1 | \chapter{Background} |
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2 | |
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3 | \vspace*{-8pt} |
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4 | |
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5 | \CFA is a backwards-compatible extension of the C programming language, therefore, it must support C-style enumerations. |
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6 | The following discussion covers C enumerations. |
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7 | |
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8 | As mentioned in \VRef{s:Aliasing}, it is common for C programmers to ``believe'' there are three equivalent forms of named constants. |
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9 | \begin{clang} |
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10 | #define Mon 0 |
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11 | static const int Mon = 0; |
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12 | enum { Mon }; |
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13 | \end{clang} |
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14 | \begin{enumerate}[leftmargin=*] |
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15 | \item |
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16 | For @#define@, the programmer has to explicitly manage the constant name and value. |
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17 | Furthermore, these C preprocessor macro names are outside of the C type-system and can incorrectly change random text in a program. |
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18 | \item |
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19 | The same explicit management is true for the @const@ declaration, and the @const@ variable cannot appear in constant-expression locations, like @case@ labels, array dimensions,\footnote{ |
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20 | C allows variable-length array-declarations (VLA), so this case does work, but it fails in \CC, which does not support VLAs, unless it is \lstinline{g++}.} immediate oper\-ands of assembler instructions, and occupy storage. |
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21 | \begin{clang} |
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22 | $\$$ nm test.o |
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23 | 0000000000000018 r Mon |
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24 | \end{clang} |
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25 | \item |
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26 | Only the @enum@ form is managed by the compiler, is part of the language type-system, works in all C constant-expression locations, and normally does not occupy storage. |
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27 | \end{enumerate} |
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28 | |
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29 | |
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30 | \section{C \lstinline{const}} |
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31 | \label{s:Cconst} |
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32 | |
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33 | C can simulate the aliasing @const@ declarations \see{\VRef{s:Aliasing}}, with static and dynamic initialization. |
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34 | \begin{cquote} |
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35 | \begin{tabular}{@{}ll@{}} |
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36 | \multicolumn{1}{@{}c}{\textbf{static initialization}} & \multicolumn{1}{c@{}}{\textbf{dynamic intialization}} \\ |
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37 | \begin{clang} |
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38 | static const int one = 0 + 1; |
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39 | static const void * NIL = NULL; |
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40 | static const double PI = 3.14159; |
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41 | static const char Plus = '+'; |
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42 | static const char * Fred = "Fred"; |
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43 | static const int Mon = 0, Tue = Mon + 1, Wed = Tue + 1, |
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44 | Thu = Wed + 1, Fri = Thu + 1, Sat = Fri + 1, Sun = Sat + 1; |
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45 | \end{clang} |
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46 | & |
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47 | \begin{clang} |
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48 | void foo() { |
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49 | // auto scope only |
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50 | const int r = random() % 100; |
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51 | int va[r]; |
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52 | } |
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53 | \end{clang} |
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54 | \end{tabular} |
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55 | \end{cquote} |
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56 | However, statically initialized identifiers cannot appear in constant-expression contexts, \eg @case@. |
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57 | Dynamically initialized identifiers may appear in initialization and array dimensions in @g++@, which allows variable-sized arrays on the stack. |
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58 | Again, this form of aliasing is not an enumeration. |
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59 | |
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60 | \section{C Enumeration} |
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61 | \label{s:CEnumeration} |
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62 | |
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63 | The C enumeration has the following syntax~\cite[\S~6.7.2.2]{C11}. |
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64 | \begin{clang}[identifierstyle=\linespread{0.9}\it] |
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65 | $\it enum$-specifier: |
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66 | enum identifier$\(_{opt}\)$ { enumerator-list } |
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67 | enum identifier$\(_{opt}\)$ { enumerator-list , } |
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68 | enum identifier |
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69 | enumerator-list: |
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70 | enumerator |
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71 | enumerator-list , enumerator |
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72 | enumerator: |
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73 | enumeration-constant |
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74 | enumeration-constant = constant-expression |
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75 | \end{clang} |
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76 | The terms \emph{enumeration} and \emph{enumerator} used in this work \see{\VRef{s:Terminology}} come from the grammar. |
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77 | The C enumeration semantics are discussed using examples. |
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78 | |
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79 | |
