Programming in Standard ML (11.02.11 draft)

297 Pages·0.72 MB·English

by  Robert Harper

Programming in Standard ML
(DRAFT: VERSION 1.2 OF 11.02.11.)
Robert Harper
Carnegie Mellon University
Spring Semester, 2011
Copyright(cid:13)c 2011byRobertHarper.
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Preface
This book is an introduction to programming with the Standard ML pro-
gramming language. It began life as a set of lecture notes for Computer
Science15–212: PrinciplesofProgramming,thesecondsemesterofthein-
troductorysequenceintheundergraduatecomputersciencecurriculumat
Carnegie MellonUniversity. It hassubsequently beenused inmany other
courses at Carnegie Mellon, and at a number of universities around the
world. It is intended to supersede my Introduction to Standard ML, which
hasbeenwidelycirculatedoverthelasttenyears.
Standard ML is a formally defined programming language. The Defi-
nition of Standard ML (Revised) is the formal definition of the language. It
is supplemented by the Standard ML Basis Library, which defines a com-
monbasisoftypesthataresharedbyallimplementationsofthelanguage.
CommentaryonStandardMLdiscussessomeofthedecisionsthatwentinto
thedesignofthefirstversionofthelanguage.
ThereareseveralimplementationsofStandardMLavailableforawide
variety of hardware and software platforms. The best-known compilers
are Standard ML of New Jersey, MLton, Moscow ML, MLKit, and PolyML.
These are all freely available on the worldwide web. Please refer to The
Standard ML Home Page for up-to-date information on Standard ML and
itsimplementations.
Numerous people have contributed directly and indirectly to this text.
I am especially grateful to the following people for their helpful com-
ments and suggestions: Brian Adkins, Nels Beckman, Marc Bezem, James
Bostock, Terrence Brannon, Franck van Breugel, Chris Capel, Matthew
William Cox, Karl Crary, Yaakov Eisenberg, Matt Elder, Mike Erdmann,
MatthiasFelleisen,AndreiFormiga,StephenHarris,NilsJa¨hnig,JoelJones,
David Koppstein, John Lafferty, Johannes Laire, Flavio Lerda, Daniel R.
Licata, Adrian Moos, Bryce Nichols, Michael Norrish, Arthur J. O’Dwyer,
Frank Pfenning, Chris Stone, Dave Swasey, Michael Velten, Johan Wallen,
ScottWilliams,andJeannetteWing. RichardC.Cobbehelpedwithfontse-
lection. I am also grateful to the many students of 15-212 who used these
notesandsentintheirsuggestionsovertheyears.
These notes are a work in progress. Corrections, comments and sug-
gestionsaremostwelcome.

