Changeset bd67442


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Timestamp:
Feb 2, 2024, 10:46:41 AM (3 months ago)
Author:
Peter A. Buhr <pabuhr@…>
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master
Children:
be4335b
Parents:
020fa10
Message:

more proofreading, related-work section still needs work

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  • doc/proposals/enum.tex

    r020fa10 rbd67442  
    121121Naming values is a common practice in mathematics and engineering, e.g., $\pi$, $\tau$ (2$\pi$), $\phi$ (golden ratio), MHz (1E6), etc.
    122122Naming is also commonly used to represent many other numerical phenomenon, such as days of the week, months of a year, floors of a building (basement), time (noon, New Years).
    123 Many programming languages capture this important capability through a mechanism called an \newterm{enumeration}.
     123Many programming languages capture this important software-engineering capability through a mechanism called an \newterm{enumeration}.
    124124An enumeration is similar to other programming-language types by providing a set of constrained values, but adds the ability to name \emph{all} the values in its set.
    125125Note, all enumeration names must be unique but different names can represent the same value (eight note, quaver), which are synonyms.
    126126
    127 Specifically, an enumerated type is a type whose values are restricted to a fixed set of named constants.
     127Specifically, an enumerated type restricts its values to a fixed set of named constants.
    128128Fundamentally, all types are restricted to a fixed set of values because of the underlying von Neumann architecture, and hence, to a corresponding set of constants, e.g., @3@, @3.5@, @3.5+2.1i@, @'c'@, @"abc"@, etc.
    129129However, the values for basic types are not named, other than the programming-language supplied constants.
     
    132132\section{C-Style Enum}
    133133
    134 The C-Style enumeration has the following syntax and semantics.
     134The C-Style enumeration has the following syntax and semantics, and is representative of enumerations in many other programming languages (see Section~\ref{s:RelatedWork}).
    135135\begin{lstlisting}[label=lst:weekday]
    136136enum Weekday { Monday, Tuesday, Wednesday, Thursday@ = 10@, Friday, Saturday, Sunday };
     
    139139\end{lstlisting}
    140140Here, the enumeration type @Weekday@ defines the ordered \newterm{enumerator}s @Monday@, @Tuesday@, @Wednesday@, @Thursday@, @Friday@, @Saturday@ and @Sunday@.
    141 The successor of @Tuesday@ is @Monday@ and the predecessor of @Tuesday@ is @Wednesday@.
    142 A C enumeration is implemented by an integral type, with consecutive enumerator values assigned by the compiler starting at zero or the next explicitly initialized value.
    143 For example, @Monday@ to @Wednesday@ have values 0--2 implicitly set by the compiler, @Thursday@ is explicitly set to @10@, and @Friday@ to @Sunday@ have values 11--13 implicitly set by the compiler.
    144 
    145 There are 3 attributes for an enumeration: \newterm{position}, \newterm{label}, and \newterm{value}:
     141By convention, the successor of @Tuesday@ is @Monday@ and the predecessor of @Tuesday@ is @Wednesday@, independent of the associated enumerator constants.
     142Because an enumerator is a constant, it cannot appear in a mutable context, e.g. @Mon = Sun@ is meaningless, and has no address, it is an rvalue\footnote{
     143The term rvalue defines an expression that can only appear on the right-hand side of an assignment.}.
     144Enumerators without explicitly designated constants are auto-initialized by the compiler: from left to right, starting at zero or the next explicitly initialized constant, incrementing by @1@.
     145For example, @Monday@ to @Wednesday@ are implicitly assigned with constants 0--2, @Thursday@ is explicitly set to constant @10@, and @Friday@ to @Sunday@ are implicitly assigned with constants 11--13.
