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Copyright c○2011 by Robert Harper. All Rights Reserved. This work is licensed under the Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-nd/3.0/us/, or send a letter to Creative Commons, 171 Second Street, Suite 300, San Francisco, California, 94105, USA.
Preface This book is an introduction to programming with the Standard ML programming language. It began life as a set of lecture notes for Computer Science 15–212: Principles of Programming, the second semester of the introductory sequence in the undergraduate computer science curriculum at Carnegie Mellon University. It has subsequently been used in many 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 has been widely circulated over the last ten years. Standard ML is a formally defined programming language. The Definition of Standard ML (Revised) is the formal definition of the language. It is supplemented by the Standard ML Basis Library, which defines a common basis of types that are shared by all implementations of the language. Commentary on Standard ML discusses some of the decisions that went into the design of the first version of the language. There are several implementations of Standard ML available for a wide 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 its implementations. Numerous people have contributed directly and indirectly to this text. I am especially grateful to the following people for their helpful comments 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, Matthias Felleisen, Andrei Formiga, Stephen Harris, Nils Jähnig, Joel Jones, David Koppstein, John Lafferty, Johannes Laire, Flavio Lerda, Daniel R. Licata, Adrian Moos, Bryce Nichols, Michael Norrish, Arthur J. O’Dwyer,
Page 1: Programming in Standard ML (DRAFT:
Page 6 and 7: Contents Preface ii I Overview 1 1
Page 8 and 9: CONTENTS vii 9 Programming with Lis
Page 10 and 11: CONTENTS ix 20.3 Transparent Ascrip
Page 12: CONTENTS xi 34 Modularity and Reuse
Page 15 and 16: 2 Standard ML is a type-safe progra
Page 17 and 18: 1.1 A Regular Expression Package 4
Page 25 and 26: 1.2 Sample Code 12 by the iteration
Page 27 and 28: 14 All Standard ML is divided into
Page 29 and 30: 2.2 The ML Computation Model 16 str
Page 31 and 32: 2.2 The ML Computation Model 18 Oft
Page 33 and 34: 2.2 The ML Computation Model 20 the
Page 35 and 36: 2.3 Types, Types, Types 22 3+3.14 i
Page 37 and 38: Chapter 3 Declarations 3.1 Variable
Page 39 and 40: 3.2 Basic Bindings 26 3.2.2 Value B
Page 41 and 42: 3.4 Limiting Scope 28 are nested wi
Page 43 and 44: 3.5 Typing and Evaluation 30 enviro
Page 45 and 46: 3.6 Sample Code 32 In words, if the
Page 47 and 48: 4.2 Functions and Application 34 al
Page 49 and 50: 4.2 Functions and Application 36 wh
Page 51 and 52: 4.3 Binding and Scope, Revisited 38
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Chapter 5 Products and Records 5.1
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5.1 Product Types 42 val pair : int
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5.1 Product Types 44 val (m:int,n:i
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5.2 Record Types 46 val {lab 1 =pat
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5.3 Multiple Arguments and Multiple
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5.4 Sample Code 50 5.4 Sample Code
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6.2 Clausal Function Expressions 52
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6.4 Exhaustiveness and Redundancy 5
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6.5 Sample Code 56 When applied to,
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7.1 Self-Reference and Recursion 58
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7.1 Self-Reference and Recursion 60
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7.3 Inductive Reasoning 62 local in
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7.3 Inductive Reasoning 64 factoria
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7.5 Sample Code 66 are said to be m
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8.1 Type Inference 68 missing type
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8.2 Polymorphic Definitions 70 is a
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8.2 Polymorphic Definitions 72 the
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8.3 Overloading 74 1. Declare the e
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8.4 Sample Code 76 because what hap
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9.1 List Primitives 78 to get anoth
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9.2 Computing With Lists 80 fun rev
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Chapter 10 Concrete Data Types 10.1
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10.2 Non-Recursive Datatypes 84 dat
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10.3 Recursive Datatypes 86 (Incide
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10.4 Heterogeneous Data Structures
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10.5 Abstract Syntax 90 datatype ex
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Chapter 11 Higher-Order Functions 1
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11.2 Binding and Scope 94 val x = 2
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11.3 Returning Functions 96 “retr
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11.4 Patterns of Control 98 fun red
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11.5 Staging 100 fun staged reduce
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11.6 Sample Code 102 11.6 Sample Co
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12.1 Exceptions as Errors 104 12.1
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12.1 Exceptions as Errors 106 in me
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12.2 Exception Handlers 108 exc is
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12.3 Value-Carrying Exceptions 110
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12.4 Sample Code 112 exn as argumen
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13.1 Reference Cells 114 contrast t
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13.3 Identity 116 An alternative to
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13.4 Aliasing 118 val r = ref () va
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13.5 Programming Well With Referenc
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13.5 Programming Well With Referenc
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13.6 Mutable Arrays 124 The last st
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13.7 Sample Code 126 end of SOME r
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14.1 Textual Input/Output 128 sink.
