Compositional Predicate Abstraction from Game Semantics

  • Adam Bakewell
  • Dan R. Ghica
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5505)


We introduce a technique for using conventional predicate abstraction methods to reduce the state-space of models produced using game semantics. We focus on an expressive procedural language that has both local store and local control, a language which enjoys a simple game-semantic model yet is expressive enough to allow non-trivial examples. Our compositional approach allows the verification of incomplete programs (e.g. libraries) and offers the opportunity for new heuristics for improved efficiency. Game-semantic predicate abstraction can be embedded in an abstraction-refinement cycle in a standard way, resulting in an improved version of our experimental model-checking tool Mage, and we illustrate it with several toy examples.


  1. 1.
    Ball, T., Cook, B., Levin, V., Rajamani, S.K.: Slam and static driver verifier: Technology transfer of formal methods inside Microsoft. In: IFM, pp. 1–20 (2004)Google Scholar
  2. 2.
    Henzinger, T.A., Jhala, R., Majumdar, R.: The BLAST software verification system. In: Godefroid, P. (ed.) SPIN 2005. LNCS, vol. 3639, pp. 25–26. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  3. 3.
    Abramsky, S., Ghica, D.R., Murawski, A.S., Ong, C.-H.L.: Applying game semantics to compositional software modeling and verification. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 421–435. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  4. 4.
    Dimovski, A., Ghica, D.R., Lazić, R.S.: Data-abstraction refinement: A game semantic approach. In: Hankin, C., Siveroni, I. (eds.) SAS 2005. LNCS, vol. 3672, pp. 102–117. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  5. 5.
    Ghica, D.R., Murawski, A.S.: Compositional model extraction for higher-order concurrent programs. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 303–317. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Bakewell, A., Ghica, D.R.: On-the-fly techniques for game-based software model checking. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 78–92. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  7. 7.
    Abramsky, S., Jagadeesan, R., Malacaria, P.: Full abstraction for PCF. Inf. Comput. 163(2), 409–470 (2000)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Hyland, J.M.E., Ong, C.H.L.: On full abstraction for PCF: I, II, and III. Inf. Comput. 163(2), 285–408 (2000)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Das, S., Dill, D.L., Park, S.: Experience with predicate abstraction. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 160–171. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  10. 10.
    Abramsky, S., McCusker, G.: Linearity, sharing and state: a fully abstract game semantics for Idealized Algol with active expressions. Electr. Notes Theor. Comput. Sci. 3 (1996)Google Scholar
  11. 11.
    Laird, J.: A fully abstract game semantics of local exceptions. In: LICS, pp. 105–114 (2001)Google Scholar
  12. 12.
    Reynolds, J.: The craft of programming. Prentice-Hall, Englewood Cliffs (1981)MATHGoogle Scholar
  13. 13.
    Pitts, A.M.: Reasoning about local variables with operationally-based logical relations. In: O’Hearn, P.W., Tennent, R.D. (eds.) Algol-Like Languages, July 1996, vol. 2, pp. 173–193. Birkhauser, Basel (1997); reprinted from Proceedings Eleventh Annual IEEE Symposium on Logic in Computer Science, Brunswick, NJ, July 1996, pp. 152–163 (2006)Google Scholar
  14. 14.
    Ghica, D.R., McCusker, G.: The regular-language semantics of second-order Idealized Algol. Theor. Comput. Sci. 309(1-3), 469–502 (2003)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Ong, C.H.L.: Observational equivalence of 3rd-order Idealized Algol is decidable. In: LICS, pp. 245–256 (2002)Google Scholar
  16. 16.
    Laird, J.: A game semantics of names and pointers. Annals of Pure and Applied Logic 151(2-3), 151–169 (2008); first Games for Logic and Programming Languages WorkshopMathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Chaki, S., Clarke, E., Groce, A., Strichman, O.: Predicate abstraction with minimum predicates. In: Geist, D., Tronci, E. (eds.) CHARME 2003. LNCS, vol. 2860, pp. 19–34. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  18. 18.
    Reynolds, J.C.: Separation logic: A logic for shared mutable data structures. In: LICS, pp. 55–74 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Adam Bakewell
    • 1
  • Dan R. Ghica
    • 1
  1. 1.University of BirminghamUK

Personalised recommendations