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1.1 A Regular Expression Package 11 end | match (Plus (r1, r2)) cs k = match r1 cs k orelse match r2 cs k | match (Times (r1, r2)) cs k = match r1 cs (fn cs’ => match r2 cs’ k) | match (Star r) cs k = let val mstar cs’ = k cs’ orelse match r cs’ mstar in mstar cs end fun accepts regexp string = match regexp (String.explode string) (fn nil => true | => false) Note that we incorporate the structure RegExp into the structure Matcher, in accordance with the requirements of the signature. The function accepts explodes the string into a list of characters (to facilitiate sequential processing of the input), then calls match with an initial continuation that ensures that the remaining input is empty to determine the result. The type of match is RegExp.regexp -> char list -> (char list -> bool) -> bool. That is, match takes in succession a regular expression, a list of characters, and a continuation of type char list -> bool; it yields as result a value of type bool. This is a fairly complicated type, but notice that nowhere did we have to write this type in the code! The type inference mechanism of ML took care of determining what that type must be based on an analysis of the code itself. Since match takes a function as argument, it is said to be a higher-order function. The simplicity of the matcher is due in large measure to the ease with which we can manipulate functions in ML. Notice that we create a new, unnamed function to pass as a continuation in the case of concatenation — it is the function that matches the second part of the regular expression to the characters remaining after matching an initial segment against the first part. We use a similar technique to implement matching against an iterated regular expression — we attempt to match the null string, but if this fails, we match against the regular expression being iterated followed REVISED 11.02.11 DRAFT VERSION 1.2
1.2 Sample Code 12 by the iteration once again. This neatly captures the “zero or more times” interpretation of iteration of a regular expression. Important: the code given above contains a subtle error. Can you find it? If not, see chapter 27 for further discussion! This completes our brief overview of Standard ML. The remainder of these notes are structured into three parts. The first part is a detailed introduction to the core language, the language in which we write programs in ML. The second part is concerned with the module language, the means by which we structure large programs in ML. The third is about programming techniques, methods for building reliable and robust programs. I hope you enjoy it! 1.2 Sample Code Here is the complete code for this chapter. REVISED 11.02.11 DRAFT VERSION 1.2
Page 1 and 2: Programming in Standard ML (DRAFT:
Page 3 and 4: Preface This book is an introductio
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 23: 1.1 A Regular Expression Package 10
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
Page 53 and 54: Chapter 5 Products and Records 5.1
Page 55 and 56: 5.1 Product Types 42 val pair : int
Page 57 and 58: 5.1 Product Types 44 val (m:int,n:i
Page 59 and 60: 5.2 Record Types 46 val {lab 1 =pat
Page 61 and 62: 5.3 Multiple Arguments and Multiple
Page 63 and 64: 5.4 Sample Code 50 5.4 Sample Code
Page 65 and 66: 6.2 Clausal Function Expressions 52
Page 67 and 68: 6.4 Exhaustiveness and Redundancy 5
Page 69 and 70: 6.5 Sample Code 56 When applied to,
Page 71 and 72: 7.1 Self-Reference and Recursion 58
Page 73 and 74: 7.1 Self-Reference and Recursion 60
Page 75 and 76:
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
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Bibliography [1] Emden R. Gansner a
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