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Chapter 15 Lazy Data Structures In
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15.1 Lazy Data Types 132 on which s
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15.2 Lazy Function Definitions 134
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15.3 Programming with Streams 136 t
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Chapter 16 Equality and Equality Ty
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Part III The Module Language
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Chapter 18 Signatures and Structure
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18.1 Signatures 144 where sigid is
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18.1 Signatures 146 signature QUEUE
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18.2 Structures 148 evaluating the
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18.3 Sample Code 150 Another proble
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19.1 Principal Signatures 152 19.1
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19.2 Matching 154 The candidate may
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19.2 Matching 156 value components
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Chapter 20 Signature Ascription Sig
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20.2 Opaque Ascription 160 The use
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20.3 Transparent Ascription 162 cas
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20.4 Sample Code 164 The ascription
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21.1 Substructures 166 To see how s
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21.1 Substructures 168 Node of ’a
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21.1 Substructures 170 struct type
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21.1 Substructures 172 end Similarl
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Chapter 22 Sharing Specifications I
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22.1 Combining Abstractions 176 As
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22.1 Combining Abstractions 178 str
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22.1 Combining Abstractions 180 But
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Chapter 23 Parameterization To supp
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23.1 Functor Bindings and Applicati
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23.2 Functors and Sharing Specifica
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23.3 Avoiding Sharing Specification
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23.3 Avoiding Sharing Specification
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Part IV Programming Techniques
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Chapter 24 Specifications and Corre
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24.2 Correctness Proofs 196 in (a+b
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24.2 Correctness Proofs 198 branch
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24.3 Enforcement and Compliance 200
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Chapter 25 Induction and Recursion
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25.1 Exponentiation 204 expressing
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25.1 Exponentiation 206 if n ≥ 0,
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25.2 The GCD Algorithm 208 then eit
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25.2 The GCD Algorithm 210 let in e
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Chapter 26 Structural Induction The
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26.2 Lists 214 representation. This
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26.4 Generalizations and Limitation
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26.5 Abstracting Induction 218 Note
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Chapter 27 Proof-Directed Debugging
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27.2 Specifying the Matcher 222 and
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27.2 Specifying the Matcher 224 Obs
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27.2 Specifying the Matcher 226 tru
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27.3 Sample Code 228 The function
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230 because they persist after appl
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28.1 Persistent Queues 232 to be us
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28.1 Persistent Queues 234 “halve
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28.2 Amortized Analysis 236 the wor
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29.1 The n-Queens Problem 240 decis
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29.3 Solution Using Exceptions 242
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29.4 Solution Using Continuations 2
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30.1 Infinite Sequences 248 30.1 In
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30.1 Infinite Sequences 250 (* bad
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30.2 Circuit Simulation 252 datatyp
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30.3 Regular Expression Matching, R
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30.4 Sample Code 256 char list -> (
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31.1 Cacheing Results 258 where sum
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31.2 Laziness 260 so that the suspe
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31.3 Lazy Data Types in SML/NJ 262
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32.1 Dictionaries 266 32.1 Dictiona
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32.3 Balanced Binary Search Trees 2
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32.3 Balanced Binary Search Trees 2
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32.4 Abstraction vs. Run-Time Check
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Chapter 33 Representation Independe
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Chapter 35 Dynamic Typing and Dynam
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Part V Appendices
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Appendix B Compilation Management A
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Appendix C Sample Programs A number
Page 297:
Bibliography [1] Emden R. Gansner a
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