The Formal Semantics of Programming Languages - An Introduction.pdf

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Foundations of Computing Michael Garey and Albert Meyer, editors Complexity Issues in VLSI: Optimal Layouts for the Shuffle-Exchange Graph and Other Networks, Frank Thomson Leighton, 1983 Equational Logic as a Programming Language, Michael J. 0 'Donnell, 1985 General Theory of Deductive Systems and Its Applications, S. Yu Maslov, 1987 Resource Allocation Problems: Algorithmic Approaches, Toshihide Ibaraki and Naoki Katoh, 1988 Algebraic Theory of Processes, Matthew Hennessy, 1988 PX: A Computational Logic, Susumu Hayashi and Hiroshi Nakano, 1989 The Stable Marriage Problem: Structure and Algorithms, Dan Gusfield and Robert Irving, 1989 Realistic Compiler Generation, Peter Lee, 1989 Single-Layer Wire Routing and Compaction,F. Miller Maley, 1990 Basic Category Theory for Computer Scientists, Benjamin C. Pierce, 1991 Categories, Types, and Structures: An Introduction to Category Theory for the Working Computer Scientist, Andrea Asperti and Giuseppe Longo, 1991 Semantics of Programming Languages: Structures and Techniques, Carl A. Gunter, 1992 The Formal Semantics of Programming Languages: An Introduction, Glynn Winskel, 1993

The Formal Semantics of Programming Languages An Introduction Glynn Winskel The MIT Press Cambridge, Massachusetts London, England

Second printing, 1994 ©1993 Massachusetts Institute of Technology All rights reserved. No part ofthis 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. This book was printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Winskel, G. (Glynn) The formal semantics of programming languages : an introduction Glynn Winskel. p. cm. - (Foundations of computing) Includes bibliographical references and index. ISBN 0-262-23169-7 1. Programming languages (Electronic computers )-Semantics. II. Series. 1. Title. QA76.7.W555 005.13'1--dc20 1993 92-36718 CIP

To Kirsten, Sofie and Stine

Contents Series foreword Preface 1 Basic set theory 1.1 Logical notation 1.2 Sets 1.2.1 Sets and properties 1.2.2 Some important sets 1.2.3 Constructions on sets 1.2.4 The axiom of foundation 1.3 Relations and functions 1.3.1 Lambda notation 1.3.2 Composing relations and functions 1.3.3 Direct and inverse image of a relation 1.3.4 Equivalence relations 1.4 FUrther reading 2 Introduction to operational semantics IMP-a simple imperative language 2.1 2.2 The evaluation of arithmetic expressions 2.3 The evaluation of boolean expressions 2.4 The execution of commands 2.5 A simple proof 2.6 Alternative semantics 2.7 FUrther reading 3 Some principles of induction 3.1 Mathematical induction 3.2 Structural induction 3.3 Well-founded induction 3.4 Induction on derivations 3.5 Definitions by induction xiii xv 1 1 2 3 3 4 6 6 7 7 9 9 10 11 11 13 17 19 20 24 26 27 27 28 31 35 39

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