Table Of ContentProgram Design Calculi
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Series F: Computer and Systems Sciences Vol. 118
Program Design Calculi
Edited by
Manfred Bray
Institut fOr Informatik
Technische Universitat MOnchen
Arcisstr. 21, D-80333 MOnchen, Germany
Springer-Verlag Berlin Heidelberg GmbH
Proceedings of the NATO Advanced Study Institute on Program Oesign Calculi,
held in Marktoberdorf, Germany, July 28 - August 9, 1992
CR Subject Classification (1991): 0.1, 0.2.4, 0.2.10
ISBN 978-3-642-08164-4 ISBN 978-3-662-02880-3 (eBook)
DOI 10.1007/978-3-662-02880-3
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© Springer-Verlag Berlin Heidelberg 1993
Originally published by Springer-Verlag Berlin Heidelberg New York in 1993
Softcover reprint of the hardcover 1 st edition 1993
Typesetting: Camera ready by authors
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Preface
The development of information processing systems requires models, calculi, and theories
for the analysis of computations. It is well understood by now that more complex software
systems cannot and should not be constructed in one step. A careful, systematic, and
disciplined structuring of the development process is most adequate. It should start from
basic requirement specifications in which aU the relevant details of the problem to be solved
are formalized. The envisaged solution should be developed step by step by adding more
and more details and giving evidence-in the best case by formal proof-to show the
correctness of the developed steps. The development ends if a description of a solution is
obtained that has aU the required properties.
The Summer School in Marktoberdorf 1992 showed significant approaches in this area to
refinement calculi, to models of computation, and as a special issue to the treatment of
reactive timed systems. Like in the many summer schools before, the success of the 1992
Summer School was not only due to the excellent lectures, but even more due to the brilliant
students taking part in the discussions at the summer school, the exchange of different
views, and the recognition of the similarity of a number of different view points. These were
some of the most important contributions of the summer school.
fu the following the proceedings of the summer school are collected. They show the maturity
of the field in an impressive way.
It is my pleasure to thank here all the people who helped to make the summer school a full
success. This includes the members of the organizing staff, in particular Ingrid Luhn and
Ralf Steinbriiggen, and our hosts in Marktoberdorf. Special thanks go to Klaus Bergner
who did an excellent job in helping to edit this volume.
The advanced study institute was realized with financial aid of the Commission of the
European Communities and the European Research Office of the u.S. Army.
Munich, March 1993 Manfred Broy
Table of Contents
Part 1: Refinement ..................................................................................... 1
The Refinement Calculus ................................................................................ 3
Carroll Morgan
Refinement Calculus, Lattices, and Higher Order Logic .................... 53
R.J.R. Back
Refinement of Parallel and Reactive Systems ...................................... 73
R.1.R. Back
Data Refinement and the Transform ........................................................ 93
David Gries
(Inter-)Action Refinement: The Easy Way............................................. 121
Manfred Broy
Part 2: Models and Calculi of Computation ......................... 159
Algebra and Models ......................................................................................... 161
C.A.R. Hoare
The Unification of Three Calculi .................................................................. 197
Edsger W. Dijkstra
Monads for Functional Programming ....................................................... 233
Philip Wadler
How Hard Is It to Reason About Propositional Programs? ............. 265
David Harel
VIII
Part 3: Reactive Timed Systems ....................................................... 285
A Temporal Proof Methodology for Reactive Systems ..................... 287
Zohar Manna. Amir Pnueli
Timed Process Algebras: A Tutorial .......................................................... 325
Matthew Hennessy
The Semantics of Pure Esterel ..................................................................... 361
Gerard Berry
Part 1
Refinement
Program development should be done step by step. This means that more and more detailed
versions of a description of a software system are obtained. It is very important to have a
clear mathematical relationship between the different versions in the development. The
following five chapters treat such relationships under the heading of refinement. They not
only define the relationships between different versions but also give calculi to prove such a
relationship. Although sometimes looking quite different, a closer inspection shows that the
approaches are much more similar than one might see at a first glance.