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80 | \subsection{Type Name} |
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81 | \label{s:TypeName} |
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82 | |
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83 | An \emph{unnamed} enumeration is used to provide aliasing \see{\VRef{s:Aliasing}} exactly like a @const@ declaration in other languages. |
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84 | However, it is restricted to integral values. |
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85 | \begin{clang} |
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86 | enum { Size = 20, Max = 10, MaxPlus10 = Max + 10, @Max10Plus1@, Fred = -7 }; |
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87 | \end{clang} |
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88 | Here, the aliased constants are: 20, 10, 20, 21, and -7. |
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89 | Direct initialization is by a compile-time expression generating a constant value. |
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90 | Indirect initialization (without initialization, @Max10Plus1@) is \newterm{auto-initialized}: from left to right, starting at zero or the next explicitly initialized constant, incrementing by @1@. |
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91 | Because multiple independent enumerators can be combined, enumerators with the same values can occur. |
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92 | The enumerators are rvalues, so assignment is disallowed. |
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93 | Finally, enumerators are \newterm{unscoped}, \ie enumerators declared inside of an @enum@ are visible (projected) into the enclosing scope of the @enum@ type. |
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94 | For unnamed enumerations, this semantic is required because there is no type name for scoped qualification. |
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95 | |
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96 | As noted, this kind of aliasing declaration is not an enumeration, even though it is declared using an @enum@ in C. |
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97 | While the semantics is misleading, this enumeration form matches with aggregate types: |
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98 | \begin{cfa} |
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99 | typedef struct @/* unnamed */@ { ... } S; |
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100 | struct @/* unnamed */@ { ... } x, y, z; $\C{// questionable}$ |
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101 | struct S { |
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102 | union @/* unnamed */@ { $\C{// unscoped fields}$ |
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103 | int i; double d ; char ch; |
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104 | }; |
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105 | }; |
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106 | \end{cfa} |
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107 | Hence, C programmers would expect this enumeration form to exist in harmony with the aggregate form. |
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108 | |
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109 | A \emph{named} enumeration is an enumeration: |
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110 | \begin{clang} |
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111 | enum @Week@ { Mon, Tue, Wed, Thu@ = 10@, Fri, Sat, Sun }; |
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112 | \end{clang} |
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113 | and adopts the same semantics with respect to direct and auto intialization. |
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114 | For example, @Mon@ to @Wed@ are implicitly assigned with constants @0@--@2@, @Thu@ is explicitly set to constant @10@, and @Fri@ to @Sun@ are implicitly assigned with constants @11@--@13@. |
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115 | As well, initialization may occur in any order. |
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116 | \begin{clang} |
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117 | enum Week { |
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118 | Thu@ = 10@, Fri, Sat, Sun, |
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119 | Mon@ = 0@, Tue, Wed@,@ $\C{// terminating comma}$ |
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120 | }; |
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121 | \end{clang} |
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122 | Note, the comma in the enumerator list can be a terminator or a separator, allowing the list to end with a dangling comma.\footnote{ |
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123 | A terminating comma appears in other C syntax, \eg the initializer list.} |
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124 | This feature allow enumerator lines to be interchanged without moving a comma. |
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125 | Named enumerators are also unscoped. |
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126 | |
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127 | |
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128 | \subsection{Implementation} |
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129 | \label{s:CenumImplementation} |
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130 | |
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131 | In theory, a C enumeration \emph{variable} is an implementation-defined integral type large enough to hold all enumerator values. |
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132 | In practice, C defines @int@~\cite[\S~6.4.4.3]{C11} as the underlying type for enumeration variables, restricting initialization to integral constants, which have type @int@ (unless qualified with a size suffix). |
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133 | However, type @int@ is defined as: |
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134 | \begin{quote} |
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135 | A ``plain'' @int@ object has the natural size suggested by the architecture of the execution environment (large enough to contain any value in the range @INT_MIN@ to @INT_MAX@ as defined in the header @<limits.h>@).~\cite[\S~6.2.5(5)]{C11} |
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136 | \end{quote} |
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137 | Howeveer, @int@ means a 4 bytes on both 32/64-bit architectures, which does not seem like the ``natural'' size for a 64-bit architecture. |
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138 | Whereas, @long int@ means 4 bytes on a 32-bit and 8 bytes on 64-bit architectures, and @long long int@ means 8 bytes on both 32/64-bit architectures, where 64-bit operations are simulated on 32-bit architectures. |
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139 | In reality, both @gcc@ and @clang@ partially ignore this specification and type the integral size of an enumerator based its initialization. |
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140 | \begin{cfa} |
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141 | enum E { IMin = INT_MIN, IMax = INT_MAX, |
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142 | ILMin = LONG_MIN, ILMax = LONG_MAX, |
