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Reasoning in the Theory of Heap: Satisfiability and Interpolation

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Logic-Based Program Synthesis and Transformation (LOPSTR 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12561))

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Abstract

In recent work, we have proposed an SMT-LIB theory of heap tailored to Horn-clause verification. The theory makes it possible to lift verification approaches for heap-allocated data-structures to a language-independent level, and this way factor out the treatment of heap in verification tools. This paper gives an overview of the theory, and presents ongoing research on decision and interpolation procedures.

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References

  1. Backeman, P., Rümmer, P., Zeljic, A.: Bit-vector interpolation and quantifier elimination by lazy reduction. In: Bjørner, N., Gurfinkel, A. (eds.) 2018 Formal Methods in Computer Aided Design, FMCAD 2018, Austin, TX, USA, 30 October–2 November 2018, pp. 1–10. IEEE (2018). https://doi.org/10.23919/FMCAD.2018.8603023

  2. Barrett, C., Shikanian, I., Tinelli, C.: An abstract decision procedure for a theory of inductive data types. JSAT 3(1–2), 21–46 (2007)

    MathSciNet  MATH  Google Scholar 

  3. Bjørner, N., Gurfinkel, A., McMillan, K., Rybalchenko, A.: Horn clause solvers for program verification. In: Beklemishev, L.D., Blass, A., Dershowitz, N., Finkbeiner, B., Schulte, W. (eds.) Fields of Logic and Computation II. LNCS, vol. 9300, pp. 24–51. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23534-9_2

    Chapter  Google Scholar 

  4. Bjørner, N., McMillan, K., Rybalchenko, A.: On solving universally quantified horn clauses. In: Logozzo, F., Fähndrich, M. (eds.) SAS 2013. LNCS, vol. 7935, pp. 105–125. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38856-9_8

    Chapter  Google Scholar 

  5. Brillout, A., Kroening, D., Rümmer, P., Wahl, T.: Beyond quantifier-free interpolation in extensions of Presburger arithmetic. In: Jhala, R., Schmidt, D. (eds.) VMCAI 2011. LNCS, vol. 6538, pp. 88–102. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-18275-4_8

    Chapter  Google Scholar 

  6. Brillout, A., Kroening, D., Rümmer, P., Wahl, T.: An interpolating sequent calculus for quantifier-free Presburger arithmetic. J. Autom. Reasoning 47, 341–367 (2011)

    Article  MathSciNet  Google Scholar 

  7. Brummayer, R., Biere, A.: Lemmas on demand for the extensional theory of arrays. J. Satisfiability Boolean Model. Comput. 6(1–3), 165–201 (2009). https://doi.org/10.3233/sat190067

    Article  MathSciNet  MATH  Google Scholar 

  8. Bruttomesso, R., Ghilardi, S., Ranise, S.: Quantifier-free interpolation of a theory of arrays. Log. Methods Comput. Sci. 8(2) (2012). https://doi.org/10.2168/LMCS-8(2:4)2012

  9. Christ, J., Hoenicke, J.: Weakly equivalent arrays. In: Rümmer, P., Wintersteiger, C.M. (eds.) Proceedings of the 12th International Workshop on Satisfiability Modulo Theories, SMT 2014, affiliated with the 26th International Conference on Computer Aided Verification (CAV 2014), the 7th International Joint Conference on Automated Reasoning (IJCAR 2014), and the 17th International Conference on Theory and Applications of Satisfiability Testing (SAT 2014), Vienna, Austria, 17–18 July 2014. CEUR Workshop Proceedings, vol. 1163, pp. 39–49. CEUR-WS.org (2014). http://ceur-ws.org/Vol-1163/paper-06.pdf