     146Hence, there are 3 universal enumeration attributes: \newterm{position}, \newterm{label}, and \newterm{value}:
    146147\begin{cquote}
    147148\small\sf\setlength{\tabcolsep}{3pt}
    148149\begin{tabular}{rccccccccccc}
    149 @enum@ Weekday \{       & Monday,       & Tuesday,      & Wednesday,    & Thursday=10,  & Friday,       & Saturday,     & Sunday \}; \\
    150 \it position            & 0                     & 1                     & 2                             & 3                             & 4                     & 5                     & 6                     \\
    151 \it label                       & Monday        & Tuesday       & Wednesday             & Thursday              & Friday        & Saturday      & Sunday        \\
    152 \it value                       & 0                     & 1                     & 2                             & {\color{red}10}& 11           & 12            & 13
     150@enum@ Weekday \{       & Monday,       & Tuesday,      & Wednesday,    & Thursday = 10,& Friday,       & Saturday,     & Sunday \}; \\
     151\it\color{red}position          & 0                     & 1                     & 2                             & 3                             & 4                     & 5                     & 6                     \\
     152\it\color{red}label                     & Monday        & Tuesday       & Wednesday             & Thursday              & Friday        & Saturday      & Sunday        \\
     153\it\color{red}value                     & 0                     & 1                     & 2                             & {\color{red}10}& 11           & 12            & 13
    153154\end{tabular}
    154155\end{cquote}
    155 
    156 The enumerators of an enumeration are unscoped, i.e., enumerators declared inside of an @enum@ are visible in the enclosing scope of the @enum@ type.
     156Finally, C enumerators are \newterm{unscoped}, i.e., enumerators declared inside of an @enum@ are visible in the enclosing scope of the @enum@ type.
     157
     158In theory, a C enumeration \emph{variable} is an implementation-defined integral type large enough to hold all enumerated values.
     159In practice, since integral constants in C have type @int@ (unless qualified with a size suffix), C uses @int@ as the underlying type for enumeration variables.
    157160Furthermore, there is an implicit bidirectional conversion between an enumeration and integral types.
    158161\begin{lstlisting}[label=lst:enum_scope]
    159162{
    160163        enum Weekday { ... };                           $\C{// enumerators implicitly projected into local scope}$
    161         Weekday weekday = Monday;
     164        Weekday weekday = Monday;                       $\C{// weekday == 0}$
    162165        weekday = Friday;                                       $\C{// weekday == 11}$
    163         int i = Sunday                                          $\C{// i == 13}$
    164         weekday = 10000;                                        $\C{// undefined behaviour}$
     166        int i = Sunday                                          $\C{// implicit conversion to int, i == 13}$
     167        weekday = 10000;                                        $\C{// UNDEFINED! implicit conversion to Weekday}$
    165168}
    166169int j = Wednesday;                                              $\C{// ERROR! Wednesday is not declared in this scope}$
    167170\end{lstlisting}
     171The implicit conversion from @int@ to an enumeration type is an unnecessary source of error.
    168172
    169173\section{\CFA-Style Enum}
     
    175179
    176180\CFA extends the enumeration by parameterizing the enumeration with a type for the enumerators, allowing enumerators to be assigned any values from the declared type.
    177 \begin{lstlisting}[label=lst:color]
    178 enum( @char@ ) Currency { Dollar = '$\textdollar$', Euro = '$\texteuro$', Pound = '$\textsterling$'  };
    179 enum( @double@ ) Planet { Venus = 4.87, Earth = 5.97, Mars = 0.642  }; // mass
    180 enum( @char *@ ) Colour { Red = "red", Green = "green", Blue = "blue"  };
    181 enum( @Currency@ ) Europe { Euro = '$\texteuro$', Pound = '$\textsterling$' }; // intersection
    182 \end{lstlisting}
    183 The types of the enumerators are @char@, @double@, and @char *@ and each enumerator is initialized with corresponding type values.
    184 % Only types with a defined ordering can be automatically initialized (see Section~\ref{s:AutoInitializable}).
    185 
    186 % An instance of \CFA-enum (denoted as @<enum_instance>@) is a label for the defined enum name.
    187 % The label can be retrieved by calling the function @label( <enum_instance> )@.
    188 % Similarly, the @value()@ function returns the value used to initialize the \CFA-enum.
