Collecting Semantics under Predicate Abstraction in the K Framework

  • Irina Măriuca Asăvoae
  • Mihail Asăvoae
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6381)


The K framework is a specialization of rewriting logic for defining programming language semantics. This paper introduces the model checking with predicate abstraction technique into the K framework. To express this technique in K, we go to the foundations of predicate abstraction, that is abstract interpretation, and use its collecting semantics. As such, we propose a suitable description in K for collecting semantics under predicate abstraction of a simple imperative language. Next, we prove that our K specification for collecting semantics is a sound approximation of the K specification for concrete semantics. This work makes a further step towards the development of program verification methodologies in rewriting logic semantics project in general and the K framework in particular.


Abstract State Abstract Computation Structural Rule Concrete State Galois Connection 
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.
    Alba-Castro, M., Alpuente, M., Escobar, S.: Automatic certification of Java source code in rewriting logic. In: Leue, S., Merino, P. (eds.) FMICS 2007. LNCS, vol. 4916, pp. 200–217. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  2. 2.
    Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. The MIT Press, Cambridge (1999)Google Scholar
  3. 3.
    Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: Symposium on Principles of Programming Languages, pp. 238–252. ACM Press, New York (1977)Google Scholar
  4. 4.
    Das, S., Dill, D.L.: Counter-example based predicate discovery in predicate abstraction. In: Aagaard, M.D., O’Leary, J.W. (eds.) FMCAD 2002. LNCS, vol. 2517, pp. 19–32. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  5. 5.
    Eker, S., Meseguer, J., Sridharanarayanan, A.: The Maude LTL model checker. In: Gaducci, F., Montanari, U. (eds.) Workshop on Rewriting Logic and Its Applications, Electronic Notes in Theoretical Computer Science, vol. 71. Elsevier, Amsterdam (September 2002)Google Scholar
  6. 6.
    Graf, S., Saidi, H.: Construction of abstract state graphs with PVS. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 72–83. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  7. 7.
    Henzinger, T.A., Jhala, R., Majumdar, R., Sutre, G.: Lazy abstraction. SIGPLAN Notices 37(1), 58–70 (2002)CrossRefzbMATHGoogle Scholar
  8. 8.
    Hills, M., Roşu, G.: KOOL: An application of rewriting logic to language prototyping and analysis. In: Baader, F. (ed.) RTA 2007. LNCS, vol. 4533, pp. 246–256. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  9. 9.
    Martí-Oliet, N., Meseguer, J.: Rewriting logic as a logical and semantic framework. Electronic Notes in Theoretical Computer Science 4 (1996)Google Scholar
  10. 10.
    McMillan, K.L.: Lazy abstraction with interpolants. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 123–136. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  11. 11.
    Meredith, P., Hills, M., Roşu, G.: An executable rewriting logic semantics of K-scheme. In: Dube, D. (ed.) Proceedings of the 2007 Workshop on Scheme and Functional Programming (SCHEME 2007), Technical Report DIUL-RT-0701, pp. 91–103. Laval University (2007)Google Scholar
  12. 12.
    Meseguer, J.: Conditional rewriting logic as a unified model of concurrency. Theoretical Computer Science 96(1), 73–155 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Meseguer, J., Palomino, M., Martí-Oliet, N.: Equational abstraction. In: Baader, F. (ed.) CADE 2003. LNCS (LNAI), vol. 2741, pp. 2–16. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  14. 14.
    Meseguer, J., Roşu, G.: The rewriting logic semantics project. Theoretical Computer Science 373(3), 213–237 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Nielson, F., Nielson, H.R., Hankin, C.: Principles of Program Analysis. Springer, New York (1999)CrossRefzbMATHGoogle Scholar
  16. 16.
    Palomino, M.: A predicate abstraction tool for Maude. Documentation and tool,
  17. 17.
    Roşu, G., Havelund, K.: A rewriting-based framework for computations – preliminary version. Tech. Rep. Department of Computer Science UIUCDCS-R-2007-2926 and College of Engineering UILU-ENG-2007-1827, University of Illinois at Urbana-Champaign (2007)Google Scholar
  18. 18.
    Roşu, G., Schulte, W.: Matching logic — extended report. Tech. Rep. Department of Computer Science UIUCDCS-R-2009-3026, University of Illinois at Urbana-Champaign (January 2009)Google Scholar
  19. 19.
    Roşu, G., Şerbănuţă, T.F.: An overview of the K semantic framework. Journal of Logic and Algebraic Programming (submitted)Google Scholar
  20. 20.
    Şerbănuţă, T.F., Roşu, G.: K-Maude: A rewriting based tool for semantics of programming languages. In: Proceedings of the 8th International Workshop on Rewriting Logic and its Applications (WRLA 2010). LNCS, vol. 6381, pp. 104–122. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  21. 21.
    Şerbănuţă, T.F., Roşu, G., Meseguer, J.: A rewriting logic approach to operational semantics. Information and Computation 207, 305–340 (2009)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Irina Măriuca Asăvoae
    • 1
  • Mihail Asăvoae
    • 1
  1. 1.Faculty of Computer ScienceAlexandru Ioan Cuza University, IaşiRomania

Personalised recommendations