) Thirty Five Years of Automating Mathematics. Applied Logic, vol. 28, pp. 271–314. Springer, Heidelberg (2003)
Sutcliffe, G.: System description: SystemOnTPTP. In: McAllester, D. (ed.) CADE 2000. LNCS (LNAI), vol. 1831, pp. 406–410. Springer, Heidelberg (2000)
Sutcliffe, G., Chang, C., Ding, L., McGuinness, D., da Silva, P.P.: Different proofs are good proofs. In: McGuinness, D., Stump, A., Sutcliffe, G., Tinelli, C. (eds.) Workshop on Evaluation Methods for Solvers, and Quality Metrics for Solutions, pp. 1–10 (2010)
Urban, J.: MPTP 0.2: Design, implementation, and initial experiments. J. Auto. Reas. 37(1-2), 21–43 (2006)
Wampler-Doty, M.: A complete proof of the Robbins conjecture. In: Klein, G., Nipkow, T., Paulson, L. (eds.) The Archive of Formal Proofs (2010), http://afp.sf.net/entries/Robbins-Conjecture.shtml
Weidenbach, C.: Combining superposition, sorts and splitting. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, pp. 1965–2013. Elsevier, Amsterdam (2001)
Wenzel, M.: Type classes and overloading in higher-order logic. In: Gunter, E.L., Felty, A.P. (eds.) TPHOLs 1997. LNCS, vol. 1275, pp. 307–322. Springer, Heidelberg (1997)
Wenzel, M.: Parallel proof checking in Isabelle/Isar. In: Dos Reis, G., Théry, L. (eds.) Programming Languages for Mechanized Mathematics Systems, ACM Digital Library (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Blanchette, J.C., Böhme, S., Paulson, L.C. (2011). Extending Sledgehammer with SMT Solvers. In: Bjørner, N., Sofronie-Stokkermans, V. (eds) Automated Deduction – CADE-23. CADE 2011. Lecture Notes in Computer Science(), vol 6803. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22438-6_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-22438-6_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22437-9
Online ISBN: 978-3-642-22438-6
eBook Packages: Computer ScienceComputer Science (R0)