     181Figure~\ref{f:EumeratorTyping} shows a series of examples illustrating that all \CFA types can be use with an enumeration and each type's constants used to set the enumerators.
     182
     183Typed enumerates deals with \emph{harmonizing} problem between an enumeration and its companion data.
     184The following example is from the \CFA compiler, written in \CC.
     185\begin{lstlisting}
     186enum integral_types { chr, schar, uschar, sshort, ushort, sint, usint, ..., NO_OF_ITYPES };
     187char * integral_names[NO_OF_ITYPES] = {
     188        "char", "signed char", "unsigned char",
     189        "signed short int", "unsigned short int",
     190        "signed int", "unsigned int",
     191        ...
     192};
     193\end{lstlisting}
     194The \emph{harmonizing} problem occurs because the enumeration declaration is in one header file and the names are declared in another translation unit.
     195It is up to the programmer to ensure changes made in one location are harmonized with the other location (by identifying this requirement within a comment).
     196The typed enumeration largely solves this problem by combining and managing the two data types.
     197\begin{lstlisting}
     198enum( char * ) integral_types {
     199        chr = "char", schar = "signed char", uschar = "unsigned char",
     200        sshort = "signed short int", ushort = "unsigned short int",
     201        sint = "signed int", usint = "unsigned int",
     202        ...
     203};
     204\end{lstlisting}
     205
     206% \begin{lstlisting}[label=lst:color]
     207% struct S { int i, j; };
     208% enum( S ) s { A = { 3,  4 }, B = { 7,  8 } };
     209% enum( @char@ ) Currency { Dollar = '$\textdollar$', Euro = '$\texteuro$', Pound = '$\textsterling$'  };
     210% enum( @double@ ) Planet { Venus = 4.87, Earth = 5.97, Mars = 0.642  }; // mass
     211% enum( @char *@ ) Colour { Red = "red", Green = "green", Blue = "blue"  };
     212% enum( @Currency@ ) Europe { Euro = '$\texteuro$', Pound = '$\textsterling$' }; // intersection
     213% \end{lstlisting}
     214
     215\begin{figure}
     216\begin{lstlisting}
     217// integral
     218        enum( @char@ ) Currency { Dollar = '$\textdollar$', Euro = '$\texteuro$', Pound = '$\textsterling$'  };
     219        enum( @signed char@ ) srgb { Red = -1, Green = 0, Blue = 1 };
     220        enum( @long long int@ ) BigNum { X = 123_456_789_012_345,  Y = 345_012_789_456_123 };
     221// non-integral
     222        enum( @double@ ) Math { PI_2 = 1.570796, PI = 3.141597, E = 2.718282 };
     223        enum( @_Complex@ ) Plane { X = 1.5+3.4i, Y = 7+3i, Z = 0+0.5i };
     224// pointer
     225        enum( @char *@ ) Names { Fred = "Fred", Mary = "Mary", Jane = "Jane" };
     226        int i, j, k;
     227        enum( @int *@ ) ptr { I = &i,  J = &j,  K = &k };
     228        enum( @int &@ ) ref { I = i,   J = j,   K = k };
     229// tuple
     230        enum( @[int, int]@ ) { T = [ 1, 2 ] };
     231// function
     232        void f() {...}   void g() {...}
     233        enum( @void (*)()@ ) funs { F = f,  G = g };
     234// aggregate
     235        struct Person { char * name; int age, height; };
     236        enum( @Person@ ) friends { Liz = { "Elizabeth", 22, 170 }, Beth = Liz, Jon = { "Jonathan", 35, 190 } };
     237\end{lstlisting}
     238\caption{Enumerator Typing}
     239\label{f:EumeratorTyping}
     240\end{figure}
     241
     242\subsection{Pure Enumerators}
     243
     244An empty type, @enum()@, implies the enumerators are pure symbols without values;
     245hence, there is no default conversion to @int@.
