Software Abstractions: Logic, Language, and Analysis

373 Pages·2012·2.06 MB·English

by  Daniel Jackson

Software Abstractions: Logic, Language, and Analysis

Software
Abstractions

Logic, Language,
and Analysis
revised edition
Daniel Jackson

The MIT Press
Cambridge, Massachusetts
London, England
© 2012 Daniel Jackson
All rights reserved. No part of this book may be reproduced in any form by
any electronic or mechanical means (including photocopying, recording, or
information storage and retrieval) without permission in writing from the
publisher.
MIT Press books may be purchased at special quantity discounts for busi-
ness or sales promotion use. For information, please email special_sales@
mitpress.mit.edu or write to Special Sales Department, The MIT Press, 55
Hayward Street, Cambridge, MA 02142.
This book was set in Adobe Warnock and ITC Officina Sans, by the author,
using Adobe Indesign and his own software, on Apple computers. Diagrams
were drawn with OmniGraffle Pro. Printed and bound in the United States
of America.
Library of Congress Cataloging-in-Publication Data
Jackson, Daniel, 1963–
Software abstractions : logic, language, and analysis / Daniel Jackson.—Rev.
ed.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-262-01715-2 (hardcover : alk. paper) 1. Computer software—
Development. I. Title.
QA76.76.D47J29 2012 005.1—dc23 2011024317
10 9 8 7 6 5 4 3 2 1
to Claudia

Contents
Preface xi
Acknowledgments xv
Acknowledgments (revised edition) xvii
1: Introduction 1
2: A Whirlwind Tour 5
2.1 Statics: Exploring States .........................................................................6
2.2 Dynamics: Adding Operations .............................................................9
2.3 Classification Hierarchy ......................................................................17
2.4 Execution Traces...................................................................................22
2.5 Summary ................................................................................................28
3: Logic 33
3.1 Three Logics in One .............................................................................33
3.2 Atoms and Relations ............................................................................35
3.3 Snapshots ...............................................................................................48
3.4 Operators ...............................................................................................50
3.5 Constraints .............................................................................................68
3.6 Declarations and Multiplicity Constraints ......................................75
3.7 Cardinality and Integers .....................................................................80
4: Language 85
4.1 An Example: Self-Grandpas ...............................................................85
4.2 Signatures and Fields ...........................................................................93
4.3 Model Diagrams .................................................................................103
4.4 Types and Type Checking .................................................................109
4.5 Facts, Predicates, Functions, and Assertions ................................119
4.6 Commands and Scope .......................................................................130
4.7 Modules and Polymorphism ............................................................133
4.8 Integers and Arithmetic ....................................................................136
viii contents
5: Analysis 141
5.1 Scope-Complete Analysis .................................................................141
5.2 Instances, Examples, and Counterexamples .................................146
5.3 Unbounded Universal Quantifiers ..................................................157
5.4 Scope Selection and Monotonicity .................................................165
6: Examples 171
6.1 Leader Election in a Ring ..................................................................171
6.2 Hotel Room Locking ..........................................................................187
6.3 Media Asset Management ................................................................205
6.4 Memory Abstractions ........................................................................219
Appendix A: Exercises 233
A.1 Logic Exercises ....................................................................................234
A.2 Extending Simple Models .................................................................244
A.3 Classic Puzzles ....................................................................................247
A.4 Metamodels .........................................................................................250
A.5 Small Case Studies ..............................................................................251
A.6 Open-Ended Case Studies ................................................................256
Appendix B: Alloy Language Reference 259
B.1 Lexical Issues .......................................................................................259
B.2 Namespaces .........................................................................................260
B.3 Grammar ..............................................................................................261
B.4 Precedence and Associativity ...........................................................263
B.5 Semantic Basis .....................................................................................264
B.6 Types and Overloading......................................................................266
B.7 Language Features ..............................................................................270
B.8 Relational Expressions .......................................................................285
B.9 Integer Expressions ............................................................................288
B.10 Boolean Expressions ..........................................................................289
Appendix C: Kernel Semantics 295
C.1 Semantics of the Alloy Kernel ..........................................................295
Appendix D: Diagrammatic Notation 299
contents ix
Appendix E: Alternative Approaches 301
E.1 An Example ..........................................................................................303
E.2 B .............................................................................................................310
E.3 OCL .......................................................................................................316
E.4 VDM ......................................................................................................322
E.5 Z .............................................................................................................328
References 337
Index 345