Structuring Real-Time Object-Z Specifications

  • Graeme Smith
  • Ian Hayes
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1945)


This paper presents a means of structuring specifications in real-time Object-Z: an integration of Object-Z with the timed refinement calculus. Incremental modification of classes using inheritance and composition of classes to form multi-component systems are examined. Two approaches to the latter are considered: using Object-Z’s notion of object instantiation and introducing a parallel composition operator similar to those found in process algebras. The parallel composition ope- rator approach is both more concise and allows more general modelling of concurrency. Its incorporation into the existing semantics of real-time Object-Z is presented.


Process Algebra Environmental Output Cruise Control System Throttle Setting Composite Class 
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.
    J.S. Dong, J. Colton, and L. Zucconi. A formal object approach to real-time specification. In 3rd Asia-Pacific Software Engineering Conference (APSEC’96). IEEE Computer Society Press, 1996.Google Scholar
  2. 2.
    C.J. Fidge, I.J. Hayes, and B.P. Mahony. Defining differentiation and integration in Z. In J. Staples, M.G. Hinchey, and Shaoying Liu, editors, IEEE International Conference on Formal Engineering Methods (ICFEM’ 98), pages 64–73. IEEE Computer Society, 1998.Google Scholar
  3. 3.
    C.J. Fidge, I.J. Hayes, A.P. Martin, and A.K. Wabenhorst. A set-theoretic model for real-time specification and reasoning. In J. Jeuring, editor, Mathematics of Program Construction (MPC’98), volume 1422 of LNCS, pages 188–206. Springer-Verlag, 1998.CrossRefGoogle Scholar
  4. 4.
    V. Friesen. An exercise in hybrid system specification using an extension of Z. In A. Bouajjani and O. Maler, editors, Proceedings Second European Workshop on Real-Time and Hybrid Systems, pages 311–316. VERIMAG Laboratory, Grenoble, 1995.Google Scholar
  5. 5.
    B.P. Mahony. The Specification and Refinement of Timed Processes. PhD thesis, Department of Computer Science, University of Queensland, 1992.Google Scholar
  6. 6.
    B.P. Mahony. Using the refinement calculus for dataflow processes. Technical Report 94-32, Software Verification Research Centre, University of Queensland, October 1994.Google Scholar
  7. 7.
    B.P. Mahony and J.S. Dong. Blending Object-Z and Timed CSP: An introduction to TCOZ. In 20th International Conference on Software Engineering (ICSE’98), pages 95–104. IEEE Computer Society Press, 1998.Google Scholar
  8. 8.
    B.P. Mahony and J.S. Dong. Sensors and actuators in TCOZ. In J. Wing, J. Wood-cock, and J. Davies, editors, World Congress on Formal Methods (FM’99), volume 1709 of Lecture Notes in Computer Science, pages 1166–1185. Springer-Verlag, 1999.Google Scholar
  9. 9.
    B.P. Mahony and I.J. Hayes. A case-study in timed refinement: A mine pump. IEEE Transactions on Software Engineering, 18(9):817–826, September 1992.Google Scholar
  10. 10.
    K. Periyasamy and V.S. Alagar. Extending Object-Z for specifying real-time systems. In TOOLS USA’97: Technology of Object-Oriented Languages and Systems, pages 163–175. IEEE Computer Society Press, 1998.Google Scholar
  11. 11.
    G. Smith. A fully abstract semantics of classes for Object-Z. Formal Aspects of Computing, 7(3):289–313, 1995.CrossRefGoogle Scholar
  12. 12.
    G. Smith. The Object-Z Specification Language. Advances in Formal Methods. Kluwer Academic Publishers, 2000.Google Scholar
  13. 13.
    G. Smith and I. Hayes. Towards real-time Object-Z. In K. Araki, A. Galloway, and K. Taguchi, editors, 1st International Conference on Integrated Formal Methods, pages 49–65. Springer-Verlag, 1999.Google Scholar
  14. 14.
    J.M. Spivey. The Z Notation: A Reference Manual. Prentice Hall, 2nd edition, 1992.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Graeme Smith
    • 1
  • Ian Hayes
    • 2
  1. 1.Software Verification Research CentreAustralia
  2. 2.School of Computer Science and Electrical EngineeringUniversity of QueenslandAustralia

Personalised recommendations