Advertisement

Predicate Pairing with Abstraction for Relational Verification

  • Emanuele De Angelis
  • Fabio Fioravanti
  • Alberto Pettorossi
  • Maurizio Proietti
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10855)

Abstract

Relational verification is a technique that aims at proving properties that relate two different program fragments, or two different program runs. It has been shown that constrained Horn clauses (CHCs) can effectively be used for relational verification by applying a CHC transformation, called Predicate Pairing, which allows the CHC solver to infer relations among arguments of different predicates. In this paper we study how the effects of the Predicate Pairing transformation can be enhanced by using various abstract domains based on Linear Arithmetic (i.e., the domain of convex polyhedra and some of its subdomains) during the transformation. After presenting an algorithm for Predicate Pairing with abstraction, we report on the experiments we have performed on over a hundred relational verification problems by using various abstract domains. The experiments have been performed by using the VeriMAP verification system, together with the Parma Polyhedra Library (PPL) and the Z3 solver for CHCs.

Notes

Acknowledgements

We thank the anonymous referees for their constructive comments.

References

  1. 1.
    Albert, E., Gómez-Zamalloa, M., Hubert, L., Puebla, G.: Verification of Java Bytecode using analysis and transformation of logic programs. In: Hanus, M. (ed.) PADL 2007. LNCS, vol. 4354, pp. 124–139. Springer, Heidelberg (2007).  https://doi.org/10.1007/978-3-540-69611-7_8CrossRefGoogle Scholar
  2. 2.
    Bagnara, R., Hill, P.M., Ricci, E., Zaffanella, E.: Precise widening operators for convex polyhedra. Sci. Comput. Program. 58(1), 28–56 (2005)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bagnara, R., Hill, P.M., Zaffanella, E.: The Parma Polyhedra Library: Toward a complete set of numerical abstractions for the analysis and verification of hardware and software systems. Sci. Comput. Program. 72(1–2), 3–21 (2008)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Barthe, G., Crespo, J.M., Kunz, C.: Relational verification using product programs. In: Butler, M., Schulte, W. (eds.) FM 2011. LNCS, vol. 6664, pp. 200–214. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-21437-0_17CrossRefGoogle Scholar
  5. 5.
    Benton, N.: Simple relational correctness proofs for static analyses and program transformations. In: Proceedings of POPL 2004, pp. 14–25. ACM (2004)CrossRefGoogle Scholar
  6. 6.
    Cousot, P., Cousot, R.: Abstract interpretation: A unified lattice model for static analysis of programs by construction of approximation of fixpoints. In: Proceedings of POPL 1977, pp. 238–252. ACM (1977)Google Scholar
  7. 7.
    Cousot, P., Halbwachs, N.: Automatic discovery of linear restraints among variables of a program. In: Proceedings of POPL 1978, pp. 84–96. ACM (1978)Google Scholar
  8. 8.
    De Angelis, E., Fioravanti, F., Pettorossi, A., Proietti, M.: Program verification via iterated specialization. Sci. Comput. Program. 95(Part 2), 149–175 (2014)CrossRefGoogle Scholar
  9. 9.
    De Angelis, E., Fioravanti, F., Pettorossi, A., Proietti, M.: VeriMAP: a tool for verifying programs through transformations. In: Ábrahám, E., Havelund, K. (eds.) TACAS 2014. LNCS, vol. 8413, pp. 568–574. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-642-54862-8_47CrossRefGoogle Scholar
  10. 10.
    De Angelis, E., Fioravanti, F., Pettorossi, A., Proietti, M.: Proving correctness of imperative programs by linearizing constrained Horn clauses. Theory Pract. Logic Program. 15(4–5), 635–650 (2015)MathSciNetCrossRefGoogle Scholar
  11. 11.
    De Angelis, E., Fioravanti, F., Pettorossi, A., Proietti, M.: A rule-based verification strategy for array manipulating programs. Fundamenta Informaticae 140(3–4), 329–355 (2015)MathSciNetCrossRefGoogle Scholar
