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Dynamic Logic with Non-rigid Functions

A Basis for Object-Oriented Program Verification
  • Bernhard Beckert
  • André Platzer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4130)

Abstract

We introduce a dynamic logic that is enriched by non-rigid functions, i.e., functions that may change their value from state to state (during program execution), and we present a (relatively) complete sequent calculus for this logic. In conjunction with dynamically typed object enumerators, non-rigid functions allow to embed notions of object-orientation in dynamic logic, thereby forming a basis for verification of object-oriented programs. A semantical generalisation of substitutions, called state update, which we add to the logic, constitutes the central technical device for dealing with object aliasing during function modification. With these few extensions, our dynamic logic captures the essential aspects of the complex verification system KeY and, hence, constitutes a foundation for object-oriented verification with the principles of reasoning that underly the successful KeY case studies.

Keywords

Dynamic logic sequent calculus program logic software verification logical foundations of programming languages object-orientation 

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References

  1. 1.
    Abadi, M., Leino, K.R.M.: A logic of object-oriented programs. In: Bidoit, M., Dauchet, M. (eds.) CAAP 1997, FASE 1997, and TAPSOFT 1997. LNCS, vol. 1214, Springer, Heidelberg (1997)CrossRefGoogle Scholar
  2. 2.
    Ahrendt, W., Baar, T., Beckert, B., Bubel, R., Giese, M., Hähnle, R., Menzel, W., Mostowski, W., Roth, A., Schlager, S., Schmitt, P.H.: The KeY tool. Software and System Modeling 4, 32–54 (2005)CrossRefGoogle Scholar
  3. 3.
    Barnett, M., Leino, K.R.M., Schulte, W.: The Spec# programming system: An overview. In: Barthe,, et al. (eds.) [4] (2004)Google Scholar
  4. 4.
    Barthe, G., Burdy, L., Huisman, M., Lanet, J.-L., Muntean, T. (eds.): CASSIS 2004. LNCS, vol. 3362. Springer, Heidelberg (2005)Google Scholar
  5. 5.
    Beckert, B.: A dynamic logic for the formal verification of Java Card programs. In: Attali, I., Jensen, T. (eds.) JavaCard 2000. LNCS, vol. 2041, pp. 6–24. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  6. 6.
    Beckert, B., Mostowski, W.: A program logic for handling Java Card’s transaction mechanism. In: Pezzé, M. (ed.) ETAPS 2003 and FASE 2003. LNCS, vol. 2621, Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Beckert, B., Schlager, S.: A sequent calculus for first-order dynamic logic with trace modalities. In: Goré, R., Leitsch, A., Nipkow, T. (eds.) IJCAR 2001. LNCS (LNAI), vol. 2083, pp. 626–641. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  8. 8.
    Beckert, B., Schlager, S.: Software verification with integrated data type refinement for integer arithmetic. In: Boiten, E.A., Derrick, J., Smith, G. (eds.) IFM 2004. LNCS, vol. 2999, pp. 207–226. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    Cok, D.R., Kiniry, J.: ESC/Java2: Uniting ESC/Java and JML. In: Barthe,, et al. (eds.) [4], pp. 108–128 (2004)Google Scholar
  10. 10.
    Fitting, M., Mendelsohn, R.L.: First-Order Modal Logic. Kluwer Academic Publishers, Dordrecht (1999)Google Scholar
  11. 11.
    Harel, D.: First-Order Dynamic Logic. Springer, New York (1979)MATHGoogle Scholar
  12. 12.
    Igarashi, A., Pierce, B.C., Wadler, P.: Featherweight Java: A minimal core calculus for Java and GJ. ACM Trans. Program. Lang. Syst. 23(3), 396–450 (2001)CrossRefGoogle Scholar
  13. 13.
    Jacobs, B., Poll, E.: A logic for the Java modeling language JML. In: Hussmann, H. (ed.) ETAPS 2001 and FASE 2001. LNCS, vol. 2029, pp. 284–299. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  14. 14.
    Miller, R., Tripathi, A.: Issues with exception handling in object-oriented systems. In: Aksit, M., Matsuoka, S. (eds.) ECOOP 1997. LNCS, vol. 1241, pp. 85–103. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  15. 15.
    Mostowski, W.: Formal Development of Safe and Secure Java Card Applets. PhD thesis, Chalmers University of Technology, Göteborg, Sweden (February 2005)Google Scholar
  16. 16.
    Nipkow, T.: Jinja: Towards a comprehensive formal semantics for a Java-like language. In: Proc. Marktoberdorf Summer School (2003)Google Scholar
  17. 17.
    Pierik, C., de Boer, F.S.: A syntax-directed Hoare logic for object-oriented programming concepts. In: Najm, E., Nestmann, U., Stevens, P. (eds.) FMOODS 2003. LNCS, vol. 2884, pp. 64–78. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  18. 18.
    Platzer, A.: An object-oriented dynamic logic with updates. Master’s thesis, University of Karlsruhe (September 2004), available at www.key-project.org
  19. 19.
    Poetzsch-Heffter, A., Müller, P.: A programming logic for sequential Java. In: Swierstra, D. (ed.) ESOP 1999 and ETAPS 1999. LNCS, vol. 1576, Springer, Heidelberg (1999)CrossRefGoogle Scholar
  20. 20.
    Stärk, R., Nanchen, S.: A logic for abstract state machines. J. UCS 7(11) (2001)Google Scholar
  21. 21.
    van den Berg, J., Huisman, M., Jacobs, B., Poll, E.: A type-theoretic memory model for verification of sequential Java programs. In: Bert, D., Choppy, C., Mosses, P.D. (eds.) WADT 1999. LNCS, vol. 1827, pp. 1–21. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  22. 22.
    von Oheimb, D., Nipkow, T.: Hoare logic for NanoJava: Auxiliary variables, side effects, and virtual methods revisited. In: Eriksson, L.-H., Lindsay, P.A. (eds.) FME 2002. LNCS, vol. 2391, pp. 89–105. Springer, Heidelberg (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Bernhard Beckert
    • 1
  • André Platzer
    • 2
  1. 1.Department of Computer ScienceUniversity of Koblenz-Landau 
  2. 2.Department of Computing ScienceUniversity of Oldenburg 

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