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Texts and Monographs in Computer Science,Study Edition. Edward Cohen, Programming in the 1990s An Introduction to the Calculation of Programs. 1990 XV 265 pages,SuadAlagie,Object Oriented Database Programming. 1989 XV 320 pages 84 iUus,SuadAlagie,Relational Database Technology. 1986 XI 259 pages 114 iUus,Suad Alagie and Michael A Arbib.
The Design of Well Structured and Correct Programs. 1978 X 292 pages 68 iUus,S Thomas Alexander, Adaptive Signal Processing Theory and Applications. 1986 IX 179 pages 42 iUus,Michael A Arbib AJ Kfoury and Robert N Moll. A Basis for Theoretical Computer Science,1981 VIII 220 pages 49 iUus. Friedrich L Bauer and Hans Wtissner,Algorithmic Language and Program Development. 1982 XVI 497 pages 109 illus,Kaare Christian,A Guide to Modula 2.
1986 XIX 436 pages 46 illus,Edsger W Dijkstra, Selected Writings on Computing A Personal Perspective. 1982 XVII 362 pages 13 illus,Edsger W Dijkstra and Carel S Scholten. Predicate Calculus and Program Semantics,1990 XII 220 pages. W H J Feijen AJ M van Gasteren D Gries and J Misra Eds. Beauty Is Our Business A Birthday Salute to Edsger W Dijkstra. 1990 XX 453 pages 21 illus,Melvin Fitting,First Order Logic and Automated Theorem Proving. 1990 XIV 242 pages 26 illus,continued after index,Programming.
in the 19908,An Introduction to the,Calculation of Programs. Edward Cohen,Springer Verlag,New York Berlin Heidelberg. London Paris Tokyo Hong Kong,Edward Cohen,Software Logic Limited. P O Box 565,Brookline Massachusetts 02146,Series Editor. David Gries,Department of Computer Science,Cornell University.
Ithaca NY 14853, Library of Congress Cataloging in Pubilcation Data. Cohen Edward, Programming in the 1990s an introduction to the calculation of. programs Edward Cohen Study ed,p cm Texts and monographs in computer science. Includes bibliographical references and index, l Electronic digital computers Programming I Title. QA 76 6 C6235 1990,005 dc20 90 10152,Printed on acid free paper.
1990 Springer Verlag New York Inc, All rights reserved This work may not be translated or copied in whole or in part without the. written permission of the publisher Springer Verlag New York Inc 175 Fifth Avenue New. York NY 10010 USA except for brief excerpts in connection with reviews or scholarly analy. sis Use in connection with any form of information storage and retrieval electronic adaptation. computer software or by similar or dissimilar methodology now known or hereafter developed is. The use of general descriptive names trade names trademarks etc in this publication even if. the former are not especially identified is not to be taken as a sign that such names as under. stood by the Trade Marks and Merchandise Marks Act may accordingly be used freely by. Photocomposed copy prepared by the author using LaTEX. 9 8 7 6 5 4 3 2 I, ISBN 13 978 0 387 97382 1 e ISBN 13 978 1 4613 9706 9. DOl 10 1007 978 1 4613 9706 9,To my grandmother,and to my parents. Programming is a fascinating and challenging subject Unfortunately it is. rarely presented as such Most often it is taught by induction features. of some famous programming language are given operational meaning e g. a loop goes round and round a number of examples are shown and by. induction we are asked to develop other programs often radically different. from the ones we ve seen Basically we are taught to guess our programs. and then to patch up our guesses Our errors are given the cute name of. bugs Fixing them becomes puzzle solving as does finding tricks that. exploit or avoid poorly designed features of the programming language. The entire process is time consuming and expensive And even so we are. never quite sure if our programs really work in all cases. When approached in this way programming is indeed a dull activity. There is however another approach to programming an approach in which. programs can be developed reliably with attention to the real issues It is a. practical approach based on methodically developing programs from their. specifications Besides being practical it is exciting Many programs can. be developed with relative ease Once difficult problems can be solved by. beginners Elegant solutions bring great satisfaction. This is our subject We are interested in making programming an exciting. The material in this book is of course not pulled from thin air It is due. to a number of serious expert programmers the best known being E W. Dijkstra and D Gries and has been developed in Europe and the U S over. many years The examples come from a number of sources. The text is self contained and is designed to be comfortably explored in a. single semester It can be used in a number of ways. Because it is self contained it is well suited for an introductory course. on programming Realizing that the recent advances in programming. viii Preface, are unfamiliar to many people it is also appropriate for a second or. third course either undergraduate or graduate or for self study by. practicing programmers interested in keeping up to date. Because of its size it can be used in a single semester course or can be. covered slowly over two semesters For a two semester course it can. also be supplemented Suggested sources of supplemental material are. mentioned at the end, Although a book about programming and not about programming in.