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143 | ILLMin = LLONG_MIN, ILLMax = LLONG_MAX }; |
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144 | int main() { |
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145 | printf( "%zd %d %d\n%zd %ld %ld\n%zd %ld %ld\n", |
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146 | sizeof(IMin), IMin, IMax, |
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147 | sizeof(ILMin), ILMin, ILMax, |
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148 | sizeof(ILLMin), ILLMin, ILLMax ); |
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149 | } |
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150 | 4 -2147483648 2147483647 |
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151 | 8 -9223372036854775808 9223372036854775807 |
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152 | 8 -9223372036854775808 9223372036854775807 |
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153 | \end{cfa} |
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154 | Hence, initialization in the range @INT_MIN@..@INT_MAX@ is 4 bytes, and outside this range is 8 bytes. |
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155 | |
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156 | \subsection{Usage} |
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157 | \label{s:Usage} |
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158 | |
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159 | C proves an implicit \emph{bidirectional} conversion between an enumeration and its integral type. |
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160 | \begin{clang} |
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161 | enum Week week = Mon; $\C{// week == 0}$ |
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162 | week = Fri; $\C{// week == 11}$ |
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163 | int i = Sun; $\C{// implicit conversion to int, i == 13}$ |
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164 | @week = 10000;@ $\C{// UNDEFINED! implicit conversion to Week}$ |
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165 | \end{clang} |
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166 | While converting an enumerator to its underlying type is useful, the implicit conversion from the base type to an enumeration type is a common source of error. |
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167 | |
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168 | Enumerators can appear in @switch@ and looping statements. |
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169 | \begin{cfa} |
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170 | enum Week { Mon, Tue, Wed, Thu, Fri, Sat, Sun }; |
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171 | switch ( week ) { |
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172 | case Mon ... Fri: $\C{// gcc case range}$ |
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173 | printf( "weekday\n" ); |
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174 | case Sat: case Sun: |
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175 | printf( "weekend\n" ); |
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176 | } |
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177 | for ( enum Week day = Mon; day <= Sun; day += 1 ) { $\C{// step of 1}$ |
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178 | printf( "day %d\n", day ); // 0-6 |
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179 | } |
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180 | \end{cfa} |
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181 | For iterating to make sense, the enumerator values \emph{must} have a consecutive ordering with a fixed step between values. |
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182 | For example, a gap introduced by @Thu = 10@, results in iterating over the values 0--13, where values 3--9 are not @Week@ values. |
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183 | Note, it is the bidirectional conversion that allows incrementing @day@: @day@ is converted to @int@, integer @1@ is added, and the result is converted back to @Week@ for the assignment to @day@. |
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184 | For safety, \CC does not support the bidirectional conversion, and hence, an unsafe cast is necessary to increment @day@: @day = (Week)(day + 1)@. |
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185 | |
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186 | There is a C idiom to automatically compute the number of enumerators in an enumeration. |
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187 | \begin{cfa} |
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188 | enum E { A, B, C, D, @N@ }; // N == 4 |
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189 | for ( enum E e = A; e < @N@; e += 1 ) ... |
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190 | \end{cfa} |
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191 | Here, the auto-incrementing counts the number of enumerators and puts the total into the last enumerator @N@. |
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192 | @N@ is often used as the dimension for an array assocated with the enumeration. |
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193 | \begin{cfa} |
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194 | E array[@N@]; |
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195 | for ( enum E e = A; e < N; e += 1 ) { |
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196 | array[e] = e; |
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197 | } |
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198 | \end{cfa} |
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199 | However, for non-integral typed enumerations, \see{\VRef{f:EumeratorTyping}}, this idiom fails. |
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200 | |
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201 | This idiom is used in another C idiom for matching companion information. |
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202 | For example, an enumeration is linked with a companion array of printable strings. |
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203 | \begin{cfa} |
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204 | enum Integral_Type { chr, schar, uschar, sshort, ushort, sint, usint, ..., NO_OF_ITYPES }; |
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205 | char * Integral_Name[@NO_OF_ITYPES@] = { |
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206 | "char", "signed char", "unsigned char", |
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207 | "signed short int", "unsigned short int", |
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208 | "signed int", "unsigned int", ... |
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209 | }; |
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210 | enum Integral_Type integral_type = ... |
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211 | printf( "%s\n", Integral_Name[@integral_type@] ); // human readable type name |
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212 | \end{cfa} |
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213 | However, the companion idiom results in the \emph{harmonizing} problem because an update to the enumeration @Integral_Type@ often requires a corresponding update to the companion array \snake{Integral_Name}. |
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214 | The need to harmonize is at best indicated by a comment before the enumeration. |