     246
     247\begin{lstlisting}
     248enum() Mode { O_RDONLY, O_WRONLY, O_CREAT, O_TRUNC, O_APPEND };
     249Mode iomode = O_RDONLY;
     250int i = iomode;                                                 $\C{\color{red}// disallowed}$
     251sout | O_TRUNC;                                                 $\C{\color{red}// disallowed}$
     252\end{lstlisting}
     253
     254\subsection{Enumerator Subset}
     255
     256If follows from enumerator typing that the type of the enumerators can be another enumerator.
     257\begin{lstlisting}
     258enum( char ) Letter { A = 'A',  B = 'B', C = 'C', ..., Z = 'Z' };
     259enum( Letter ) Greek { Alph = A, Beta = B, ..., Zeta = Z }; // alphabet intersection
     260Letter letter = A;
     261Greak greek = Alph;
     262letter = Alph;                                                  $\C{// allowed}$
     263greek = A;                                                              $\C{\color{red}// disallowed}$
     264\end{lstlisting}
     265Enumeration @Greek@ may have more or less enumerators than @Letter@, but the enumerator values must be from @Letter@.
     266Therefore, @Greek@ enumerators are a subset of type @Letter@ and are type compatible with enumeration @Letter@, but @Letter@ enumerators are not type compatible with enumeration @Greek@.
     267
     268\subsection{Enumeration Inheritance}
     269
     270\CFA Plan-9 inheritance may be used with enumerations.
     271\begin{lstlisting}
     272enum( char * ) Name2 { @inline Name@, Jack = "Jack", Jill = "Jill" };
     273enum /* inferred */ Name3 { @inline Name2@, Sue = "Sue", Tom = "Tom" };
     274\end{lstlisting}
     275Enumeration @Name2@ inherits all the enumerators and their values from enumeration @Name@ by containment, and a @Name@ enumeration is a subtype of enumeration @Name2@.
     276Note, enumerators must be unique in inheritance but enumerator values may be repeated.
     277
     278The enumeration type for the inheriting type must be the same as the inherited type;
     279hence the enumeration type may be omitted for the inheriting enumeration and it is inferred from the inherited enumeration, as for @Name3@.
     280When inheriting from integral types, automatic numbering may be used, so the inheritance placement left to right is important.
     281
     282Specifically, the inheritance relationship for Names is:
     283\begin{lstlisting}
     284Name $\(\subset\)$ Name2 $\(\subset\)$ Name3 $\(\subset\)$ const char *         // enum type of Name
     285\end{lstlisting}
     286For the given function prototypes, the following calls are valid.
     287\begin{cquote}
     288\begin{tabular}{ll}
     289\begin{lstlisting}
     290void f( Name );
     291void g( Name2 );
     292void h( Name3 );
     293void j( const char * );
     294\end{lstlisting}
     295&
     296\begin{lstlisting}
     297f( Fred );
     298g( Fred );   g( Jill );
     299h( Fred );   h( Jill );   h( Sue );
     300j( Fred );   j( Jill );   j( Sue );   j( "Will" );
     301\end{lstlisting}
     302\end{tabular}
     303\end{cquote}
     304Note, the validity of calls is the same for call-by-reference as for call-by-value, and const restrictions are the same as for other types.
    189305
    190306\subsection{Enumerator Scoping}
     
    220336Enumeration Greek may have more or less enumerators than Letter, but the enumerator values must be from Letter.
    221337Therefore, Greek enumerators are a subset of type Letter and are type compatible with enumeration Letter, but Letter enumerators are not type compatible with enumeration Greek.
     338
     339% An instance of \CFA-enum (denoted as @<enum_instance>@) is a label for the defined enum name.
     340% The label can be retrieved by calling the function @label( <enum_instance> )@.
     341% Similarly, the @value()@ function returns the value used to initialize the \CFA-enum.
    222342
    223343\subsubsection{\lstinline{enumerate()}}
     
    9261046
    9271047\section{Related Work}
    928 
    929 Enumerations exist in many popular programming languages, e.g., Pascal, Ada, \Csharp, \CC, Go, Java, Modula-3, Rust, Swift, Python, and Algebraic data type in functional programming.
    930 There are a large set of overlapping features for all the languages, but each language has its own unique restrictions and extensions.
