Floats .................................................................................................. 61

Complex Numbers ................................................................................ 65

3.6 Indexed Expressions .............................................................................. 69

3.7 Member Selection ................................................................................. 74

3.8 Functions ............................................................................................ 75

Calls to Procedures ................................................................................ 77

3.9 Arithmetic Expressions .......................................................................... 77

Arithmetic Operators ............................................................................. 77

Noncommutative Multiplication ............................................................... 90

Factorials ............................................................................................. 92

Forming Sums and Products .................................................................... 93

3.10 Boolean and Relational Expressions ........................................................ 94

Boolean Constants ................................................................................. 94

Boolean Operators ................................................................................. 94

Relational Operators .............................................................................. 98

Efcient Boolean Iteration .................................................................... 102

3.11 Expressions for Data Structures ............................................................ 103

Sequences .......................................................................................... 103

Lists .................................................................................................. 105

Sets .................................................................................................. 107

Tables ............................................................................................... 107

Rectangular Tables .............................................................................. 108

3.12 Set-Theoretic Expressions ................................................................... 109

Membership ....................................................................................... 110

Set Inclusion ....................................................................................... 110

Other Binary Operators for Sets ............................................................. 111

3.13 Other Expressions .............................................................................. 113

Functional Operators ............................................................................ 113

Composition ....................................................................................... 114

Neutral Operators ................................................................................ 116

Ranges .............................................................................................. 116

The Concatenation Operator .................................................................. 119

The Double Colon Operator ................................................................... 121

Series ................................................................................................ 122

3.14 Attributes ......................................................................................... 124

3.15 Using Expressions ............................................................................. 126

Evaluating and Simplifying Expressions .................................................. 126

Substituting Subexpressions .................................................................. 127

Structured Types ................................................................................. 130

3.16 Exercises ......................................................................................... 134

4 Basic Data Structures ................................................................................. 135

4.1 In This Chapter ................................................................................... 135

4.2 Introduction ....................................................................................... 135

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