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Z User Workshop, York 1991

Proceedings of the Sixth Annual Z User Meeting, York 16–17 December 1991

  • J. E. Nicholls

Part of the Workshops in Computing book series (WORKSHOPS COMP.)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Theoretical Foundations

    1. Front Matter
      Pages 1-1
    2. Alf Smith
      Pages 3-39
    3. R. D. Arthan
      Pages 40-58
    4. Antoni Diller
      Pages 59-76
    5. J. C. P. Woodcock, S. M. Brien
      Pages 77-96
  3. Scope of Use

    1. Front Matter
      Pages 97-97
    2. Rosalind Barden, Susan Stepney, David Cooper
      Pages 99-124
    3. Paul A. Swatman, Danielle Fowler, C. Y. Michael Gan
      Pages 125-144
    4. J. E. Nicholls
      Pages 145-156
    5. Samuel H. Valentine
      Pages 157-187
  4. Special Applications

    1. Front Matter
      Pages 189-189
    2. Michael Harrison
      Pages 191-204
  5. Tools

    1. Front Matter
      Pages 221-221
    2. Mark Saaltink
      Pages 223-242
    3. Dave Neilson, Divya Prasad
      Pages 243-258
  6. Structured Methods and Object-Oriented Approaches

    1. Front Matter
      Pages 259-259
    2. Roberto S. M. de Barros, David J. Harper
      Pages 261-286
    3. Fiona Polack, Mark Whiston, Peter Hitchcock
      Pages 287-328
    4. David Carrington
      Pages 352-364
  7. Bibliography etc

    1. Front Matter
      Pages 365-365
    2. Jonathan Bowen
      Pages 367-397
  8. Back Matter
    Pages 398-405

About these proceedings

Introduction

In ordinary mathematics, an equation can be written down which is syntactically correct, but for which no solution exists. For example, consider the equation x = x + 1 defined over the real numbers; there is no value of x which satisfies it. Similarly it is possible to specify objects using the formal specification language Z [3,4], which can not possibly exist. Such specifications are called inconsistent and can arise in a number of ways. Example 1 The following Z specification of a functionf, from integers to integers "f x : ~ 1 x ~ O· fx = x + 1 (i) "f x : ~ 1 x ~ O· fx = x + 2 (ii) is inconsistent, because axiom (i) gives f 0 = 1, while axiom (ii) gives f 0 = 2. This contradicts the fact that f was declared as a function, that is, f must have a unique result when applied to an argument. Hence no suchfexists. Furthermore, iff 0 = 1 andfO = 2 then 1 = 2 can be deduced! From 1 = 2 anything can be deduced, thus showing the danger of an inconsistent specification. Note that all examples and proofs start with the word Example or Proof and end with the symbol.1.

Keywords

calculus database formal method formal methods high-integrity software logic programming structured analysis

Editors and affiliations

  • J. E. Nicholls
    • 1
  1. 1.Programming Research GroupOxford University Computing LaboratoryOxfordUK

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-3203-5
  • Copyright Information Springer-Verlag London 1992
  • Publisher Name Springer, London
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-19780-5
  • Online ISBN 978-1-4471-3203-5
  • Series Print ISSN 1431-1682
  • Buy this book on publisher's site