Types and Programming Languages

645 Pages·2002·1.74 MB·english

by  Benjamin C. Pierce

Types and Programming Languages

Types and Programming Languages
Benjamin C. Pierce
TheMITPress
Cambridge,Massachusetts
London,England
©2002BenjaminC.Pierce
All rights reserved. No part of this book may be reproduced in any form by
any electronic of mechanical means (including photocopying, recording, or
information storage and retrieval) without permission in writing from the
publisher.
This book was set in Lucida Bright by the author using the LATEX document
preparationsystem.
PrintedandboundintheUnitedStatesofAmerica.
LibraryofCongressCataloging-in-PublicationData
Pierce,BenjaminC.
Typesandprogramminglanguages/BenjaminC.Pierce
p. cm.
Includesbibliographicalreferencesandindex.
ISBN0-262-16209-1(hc.:alk.paper)
1.Programminglanguages(Electroniccomputers). I.Title.
QA76.7.P54 2002
005.13—dc21
2001044428
Contents
Preface xiii
1 Introduction 1
1.1 TypesinComputerScience 1
1.2 WhatTypeSystemsAreGoodFor 4
1.3 TypeSystemsandLanguageDesign 9
1.4 CapsuleHistory 10
1.5 RelatedReading 12
2 MathematicalPreliminaries 15
2.1 Sets,Relations,andFunctions 15
2.2 OrderedSets 16
2.3 Sequences 18
2.4 Induction 19
2.5 BackgroundReading 20
I Untyped Systems 21
3 UntypedArithmeticExpressions 23
3.1 Introduction 23
3.2 Syntax 26
3.3 InductiononTerms 29
3.4 SemanticStyles 32
3.5 Evaluation 34
3.6 Notes 43
vi Contents
4 AnMLImplementationofArithmeticExpressions 45
4.1 Syntax 46
4.2 Evaluation 47
4.3 TheRestoftheStory 49
5 TheUntypedLambda-Calculus 51
5.1 Basics 52
5.2 ProgrammingintheLambda-Calculus 58
5.3 Formalities 68
5.4 Notes 73
6 NamelessRepresentationofTerms 75
6.1 TermsandContexts 76
6.2 ShiftingandSubstitution 78
6.3 Evaluation 80
7 AnMLImplementationoftheLambda-Calculus 83
7.1 TermsandContexts 83
7.2 ShiftingandSubstitution 85
7.3 Evaluation 87
7.4 Notes 88
II Simple Types 89
8 TypedArithmeticExpressions 91
8.1 Types 91
8.2 TheTypingRelation 92
8.3 Safety=Progress+Preservation 95
9 SimplyTypedLambda-Calculus 99
9.1 FunctionTypes 99
9.2 TheTypingRelation 100
9.3 PropertiesofTyping 104
9.4 TheCurry-HowardCorrespondence 108
9.5 ErasureandTypability 109
9.6 Curry-Stylevs.Church-Style 111
9.7 Notes 111
10 AnMLImplementationofSimpleTypes 113
10.1 Contexts 113
10.2 TermsandTypes 115
10.3 Typechecking 115
Contents vii
11 SimpleExtensions 117
11.1 BaseTypes 117
11.2 TheUnitType 118
11.3 DerivedForms:SequencingandWildcards 119
11.4 Ascription 121
11.5 LetBindings 124
11.6 Pairs 126
11.7 Tuples 128
11.8 Records 129
11.9 Sums 132
11.10 Variants 136
11.11 GeneralRecursion 142
11.12 Lists 146
12 Normalization 149
12.1 NormalizationforSimpleTypes 149
12.2 Notes 152
13 References 153
13.1 Introduction 153
13.2 Typing 159
13.3 Evaluation 159
13.4 StoreTypings 162
13.5 Safety 165
13.6 Notes 170
14 Exceptions 171
14.1 RaisingExceptions 172
14.2 HandlingExceptions 173
14.3 ExceptionsCarryingValues 175
III Subtyping 179
15 Subtyping 181
15.1 Subsumption 181
15.2 TheSubtypeRelation 182
15.3 PropertiesofSubtypingandTyping 188
15.4 TheTopandBottomTypes 191
15.5 SubtypingandOtherFeatures 193
15.6 CoercionSemanticsforSubtyping 200
15.7 IntersectionandUnionTypes 206
15.8 Notes 207
viii Contents
16 MetatheoryofSubtyping 209
16.1 AlgorithmicSubtyping 210
16.2 AlgorithmicTyping 213
16.3 JoinsandMeets 218
16.4 AlgorithmicTypingandtheBottomType 220
17 AnMLImplementationofSubtyping 221
17.1 Syntax 221
17.2 Subtyping 221
17.3 Typing 222
18 CaseStudy:ImperativeObjects 225
18.1 WhatIsObject-OrientedProgramming? 225
18.2 Objects 228
18.3 ObjectGenerators 229
18.4 Subtyping 229
18.5 GroupingInstanceVariables 230
18.6 SimpleClasses 231
18.7 AddingInstanceVariables 233
18.8 CallingSuperclassMethods 234
18.9 ClasseswithSelf 234
18.10 OpenRecursionthroughSelf 235
18.11 OpenRecursionandEvaluationOrder 237
18.12 AMoreEfficientImplementation 241
18.13 Recap 244
18.14 Notes 245
19 CaseStudy:FeatherweightJava 247
19.1 Introduction 247
19.2 Overview 249
19.3 NominalandStructuralTypeSystems 251
19.4 Definitions 254
19.5 Properties 261
19.6 Encodingsvs.PrimitiveObjects 262
19.7 Notes 263