    931 
    932 \subsection{Pascal}
     1048\label{s:RelatedWork}
     1049
     1050Enumerations exist in many popular programming languages, e.g., Pascal, Ada, \Csharp, \CC, Go, Java, Modula-3, Rust, Swift, Python, and the algebraic data-type in functional programming.
     1051There are a large set of overlapping features among these languages, but each language has its own unique restrictions and extensions.
     1052
     1053\subsection{(Free) Pascal}
     1054
     1055Free Pascal is a modern object-oriented version of the classic Pascal programming language.
     1056It allows a C-style enumeration type, where enumerators must be in assigned in ascending numerical order with a constant expression and the range can be non-consecutive.
     1057\begin{lstlisting}[language=pascal,{moredelim=**[is][\color{red}]{@}{@}}]
     1058Type EnumType = ( one, two, three, forty @= 40@, fortyone );
     1059\end{lstlisting}
     1060Pseudo-functions @Pred@ and @Succ@ can only be used if the range is consecutive.
     1061The underlying type is an implementation-defined integral type large enough to hold all enumerated values; it does not have to be the smallest possible type.
     1062The size underlying integral type can be explicitly specified using compiler directive @$PACKENUM@~$N$, where $N$ is the number of bytes, e.g.:
     1063\begin{lstlisting}[language=pascal,{moredelim=**[is][\color{red}]{@}{@}}]
     1064Type @{$\color{red}\$$PACKENUM 1}@ SmallEnum = ( one, two, three );
     1065            @{$\color{red}\$$PACKENUM 4}@ LargeEnum = ( BigOne, BigTwo, BigThree );
     1066Var S : SmallEnum; { 1 byte }
     1067          L : LargeEnum; { 4 bytes}
     1068\end{lstlisting}
     1069
    9331070
    9341071\subsection{Ada}
    9351072
     1073An enumeration type is defined as a list of possible values:
     1074\begin{lstlisting}[language=ada]
     1075type RGB is (Red, Green, Blue);
     1076\end{lstlisting}
     1077Like for numeric types, where e.g., 1 is an integer literal, @Red@, @Green@ and @Blue@ are called the literals of this type.
     1078There are no other values assignable to objects of this type.
     1079
     1080\paragraph{Operators and attributes} ~\newline
     1081Apart from equality (@"="@), the only operators on enumeration types are the ordering operators: @"<"@, @"<="@, @"="@, @"/="@, @">="@, @">"@, where the order relation is given implicitly by the sequence of literals:
     1082Each literal has a position, starting with 0 for the first, incremented by one for each successor.
     1083This position can be queried via the @'Pos@ attribute; the inverse is @'Val@, which returns the corresponding literal. In our example:
     1084\begin{lstlisting}[language=ada]
     1085RGB'Pos (Red) = 0
     1086RGB'Val (0)   = Red
     1087\end{lstlisting}
     1088There are two other important attributes: @Image@ and @Value@.
     1089@Image@ returns the string representation of the value (in capital letters), @Value@ is the inverse:
     1090\begin{lstlisting}[language=ada]
     1091RGB'Image ( Red ) = "RED"
     1092RGB'Value ("Red") =  Red
     1093\end{lstlisting}
     1094These attributes are important for simple IO (there are more elaborate IO facilities in @Ada.Text_IO@ for enumeration types).
     1095Note that, since Ada is case-insensitive, the string given to @'Value@ can be in any case.
     1096
     1097\paragraph{Enumeration literals} ~\newline
     1098Literals are overloadable, i.e. you can have another type with the same literals.
     1099\begin{lstlisting}[language=ada]
     1100type Traffic_Light is (Red, Yellow, Green);
     1101\end{lstlisting}
     1102Overload resolution within the context of use of a literal normally resolves which @Red@ is meant.
     1103Only if you have an unresolvable overloading conflict, you can qualify with special syntax which @Red@ is meant:
     1104\begin{lstlisting}[language=ada]
     1105RGB'(Red)
     1106\end{lstlisting}
     1107Like many other declarative items, enumeration literals can be renamed.
