Computer Program Synthesis Methodologies: Proceedings of the NATO Advanced Study Institute held at Bonas, France, September 28–October 10, 1981

378 Pages·1983·18.252 MB·English

by  Manfred Broy (auth.), Alan W. Biermann, Gérard Guiho (eds.)

Computer Program Synthesis Methodologies
NATO ADVANCED STUDY INSTITUTES SERIES
Proceedings of the Advanced Study Institute Programme, which aims
at the dissemination ofa dvanced knowledge and
the formation of contacts among scientists [rom different countries
The series is published by an international board of publishers in conjunction
with NATO Scientific Affairs Division
A Life Sciences Plenum Publishing Corporation
B Physics London and New York
C Mathematical D. Reidel Publishing Company
and Physical Dordrecht, Boston and London
Sciences
D Behavioural and
Social Sciences Martinus Nijhoff Publishers
E Engineering and The Hague, London and Boston
Materials Sciences
F Computer and Springer Verlag
Systems Sciences Heidelberg
G Ecological Sciences
Series C - Mathematical and Physical Sciences
Volume 95 - Computer Program Synthesis Methodologies
Computer Program
Synthesis Methodologies
Proceedings oft he NATO Advanced Study Institute
held at Bonas, France, September 28 -October 10, 1981
edited by
ALAN W. BIERMANN
Duke University, Department of Computer Science, Durham, NC, U.S.A.
and
GERARD GUIHO
Laboratoire de Recherche en Informatique, Universite de Paris-Sud, Orsay, France
D. Reidel Publishing Company
Dordrecht: Holland / Boston: U.S.A. / London: England
Published in cooperation with NATO Scientific Affairs Division
library of Congress cataloging in Publication Data
NATO Advanced Study Institute (1981 : Bonas, France)
Computer program synthesis methodologies.
(NATO advanced study institutes series. Series C, Mathematical
and physical sciences; v. 95)
"Published in cooperation with NATO Scientific Affairs Division."
Includes indexes.
1. Electronic digital computers-Programming-Congresses.
I. Biermann, Alan W., 1939- II. Guiho, Gerard, 1945-
III. Title. IV. Series.
QA76.6.N378 1981 001.64'2 82-16704
ISBN-\3: 978-94-009-7021-2 e-ISBN-\3: 978-94-009-7019-9
DOl: 10.1007/978-94-009-7019-9
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TABLE OF CONTENTS
Preface vii
M. BROY / Program Construction by Transformations:
A Family Tree of Sorting Programs
M. SINTZOFF / Issues in the Methodical Design of
Concurrent Programs 51
R. BACKHOUSE / An Analysis of Choice in Program Design 79
P. C. GOLDBERG / The Design of Very High Level Languages 125
•
P. C. GOLDBERG / Implementation Considerations 1n
Very High Level Languages 147
H. GALLAIRE / A Study of Prolog 173
J.-P. JOUANNAUD and Y. KODRATOFF / Program Synthesis
from Examples of Behavior 213
Z. MANNA and R. WALDINGER / Deductive Synthesis of
the Unification Algorithm 251
J. DARLINGTON / The Synthesis of Implementations
for Abstract Data Types,
A Program Transformation Tactic 309
A. W. BIERMANN / Natural Language Programming 335
AUTHOR INDEX 369
SUBJECT INDEX 373
PRE F ACE
Ever since the early days of computing, programmers have
been seeking ways to automate portions of the programming task.
The first major step was the invention of assemblers which
allowed mneumonic operation codes,handled certain addressing
tasks and offered other functions. Next came a vast array of
compiled and interpreted languages which implemented many data
structures, flow-of-control features, and notational conveniences.
In an attempt to continue this trend today. a number researchers
are developing program synthesis methodologies which aim at
making further automation possible. Most of these methodologies
fall into one of the categories:
a) extensions to traditional programming methods,
b) synthesis of programs from examples,
c) synthesis from formal input-output specifications,
d) program construction from natural language dialogue.