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215 | This issue is exacerbated if enumeration and companion array are in different translation units. |
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216 | |
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217 | \bigskip |
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218 | While C provides a true enumeration, it is restricted, has unsafe semantics, and does not provide useful enumeration features in other programming languages. |
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219 | |
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220 | \section{\CFA Polymorphism} |
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221 | \subsection{Function Overloading} |
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222 | Function overloading is programming languages feature wherein functions may share the same name, but with different function signatures. In both C++ and \CFA, function names can be overloaded |
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223 | with different entities as long as they are different in terms of the number and type of parameters. |
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224 | |
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225 | \begin{cfa} |
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226 | void f(); // (1) |
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227 | void f(int); // (2); Overloaded on the number of parameters |
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228 | void f(char); // (3); Overloaded on parameter type |
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229 | |
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230 | f('A'); |
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231 | \end{cfa} |
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232 | In this case, the name f is overloaded with a nullity function and two arity functions with different parameters types. Exactly which precedures being executed |
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233 | is determined based on the passing arguments. The last expression of the preceding example calls f with one arguments, narrowing the possible candidates down to (2) and (3). |
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234 | Between those, function argument 'A' is an exact match to the parameter expected by (3), while needing an @implicit conversion@ to call (2). The compiler determines (3) is the better candidates among |
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235 | and procedure (3) is being executed. |
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236 | |
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237 | \begin{cfa} |
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238 | int f(int); // (4); Overloaded on return type |
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239 | [int, int] f(int); // (5) Overloaded on the number of return value |
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240 | \end{cfa} |
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241 | The function declarations (4) and (5) show the ability of \CFA functions overloaded with different return value, a feature that is not shared by C++. |
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242 | |
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243 | |
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244 | \subsection{Operator Overloading} |
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245 | Operators in \CFA are specialized function and are overloadable by with specially-named functions represents the syntax used to call the operator. |
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246 | % For example, @bool ?==?T(T lhs, T rhs)@ overloads equality operator for type T, where @?@ is the placeholders for operands for the operator. |
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247 | \begin{cfa} |
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248 | enum Weekday { Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday }; |
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249 | bool ?<?(const Weekday a, const Weekday b) { |
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250 | return ((int)a + 1); |
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251 | } |
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252 | Monday < Sunday; // False |
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253 | ?<?( Monday, Sunday ); // Equivalent syntax |
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254 | \end{cfa} |
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255 | Unary operators are functions that takes one argument and have name @operator?@ or @?operator@, where @?@ is the placeholders for operands. |
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256 | Binary operators are function with two parameters. They are overloadable with function name @?operator?@. |
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257 | |
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258 | \subsection{Constructor and Destructor} |
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259 | In \CFA, all objects are initialized by @constructors@ during its allocation, including basic types, |
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260 | which are initialized by auto-generated basic type constructors. |
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261 | |
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262 | Constructors are overloadable functions with name @?{}@, return @void@, and have at least one parameter, which is a reference |
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263 | to the object being constructored (Colloquially referred to "this" or "self" in other language). |
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264 | |
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265 | \begin{cfa} |
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266 | struct Employee { |
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267 | const char * name; |
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268 | double salary; |
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269 | }; |
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270 | |
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271 | void ?{}( Employee& this, const char * name, double salary ) { |
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272 | this.name = name; |
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273 | this.salary = salary; |
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274 | } |
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275 | |
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276 | Employee Sara { "Sara Schmidt", 20.5 }; |
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277 | \end{cfa} |
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278 | Like Python, the "self" reference is implicitly passed to a constructor. The Employee constructors takes two additional arugments used in its |
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279 | field initialization. |
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280 | |
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281 | A destructor in \CFA is a function that has name @^?{}@. It returns void, and take only one arugment as its "self". |
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282 | \begin{cfa} |
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283 | void ^?{}( Employee& this ) { |
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284 | free(this.name); |