language X for whatever X a notation had to be chosen for writing. down programs Dijkstra s guarded commands was the choice Frankly. this choice was so obvious that nothing else was considered They are an. ideal vehicle For one thing they are simple only one type of loop only one. type of if statement so we don t get bogged down in a myriad of some. times questionable programming language features But the main thing. was that they were designed to nicely accomodate program development. An instructor can of course substitute another programming language. but I wouldn t recommend it Readers familiar with other languages can. easily translate their programs And when the text is used in an introduc. tory course in a curriculum requiring proficiency in Pascal say the text. can be supplemented with lectures and exercises on that language This. approach has a number of advantages Because they will already be famil. iar with programming students will be able to master the language with. ease Further they will be in a position to evaluate its advantages and dis. advantages We mention this because many introductory courses do not. distinguish programming from programming in language X In such. cases X must be taken for granted, The exercises are exceedingly important This cannot be overstated Exer. cises are the only way the material goes from the head to the fingertips I. have found it beneficial to scatter certain exercises especially those involv. ing predicates throughout the semester Such reinforcement helps students. become comfortable with the manipulations, I hope that this book is enjoyable and hope that many things are learned. My main hope however is that programming is revealed for what it really. is a fascinating subject worthy of further study,ACKNOWLEDGEMENTS. My deepest gratitude goes to three people, o Professor Wim H J Feijen University of Technology Eindhoven The. Preface ix, Netherlands whose good taste clear writing and ongoing quest for per.
fection in programming have been a great inspiration to me It was his. suggestion that I undertake this project and while in progress he spent. many hours showing me many improvements His influence is on every. o Professor David Gries Cornell University Ithaca NY USA who first. taught me that programming properly approached is a science and that. programs can be developed in a reliable and elegant way Without this. exposure I would been bored years ago Instead I have been continuously. rewarded In the years since he has helped me many times. o Professor Edsger W Dijkstra University of Texas Austin TX USA. whose lectures and writings have inspired me over many years The central. ideas in this book are his as are most of the techniques shown His contri. butions are many and are fundamental Along the way he has generously. answered all my questions, Very special thanks to Vit Novak whose high standards and good sense. have helped at every step from the lectures that led to this book to the. book itself Thanks also to Mike Sheldon who offered excellent comments. on successive drafts of each chapter to Mark Schneider and Ted Czotter for. never being satisfied with anything that I did always forcing me to improve. my presentations and never allowing me to wave my hands Thanks to Kaia. Cornell for comments on an early draft of the manuscript to Edgar Knapp. for desperately needed u TEX help to Professor Fred B Schneider Cornell. University Ithaca NY USA for his comments on the almost final version. and to Gerhard Rossbach of Springer Verlag, Finally I would like to thank the CSCI 264 students at Harvard Extension. Edward Cohen,Boston MA USA,April 1990,Preface Vll,o What can we learn from a cake 1. 0 0 Introduction 1,0 1 What can we learn from a cake 1. 1 Preliminary notions notations and terminology 9,1 0 Introduction 9.
