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continued on back page ...
J.E. Nicholls (Ed.)
Z User Workshop,
York 1991
Proceedings of the Sixth Annual Z User
Meeting, York
16-17 December 1991
M
Published in collaboration with the ...
British Computer Society
Springer-Verlag
London Berlin Heidelberg New York
Paris Tokyo Hong Kong
Barcelona Budapest
J .E. Nicholls. MA
Oxford University Computing Laboratory
Programming Research Group
8-11 Keble Road
Oxford. OXI3QD. UK
ISBN-13: 978-3-540-19780-5 e-ISBN-13: 978-1-4471-3203-5
DOl: 10.1007/978-1-4471-3203-5
British Library Cataloguing in Publication Data
Z User Workshop, York, 1991 : Proceedings of the Sixth Annual Z User Meeting,
York. 16-17 December 1991. - (Workshops in Computing Series)
I. Nicholls, IE. II. Series
005.133
Library of Congress Cataloging-in-Publication Data
A catalog record for this book is available from the Library of Congress
Apart from any fair dealing for the purposes of research or private study, or
criticism or review, as permitted under the Copyright, Designs and Patents Act
1988, this publication may only be reproduced, stored or transmitted, in any form
or by any means. with the prior permission in writing of the publishers, or in the
case of repro graphic reproduction in accordance with the terms of licences issued
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©British Computer Society 1992
The use of registered names, trademarks etc. in this publication does not imply,
even in the absence of a specific statement, that such names are exempt from the
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The publisher makes no representation, express or implied, with regard to the
accuracy of the information contained in this book and cannot accept any legal
responsibility or liability for any errors or omissions that may be made.
34/3830-543210 Printed on acid-free paper
Contents
Theoretical Foundations
On Recursive Free Types in Z
A. Smith ............................................................................................... 3
On Free Type Definitions in Z
R.D. Arthan ......................................................................................... 40
Z and Hoare Logics
A. Diller ........... ..... ....... ..... ....... ........................ ..... ....... ............ ..... ....... 59
w:
A Logic for Z
J.C.P. Woodcock and S.M. Brien ....................................................... 77
Scope of Use
The UseofZ
R. Barden. S. Stepney and D. Cooper ............................................... 99
Extending the Useful Application Domain for Formal Methods
P.A. Swatman. D. Fowler and C.Y.M. Can ....................................... 125
Domains of Application for Formal Methods
J.E. Nicholls ........................................................................................ 145
Z--. an Executable Subset of Z
S.H. Valentine ..................................................................................... 157
Special Applications
Engineering Human-Error Tolerant Software
M. Harrison. Invited Speaker ............................................................ 191
Techniques for Partial Specification and Specification of
Switching Systems
P. Zave and M. Jackson
Presented by M. Jackson. Invited Speaker ........................................ 205
vi Contents
Tools
Z and Eves
M. Saaltink. Invited Speaker .............................................................. 223
zedB: A Proof Tool for Z Built on B
D. Neilson andD. Prasad ................................................................... 243
Structured Methods and Object-Oriented Approaches
A Method for the Specification of Relational Database
Applications
R.S.M. de Barros and D.J. Harper .................................................... 261
Structured Analysis - A Draft Method for Writing Z
Specifications
F. Polack. M. Whiston and P. Hitchcock ........................................... 287
Enhancing the Structure of Z Specifications
D. Duke ............................................................................................... 329
ZOOM Workshop Report
D. Carrington ..................................................................................... 352
Bibliography etc
Select Z Bibliography and Frequently Asked Questions
J. Bowen .............................................................................................. 367
Author Index ..................................................................................... 403
Introduction and Opening Remarks
J. E. Nicholls
(Chairman, Programme Committee)
Oxford University Computing Laboratory
Programming Research Group
This was the sixth in the series of Z User Meetings, and was held in the University of
York, one of the centres of excellence of Z in the U.K. We are grateful to Professor
John McDermid for the invitation to meet in York and for the help given by Sue
Helliwell in local arrangements.