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285 | this.name = 0p; |
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286 | this.salary = 0; |
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287 | } |
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288 | \end{cfa} |
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289 | Destructor can be explicitly evoked as a function call, or implicitly called at the end of the block in which the object is delcared. |
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290 | \begin{cfa} |
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291 | { |
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292 | ^Sara{}; |
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293 | Sara{ "Sara Craft", 20 }; |
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294 | } // ^Sara{} |
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295 | \end{cfa} |
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296 | |
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297 | \subsection{Variable Overloading} |
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298 | C and C++ disallow more than one variable declared in the same scope with the same name. When a variable declare in a inner scope has the same name as |
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299 | a variable in an outer scope, the outer scope variable is "shadowed" by the inner scope variable and cannot be accessed directly. |
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300 | |
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301 | \CFA has variable overloading: multiple variables can share the same name in the same scope, as long as they have different type. Name shadowing only |
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302 | happens when the inner scope variable and the outer scope ones have the same type. |
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303 | \begin{cfa} |
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304 | double i = 6.0; |
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305 | int i = 5; |
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306 | void foo( double i ) { sout | i; } // 6.0 |
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307 | \end{cfa} |
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308 | |
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309 | \subsection{Special Literals} |
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310 | Literal 0 has special meanings within different contexts: it can means "nothing" or "empty", an additive identity in arithmetic, a default value as in C (null pointer), |
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311 | or an initial state. |
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312 | Awaring of its significance, \CFA provides a special type for the 0 literal, @zero_t@, to define the logical @zero@ for custom types. |
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313 | \begin{cfa} |
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314 | struct S { int i, j; }; |
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315 | void ?{}( S & this, @zero_t@ ) { this.i = 0; this.j = 0; } // zero_t, no parameter name allowed |
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316 | S s0 = @0@; |
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317 | \end{cfa} |
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318 | Overloading @zero_t@ for S provides new definition for @zero@ of type S. |
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319 | |
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320 | According to the C standard, @0@ is the @only@ false value. Any values compares equals to @0@ is false, and not euqals @0@ is true. As a consequence, control structure |
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321 | such as @if()@ and @while()@ only runs it true clause when its predicate @not equals@ to @0@. |
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322 | |
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323 | \CFA generalizes this concept and allows to logically overloads the boolean value for any type by overloading @not equal@ comparison against @zero_t@. |
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324 | \begin{cfa} |
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325 | int ?@!=@?( S this, @zero_t@ ) { return this.i != 0 && this.j != 0; } |
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326 | \end{cfa} |
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327 | |
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328 | % In C, the literal 0 represents the Boolean value false. The expression such as @if (x)@ is equivalent to @if (x != 0)@ . |
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329 | % \CFA allows user to define the logical zero for a custom type by overloading the @!=@ operation against a special type, @zero_t@, |
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330 | % so that an expression with the custom type can be used as a predicate without the need of conversion to the literal 0. |
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331 | % \begin{cfa} |
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332 | % struct S s; |
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333 | % int ?!=?(S, zero_t); |
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334 | % if (s) {} |
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335 | % \end{cfa} |
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336 | Literal 1 is also special. Particularly in C, the pre-increment operator and post-increment operator can be interpreted in terms of @+= 1@. |
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337 | The logical @1@ in \CFA is represented by special type @one_t@. |
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338 | \begin{cfa} |
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339 | void ?{}( S & this, one_t ) { this.i = 1; this.j = 1; } // one_t, no parameter name allowed |
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340 | S & ?+=?( S & this, one_t ) { this.i += 1; this.j += 1; return op; } |
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341 | \end{cfa} |
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342 | Without explictly overloaded by a user, \CFA uses the user-defined @+=(S&, one_t)@ to interpret @?++@ and @++?@, as both are polymorphic functions in \CFA. |
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343 | |
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344 | \subsection{Polymorphics Functions} |
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345 | Parametric-Polymorphics functions are the functions that applied to all types. \CFA functions are parametric-polymorphics when |
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346 | they are written with the @forall@ clause. |
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347 | |
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348 | \begin{cfa} |
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349 | forall(T) |
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350 | T identity(T x) { return x; } |
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351 | identity(42); |
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352 | \end{cfa} |
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353 | The identity function accepts a value from any type as an arugment, and the type parameter @T@ is bounded to @int@ when the function |
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354 | is called with 42. |
