Disproving Inductive Entailments in Separation Logic via Base Pair Approximation

  • James Brotherston
  • Nikos Gorogiannis
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9323)


We give a procedure for establishing the invalidity of logical entailments in the symbolic heap fragment of separation logic with user-defined inductive predicates, as used in program verification. This disproof procedure attempts to infer the existence of a countermodel to an entailment by comparing computable model summaries, a.k.a. bases (modified from earlier work), of its antecedent and consequent. Our method is sound and terminating, but necessarily incomplete.

Experiments with the implementation of our disproof procedure indicate that it can correctly identify a substantial proportion of the invalid entailments that arise in practice, at reasonably low time cost. Accordingly, it can be used, e.g., to improve the output of theorem provers by returning “no” answers in addition to “yes” and “unknown” answers to entailment questions, and to speed up proof search or automated theory exploration by filtering out invalid entailments.


Base Pair Inductive Rule Separation Logic Proof Search Model Check Procedure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Cyclist: software distribution for this paper,
  2. 2.
    The first Separation Logic Competition (SL-COMP14),
  3. 3.
    Antonopoulos, T., Gorogiannis, N., Haase, C., Kanovich, M., Ouaknine, J.: Foundations for decision problems in separation logic with general inductive predicates. In: Muscholl, A. (ed.) FOSSACS 2014 (ETAPS). LNCS, vol. 8412, pp. 411–425. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  4. 4.
    Bell, E.: Exponential numbers. The American Mathematical Monthly 41(7), 411–419 (1934)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Berdine, J., Calcagno, C., O’Hearn, P.W.: A decidable fragment of separation logic. In: Lodaya, K., Mahajan, M. (eds.) FSTTCS 2004. LNCS, vol. 3328, pp. 97–109. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  6. 6.
    Berdine, J., Calcagno, C., O’Hearn, P.W.: Symbolic execution with separation logic. In: Yi, K. (ed.) APLAS 2005. LNCS, vol. 3780, pp. 52–68. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. 7.
    Berdine, J., Cook, B., Ishtiaq, S.: SLAyer: Memory safety for systems-level code. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 178–183. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  8. 8.
    Bornat, R., Calcagno, C., O’Hearn, P., Parkinson, M.: Permission accounting in separation logic. In: Proc. POPL-32, pp. 59–70. ACM (2005)Google Scholar
  9. 9.
    Brotherston, J.: Formalised inductive reasoning in the logic of bunched implications. In: Riis Nielson, H., Filé, G. (eds.) SAS 2007. LNCS, vol. 4634, pp. 87–103. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  10. 10.
    Brotherston, J., Fuhs, C., Gorogiannis, N., Navarro Pérez, J.: A decision procedure for satisfiability in separation logic with inductive predicates. In: Proc. CSL-LICS, pp. 25:1–25:10. ACM (2014)Google Scholar
  11. 11.
    Brotherston, J., Gorogiannis, N.: Cyclic abduction of inductively defined safety and termination preconditions. In: Müller-Olm, M., Seidl, H. (eds.) SAS 2014. LNCS, vol. 8723, pp. 68–84. Springer, Heidelberg (2014)Google Scholar
  12. 12.
    Brotherston, J., Gorogiannis, N., Kanovich, M., Rowe, R.: Model checking for symbolic-heap separation logic with inductive predicates (2015) (submitted)Google Scholar
  13. 13.
    Brotherston, J., Gorogiannis, N., Petersen, R.L.: A generic cyclic theorem prover. In: Jhala, R., Igarashi, A. (eds.) APLAS 2012. LNCS, vol. 7705, pp. 350–367. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  14. 14.
    Calcagno, C., Distefano, D., O’Hearn, P., Yang, H.: Compositional shape analysis by means of bi-abduction. Journal of the ACM 58(6) (2011)Google Scholar
  15. 15.
    Chin, W.-N., David, C., Nguyen, H.H., Qin, S.: Automated verification of shape, size and bag properties via user-defined predicates in separation logic. Science of Computer Programming 77(9), 1006–1036 (2012)CrossRefzbMATHGoogle Scholar
  16. 16.
    Claessen, K., Johansson, M., Rosén, D., Smallbone, N.: Automating inductive proofs using theory exploration. In: Bonacina, M.P. (ed.) CADE 2013. LNCS, vol. 7898, pp. 392–406. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  17. 17.
    Cook, B., Haase, C., Ouaknine, J., Parkinson, M., Worrell, J.: Tractable reasoning in a fragment of separation logic. In: Katoen, J.-P., König, B. (eds.) CONCUR 2011. LNCS, vol. 6901, pp. 235–249. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  18. 18.
    Hurlin, C., Bobot, F., Summers, A.J.: Size does matter: Two certified abstractions to disprove entailment in intuitionistic and classical separation logic. In: Proc. IWACO, pp. 5:1–5:6. ACM (2009)Google Scholar
  19. 19.
    Iosif, R., Rogalewicz, A., Simacek, J.: The tree width of separation logic with recursive definitions. In: Bonacina, M.P. (ed.) CADE 2013. LNCS, vol. 7898, pp. 21–38. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  20. 20.
    Jacobs, B., Smans, J., Philippaerts, P., Vogels, F., Penninckx, W., Piessens, F.: VeriFast: A powerful, sound, predictable, fast verifier for C and Java. In: Bobaru, M., Havelund, K., Holzmann, G.J., Joshi, R. (eds.) NFM 2011. LNCS, vol. 6617, pp. 41–55. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  21. 21.
    Magill, S., Tsai, M.-H., Lee, P., Tsay, Y.-K.: Automatic numeric abstractions for heap-manipulating programs. In: Proc. POPL-37, pp. 211–222. ACM (2010)Google Scholar
  22. 22.
    Pek, E., Qiu, X., Madhusudan, P.: Natural proofs for data structure manipulation in C using separation logic. In: Proc. PLDI-35, pp. 440–451. ACM (2014)Google Scholar
  23. 23.
    Reynolds, J.C.: Separation logic: A logic for shared mutable data structures. In: Proc. LICS-17, pp. 55–74. IEEE Computer Society (2002)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • James Brotherston
    • 1
  • Nikos Gorogiannis
    • 2
  1. 1.Dept. of Computer ScienceUniversity College LondonLondonUK
  2. 2.Dept. of Computer ScienceMiddlesex University LondonLondonUK

Personalised recommendations