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International Static Analysis Symposium

SAS 2013: Static Analysis pp 105–125Cite as

On Solving Universally Quantified Horn Clauses

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 7935))

Abstract

Program proving can be viewed as solving for unknown relations (such as loop invariants, procedure summaries and so on) that occur in the logical verification conditions of a program, such that the verification conditions are valid. Generic logical tools exist that can solve such problems modulo certain background theories, and therefore can be used for program analysis. Here, we extend these techniques to solve for quantified relations. This makes it possible to guide the solver by constraining the form of the proof, allowing it to converge when it otherwise would not. We show how to simulate existing abstract domains in this way, without having to directly implement program analyses or make certain heuristic choices, such as the terms and predicates that form the parameters of the abstract domain. Moreover, the approach gives the flexibility to go beyond these domains and experiment quickly with various invariant forms.

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References

  1. Albarghouthi, A., McMillan, K.L.: Beautiful interpolants. In: CAV (2013)

    Google Scholar 

  2. Alberti, F., Bruttomesso, R., Ghilardi, S., Ranise, S., Sharygina, N.: Lazy abstraction with interpolants for arrays. In: Bjørner, N., Voronkov, A. (eds.) LPAR-18 2012. LNCS, vol. 7180, pp. 46–61. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  3. Beyene, T.A., Popeea, C., Rybalchenko, A.: Solving existentially quantified Horn clauses. In: CAV (2013)

    Google Scholar 

  4. Bjørner, N., McMillan, K.L., Rybalchenko, A.: Program verification as Satisfiability Modulo Theories. In: SMT (2012)

    Google Scholar 

  5. Cousot, P.: Verification by abstract interpretation. In: Dershowitz, N. (ed.) Verification (Manna Festschrift). LNCS, vol. 2772, pp. 243–268. Springer, Heidelberg (2004)

    Google Scholar 

  6. Cousot, P., Cousot, R., Logozzo, F.: A parametric segmentation functor for fully automatic and scalable array content analysis. In: POPL (2011)

    Google Scholar 

  7. Delzanno, G., Podelski, A.: Model Checking in CLP. In: Cleaveland, W.R. (ed.) TACAS 1999. LNCS, vol. 1579, pp. 223–239. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  8. Detlefs, D., Nelson, G., Saxe, J.B.: Simplify: a theorem prover for program checking. J. ACM 52(3) (2005)

    Google Scholar 

  9. Dillig, I., Dillig, T., Aiken, A.: Fluid updates: Beyond strong vs. weak updates. In: Gordon, A.D. (ed.) ESOP 2010. LNCS, vol. 6012, pp. 246–266. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  10. Flanagan, C.: Automatic software model checking using clp. In: Degano, P. (ed.) ESOP 2003. LNCS, vol. 2618, pp. 189–203. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  11. Flanagan, C., Qadeer, S.: Predicate abstraction for software verification. In: POPL, pp. 191–202 (2002)

    Google Scholar 

  12. Graf, S., Saïdi, H.: Construction of abstract state graphs with PVS. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 72–83. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  13. Grebenshchikov, S., Lopes, N.P., Popeea, C., Rybalchenko, A.: Synthesizing software verifiers from proof rules. In: PLDI (2012)

    Google Scholar 

  14. Gulwani, S., McCloskey, B., Tiwari, A.: Lifting abstract interpreters to quantified logical domains. In: Necula, G.C., Wadler, P. (eds.) POPL, pp. 235–246. ACM (2008)

    Google Scholar 

  15. Gupta, A., Popeea, C., Rybalchenko, A.: Solving recursion-free Horn clauses over LI+UIF. In: Yang, H. (ed.) APLAS 2011. LNCS, vol. 7078, pp. 188–203. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  16. Hermenegildo, M., Puebla, G., Bueno, F., López-García, P.: Program development using abstract interpretation (and the ciao system preprocessor). In: Cousot, R. (ed.) SAS 2003. LNCS, vol. 2694, pp. 127–152. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  17. Hoder, K., Bjørner, N.: Generalized property directed reachability. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 157–171. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  18. Hoder, K., Kovács, L., Voronkov, A.: Case studies on invariant generation using a saturation theorem prover. In: Batyrshin, I., Sidorov, G. (eds.) MICAI 2011, Part I. LNCS, vol. 7094, pp. 1–15. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  19. Hojjat, H., Konečný, F., Garnier, F., Iosif, R., Kuncak, V., Rümmer, P.: A verification toolkit for numerical transition systems - tool paper. In: Giannakopoulou, D., Méry, D. (eds.) FM 2012. LNCS, vol. 7436, pp. 247–251. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  20. Jaffar, J., Maher, M.J.: Constraint logic programming: A survey. J. Log. Program. 19(20), 503–581 (1994)

    Article  MathSciNet  Google Scholar 

  21. Jaffar, J., Murali, V., Navas, J.A., Santosa, A.E.: Tracer: A symbolic execution tool for verification. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 758–766. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  22. Jaffar, J., Santosa, A.E., Voicu, R.: Modeling Systems in CLP. In: Gabbrielli, M., Gupta, G. (eds.) ICLP 2005. LNCS, vol. 3668, pp. 412–413. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  23. 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 

  24. Komuravelli, A., Gurfinkel, A., Chaki, S., Clarke, E.: Automatic Abstraction in SMT-Based Unbounded Software Model Checking. In: CAV (2013)

    Google Scholar 

  25. Larraz, D., Rodríguez-Carbonell, E., Rubio, A.: SMT-Based Array Invariant Generation. In: Giacobazzi, R., Berdine, J., Mastroeni, I. (eds.) VMCAI 2013. LNCS, vol. 7737, pp. 169–188. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  26. McMillan, K.L.: An interpolating theorem prover. Theor. Comput. Sci. 345(1) (2005)

    Google Scholar 

  27. McMillan, K.L.: Lazy abstraction with interpolants. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 123–136. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  28. 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 

  29. McMillan, K.L.: Interpolants from Z3 proofs. In: FMCAD (2011)

    Google Scholar 

  30. McMillan, K.L., Rybalchenko, A.: Computing relational fixed points using interpolation. Technical Report MSR-TR-2013-6, Microsoft Research (2013), http://research.microsoft.com/apps/pubs/?id=180055

  31. Pnueli, A., Ruah, S., Zuck, L.D.: Automatic deductive verification with invisible invariants. In: Margaria, T., Yi, W. (eds.) TACAS 2001. LNCS, vol. 2031, pp. 82–97. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  32. Rümmer, P., Hojjat, H., Kuncak, V.: Disjunctive interpolants for horn-clause verification. In: CAV (2013)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Microsoft Research, USA

    Nikolaj Bjørner, Ken McMillan & Andrey Rybalchenko

  2. Technische Universität München, Germany

    Andrey Rybalchenko

Authors
  1. Nikolaj Bjørner
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  2. Ken McMillan
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  3. Andrey Rybalchenko
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Editor information

Editors and Affiliations

  1. Microsoft Research, One Microsoft Way, 98052, Redmond, WA, USA

    Francesco Logozzo

  2. One Microsoft Way, Microsoft Research, 98052, Redmond,, WA,, USA

    Manuel Fähndrich

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Bjørner, N., McMillan, K., Rybalchenko, A. (2013). On Solving Universally Quantified Horn Clauses. In: Logozzo, F., Fähndrich, M. (eds) Static Analysis. SAS 2013. Lecture Notes in Computer Science, vol 7935. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38856-9_8

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  • DOI: https://doi.org/10.1007/978-3-642-38856-9_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38855-2

  • Online ISBN: 978-3-642-38856-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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