  10. Craig, W.: Linear reasoning. A new form of the Herbrand-Gentzen theorem. J. Symbolic Log. 22(3), 250–268 (1957)

    Article  MathSciNet  Google Scholar 

  11. De Angelis, E., Fioravanti, F., Pettorossi, A., Proietti, M.: Program verification using constraint handling rules and array constraint generalizations. Fundam. Inform. 150(1), 73–117 (2017). https://doi.org/10.3233/FI-2017-1461

    Article  MathSciNet  MATH  Google Scholar 

  12. Esen, Z., Rümmer, P.: Towards an SMT-LIB theory of heap. In: Fribourg, L., Heizmann, M. (eds.) Proceedings 8th International Workshop on Verification and Program Transformation and 7th Workshop on Horn Clauses for Verification and Synthesis, VPT/HCVS@ETAPS 2020 2020, and 7th Workshop on Horn Clauses for Verification and SynthesisDublin, Ireland, 25–26th April 2020. EPTCS, vol. 320 (2020)

    Google Scholar 

  13. Fitting, M.C.: First-Order Logic and Automated Theorem Proving. TCS, 2nd edn. Springer, New York (1996). https://doi.org/10.1007/978-1-4612-2360-3

    Book  MATH  Google Scholar 

  14. Hoenicke, J., Schindler, T.: Efficient interpolation for the theory of arrays. In: Galmiche, D., Schulz, S., Sebastiani, R. (eds.) IJCAR 2018. LNCS (LNAI), vol. 10900, pp. 549–565. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-94205-6_36

    Chapter  Google Scholar 

  15. Hojjat, H., Rümmer, P.: Deciding and interpolating algebraic data types by reduction. In: Jebelean, T., Negru, V., Petcu, D., Zaharie, D., Ida, T., Watt, S.M. (eds.) 19th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2017, Timisoara, Romania, 21–24 September 2017, pp. 145–152. IEEE Computer Society (2017). https://doi.org/10.1109/SYNASC.2017.00033

  16. Hojjat, H., Rümmer, P.: The ELDARICA horn solver. In: Bjørner, N., Gurfinkel, A. (eds.) 2018 Formal Methods in Computer Aided Design, FMCAD 2018, Austin, TX, USA, 30 October–2 November 2018, pp. 1–7. IEEE (2018). https://doi.org/10.23919/FMCAD.2018.8603013

  17. Kahsai, T., Kersten, R., Rümmer, P., Schäf, M.: Quantified heap invariants for object-oriented programs. In: Eiter, T., Sands, D. (eds.) LPAR-21, 21st International Conference on Logic for Programming, Artificial Intelligence and Reasoning, Maun, Botswana, 7–12 May 2017. EPiC Series in Computing, vol. 46, pp. 368–384. EasyChair (2017) https://easychair.org/publications/paper/Pmh

  18. Kapur, D., Majumdar, R., Zarba, C.G.: Interpolation for data structures. In: SIGSOFT 2006/FSE-14, pp. 105–116. ACM, New York (2006)

    Google Scholar 

  19. Komuravelli, A., Bjørner, N., Gurfinkel, A., McMillan, K.L.: Compositional verification of procedural programs using Horn clauses over integers and arrays. In: Kaivola, R., Wahl, T. (eds.) Formal Methods in Computer-Aided Design, FMCAD 2015, Austin, Texas, USA, 27–30 September 2015, pp. 89–96. IEEE (2015)

    Google Scholar 

  20. Komuravelli, A., Gurfinkel, A., Chaki, S., Clarke, E.M.: Automatic abstraction in SMT-based unbounded software model checking. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 846–862. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39799-8_59

    Chapter  Google Scholar 

  21. McMillan, K.L.: An interpolating theorem prover. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 16–30. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24730-2_2

    Chapter  Google Scholar 

  22. Monniaux, D., Gonnord, L.: Cell morphing: from array programs to array-free horn clauses. In: Rival, X. (ed.) SAS 2016. LNCS, vol. 9837, pp. 361–382. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53413-7_18