     1108In fact, such a literal is actually a function, so it has to be renamed as such:
     1109\begin{lstlisting}[language=ada]
     1110function Red return P.RGB renames P.Red;
     1111\end{lstlisting}
     1112Here, @RGB@ is assumed to be defined in package @P@, which is visible at the place of the renaming declaration.
     1113Renaming makes @Red@ directly visible without necessity to resort the use-clause.
     1114
     1115Note that redeclaration as a function does not affect the staticness of the literal.
     1116
     1117\paragraph{Characters as enumeration literals} ~\newline
     1118Rather unique to Ada is the use of character literals as enumeration literals:
     1119\begin{lstlisting}[language=ada]
     1120type ABC is ('A', 'B', 'C');
     1121\end{lstlisting}
     1122This literal @'A'@ has nothing in common with the literal @'A'@ of the predefined type @Character@ (or @Wide_Character@).
     1123
     1124Every type that has at least one character literal is a character type.
     1125For every character type, string literals and the concatenation operator @"&"@ are also implicitly defined.
     1126\begin{lstlisting}[language=ada]
     1127type My_Character is (No_Character, 'a', Literal, 'z');
     1128type My_String is array (Positive range <>) of My_Character;
     1129
     1130S: My_String := "aa" & Literal & "za" & 'z';
     1131T: My_String := ('a', 'a', Literal, 'z', 'a', 'z');
     1132\end{lstlisting}
     1133In this example, @S@ and @T@ have the same value.
     1134
     1135Ada's @Character@ type is defined that way.
     1136See Ada Programming/Libraries/Standard.
     1137
     1138\paragraph{Booleans as enumeration literals} ~\newline
     1139Also Booleans are defined as enumeration types:
     1140\begin{lstlisting}[language=ada]
     1141type Boolean is (False, True);
     1142\end{lstlisting}
     1143There is special semantics implied with this declaration in that objects and expressions of this type can be used as conditions.
     1144Note that the literals @False@ and @True@ are not Ada keywords.
     1145
     1146Thus it is not sufficient to declare a type with these literals and then hope objects of this type can be used like so:
     1147\begin{lstlisting}[language=ada]
     1148type My_Boolean is (False, True);
     1149Condition: My_Boolean;
     1150
     1151if Condition then -- wrong, won't compile
     1152\end{lstlisting}
     1153
     1154If you need your own Booleans (perhaps with special size requirements), you have to derive from the predefined Boolean:
     1155\begin{lstlisting}[language=ada]
     1156type My_Boolean is new Boolean;
     1157Condition: My_Boolean;
     1158
     1159if Condition then -- OK
     1160\end{lstlisting}
     1161
     1162\paragraph{Enumeration subtypes} ~\newline
     1163You can use range to subtype an enumeration type:
     1164\begin{lstlisting}[language=ada]
     1165subtype Capital_Letter is Character range 'A' .. 'Z';
     1166type Day_Of_Week is (Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday);
     1167subtype Working_Day is Day_Of_Week range Monday .. Friday;
     1168\end{lstlisting}
     1169
     1170\paragraph{Using enumerations} ~\newline
     1171Enumeration types being scalar subtypes, type attributes such as @First@ and @Succ@ will allow stepping through a subsequence of the values.
     1172\begin{lstlisting}[language=ada]
     1173case Day_Of_Week'First is
     1174        when Sunday =>
     1175           ISO (False);
     1176        when Day_Of_Week'Succ(Sunday) =>
     1177           ISO (True);
     1178        when Tuesday .. Saturday =>
     1179           raise Program_Error;
     1180end case;
     1181\end{lstlisting}
     1182A loop will automatically step through the values of the subtype's range.