These program synthesis methodologies are the subject of
this book.
The first three chapters examine the program synthesis issue
largely without regard to the automation problem. Systematic
means are described for constructing programs with emphasis on
what is the nature of the synthesis task and how can it be
approached. M. BROY describes a transformational technique for
deriving programs from their specifications. M. SINTZOFF
describes central issues in the design of concurrent programs,
and R. BACKHOUSE gives a methodology for decision making in
program design that accounts both for correctness and efficiency.
The later chapters of the book sequentially address the
four approaches to synthesis given above. Extensions to
traditional programming methods often involve the construction
of very high level languages to deal with larger objects (data
structures) than traditional languages with appropriately more
vii
A. W. Biermann and G. Guiho (eds.). Computer Program Synthesis Methodologies, vii-ix.
Copyright © 1983 by D. Reidel Publishing Company.
viii PREFACE
powerful operations on them. An early step in this direction
was the development of APl, and more recent examples have been
SETl which enables a user to code in terms of mathematical enti
ties such as sets and BDl which allows a user, presumably a
businessman, to specify a computation in terms of a series of
tabular forms and a series of processing paths through which
data flows. The design and implementation of such languages are
examined in chapters by P. GOLDBERG.
Another extension to traditional methods is made possible
by systems designed to automatically handle low level flow-of
control decisions. All the above higher level languages do
this implicitly with their built in operators. PROLOG is a
language which does this with a theorem proving mechanism
employing primarily unification and backtracking. The programmer
specifies the problem to be solved with a set of formal logic
statements including a theorem to be proved. The theorem proving
system finds a way to combine the axioms to prove the theorem,
and in the process, it completes the desired calculation.
H. GAllAIRE has contributed a chapter describing PROLOG giving
many examples of its usage.
There are many situations in machine programming where it
is more natural to give examples of what is wanted than to give
programs. As an illustration, the operator of an automatic machine
tool would probably prefer to manually direct the device
through an example machining sequence and have it self program
to do that sequence than to code the sequence using a symbolic
language. The machine operator can be sure in the example
sequence that all processes occur as desired and will probably
produce a more reliable control program than if he or she had
written the program directly. As a illustration, a person
s~cond
formating a piece of text would probably much rather organize
the page using a manual graphics device of some kind and then
have an automatic editor create the command sequence to actually
space out and format the text items correctly. A fascinating
domain for these kinds of studies has been in the synthesis of
IISP programs from examples of their input-output behaviors.
J.P. JOUANNAUD and Y. KODRATOFF have included a chapter describing
some of this work.
Another way to construct programs automatically is to
deduce them from their input-output specifications. The speci
fications are given with a formal language but they do not
give the method for doing the computation. The automatic
system attempts to transform the specifications in a sequence
of steps to the target program. The result program is guaranteed
to implement the specifications and to terminate on legitimate
inputs. Z. MANNA and R. WALDINGER give a deductive method for
this type of synthesis where a theorem is proved and the target
PREFACE ix
program is a by-product of the theorem proving process. The
following chapter by J. DARLINGTON describes a transformational
approach.
One of the ways in which nonprogrammers will be able to
interact with computers of the future will be via typed or spoken
natural language. While this may seem to be an impractical alter
native in the near term, some progress has been made. The final
chapter by A. BIERMANN discusses a system for natural language
programming that has been developed to the pOint that college
students can use it to solve problems typical of a first course
in programming.
ACKNOWLEDGEMENTS
This book is the proceedings of the 1981 NATO Advanced Study
Institute on Automatic Program Construction which was held in
October 1981. This meeting has been made possible through the
financial support and the framework provided by the NATO
Scientific Affairs Division.