    Chapter  Google Scholar 

  23. 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). https://doi.org/10.1007/978-3-540-78800-3_24

    Chapter  Google Scholar 

  24. de Moura, L.M., Bjørner, N.: Generalized, efficient array decision procedures. In: Proceedings of 9th International Conference on Formal Methods in Computer-Aided Design, FMCAD 2009, Austin, Texas, USA, 15–18 November 2009, pp. 45–52. IEEE (2009). https://doi.org/10.1109/FMCAD.2009.5351142

  25. Reynolds, A., Blanchette, J.C.: A decision procedure for (co)datatypes in SMT solvers. J. Autom. Reasoning 58(3), 341–362 (2017). https://doi.org/10.1007/s10817-016-9372-6

    Article  MathSciNet  MATH  Google Scholar 

  26. Rondon, P.M., Kawaguchi, M., Jhala, R.: Liquid types. In: Gupta, R., Amarasinghe, S.P. (eds.) Proceedings of the ACM SIGPLAN 2008 Conference on Programming Language Design and Implementation, Tucson, AZ, USA, 7–13 June 2008, pp. 159–169. ACM (2008). https://doi.org/10.1145/1375581.1375602

  27. Rümmer, P.: A constraint sequent calculus for first-order logic with linear integer arithmetic. In: Cervesato, I., Veith, H., Voronkov, A. (eds.) LPAR 2008. LNCS (LNAI), vol. 5330, pp. 274–289. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-89439-1_20

    Chapter  MATH  Google Scholar 

  28. Rümmer, P.: Competition report: CHC-COMP-20. In: Fribourg, L., Heizmann, M. (eds.) Proceedings 8th International Workshop on Verification and Program Transformation and 7th Workshop on Horn Clauses for Verification and Synthesis, VPT/HCVS@ETAPS 2020 2020, and 7th Workshop on Horn Clauses for Verification and SynthesisDublin, Ireland, 25–26th April 2020. EPTCS, vol. 320, pp. 197–219 (2020). https://doi.org/10.4204/EPTCS.320.15

  29. Rümmer, P., Hojjat, H., Kuncak, V.: Disjunctive interpolants for horn-clause verification. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 347–363. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39799-8_24

    Chapter  Google Scholar 

  30. Stump, A., Barrett, C.W., Dill, D.L., Levitt, J.R.: A decision procedure for an extensional theory of arrays. In: 16th Annual IEEE Symposium on Logic in Computer Science, Boston, Massachusetts, USA, 16–19 June 2001, Proceedings, pp. 29–37. IEEE Computer Society (2001). https://doi.org/10.1109/LICS.2001.932480

  31. Suter, P., Dotta, M., Kuncak, V.: Decision procedures for algebraic data types with abstractions. In: SIGPLAN Not., vol. 45, no. 1, pp. 199–210 (2010)

    Google Scholar 

  32. Totla, N., Wies, T.: Complete instantiation-based interpolation. J. Autom. Reasoning 57(1), 37–65 (2016). https://doi.org/10.1007/s10817-016-9371-7

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work was supported by the Swedish Research Council (VR) under grant 2018-04727, and by the Swedish Foundation for Strategic Research (SSF) under the project WebSec (Ref. RIT17-0011).

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  1. Uppsala University, Uppsala, Sweden

    Zafer Esen & Philipp Rümmer

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  1. Zafer Esen
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Correspondence to Philipp Rümmer .

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  1. King’s College London, London, UK

    Maribel Fernández

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Esen, Z., Rümmer, P. (2021). Reasoning in the Theory of Heap: Satisfiability and Interpolation. In: Fernández, M. (eds) Logic-Based Program Synthesis and Transformation. LOPSTR 2020. Lecture Notes in Computer Science(), vol 12561. Springer, Cham. https://doi.org/10.1007/978-3-030-68446-4_9

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  • DOI: https://doi.org/10.1007/978-3-030-68446-4_9

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