Table Of ContentLogic of Programming and
Calculi of Discrete Design
NATO ASI Series
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Series F: Computer and Systems Sciences Vol. 36
Logic of Programming and
Calculi of Discrete Design
International Summer School directed by
F. L. Bauer, M. Broy, E. W. Dijkstra, C.A. R. Hoare
Edited by
Manfred Broy
Fakultat iUr Mathematik und Informatik, Universitat Passau
Postfach 2540, 8390 Passau, Federal Republic of Germany
Springer -Verlag
Berlin Heidelberg New York London Paris Tokyo
Published in cooperation with NATO Scientific Affairs Divison
Proceedings of the NATO Advanced Study Institute on Logic of Programming and
Calculi of Discrete Design held in Marktoberdorf, Federal Republic of Germany,
July 29-August 10, 1986
Library of Congress Cataloging in Publication Data. NATO Advanced Study Institute on Logic of Program
ming and Calculi of Discrete Design (1986 : Marktoberdorf, Germany) Logic of programming and calculi of
discrete design. (NATO ASI series. Series F, Computer and systems sciences; vol. 36) "Published in
cooperation with NATO Scientific Affairs Division." "Proceedings of the NATO Advanced Study Institute on
Logic of Programming and Calculi of Discrete Design held in Marktoberdorf, Federal Republic of Ger
many, July 29-August 10, 1986"-Verso t.p. 1. Formal languages-Congresses. I. Broy, M., 1949-. II. North
Atlantic Treaty Organization. Scientific Affairs Division. III. Title. IV. Series: NATO ASI series. Series F,
Computer and system sciences; no. 36. QA267.3.N38 1986005.13'1 87-20638
ISBN-13: 978-3-642-87376-8 e-ISBN-13: 978-3-642-87374-4
DOl: 10.1007/978-3-642-87374-4
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Softcover reprint of the hardcover 1st edition 1987
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Preface
In computing science design plays an eminently important role. By now, it is quite clear that the
issue of proper design of programs within a formal calculus is one of the most interesting and most
difficult parts of computing science. Many demanding problems have to be envisaged here such as
notations, rules and calculi, and the study of semantic models. We are 'far away from
comprehensive and widely accepted solutions in these areas. Discussions at the summer school
have clearly shown that people have quite different perspectives and priorities with respect to these
three main areas.
There is a general agreement that notation is very important. Here, notation is not so much used in
the sense of "syntactic sugar", but rather in the sense of abstract syntax, in the sense of language
constructs. Proper notation can significantly improve our understanding of the nature of the objects
that we are dealing with and simplify the formal manipulation of these objects. However,
influenced by educational background, habits, and schools of thought there are quite different tastes
with respect to notation. The papers in these proceedings show very clearly how different those
notations can be even when talking about quite similar objects.
There is also a general agreement that rules of inference, transformation rules, and rewriting rules,
forming calculi for proving and designing, are of major interest. But here, again, people might find
quite different opinions as to which forms of rules are best suited, which levels of reasoning are
best suited, how formal the reasoning should be. However, it is necessary to underline once more
that at least the machine needs a completely formal system when computing with information.
Computation in an abstract view always means working in a deductive theory with a concrete
control strategy.
Besides deductive theories, notations can refer to or express mathematical models, as is done, for
example, in denotational semantics. Basically, in this way, the meaning of the considered notation
is given in terms of well-known and well-understood mathematical concepts.
There was a lot of discussion within the summer school on the question "what is a mathematical or
semantic model good for?" Some people argued that semantic models should not be used at all
since they do not help us in formal reasoning. Other people argued that mathematical models are
necessary for our understanding of deductive theories and that as an ultimate goal understanding is
more important than formal manipulation. It is quite clear that the discussions within the summer
school did not come to a particular conclusion in that point. I invite the reader of this volume to go
through the articles and to make up his mind by himself. By doing so he may come to the
conclusion that model-oriented and deduction-oriented treatments of formalisms are not competing
but complementary approaches.
The individual lecture notes in this volume exhibit a wide spectrum of aspects of logic of
programming and calculi of discrete design. They range from general questions of logic and design
calculi to foundations of logic programming and questions of specification and verification of
programs, from algebraic specifications to special design calculi for particular structures such as
distributed systems, programs working with lists, or the logic of switching circuits.
Like each previous summer school in Marktoberdorf, this one also proved to be an undertaking that
benefited almost more from the ideas and understanding of the participants than it did from those of
the lecturers. The participants were motivated in following the lectures in a way which was hard to
believe, in attending discussions, in criticizing approaches and working hard on understanding and
maybe even improving the presented material. But also the lecturers gave outstanding presentations
such that the summer school again became a defmite highlight in our academic life.
This was complemented through the excellent organization and the perfect environment that we
again found in Marktoberdorf. Therefore I would like to thank here, once more, all the people who
worked hard to make this summer school a success and to prepare these fine proceedings which
give an excellent overview of the state of the art.
Passau, April 1987 Manfred Broy
Table of Contents
Part I: Programming Calculi 3
An Introduction to the Theory of Lists
R.S. Bird 5
A Heuristic Explanation of Batcher's Baffler
E.W. Dijkstra 43
Predicative Methodology
E.CR. Hehner, L.E. Gupta, andAJ. Malton 51
Termination Conventions and Comparative Semantics
E.CR. Hehner and AJ. Malton 79
Predicative Communications
E.CR. Hehner 99
Notes on Logic Programming
J A. Robinson 109
Part II: Specification and Verification Calculi 147
Program Specification and Verification in VDM
C.B. Jones: 149
Equational Specification of Partial Higher Order Algebras
M. Broy 185
Extreme Solutions of Equations
E. W. Dijkstra 243
Logic Based on Programming
E.CR. Hehner 261
Algebraic Specifications and Proofs for Communicating Sequential Processes
C.A.R. Hoare 277
Part ill: Design and Construction Calculi 303
Deduction and Computation
G.Huet 305
Expressing Program Developments in a Design Calculus
M. SintzofJ 343
Models and Logic of MOS Circuits
G. Winskel 367
List of Lecturers 415
F.L. Bauer
E.W. Dijkstra
2
E.C.R. Hehner
R.S. Bird
J.A. Robinson
Part I
Programming Calculi
Computation is just a special form of schematic deduction which may be called reduction.
Programming, which means the formal specification of computation patterns, can therefore be
viewed as the description of a schematic reduction process. In a computation certain rules are
applied that help to reduce a given term to a special"normal" form. The applied rules are part of the
theory underlying the basic computation structures that are also used as the basic programming
structures. The set of these rules forms a programming calculus which can be used for the
derivation of programs.