As Directors of the NATO Institute, we would like to thank
all the participants for their valuable participation in the dis
cussions and panel presentations which finally made a great success
of this Institute. We are grateful to our host and hostess at the
Chateau Professor and Mrs. J.C. SIMON, animateur of the Centre
Culturel de Bonas, for providing a delightful environment for the
Institute. We would also like to thank the chapter authors for
their careful preparation of the chapters and the secretarial staff
at the Laboratoire de Recherche en Informatique d'Orsay for their
help in assembling this volume.
PROGRAM CONSTRUCTION BY TRANSFORMATIONS A FAMILY TREE OF
SORTING PROGRAMS.
Manfred BROY
Technische Universitat Munchen
Institut fur Informatik
Postfach 20 24 20
D-8000 MUNCHEN 2
The construction of a program is considered as a process consis
ting of a sequence of formal steps. Each step is characterized by a
particular transformation rule. In general, the development starts
with a formal specification and ends with an efficient program.
In the first part of this paper this methodology and its formal
foundations are briefly outlined. In the second part a number of
sorting programs is developed along these lines leading to a deci
sion tree of the program family of different sorting programs.
1. PROGRAM CONSTRUCTION BY TRANSFORMATIONS
In order to manage the enormous complexity of the activity of
writing a program it seems indispensable to organize the develop
ment process in a formal way leading through a series of more and
more detailed versions (cf. (4». The switch from one version
to the other is called a program transformation, an instruction
how to perform this switch is called a transformation rule.
The reliability and understandability of the development and thus
our confidence in the resulting piece of software obviously can
be increased if both the steps and the single versions are repre
sented in formal notation, such that all development stages can
always be properly verified. A rigorous observation of this pro
ceding leads to considering programming as a formal activity
(cf. (17». Using formal notations moreover allows conveniently to
support the development process by an interactive development sys
tem.
This wopk was oappied out within the Sondepfopsohungsbepeioh 49 -
"Progparroniepteohnik" - Munioh. .
A. W. Biermann and G. Guiho (eds.), Computer Program Synthesis Methodologies, 1-49.
Copyright © 1983 by D. Reidel Publishing Company.
2 M.BROY
A first approach to a system for program development by transfor
mations has been undertaken by R.M. Burstall and J. Darlington
(see e.g. (28), (23». In the meanwhile related efforts have been
made elsewhere (33), (51), (54), (I), (2), (39), for a comprehen
sive survey see (46).
Of course, the basic motivations of the different groups working
in the fiels of program transformations are rather different.
First there are groups which are only interested in small local
program transformations as part of an optimizing compiler. They
only want to liberate the programmer from doing these tricky and
burdensone local optimizations by hand. Second there are projects
which consider program transformations as a tool in program design
and development, i.e. as being part of the discipline of program
ming. Third there are people which try to automatize the process
of program construction as much as possible leading to program
synthesis.
Of course, there are no sharp boundaries between these three
approaches. In their extreme cases the first approach is not very
interesting for program development and the third one may not be
very realistic on account of the undecidability results of for
mal logics.
In this paper we follow the second approach, trying to show the
power of program transformations as a design tool in the process
of program construction.
1.1. Significance of notation
Program development by transformation, of course, is independent
from particular notations or programming languages. Both the rules
and the program versions may be described informally in natural
language. However, in man-machine communication or if a mathema
tically proper proof is aimed at, both the programs to be trans
formed and the resp. rules have to be represented by a formal lan
guage. In principle, any programming language could be used, but
not all languages are equally well suited, at least for particu
lar problem areas or particular levels of abstraction. To gain
optimal freedom, flexibility and formal soundness by allowing
smooth transitions between different levels of abstraction a spe
cial "Wide Spectrum Language" called CIP-L has been designed
within the project CIP (cf (8), (10». This language comprises
constructs for problem specification, applicative and procedural
programming. Hence the programmer can very flexibly choose the
appropriate style for his specific problem.
1.2. Transformation rules
Basically, a transformation is the generation of a new piece of
program from a given one; it is said to be correct, if both pro-