The Z Notation

  • V. S. Alagar
  • K. Periyasamy
Part of the Graduate Texts in Computer Science book series (TCS)


The Z notation (pronounced as zed, named after the German mathematician Ernst Zermelo) originated at the Oxford University Computing Laboratory, UK, and has evolved over the last decade into a conceptually clear and mathematically welldefined specification language. The mathematical bases for Z notation are ZF set theory and the classical two-valued predicate logic. An interesting feature of the Z specification language is the schema notation. Using schemas, one can develop modular specifications in Z and compose them using schema calculus.


Global Constraint Resource Type Operation Schema Proof Obligation Predicate Part 
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.


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  1. [1]
    VS. Alagar and K. Periyasamy, “Real-Time Object-Z: A Language for the Specification and Design of Real-Time Reactive Systems,” Technical Report, Department of Computer Science, Concordia University, Montreal, Canada, June 1996.Google Scholar
  2. [2]
    P. Baumann and K. Lermer, “A Framework for the Specification of Reactive and Concurrent Systems in Z,” Proceedings of the Fifteenth Conference on Foundations of Software Technology and Theoretical Computer Science; published as Lecture Notes in Computer Science Series, Vol. 1026, Springer-Verlag, 1995, pp. 62–79.MathSciNetCrossRefGoogle Scholar
  3. [3]
    J.M. Carrido, “Specification of Real-Time Systems with Extensions to Object-Z,” Proceedings of Technology of Object-Oriented Languages and Systems (TOOLS USA), Santa Barbara, CA, 1995, pp. 167–179.Google Scholar
  4. [4]
    A.C. Coombes and J.A. McDermid, “Specifying Temporal Requirements for Distributed Real-Time Systems in Z,” Technical Report YCS176, Computer Science Department, University of York, Heslington, York, England, 1992.Google Scholar
  5. [5]
    R. Duke, G. Rose, and G. Smith, “Object-Z: A Specification Language for the Description of Standards,” Computer Standards & Interfaces, Vol. 17, 1995, pp. 511–533.CrossRefGoogle Scholar
  6. [6]
    I.J. Hayes (Ed.), Specification Case Studies, Prentice Hall International (UK), 1987.Google Scholar
  7. [7]
    B.P. Mahony and I.J. Hayes, “A Case-Study in Timed Refinement: A Mine Pump,” IEEE Transactions on Software Engineering, Vol. 18, No. 9, September 1992, pp. 817–826.CrossRefGoogle Scholar
  8. [8]
    S.L. Meira and A.L.C. Cavalcanti, “The MooZ Specification Language,” Technical Report, Departamento de Informática, Universidade Federal de Pernambuco, Recife — PE, Brasil, 1992.Google Scholar
  9. [9]
    C. Morgan and T. Vickers (Eds.), On the Refinement Calculus, Springer-Verlag, London, England, 1994.Google Scholar
  10. [10]
    B. Potter, J. Sinclair, and D. Till, An Introduction to Formal Specification and Z, Prentice Hall International (UK), 1991.MATHGoogle Scholar
  11. [11]
    J.M. Spivey, The fuzz Reference Manual, J.M. Spivey Computing Science Consultancy, Oxford OX44 9AN, U.K., 1992.Google Scholar
  12. [12]
    J.M. Spivey, The Z Notation — A Reference Manual (second edition), Prentice Hall International (UK), 1992.Google Scholar
  13. [13]
    S. Stepney, R. Barden, and D. Cooper (Eds.), Object-Orientation in Z, Workshops in Computing Series, Springer-Verlag, London, England, 1992.Google Scholar
  14. [14]
    J.C.P. Woodcock and J. Davies, Using Z: Specification, Refinement and Proof, Prentice Hall International (UK), 1996.MATHGoogle Scholar
  15. [15]
    J.B. Wordsworth, Software Development with Z, Addison-Wesley Publishing Company, International Computer Science Series, 1992.Google Scholar
  16. [16]
    The Z Notation, ISO/IEC JTC 1/SC22 CD 13568, September 1995.Google Scholar

Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • V. S. Alagar
    • 1
  • K. Periyasamy
    • 2
  1. 1.Department of Computer ScienceConcordia UniversityMontrealCanada
  2. 2.Department of Computer ScienceUniversity of ManitobaWinnipegCanada

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