     1183Filtering week days to include only working days with an even position number:
     1184\begin{lstlisting}[language=ada]
     1185        for Day in Working_Day loop
     1186                if Day_Of_Week'Pos(Day) mod 2 = 0 then
     1187                        Work_In_Backyard;
     1188                end if;
     1189        end loop;
     1190\end{lstlisting}
     1191Enumeration types can be used as array index subtypes, yielding a table feature:
     1192\begin{lstlisting}[language=ada]
     1193type Officer_ID is range 0 .. 50;
     1194type Schedule is array (Working_Day) of Officer_ID;
     1195\end{lstlisting}
     1196
     1197\begin{lstlisting}[language=ada]
     1198type Subtype_Name is (Id1, Id2, Id3 ... );
     1199\end{lstlisting}
     1200where @Id1@, @Id2@, etc. are identifiers or characters literals.
     1201In either case, the legal values of the type are referred to as "enumeration literals."
     1202Each of these values has a "position number" corresponding to its position in the list such that @Id1@ has position 0, @Id2@ has position 1, and the Nth value has position N-1.
     1203
     1204\paragraph{Attributes of Enumeration Types} ~\newline
     1205An enumeration type, @T@, has the following attributes: @T'First@, @T'Last@, @T'Range@, @T'Pred@, @T'Succ@, @T'Min@, @T'Max@, @T'Image@, @T'Wide_Image@, @T'Value@, @T'Wide_Value@, @T'Pos@, and @T'Val@ (pronounced "T tick first", "T tick last", etc.).
     1206Most of these are illustrated in the example program given below, and most of them produce what you would intuitively expect based on their names.
     1207
     1208@T'Image@ and @T'Value@ form a complementary pair of attributes.
     1209The former takes a value in @T@ and returns a String representation of that value.
     1210The latter takes a @String@ that is a representation of a value in @T@ and returns that value.
     1211
     1212@T'Pos@ and @T'Val@ form another complementary pair.
     1213The former takes a value in @T@ and returns its position number.
     1214The latter takes a position number and returns the corresponding value of type @T@.
     1215
     1216
    9361217\subsection{\Csharp}
    9371218
    9381219\subsection{\CC}
    9391220
    940 Because \CC is backwards compatible with C, it inherited C's enumerations, except there is no implicit conversion from an integral value to an enumeration;
    941 hence, the values in a \CC enumeration can only be its enumerators.
    942 
    943 \CC{11} extended enumeration with a scoped enumeration, \lstinline[language=c++]{enum class} (or \lstinline[language=c++]{enum struct}), where the enumerators are local to the enumeration and are accessed using type qualification, e.g., @Weekday::Monday@.
     1221\CC is backwards compatible with C, so it inherited C's enumerations, except there is no implicit conversion from an integral value to an enumeration;
     1222hence, the values in a \CC enumeration can only be its enumerators (without a cast).
     1223There is no mechanism to iterate through an enumeration.
     1224
     1225\CC{11} added a scoped enumeration, \lstinline[language=c++]{enum class} (or \lstinline[language=c++]{enum struct}), so the enumerators are local to the enumeration and must be accessed using type qualification, e.g., @Weekday::Monday@.
    9441226\CC{20} supports unscoped access with a \lstinline[language=c++]{using enum} declaration.
    9451227
    946 For both unscoped and scoped enumerations, the underlying type is an implementation-defined integral type that is large enough to hold all enumerated values; it does not have to be the smallest possible type.
    947 The underlying integral type can be explicitly specified:
     1228For both unscoped and scoped enumerations, the underlying type is an implementation-defined integral type large enough to hold all enumerated values; it does not have to be the smallest possible type.
     1229In \CC{11}, the underlying integral type can be explicitly specified:
    9481230\begin{lstlisting}[language=c++,{moredelim=**[is][\color{red}]{@}{@}}]
    9491231enum class RGB : @long@ { Red, Green, Blue };
    9501232enum class rgb : @char@ { Red = 'r', Green = 'g', Blue = 'b' };
    9511233enum class srgb : @signed char@ { Red = -1, Green = 0, Blue = 1 };
     1234RGB colour1 = @RGB::@Red;
     1235rgb colour2 = @rgb::@Red;
     1236srgb colour3 = @srgb::@Red;
    9521237\end{lstlisting}
    9531238
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