Contents
Preface ii
I Overview 1
1 ProgramminginStandardML 3
1.1 ARegularExpressionPackage . . . . . . . . . . . . . . . . . 3
1.2 SampleCode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
II The Core Language 13
2 Types,Values,andEffects 15
2.1 EvaluationandExecution . . . . . . . . . . . . . . . . . . . . 15
2.2 TheMLComputationModel . . . . . . . . . . . . . . . . . . 16
2.2.1 TypeChecking . . . . . . . . . . . . . . . . . . . . . . 17
2.2.2 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3 Types,Types,Types . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4 TypeErrors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.5 SampleCode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3 Declarations 24
3.1 Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 BasicBindings . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2.1 TypeBindings . . . . . . . . . . . . . . . . . . . . . . . 25
3.2.2 ValueBindings . . . . . . . . . . . . . . . . . . . . . . 26
3.3 CompoundDeclarations . . . . . . . . . . . . . . . . . . . . . 27
3.4 LimitingScope . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
CONTENTS vi
3.5 TypingandEvaluation . . . . . . . . . . . . . . . . . . . . . . 29
3.6 SampleCode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4 Functions 33
4.1 FunctionsasTemplates . . . . . . . . . . . . . . . . . . . . . . 33
4.2 FunctionsandApplication . . . . . . . . . . . . . . . . . . . . 34
4.3 BindingandScope,Revisited . . . . . . . . . . . . . . . . . . 37
4.4 SampleCode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5 ProductsandRecords 40
5.1 ProductTypes . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5.1.1 Tuples . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5.1.2 TuplePatterns . . . . . . . . . . . . . . . . . . . . . . . 42
5.2 RecordTypes . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.3 MultipleArgumentsandMultipleResults . . . . . . . . . . . 48
5.4 SampleCode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
6 CaseAnalysis 51
6.1 HomogeneousandHeterogeneousTypes . . . . . . . . . . . 51
6.2 ClausalFunctionExpressions . . . . . . . . . . . . . . . . . . 52
6.3 BooleansandConditionals,Revisited . . . . . . . . . . . . . 53
6.4 ExhaustivenessandRedundancy . . . . . . . . . . . . . . . . 54
6.5 SampleCode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
7 RecursiveFunctions 57
7.1 Self-ReferenceandRecursion . . . . . . . . . . . . . . . . . . 58
7.2 Iteration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
7.3 InductiveReasoning . . . . . . . . . . . . . . . . . . . . . . . 62
7.4 MutualRecursion . . . . . . . . . . . . . . . . . . . . . . . . . 65
7.5 SampleCode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
8 TypeInferenceandPolymorphism 67
8.1 TypeInference . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
8.2 PolymorphicDefinitions . . . . . . . . . . . . . . . . . . . . . 70
8.3 Overloading . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
8.4 SampleCode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
REVISED 11.02.11 DRAFT VERSION 1.2
CONTENTS vii
9 ProgrammingwithLists 77
9.1 ListPrimitives . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
9.2 ComputingWithLists . . . . . . . . . . . . . . . . . . . . . . 79
9.3 SampleCode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
10 ConcreteDataTypes 82
10.1 DatatypeDeclarations . . . . . . . . . . . . . . . . . . . . . . 82
10.2 Non-RecursiveDatatypes . . . . . . . . . . . . . . . . . . . . 83
10.3 RecursiveDatatypes . . . . . . . . . . . . . . . . . . . . . . . 85
10.4 HeterogeneousDataStructures . . . . . . . . . . . . . . . . . 88
10.5 AbstractSyntax . . . . . . . . . . . . . . . . . . . . . . . . . . 89
10.6 SampleCode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
11 Higher-OrderFunctions 92
11.1 FunctionsasValues . . . . . . . . . . . . . . . . . . . . . . . . 92
11.2 BindingandScope . . . . . . . . . . . . . . . . . . . . . . . . 93
11.3 ReturningFunctions . . . . . . . . . . . . . . . . . . . . . . . 95
11.4 PatternsofControl . . . . . . . . . . . . . . . . . . . . . . . . 97
11.5 Staging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
11.6 SampleCode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
12 Exceptions 103
12.1 ExceptionsasErrors . . . . . . . . . . . . . . . . . . . . . . . 104
12.1.1 PrimitiveExceptions . . . . . . . . . . . . . . . . . . . 104
12.1.2 User-DefinedExceptions . . . . . . . . . . . . . . . . . 105
12.2 ExceptionHandlers . . . . . . . . . . . . . . . . . . . . . . . . 107
12.3 Value-CarryingExceptions . . . . . . . . . . . . . . . . . . . . 110
12.4 SampleCode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
13 MutableStorage 113
13.1 ReferenceCells . . . . . . . . . . . . . . . . . . . . . . . . . . 113
13.2 ReferencePatterns . . . . . . . . . . . . . . . . . . . . . . . . 115
13.3 Identity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
13.4 Aliasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
13.5 ProgrammingWellWithReferences . . . . . . . . . . . . . . 119
13.5.1 PrivateStorage . . . . . . . . . . . . . . . . . . . . . . 120
13.5.2 MutableDataStructures . . . . . . . . . . . . . . . . . 122
13.6 MutableArrays . . . . . . . . . . . . . . . . . . . . . . . . . . 124
REVISED 11.02.11 DRAFT VERSION 1.2
CONTENTS viii
13.7 SampleCode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
14 Input/Output 127
14.1 TextualInput/Output . . . . . . . . . . . . . . . . . . . . . . 127
14.2 SampleCode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
15 LazyDataStructures 130
15.1 LazyDataTypes . . . . . . . . . . . . . . . . . . . . . . . . . . 132
15.2 LazyFunctionDefinitions . . . . . . . . . . . . . . . . . . . . 133
15.3 ProgrammingwithStreams . . . . . . . . . . . . . . . . . . . 135
15.4 SampleCode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
16 EqualityandEqualityTypes 138
16.1 SampleCode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
17 Concurrency 139
17.1 SampleCode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
III The Module Language 140
18 SignaturesandStructures 142
18.1 Signatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
18.1.1 BasicSignatures . . . . . . . . . . . . . . . . . . . . . . 143
18.1.2 SignatureInheritance . . . . . . . . . . . . . . . . . . . 144
18.2 Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
18.2.1 BasicStructures . . . . . . . . . . . . . . . . . . . . . . 147
18.2.2 LongandShortIdentifiers . . . . . . . . . . . . . . . . 148
18.3 SampleCode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
19 SignatureMatching 151
19.1 PrincipalSignatures . . . . . . . . . . . . . . . . . . . . . . . . 152
19.2 Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
19.3 Satisfaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
19.4 SampleCode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
20 SignatureAscription 158
20.1 AscribedStructureBindings . . . . . . . . . . . . . . . . . . . 158
20.2 OpaqueAscription . . . . . . . . . . . . . . . . . . . . . . . . 159
REVISED 11.02.11 DRAFT VERSION 1.2
CONTENTS ix
20.3 TransparentAscription . . . . . . . . . . . . . . . . . . . . . . 162
20.4 SampleCode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
21 ModuleHierarchies 165
21.1 Substructures . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
21.2 SampleCode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
22 SharingSpecifications 174
22.1 CombiningAbstractions . . . . . . . . . . . . . . . . . . . . . 174
22.2 SampleCode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
23 Parameterization 182
23.1 FunctorBindingsandApplications . . . . . . . . . . . . . . . 182
23.2 FunctorsandSharingSpecifications . . . . . . . . . . . . . . 185
23.3 AvoidingSharingSpecifications . . . . . . . . . . . . . . . . . 187
23.4 SampleCode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
IV Programming Techniques 192
24 SpecificationsandCorrectness 194
24.1 Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
24.2 CorrectnessProofs . . . . . . . . . . . . . . . . . . . . . . . . 196
24.3 EnforcementandCompliance . . . . . . . . . . . . . . . . . . 199
25 InductionandRecursion 202
25.1 Exponentiation . . . . . . . . . . . . . . . . . . . . . . . . . . 202
25.2 TheGCDAlgorithm . . . . . . . . . . . . . . . . . . . . . . . 207
25.3 SampleCode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
26 StructuralInduction 212
26.1 NaturalNumbers . . . . . . . . . . . . . . . . . . . . . . . . . 212
26.2 Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
26.3 Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
26.4 GeneralizationsandLimitations . . . . . . . . . . . . . . . . 216
26.5 AbstractingInduction . . . . . . . . . . . . . . . . . . . . . . 217
26.6 SampleCode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
REVISED 11.02.11 DRAFT VERSION 1.2