Advertisement

Spatial Interpolants

  • Aws Albargouthi
  • Josh Berdine
  • Byron Cook
  • Zachary Kincaid
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9032)

Abstract

We propose SplInter, a new technique for proving properties of heap-manipulating programs that marries (1) a new separation logic–based analysis for heap reasoning with (2) an interpolation-based technique for refining heap-shape invariants with data invariants. SplInter is property directed, precise, and produces counterexample traces when a property does not hold. Using the novel notion of spatial interpolants modulo theories, SplInter can infer complex invariants over general recursive predicates, e.g., of the form all elements in a linked list are even or a binary tree is sorted. Furthermore, we treat interpolation as a black box, which gives us the freedom to encode data manipulation in any suitable theory for a given program (e.g., bit vectors, arrays, or linear arithmetic), so that our technique immediately benefits from any future advances in SMT solving and interpolation.

Keywords

Spatial Interpolation Horn Clause Symbolic Execution Abstract Domain Separation Logic 
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.

References

  1. 1.
    Albarghouthi, A., McMillan, K.L.: Beautiful interpolants. In: Sharygina and Veith [37]Google Scholar
  2. 2.
    Albargouthi, A., Berdine, J., Cook, B., Kincaid, Z.: Spatial interpolants. Tech. Rep. MSR-TR-2015-4 (January 2015), http://research.microsoft.com/apps/pubs/default.aspx?id=238328
  3. 3.
    Ball, T., Jones, R.B. (eds.): CAV 2006. LNCS, vol. 4144. Springer, Heidelberg (2006)Google Scholar
  4. 4.
    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)Google Scholar
  5. 5.
    Beyer, D., Henzinger, T.A., Majumdar, R., Rybalchenko, A.: Path invariants. In: Ferrante, J., McKinley, K.S. (eds.) PLDI, ACM (2007)Google Scholar
  6. 6.
    Beyer, D., Henzinger, T.A., Théoduloz, G.: Lazy shape analysis. In: Ball and Jones [3]Google Scholar
  7. 7.
    Bogudlov, I., Lev-Ami, T., Reps, T., Sagiv, M.: Revamping TVLA: Making parametric shape analysis competitive. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 221–225. Springer, Heidelberg (2007)Google Scholar
  8. 8.
    Botincan, M., Dodds, M., Magill, S.: Abstraction refinement for separation logic program analyses, http://www.cl.cam.ac.uk/~mb741/papers/abs_ref_draft.pdf
  9. 9.
    Bouajjani, A., Drăgoi, C., Enea, C., Rezine, A., Sighireanu, M.: Invariant synthesis for programs manipulating lists with unbounded data. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 72–88. Springer, Heidelberg (2010)Google Scholar
  10. 10.
    Bouajjani, A., Drăgoi, C., Enea, C., Sighireanu, M.: Abstract domains for automated reasoning about list-manipulating programs with infinite data. In: Kuncak, V., Rybalchenko, A. (eds.) VMCAI 2012. LNCS, vol. 7148, pp. 1–22. Springer, Heidelberg (2012)Google Scholar
  11. 11.
    Calcagno, C., Distefano, D., O’Hearn, P.W., Yang, H.: Compositional shape analysis by means of bi-abduction. In: Shao, Z., Pierce, B.C. (eds.) POPL. ACM (2009)Google Scholar
  12. 12.
    Chang, B.Y.E.: Personal communicationGoogle Scholar
  13. 13.
    Chang, B.E., Rival, X.: Relational inductive shape analysis. In: Necula, G.C., Wadler, P. (eds.) POPL. ACM (2008)Google Scholar
  14. 14.
    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)Google Scholar
  15. 15.
    Distefano, D., O’Hearn, P.W., Yang, H.: A local shape analysis based on separation logic. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 287–302. Springer, Heidelberg (2006)Google Scholar
  16. 16.
    Garg, P., Löding, C., Madhusudan, P., Neider, D.: Learning universally quantified invariants of linear data structures. In: Sharygina and Veith [37]Google Scholar