  12. 12.
    De Angelis, E., Fioravanti, F., Pettorossi, A., Proietti, M.: Relational verification through Horn clause transformation. In: Rival, X. (ed.) SAS 2016. LNCS, vol. 9837, pp. 147–169. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53413-7_8CrossRefGoogle Scholar
  13. 13.
    De Angelis, E., Fioravanti, F., Pettorossi, A., Proietti, M.: Semantics-based generation of verification conditions by program specialization. Sci. Comput. Program. 147, 78–108 (2017)CrossRefGoogle Scholar
  14. 14.
    De Angelis, E., Fioravanti, F., Pettorossi, A., Proietti, M.: Predicate pairing for program verification. Theory Pract. Logic Program., 1–41 (2017).  https://doi.org/10.1017/S1471068417000497
  15. 15.
    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_24CrossRefGoogle Scholar
  16. 16.
    De Schreye, D., Glück, R., Jørgensen, J., Leuschel, M., Martens, B., Sørensen, M.H.: Conjunctive partial deduction: Foundations, control, algorithms, and experiments. J. Logic Program. 41(2–3), 231–277 (1999)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Etalle, S., Gabbrielli, M.: Transformations of CLP modules. Theoret. Comput. Sci. 166, 101–146 (1996)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Felsing, D., Grebing, S., Klebanov, V., Rümmer, P., Ulbrich, M.: Automating regression verification. In: Proceedings of ASE 2014, pp. 349–360. ACM (2014)Google Scholar
  19. 19.
    Hojjat, H., Konečný, F., Garnier, F., Iosif, R., Kuncak, V., Rümmer, P.: A verification toolkit for numerical transition systems. In: Giannakopoulou, D., Méry, D. (eds.) FM 2012. LNCS, vol. 7436, pp. 247–251. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-32759-9_21CrossRefGoogle Scholar
  20. 20.
    Kafle, B., Gallagher, J.P.: Constraint specialisation in Horn clause verification. Sci. Comput. Program. 137, 125–140 (2017)CrossRefGoogle Scholar
  21. 21.
    Kafle, B., Gallagher, J.P.: Horn clause verification with convex polyhedral abstraction and tree automata-based refinement. Comput. Lang. Syst. Struct. 47, 2–18 (2017)zbMATHGoogle Scholar
  22. 22.
    Lahiri, S.K., McMillan, K.L., Sharma, R., Hawblitzel, C.: Differential assertion checking. In: Proceedings of ESEC/FSE 2013, pp. 345–355. ACM (2013)Google Scholar
  23. 23.
    Leuschel, M.: A framework for the integration of partial evaluation and abstract interpretation of logic programs. ACM TOPLAS 26(3), 413–463 (2004)CrossRefGoogle Scholar
  24. 24.
    McMillan, K.L., Rybalchenko, A.: Solving constrained Horn clauses using interpolation. MSR Technical Report 2013-6, Microsoft Report (2013)Google Scholar
  25. 25.
    Méndez-Lojo, M., Navas, J., Hermenegildo, M.V.: A flexible, (C)LP-based approach to the analysis of object-oriented programs. In: King, A. (ed.) LOPSTR 2007. LNCS, vol. 4915, pp. 154–168. Springer, Heidelberg (2008).  https://doi.org/10.1007/978-3-540-78769-3_11CrossRefzbMATHGoogle Scholar
  26. 26.
    Miné, A.: The octagon abstract domain. Higher-Order Symbolic Comput. 19(1), 31–100 (2006)CrossRefGoogle Scholar
  27. 27.
    Mordvinov, D., Fedyukovich, G.: Synchronizing constrained Horn clauses. In: Proceedings of LPAR 2017. EPiC Series in Computing, vol. 46, pp. 338–355. EasyChair (2017)Google Scholar
  28. 28.
    Peralta, J.C., Gallagher, J.P., Sağlam, H.: Analysis of imperative programs through analysis of constraint logic programs. In: Levi, G. (ed.) SAS 1998. LNCS, vol. 1503, pp. 246–261. Springer, Heidelberg (1998).  https://doi.org/10.1007/3-540-49727-7_15CrossRefGoogle Scholar
  29. 29.
    Pettorossi, A., Proietti, M.: Transformation of logic programs: foundations and techniques. J. Logic Program. 19(20), 261–320 (1994)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.DECUniversity ‘G. d’Annunzio’Chieti-PescaraItaly
  2. 2.DICIIUniversity of Rome ‘Tor Vergata’RomeItaly
  3. 3.IASI-CNRRomeItaly

Personalised recommendations