Lazy Behavioral Subtyping

  • Johan Dovland
  • Einar Broch Johnsen
  • Olaf Owe
  • Martin Steffen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5014)

Abstract

Late binding allows flexible code reuse but complicates formal reasoning significantly, as a method call’s receiver class is not statically known. This is especially true when programs are incrementally developed by extending class hierarchies. This paper develops a novel method to reason about late bound method calls. In contrast to traditional behavioral subtyping, reverification is avoided without restricting method overriding to fully behavior-preserving redefinition. The approach ensures that when analyzing the methods of a class, it suffices to consider that class and its superclasses. Thus, the full class hierarchy is not needed, and incremental reasoning is supported. We formalize this approach as a calculus which lazily imposes context-dependent subtyping constraints on method definitions. The calculus ensures that all method specifications required by late bound calls remain satisfied when new classes extend a class hierarchy. The calculus does not depend on a specific program logic, but the examples in the paper use a Hoare-style proof system. We show soundness of the analysis method.

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References

  1. 1.
    Abadi, M., Leino, K.R.M.: A Logic of Object-Oriented Programs. In: Dershowitz, N. (ed.) Verification: Theory and Practice. LNCS, vol. 2772, pp. 11–41. Springer, Heidelberg (2004)Google Scholar
  2. 2.
    America, P.: Designing an object-oriented programming language with behavioural subtyping. In: de Bakker, J.W., de Roever, W.-P., Rozenberg, G. (eds.) Foundations of Object-Oriented Languages, pp. 60–90. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  3. 3.
    Apt, K.R.: Ten years of Hoare’s logic: A survey — Part I. ACM Transactions on Programming Languages and Systems 3(4), 431–483 (1981)MATHCrossRefGoogle Scholar
  4. 4.
    Apt, K.R., Olderog, E.-R.: Verification of Sequential and Concurrent Systems. In: Texts and Monographs in Computer Science, Springer, Heidelberg (1991)Google Scholar
  5. 5.
    Barnett, M., Leino, K.R.M., Schulte, W.: The Spec# Programming System: An Overview. In: Barthe, G., Burdy, L., Huisman, M., Lanet, J.-L., Muntean, T. (eds.) CASSIS 2004. LNCS, vol. 3362, pp. 49–69. Springer, Heidelberg (2005)Google Scholar
  6. 6.
    Beckert, B., Hähnle, R., Schmitt, P.H. (eds.): Verification of Object-Oriented Software. LNCS (LNAI), vol. 4334. Springer, Heidelberg (2007)Google Scholar
  7. 7.
    Burdy, L., Cheon, Y., Cok, D.R., Ernst, M., Kiniry, J., Leavens, G.T., Leino, K.R.M., Poll, E.: An overview of JML tools and applications. In: Arts, T., Fokkink, W. (eds.) Proceedings of FMICS 2003. ENTCS, vol. 80, Elsevier, Amsterdam (2003)Google Scholar
  8. 8.
    Dahl, O.-J., Myhrhaug, B., Nygaard, K. (Simula 67) Common Base Language. Technical Report S-2, Norsk Regnesentral (Norwegian Computing Center), Oslo, Norway (May 1968)Google Scholar
  9. 9.
    de Boer, F.S.: A WP-calculus for OO. In: Thomas, W. (ed.) ETAPS 1999 and FOSSACS 1999. LNCS, vol. 1578, pp. 135–149. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  10. 10.
    de Boer, F.S., Clarke, D., Johnsen, E.B.: A Complete Guide to the Future. In: De Nicola, R. (ed.) ESOP 2007. LNCS, vol. 4421, pp. 316–330. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  11. 11.
    Dovland, J., Johnsen, E.B., Owe, O., Steffen, M.: Lazy behavioral subtyping. Research Report 368, Dept. of Informatics, University of Oslo (November 2007), heim.ifi.uio.no/creol
  12. 12.
    Hoare, C.A.R.: An Axiomatic Basis of Computer Programming. Communications of the ACM 12, 576–580 (1969)MATHCrossRefGoogle Scholar
  13. 13.
    Hoare, C.A.R.: Procedures and parameters: An axiomatic approach. In: Engeler, E. (ed.) Symposium On Semantics of Algorithmic Languages. Lecture Notes in Mathematics, vol. 188, pp. 102–116. Springer, Heidelberg (1971)CrossRefGoogle Scholar
  14. 14.
    Huisman, M.: Java Program Verification in Higher-Order Logic with PVS and Isabelle. PhD thesis, University of Nijmegen (2001)Google Scholar
  15. 15.
    Igarashi, A., Pierce, B.C., Wadler, P.: Featherweight Java: a minimal core calculus for Java and GJ. ACM Transactions on Programming Languages and Systems 23(3), 396–450 (2001)CrossRefGoogle Scholar
  16. 16.
    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
  17. 17.
    Johnsen, E.B., Owe, O.: An asynchronous communication model for distributed concurrent objects. Software and Systems Modeling 6(1), 35–58 (2007)Google Scholar
  18. 18.
    Leavens, G.T., Leino, K.R.M., Müller, P.: Specification and verification challenges for sequential object-oriented programs. Formal Aspects of Computing 19(2), 159–189 (2007)MATHCrossRefGoogle Scholar
  19. 19.
    Leavens, G.T., Naumann, D.A.: Behavioral subtyping, specification inheritance, and modular reasoning. Technical Report 06-20a, Department of Computer Science, Iowa State University, Ames, Iowa (2006)Google Scholar
  20. 20.
    Liskov, B.H., Wing, J.M.: A behavioral notion of subtyping. ACM Transactions on Programming Languages and Systems 16(6), 1811–1841 (1994)CrossRefGoogle Scholar
  21. 21.
    Mikhajlov, L., Sekerinski, E.: A Study of the Fragile Base Class Problem. In: Jul, E. (ed.) ECOOP 1998. LNCS, vol. 1445, pp. 355–382. Springer, Heidelberg (1998)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
  23. 23.
    Owicki, S., Gries, D.: An axiomatic proof technique for parallel programs I. Acta Informatica 6(4), 319–340 (1976)MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Pierik, C., de Boer, F.S.: A proof outline logic for object-oriented programming. Theoretical Computer Science 343(3), 413–442 (2005)MATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    Poetzsch-Heffter, A., Müller, P.: A programming logic for sequential Java. In: Swierstra, S.D. (ed.) ESOP 1999 and ETAPS 1999. LNCS, vol. 1576, pp. 162–176. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  26. 26.
    Soundarajan, N., Fridella, S.: Inheritance: From code reuse to reasoning reuse. In: Devanbu, P., Poulin, J. (eds.) Proc. Fifth International Conference on Software Reuse (ICSR5), pp. 206–215. IEEE Computer Society Press, Los Alamitos (1998)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Johan Dovland
    • 1
  • Einar Broch Johnsen
    • 1
  • Olaf Owe
    • 1
  • Martin Steffen
    • 1
  1. 1.Dept. of InformaticsUniversity of OsloNorway

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