Compositional Verification for Object-Z

  • Kirsten Winter
  • Graeme Smith
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2651)


This paper presents a framework for compositional verification of Object-Z specifications. Its key feature is a proof rule based on decomposition of hierarchical Object-Z models. For each component in the hierarchy local properties are proven in a single proof step. However, we do not consider components in isolation. Instead, components are envisaged in the context of the referencing super-component and proof steps involve assumptions on properties of the sub-components. The framework is defined for Linear Temporal Logic (LTL).


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Eme90]
    E. A. Emerson. Temporal and modal logic. In J. van Leeuwen, editor, Handbook of Theoretical Coomputer Science, volume B. Elsevier Science Publishers, 1990.Google Scholar
  2. [GL94]
    O. Grumberg and D.E. Long. Model checking and modular verification. ACM Transactions on Programming Languages and Systems, 16(3):843–871, 1994.CrossRefGoogle Scholar
  3. [Gri97]
    A. Griffiths. Modular reasoning in Object-Z. In W. Wong and K. Leung, editors, Proc. of the Joint 1997 Asia Pacific Software Engineering Conference and International Computer Science Conference, IEEE, pages 140–149. Computer Society Press, 1997.Google Scholar
  4. [Pnu85]
    A. Pnueli. In transition from global to modular temporal reasoning about programs. In K. R. Apt, editor, Logics and Models of Concurrent Systems, volume 13 of NATO ASI Series, pages 123–144. Springer-Verlag, 1985.Google Scholar
  5. [SKS02]
    G. Smith, F. Kammüller, and T. Santen. Encoding Object-Z in Isabelle/HOL. In D. Bert, J.P. Bowen, M.C. Henson, and K. Robinson, editors, Proc. of Int. Conf. of Z and B Users (ZB 2002), volume 2272 of LNCS, pages 82–99. Springer-Verlag, 2002.Google Scholar
  6. [Smi92]
    G. Smith. An Object-Oriented Approach to Formal Specification. PhD thesis, Department of Computer Science, University of Queensland, 1992.Google Scholar
  7. [Smi95a]
    G. Smith. A fully abstract semantics of classes for Object-Z. Formal Aspects of Computing, 7(3):289–313, 1995.CrossRefGoogle Scholar
  8. [Smi95b]
    G. Smith. Reasoning about Object-Z specifications. In Proc. of the Asia-Pacific Software Engineering Conference (APSEC95), IEEE, pages 489–497. Computer Society Press, 1995.Google Scholar
  9. [Smi00]
    G. Smith. The Object-Z Specification Language. Kluwer Academic Publishers, 2000.Google Scholar
  10. [Smi02]
    G. Smith. Introducing reference semantics via refinement. In C. George and H. Miao, editors, Proc. on Int. Conference on Formal Engineering Methods (ICFEM 2002), volume 2495 of LNCS, pages 588–599. Springer-Verlag, 2002.Google Scholar
  11. [Spi92]
    J.M. Spivey. The Z Notation — A Reference Manual. Prentice Hall, 1992.Google Scholar
  12. [SW03]
    G. Smith and K. Winter. Proving temporal properties of Z specificatons using abstraction. In 3rd International Conference of Z and B USers (ZB 2003), LNCS. Springer-Verlag, 2003. This volume.Google Scholar
  13. [WB92]
    J.C.P. Woodcock and S.M. Brien. \( \mathcal{W} \) : A logic for Z. In Z User Workshop (ZUM’92), Workshops in Computing, pages 77–98. Springer-Verlag, 1992.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Kirsten Winter
    • 1
  • Graeme Smith
    • 1
  1. 1.Software Verification Research CentreUniversity of QueenslandAustralia

Personalised recommendations