Introduction to Functional Programming Through Lambda Calculus

By: GREG MICHAELSON

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Paperback | 26 August 2011

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Well-respected text for computer science students provides an accessible introduction to functional programming. Cogent examples illuminate the central ideas, and numerous exercises offer reinforcement. Includes solutions. Functional programming is rooted in lambda calculus, which constitutes the world's smallest programming language. This well-respected text offers an accessible introduction to functional programming concepts and techniques for students of mathematics and computer science. The treatment is as nontechnical as possible, and it assumes no prior knowledge of mathematics or functional programming. Cogent examples illuminate the central ideas, and numerous exercises appear throughout the text, offering reinforcement of key concepts. All problems feature complete solutions.

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Non-Fiction Mathematics Calculus & Mathematical Analysis Calculus Computing & I.T.Computer Programming & Software Development Object-Oriented Programming or OOP Programming & Scripting Languages

Preface to the Dover Edition	p. iii
Preface	p. v
Introduction	p. 1
Names and values in programming	p. 2
Names and values in imperative and functional languages	p. 2
Execution order in imperative and functional languages	p. 3
Repetition in imperative and functional languages	p. 5
Data structures in functional languages	p. 7
Functions as values	p. 8
The origins of functional languages	p. 9
Computing and the theory of computing	p. 11
? calculus	p. 13
Summary	p. 14
¿ calculus	p. 15
Abstraction	p. 16
Abstraction in programming languages	p. 19
Introducing ¿ calculus	p. 20
¿ expressions	p. 21
Simple ¿ functions	p. 23
Introducing new syntax	p. 30
Notations for naming functions and reduction	p. 31
Functions from functions	p. 31
Argument selection and argument pairing functions	p. 33
Free and bound variables	p. 33
Name clashes and ¿ conversion	p. 43
Simplification through ¿ reduction	p. 44
Summary	p. 45
Exercises	p. 47
Conditions, booleans and numbers	p. 49
Truth values and conditional expression	p. 50
NOT	p. 51
AND	p. 52
OR	p. 54
Natural numbers	p. 55
Simplified notations	p. 59
Summary	p. 61
Exercises	p. 62
Recursion and arithmetic	p. 65
Repetitions, iteration and recursion	p. 66
Recursion through definitions?	p. 68
Passing a function to itself	p. 69
Applicative order reduction	p. 72
Recursion function	p. 73
Recursion notation	p. 77
Arithmetic operations	p. 78
Summary	p. 82
Exercises	p. 84
Types	p. 87
Types and programming	p. 88
Types as objects and operations	p. 89
Representing typed objects	p. 91
Errors	p. 92
Booleans	p. 94
Typed conditional expression	p. 97
Numbers and arithmetic	p. 98
Characters	p. 101
Repetitive type checking	p. 104
Static and dynamic type checking	p. 107
Infix operators	p. 107
Case definitions and structure matching	p. 108
Summary	p. 111
Exercises	p. 113
Lists and strings	p. 115
Lists	p. 116
List representation	p. 119
Operations on lists	p. 122
List notation	p. 124
Lists and evaluation	p. 127
Deletion from a list	p. 127
List comparison	p. 129
Strings	p. 131
String comparison	p. 132
Numeric string to number conversion	p. 134
Structure matching with lists	p. 139
Ordered linear lists, insertion and sorting	p. 140
Indexed linear list access	p. 142
Mapping functions	p. 146
Summary	p. 150
Exercises	p. 151
Composite values and trees	p. 153
Composite values	p. 154
Processing composite value sequences	p. 155
Selector functions	p. 157
Generalized structure matching	p. 160
Local definitions	p. 164
Matching composite value results	p. 164
List inefficiency	p. 167
Trees	p. 168
Adding values to ordered binary trees	p. 169
Binary tree traversal	p. 173
Binary tree search	p. 174
Binary trees of composite values	p. 176
Binary tree efficiency	p. 178
Curried and uncurried functions	p. 179
Partial application	p. 181
Structures, values and functions	p. 183
Summary	p. 183
Exercises	p. 184
Evaluation	p. 187
Termination and normal form	p. 188
Normal order	p. 189
Applicative order	p. 190
Consistent applicative order use	p. 191
Delaying evaluation	p. 193
Evaluation termination, the halting problem, evaluation equivalence and the Church-Rosser theorems	p. 196
Infinite objects	p. 197
Lazy evaluation	p. 199
Summary	p. 204
Exercises	p. 205
Functional programming in Standard ML	p. 207
Types	p. 208
Lists	p. 209
Tuples	p. 210
Function types and expressions	p. 211
Standard functions	p. 212
Comparison operators	p. 218
Functions	p. 218
Making bound variables' types explicit	p. 219
Definitions	p. 220
Conditional expressions	p. 221
Recursion and function definitions	p. 221
Tuple selection	p. 222
Pattern matching	p. 223
Local definitions	p. 225
Type expressions and abbreviated types	p. 226
Type variables and polymorphism	p. 227
New types	p. 230
Trees	p. 234
¿ calculus in SML	p. 237
Other features	p. 238
Summary	p. 238
Exercises	p. 238
Functional programming and LISP	p. 243
Atoms, numbers and symbols	p. 244
Forms, expressions and function applications	p. 245
Logic	p. 245
Arithmetic and numeric comparison	p. 246
Lambda functions	p. 248
Global definitions	p. 250
Conditional expressions	p. 251
Quoting	p. 252
Lists	p. 253
List selection	p. 255
Recursion	p. 256
Local definitions	p. 257
Binary trees in LISP	p. 257
Dynamic and lexical scope	p. 259
Functions as values and arguments	p. 261
Symbols, quoting and evaluation	p. 263
¿ calculus in LISP	p. 265
¿ calculus and Scheme	p. 266
Other features	p. 268
Summary	p. 268
Exercises	p. 268
Answers to exercises	p. 273
Bibliography	p. 305
Index	p. 313
Table of Contents provided by Ingram. All Rights Reserved.

Introduction to Functional Programming Through Lambda Calculus

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