tailieunhanh - A Practical Theory of Programming

Understanding programming and programming languages requires knowledge of the underlying theoretical model. This book explores aspects of programming that are amenable to mathematical proof. The author describes a programming theory which is aspects of programming that are amenable to mathematical proof. The author describes a programming theory which is | a Practical Theory of Programming second edition Eric . Hehner -5 a Practical Theory of Programming second edition 2004 January 1 Eric . Hehner Department of Computer Science University of Toronto Toronto On M5S 2E4 The first edition of this book was published by Springer-Verlag Publishers New York 1993 ISBN 0-387-94106-1 This second edition is available free at hehner aPToP You may copy freely as long as you include all the information on this page. -4 Contents 0 Preface 0 Introduction 0 Second Edition 1 Quick Tour 1 Acknowledgements 2 1 Basic Theories 3 Boolean Theory 3 Axioms and Proof Rules 5 Expression and Proof Format 7 Monotonicity and Antimonotonicity 9 Context 10 Formalization 12 Number Theory 12 Character Theory 13 2 Basic Data Structures 14 Bunch Theory 14 Set Theory optional 17 String Theory 17 List Theory 20 Multidimensional Structures 22 3 Function Theory 23 Functions 23 Abbreviated Function Notations 25 Scope and Substitution 25 Quantifiers 26 Function Fine Points optional 28 Function Inclusion and Equality optional 30 Higher-Order Functions optional 30 Function Composition optional 31 List as Function 32 Limits and Reals optional 32 4 Program Theory 34 Specifications 34 Specification Notations 36 Specification Laws 37 Refinement 39 Conditions optional 40 Programs 41 Program Development 43 Refinement Laws 43 List Summation 43 Binary Exponentiation .