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International Joint Conference on Automated Reasoning

IJCAR 2010: Automated Reasoning pp 188–195Cite as

Interpolation and Symbol Elimination in Vampire

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6173))

Abstract

It has recently been shown that proofs in which some symbols are colored (e.g. local or split proofs and symbol-eliminating proofs) can be used for a number of applications, such as invariant generation and computing interpolants. This tool paper describes how such proofs and interpolant generation are implemented in the first-order theorem prover Vampire.

This work has been partly done while the second authors was at ETH Zürich.

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References

  1. Cimatti, A., Griggio, A., Sebastiani, R.: Efficient Interpolant Generation in Satisfiability Modulo Theories. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 397–412. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  2. 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 

  3. Gopan, D., Reps, T.W., Sagiv, M.: A Framework for Numeric Analysis of Array Operations. In: POPL, pp. 338–350 (2005)

    Google Scholar 

  4. Gulwani, S., Tiwari, A.: Combining Abstract Interpreters. In: Proc. of PLDI, pp. 376–386 (2006)

    Google Scholar 

  5. Henzinger, T.A., Jhala, R., Majumdar, R., McMillan, K.L.: Abstractions from Proofs. In: Proc. of POPL, pp. 232–244 (2004)

    Google Scholar 

  6. Jhala, R., McMillan, K.L.: Interpolant-Based Transition Relation Approximation. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 39–51. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  7. Jhala, R., McMillan, K.L.: A Practical and Complete Approach to Predicate Refinement. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 459–473. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  8. Jhala, R., McMillan, K.L.: Array Abstractions from Proofs. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 193–206. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  9. Kovacs, L., Voronkov, A.: Finding Loop Invariants for Programs over Arrays Using a Theorem Prover. In: Chechik, M., Wirsing, M. (eds.) FASE 2009. LNCS, vol. 5503, pp. 470–485. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  10. Kovacs, L., Voronkov, A.: Interpolation and Symbol Elimination. In: Schmidt, R.A. (ed.) CADE 2009. LNCS, vol. 5663, pp. 199–213. Springer, Heidelberg (2009)

    Google Scholar 

  11. Ludwig, M., Waldmann, U.: An Extension of the Knuth-Bendix Ordering with LPO-Like Properties. In: Dershowitz, N., Voronkov, A. (eds.) LPAR 2007. LNCS (LNAI), vol. 4790, pp. 348–362. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  12. McMillan, K.L.: Interpolation and SAT-Based Model Checking. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 1–13. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  13. McMillan, K.L.: Quantified Invariant Generation Using an Interpolating Saturation Prover. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 413–427. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  14. Riazanov, A., Voronkov, A.: The Design and Implementation of Vampire. AI Communications 15(2-3), 91–110 (2002)

    MATH  Google Scholar 

  15. Rybalchenko, A., Sofronie-Stokkermans, V.: Constraint Solving for Interpolation. In: Cook, B., Podelski, A. (eds.) VMCAI 2007. LNCS, vol. 4349, pp. 346–362. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  16. Srivastava, S., Gulwani, S.: Program Verification using Templates over Predicate Abstraction. In: PLDI, pp. 223–234 (2009)

    Google Scholar 

  17. Sutcliffe, G.: The TPTP Problem Library and Associated Infrastructure. The FOF and CNF Parts, v3.5.0. J. of Automated Reasoning (to appear, 2009)

    Google Scholar 

  18. Weidenbach, C., Schmidt, R.A., Hillenbrand, T., Rusev, R., Topic, D.: System Description: SpassVersion 3.0. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 514–520. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  19. Yorsh, G., Musuvathi, M.: A Combination Method for Generating Interpolants. In: Nieuwenhuis, R. (ed.) CADE 2005. LNCS (LNAI), vol. 3632, pp. 353–368. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. University of Manchester, USA

    Kryštof Hoder & Andrei Voronkov

  2. TU Vienna, Austria

    Laura Kovács

Authors
  1. Kryštof Hoder
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  2. Laura Kovács
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  3. Andrei Voronkov
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Editor information

Editors and Affiliations

  1. RWTH Aachen, LuFG Informatik, 2, Ahornstr. 55, 52074, Aachen, Germany

    Jürgen Giesl

  2. Department of Computer Science, Chalmers University of Technology, 41296, Gothenburg, Sweden

    Reiner Hähnle

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Hoder, K., Kovács, L., Voronkov, A. (2010). Interpolation and Symbol Elimination in Vampire. In: Giesl, J., Hähnle, R. (eds) Automated Reasoning. IJCAR 2010. Lecture Notes in Computer Science(), vol 6173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14203-1_16

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  • DOI: https://doi.org/10.1007/978-3-642-14203-1_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14202-4

  • Online ISBN: 978-3-642-14203-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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