During 1991 we experimented for the first time with a summer meeting. When this
was first proposed I had hopes of wooing Z users from the idea that all Z meetings
must be held in the chill of December. I'm afraid this objective didn't completely
succeed, and we have reverted to December as the usual meeting time for annual
meetings; from responses to our questionnaires, this seems to suit most people.
For this year, however, we had an additional meeting in the middle of the summer,
for which we came to Oxford and the bosky delights of Lady Margaret Hall, where we
met for two days to consider the effect of introducing object-oriented ideas in Z. This
was an invitation-only workshop, attended by those who had published papers or had
special experience of object-oriented approaches in conjunction with Z. David
Carrington, a visitor to the PRG from the University of Queensland, not only described
the Object-Z work being done in Queensland but also wrote an account of the
workshop, now included in these Proceedings. I am sure we will have further papers
and meetings on this topic, which continues to attract a great deal of attention among
Z users.
The sixth User Meeting was held at roughly the half-way point of the ZIP project,
the lED-funded project supporting research and application of Z. Several papers from
the project were presented: a description of a Survey of Z users, the outline and
objectives of an Application Compendium for Z, and a paper presenting a new Logic
for Z. These papers are included in these Proceedings and represent the latest thinking
on several aspects of the ZIP work.
In the opening remarks at the meeting I described the work on the Z Standard
being done as part of the ZIP project. We were able to give delegates to this meeting
a copy of the latest working document on the Standard. As I write these notes, things
have moved on, and I will therefore update these remarks with latest news on this
viii
aspect of the ZIP work. One thing to report is that the Z Standards project has applied
to have a standards panel set up under the BSI committee IST/5. Our case for
standardisation was based on the following:
the Z notation is mature and stable;
it is being used by numbers of industrial users;
these users have requested its standardisation.
The case for developing a Z standard under BSI was agreed technically at the IST/5
meeting on 10th March 1992. The committee stipulated that, in addition to the BSI
work, the standard should be put forward for ISO standardisation as soon as possible.
At the time of going to press we do not yet have a fully approved programme of work
but matters are proceeding in the direction of a BSI and ISO standard for Z.
Another event in 1991 was the formation of the organisation known as Formal
Methods Europe. This had evolved from the original VDM group, a group rather like
our own. As part of general support for formal methods, it is clearly an advantage to
have an organisation taking a broad view of all notations and methods, and with
international scope. At the end of this meeting in York I asked delegates their opinion
on our relationship to this new body, and found that most would like us to work
closely with FME, although some would also like us to continue as a distinctive Z
related group. During 1992 I suspect there will be continuing discussion of the role of
formal methods and the support needed for individual notations.
I should like to thank the programme committee who helped in arranging the
meeting, reviewing papers and introducing sessions:
Jonathan Bowen, Oxford University PRG
David Duce, Rutherford Appleton Laboratories
Brian Hepworth, British Aerospace
Tim Hoverd, Logica Cambridge
Darrell Ince, The Open University
Peter Lupton, IBM Hursley
John McDermid, University of York
Silvio Meira, University of Pernambuco, Brazil
John Nicholls, Oxford University PRG
Gordon Rose, University of Queensland
Chris Sennett, DRA Malvern
Jim Woodcock, Oxford University PRG
John Wordsworth, IBM Hursley
Finally I should like to acknowledge support of my own work on Z from the DTI,
under lED project No 1639 (the ZIP project).
Theoretical Foundations
ON RECURSIVE FREE TYPES IN Z
AlfSmith
DRAMalvern,
St. Andrews Road,
Great Malvern,
Worcs, WR14 3PS.
ABSTRACT
Inconsistent specifications may give rise to false conclusions in reasoning, thus
destroying the point of having a specification. This report is concerned with
inconsistent specifications which may arise when using the fonnal specification
language Z. In particular, the report is concerned with the inconsistencies that can
arise when using recursive free types, and recursive functions defmed over recursive
free types. The intended audience of the report consists of Z practitioners who wish
to avoid writing meaningless specifications.
© British Crown Copyright 1991