  17. 17.
    Garg, P., Madhusudan, P., Parlato, G.: Quantified data automata on skinny trees: An abstract domain for lists. In: Logozzo, F., Fähndrich, M. (eds.) Static Analysis. LNCS, vol. 7935, pp. 172–193. Springer, Heidelberg (2013)Google Scholar
  18. 18.
    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)Google Scholar
  19. 19.
    Heizmann, M., Hoenicke, J., Podelski, A.: Nested interpolants. In: Hermenegildo and Palsberg [21]Google Scholar
  20. 20.
    Henzinger, T.A., Jhala, R., Majumdar, R., McMillan, K.L.: Abstractions from proofs. In: Jones, N.D., Leroy, X. (eds.) POPL. ACM (2004)Google Scholar
  21. 21.
    Hermenegildo, M.V., Palsberg, J. (eds.): POPL. ACM (2010)Google Scholar
  22. 22.
    Itzhaky, S., Bjørner, N., Reps, T., Sagiv, M., Thakur, A.: Property-directed shape analysis. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 35–51. Springer, Heidelberg (2014)Google Scholar
  23. 23.
    Magill, S., Tsai, M., Lee, P., Tsay, Y.: Automatic numeric abstractions for heap-manipulating programs. In: Hermenegildo and Palsberg [21]Google Scholar
  24. 24.
    Manevich, R., Field, J., Henzinger, T.A., Ramalingam, G., Sagiv, M.: Abstract counterexample-based refinement for powerset domains. In: Reps, T., Sagiv, M., Bauer, J. (eds.) Wilhelm Festschrift. LNCS, vol. 4444, pp. 273–292. Springer, Heidelberg (2007)Google Scholar
  25. 25.
    McCloskey, B., Reps, T., Sagiv, M.: Statically inferring complex heap, array, and numeric invariants. In: Cousot, R., Martel, M. (eds.) SAS 2010. LNCS, vol. 6337, pp. 71–99. Springer, Heidelberg (2010)Google Scholar
  26. 26.
    McMillan, K.L.: Lazy abstraction with interpolants. In: Ball and Jones [3]Google Scholar
  27. 27.
    McMillan, K.L.: Interpolants from Z3 proofs. In: Bjesse, P., Slobodová, A. (eds.) FMCAD. FMCAD Inc. (2011)Google Scholar
  28. 28.
    Pérez, J.A.N., Rybalchenko, A.: Separation logic + superposition calculus = heap theorem prover. In: Hall, M.W., Padua, D.A. (eds.) PLDI. ACM (2011)Google Scholar
  29. 29.
    Navarro Pérez, J.A., Rybalchenko, A.: Separation logic modulo theories. In: Shan, C.-c. (ed.) APLAS 2013. LNCS, vol. 8301, pp. 90–106. Springer, Heidelberg (2013)Google Scholar
  30. 30.
    Piskac, R., Wies, T., Zufferey, D.: Automating separation logic using SMT. In: Sharygina and Veith [37]Google Scholar
  31. 31.
    Podelski, A., Wies, T.: Counterexample-guided focus. In: Hermenegildo and Palsberg [21]Google Scholar
  32. 32.
    Qiu, X., Garg, P., Stefanescu, A., Madhusudan, P.: Natural proofs for structure, data, and separation. In: Boehm, H., Flanagan, C. (eds.) PLDI. ACM (2013)Google Scholar
  33. 33.
    Reynolds, J.C.: Separation logic: A logic for shared mutable data structures. In: LICS. IEEE Computer Society Press (2002)Google Scholar
  34. 34.
    Rümmer, P., Hojjat, H., Kuncak, V.: Classifying and solving horn clauses for verification. In: Cohen, E., Rybalchenko, A. (eds.) VSTTE 2013. LNCS, vol. 8164, pp. 1–21. Springer, Heidelberg (2014)Google Scholar
  35. 35.
    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)Google Scholar
  36. 36.
    Sagiv, S., Reps, T.W., Wilhelm, R.: Parametric shape analysis via 3-valued logic. In: Appel, A.W., Aiken, A. (eds.) POPL. ACM (1999)Google Scholar
  37. 37.
    Sharygina, N., Veith, H. (eds.): CAV 2013. LNCS, vol. 8044. Springer, Heidelberg (2013)Google Scholar
  38. 38.

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Aws Albargouthi
    • 1
  • Josh Berdine
    • 2
  • Byron Cook
    • 3
  • Zachary Kincaid
    • 4
  1. 1.University of Wisconsin-MadisonMadisonUSA
  2. 2.Microsoft ResearchCambridgeUK
  3. 3.University College LondonLondonUK
  4. 4.University of TorontoTorontoCanada

Personalised recommendations