On transferring VDM verification techniques to Z

  • Peter A. Lindsay
Part of the Lecture Notes in Computer Science book series (LNCS, volume 873)


This paper discusses some of the necessary prerequisites for transferring specification analysis and verification techniques from VDM to Z. It starts by comparing Z and VDM in terms of the mathematical and specification notations they use. It then explains the VDM approach to reasoning about specifications, as supported by the mural tool-set, and compares VDM's Logic of Partial Functions with Classical Logic. It outlines VDM proof obligations for checking consistency and completeness of specifications, and illustrates their use on a small example, comparing the results with a Z-like analysis. The paper concludes with a brief discussion of how the W logic for Z might be modified for LPF.


Direct Acyclic Graph Classical Logic Partial Function Proof Obligation Verification Technique 
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]
    H. Barringer, J.H. Cheng, and C.B. Jones. A logic covering undefinedness in program proofs. Acta Informatica, 21:251–269, 1984.CrossRefGoogle Scholar
  2. [2]
    J.C. Bicarregui, J.S. Fitzgerald, P.A. Lindsay, R. Moore, and B. Ritchie. Proof in VDM: A Practitioner's Guide. FACIT Series. Springer-Verlag, 1994. ISBN no. 3-540-19813-X.Google Scholar
  3. [3]
    S.M. Brien and J.E. Nicholls. Z Base Standard, Version 1.0. Technical Report SRC D-132, Oxford University Programming Research Group, November 1992.Google Scholar
  4. [4]
    British Standards Institute, Working Group IST/5/19. VDM Specification Language Proto-Standard: Draft, November 1993.Google Scholar
  5. [5]
    J.H. Cheng. A logic for partial functions. Technical Report UMCS-86-7-1, University of Manchester, Department of Computer Science, 1986.Google Scholar
  6. [6]
    S. Gilmore. Correctness-Oriented Approaches to Software Development. PhD thesis, University of Edinburgh, Department of Computer Science, 1991.Google Scholar
  7. [7]
    A. Hall. A response to Florence, Dougal and Zebedee. FACS Europe, 1(1):31–32, 1993.Google Scholar
  8. [8]
    I. Hayes. VDM and Z: A comparative case study. Formal Aspects of Computing, 4(1):76–99, 1992.Google Scholar
  9. [9]
    I. Hayes, editor. Specification Case Studies. Prentice-Hall, second edition, 1993. First Edition published in 1987.Google Scholar
  10. [10]
    I.J. Hayes, C.B. Jones, and J.E. Nicholls. Understanding the differences between VDM and Z. FACS Europe, 1(1):7–30, Autumn 1993.Google Scholar
  11. [11]
    W. Hodges. Another semantics for Z. draft preprint, August 1991.Google Scholar
  12. [12]
    C.B. Jones. Systematic Software Development Using VDM. Prentice Hall, New York, second edition, 1990.Google Scholar
  13. [13]
    C.B. Jones, K.D. Jones, P.A. Lindsay, and R. Moore. Mural: A Formal Development Support System. Springer-Verlag, 1991.Google Scholar
  14. [14]
    C.B. Jones and C.A. Middelburg. A typed logic of partial functions reconstructed classically. Technical Report Logic Group Preprint Series 89, Department of Philosophy, Utrecht University, April 1993.Google Scholar
  15. [15]
    P.A. Lindsay and E. van Keulen. Case studies in the verification of specifications in Z and VDM. Technical Report TR 94-3, Software Verification Research Centre, University of Queensland, March 1994. Available by anonymous ftp from Scholar
  16. [16]
    B. Monahan and R. Shaw. Model-based specifications. In J.A. McDermid, editor, Software Engineer's Reference Book, chapter 21. Butterworth-Heinemann, London, 1991.Google Scholar
  17. [17]
    J.C.P. Woodcock. Calculating properties of Z specifications. ACM SigSoft Software Engineering Notes, 14(5):43–54, 1989.Google Scholar
  18. [18]
    J.C.P. Woodcock and S.M. Brien. W: a logic for Z. In J.E. Nicholls, editor, Z User Workshop, York 1991. Springer-Verlag, 1992. Proceedings of the Sixth Annual Z User Meeting.Google Scholar
  19. [19]
    J.B. Wordsworth. Software Development with Z: a Practical Approach to Formal Methods in Software Engineering. Addison-Wesley, Wokingham, England, 1992.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Peter A. Lindsay
    • 1
  1. 1.Software Verification Research CentreUniversity of QueenslandSt LuciaAustralia

Personalised recommendations