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355 | |
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356 | The forall clause can takes @type assertions@ that restricts the polymorphics type. |
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357 | \begin{cfa} |
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358 | forall( T | { void foo(T); } ) |
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359 | void bar(T t) { foo(t); } |
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360 | |
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361 | struct S {} s; |
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362 | void foo(struct S); |
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363 | |
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364 | bar(s); |
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365 | \end{cfa} |
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366 | The assertion on @T@ restricts the range of types for bar to only those implements foo with the matching a signature, so that bar() |
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367 | can call @foo@ in its body with type safe. |
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368 | Calling on type with no mathcing @foo()@ implemented, such as int, causes a compile time type assertion error. |
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369 | |
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370 | A @forall@ clause can asserts on multiple types and with multiple asserting functions. A common practice in \CFA is to group |
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371 | the asserting functions in to a named @trait@ . |
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372 | |
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373 | \begin{cfa} |
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374 | trait Bird(T) { |
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375 | int days_can_fly(T i); |
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376 | void fly(T t); |
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377 | }; |
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378 | |
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379 | forall(B | Bird(B)) { |
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380 | void bird_fly(int days_since_born, B bird) { |
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381 | if (days_since_born > days_can_fly(bird)) { |
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382 | fly(bird); |
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383 | } |
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384 | } |
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385 | } |
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386 | |
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387 | struct Robin {} r; |
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388 | int days_can_fly(Robin r) { return 23; } |
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389 | void fly(Robin r) {} |
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390 | |
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391 | bird_fly( r ); |
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392 | \end{cfa} |
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393 | |
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394 | Grouping type assertions into named trait effectively create a reusable interface for parametrics polymorphics types. |
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395 | |
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396 | \section{Expression Resolution} |
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397 | |
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398 | The overloading feature poses a challenge in \CFA expression resolution. Overloadeded identifiers can refer multiple |
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399 | candidates, with multiples being simultaneously valid. The main task of \CFA resolver is to identity a best candidate that |
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400 | involes less implicit conversion and polymorphism. |
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401 | |
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402 | \subsection{Conversion Cost} |
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403 | In C, functions argument and parameter type does not need to be exact match, and the compiler performs an @implicit conversion@ on argument. |
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404 | \begin{cfa} |
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405 | void foo(double i); |
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406 | foo(42); |
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407 | \end{cfa} |
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408 | The implicit conversion in C is relatively simple because of the abscence of overloading, with the exception of binary operators, for which the |
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409 | compiler needs to find a common type of both operands and the result. The pattern is known as "usual arithmetic conversions". |
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410 | |
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411 | \CFA generalizes C implicit conversion to function overloading as a concept of @conversion cost@. |
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412 | Initially designed by Bilson, conversion cost is a 3-tuple, @(unsafe, poly, safe)@, where unsafe is the number of narrowing conversion, |
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413 | poly is the count of polymorphics type binding, and safe is the sum of the degree of widening conversion. Every |
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414 | basic type in \CFA has been assigned with a @distance to Byte@, or @distance@, and the degree of widening conversion is the difference between two distances. |
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415 | |
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416 | Aaron extends conversion cost to a 7-tuple, |
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417 | @@(unsafe, poly, safe, sign, vars, specialization, reference)@@. The summary of Aaron's cost model is the following: |
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418 | \begin{itemize} |
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419 | \item Unsafe is the number of argument that implicitly convert to a type with high rank. |
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420 | \item Poly accounts for number of polymorphics binding in the function declaration. |
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421 | \item Safe is sum of distance (add reference/appendix later). |
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422 | \item Sign is the number of sign/unsign variable conversion. |
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423 | \item Vars is the number of polymorphics type declared in @forall@. |
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424 | \item Specialization is opposite number of function declared in @forall@. More function declared implies more constraint on polymorphics type, and therefore has the lower cost. |
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425 | \item Reference is number of lvalue-to-rvalue conversion. |
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426 | \end{itemize} |
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