1 1 The shapes of our calculations 9,1 2 Laws and so on 11. 1 3 On avoiding parentheses 12,1 4 On carrying out calculations 14. 1 5 Three new arithmetic operators 20,1 6 The problem with the three dots 21. 1 7 What are the natural numbers 22,1 8 A bit about function application 23. 1 9 What next 25,2 Predicates A Boolean operators 27.
2 0 Introduction 27,2 1 The equivalence 27,xii Contents. 2 2 The disjunction 29,2 3 Intermezzo on some interesting formulae 30. 2 4 The conjunction 31,2 5 The implication 34,2 6 The consequence 36. 2 7 The negation 37,2 8 The discrepancy 40,2 9 Summary of binding powers 41. 2 10 Final comments 41,2 11 Exercises 41,3 Predicates B Quantified expressions 45.
3 0 How to write quantified expressions 45,3 1 Laws for quantified expressions 46. 3 2 Universal quantification 52,3 3 Existential quantification 54. 3 4 Some arithmetic quantifications 56,3 5 Other quantified expressions 58. 3 6 Additional exercises 58,4 Specifications 61,4 0 Introduction 61. 4 1 Assigning meaning to our predicates 61,4 2 Towards writing specifications 65.
4 3 Examples of specifications 68,4 4 Intermezzo on the array 70. 4 5 More examples of specifications 71,Contents xiii. 4 6 Intermezzo on ascending functions 73,4 7 Even more examples of specifications 74. 4 8 Other notations for functional specifications 76. 4 9 Comments on specifications 77,5 The shapes of programs 81. 5 0 Introduction 81,5 1 The shapes of programs 81,5 2 When is a program correct 83.
5 3 A bit about wp S 85,5 4 Defining wp S for all programs S 87. 5 4 0 The skip and the abort 87,5 4 1 The composition 88. 5 4 2 The assignment 89,5 4 3 The alternation 92,5 4 4 The repetition 96. 6 Intermezzo on calculations 101,7 Developing loopless programs 109. 7 0 Introduction 109,7 1 Calculating expressions in assignments 109.
7 2 Developing IFs 113,8 Developing loops an introduction 123. 9 Loops A On deleting a conjunct 127,9 0 Introduction 127. 9 1 An example Integer division 128,XIV Contents,9 2 An example The linear search. and its billions of uses 131,9 3 An example 3 tuple sort. and avoiding avoidable case analyses 138,9 4 An example Integer division improved.
and postponing design decisions 144, 10 Loops B On replacing constants by fresh variables 149. 10 0 Introduction 149,10 1 An example Evaluating a polynomial 150. 10 2 An example The minimum value 154,10 3 An example Determining the multiple 159. 10 4 An example A table of cubes 161,10 5 An example The maximum section sum 166. 10 6 An example The binary search,and its numerous applications 171.
10 7 An example Rearranging an array 182,10 8 An example The bounded linear search 187. 11 Mainly on recursion 195,11 0 Introduction 195,11 1 The general solution 196. 11 2 An example The sum of digits 197,11 3 An example Exponentiation 199. 11 4 Introducing four new types 203,11 5 An example Reversing a sequence. and the importance of good notation 205, 11 6 An example The post order of a binary tree 209.
11 7 An example The depth of a binary tree 213,Contents xv. 11 8 Exercises 217,12 Back to scratch 221,12 0 Introduction 221. 12 1 An example Evaluating a polynomial,and the discovery of nice specifications 221. 12 2 An example Greatest common divisors,and the discovery of useful properties 224. 12 3 An example All shortest paths,and the specification as logical firewall 230.
12 4 A final example Shiloach s algorithm 237,12 5 Additional exercises 245. 13 Where to go from here 249,13 0 On what we have learned 249. 13 1 Where to go from here 251,13 2 Be a little discriminating 253. 13 3 Inspirations and acknowledgements 254,13 4 Selected references 258.


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