Changeset 0030b508 for doc


Ignore:
Timestamp:
Nov 13, 2023, 3:43:31 AM (7 months ago)
Author:
JiadaL <j82liang@…>
Branches:
master
Children:
fc12f05
Parents:
6bd9f9e
Message:

some updates

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1 edited

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  • doc/proposals/enum.tex

    r6bd9f9e r0030b508  
    1 %%
    2 %% This is file `sample-manuscript.tex',
    3 %% generated with the docstrip utility.
    4 %%
    5 %% The original source files were:
    6 %%
    7 %% samples.dtx  (with options: `manuscript')
    8 %%
    9 %% IMPORTANT NOTICE:
    10 %%
    11 %% For the copyright see the source file.
    12 %%
    13 %% Any modified versions of this file must be renamed
    14 %% with new filenames distinct from sample-manuscript.tex.
    15 %%
    16 %% For distribution of the original source see the terms
    17 %% for copying and modification in the file samples.dtx.
    18 %%
    19 %% This generated file may be distributed as long as the
    20 %% original source files, as listed above, are part of the
    21 %% same distribution. (The sources need not necessarily be
    22 %% in the same archive or directory.)
    23 %%
    24 %% Commands for TeXCount
    25 %TC:macro \cite [option:text,text]
    26 %TC:macro \citep [option:text,text]
    27 %TC:macro \citet [option:text,text]
    28 %TC:envir table 0 1
    29 %TC:envir table* 0 1
    30 %TC:envir tabular [ignore] word
    31 %TC:envir displaymath 0 word
    32 %TC:envir math 0 word
    33 %TC:envir comment 0 0
    34 %%
    35 %%
    36 %% The first command in your LaTeX source must be the \documentclass command.
    37 \documentclass[manuscript,screen,review]{acmart}
     1\documentclass[12pt]{article}
     2\usepackage{fullpage,times}
     3\usepackage{pslatex}                    % reduce size of san serif font
    384\usepackage{xcolor}
    395\usepackage{listings}
    40 \usepackage[ligature, inference]{semantic}
    41 \usepackage{array}
    42 
    43 \definecolor{mGreen}{rgb}{0,0.6,0}
    44 \definecolor{mGray}{rgb}{0.5,0.5,0.5}
    45 \definecolor{mPurple}{rgb}{0.58,0,0.82}
    46 \definecolor{backgroundColour}{rgb}{0.95,0.95,0.92}
     6%\usepackage{array}
     7\usepackage{graphics}
     8\usepackage{xspace}
     9
     10\makeatletter
     11\renewcommand\section{\@startsection{section}{1}{\z@}{-3.0ex \@plus -1ex \@minus -.2ex}{1.5ex \@plus .2ex}{\normalfont\large\bfseries}}
     12\renewcommand\subsection{\@startsection{subsection}{2}{\z@}{-2.75ex \@plus -1ex \@minus -.2ex}{1.25ex \@plus .2ex}{\normalfont\normalsize\bfseries}}
     13\renewcommand\subsubsection{\@startsection{subsubsection}{3}{\z@}{-2.5ex \@plus -1ex \@minus -.2ex}{1.0ex \@plus .2ex}{\normalfont\normalsize\bfseries}}
     14\renewcommand\paragraph{\@startsection{paragraph}{4}{\z@}{-2.0ex \@plus -1ex \@minus -.2ex}{-1em}{\normalfont\normalsize\bfseries}}
     15\renewcommand\subparagraph{\@startsection{subparagraph}{4}{\z@}{-1.5ex \@plus -1ex \@minus -.2ex}{-1em}{\normalfont\normalsize\bfseries\itshape}}
     16\makeatother
     17
     18\newenvironment{cquote}{%
     19        \list{}{\lstset{resetmargins=true,aboveskip=0pt,belowskip=0pt}\topsep=4pt\parsep=0pt\leftmargin=\parindent\rightmargin\leftmargin}%
     20        \item\relax
     21}{%
     22        \endlist
     23}% cquote
     24
     25\setlength{\topmargin}{-0.45in}                                                 % move running title into header
     26\setlength{\headsep}{0.25in}
     27\setlength{\textheight}{9.0in}
     28
     29\newcommand{\CFAIcon}{\textsf{C\raisebox{\depth}{\rotatebox{180}A}}} % Cforall icon
     30\newcommand{\CFA}{\protect\CFAIcon\xspace}                              % CFA symbolic name
     31\newcommand{\PAB}[1]{{\color{red}PAB: #1}}
     32
     33% \definecolor{mGreen}{rgb}{0,0.6,0}
     34% \definecolor{mGray}{rgb}{0.5,0.5,0.5}
     35% \definecolor{mPurple}{rgb}{0.58,0,0.82}
     36% \definecolor{backgroundColour}{rgb}{0.95,0.95,0.92}
    4737
    4838\lstdefinestyle{CStyle}{
    49     backgroundcolor=\color{backgroundColour},   
    50     commentstyle=\color{mGreen},
    51     keywordstyle=\color{magenta},
    52     numberstyle=\tiny\color{mGray},
    53     stringstyle=\color{mPurple},
    54     basicstyle=\footnotesize,
     39%    backgroundcolor=\color{backgroundColour},   
     40%    commentstyle=\color{mGreen},
     41%    keywordstyle=\color{magenta},
     42        stringstyle=\small\tt,                                  % use typewriter font
     43%    stringstyle=\color{mPurple},
     44    columns=fullflexible,
     45    basicstyle=\small\linespread{0.9}\sf,       % reduce line spacing and use sanserif font
     46%   basicstyle=\footnotesize,
    5547    breakatwhitespace=false,         
    56     breaklines=true,                 
     48%    breaklines=true,                 
    5749    captionpos=b,                   
    5850    keepspaces=true,                 
    59     numbers=left,                   
    60     numbersep=5pt,                 
    61     showspaces=false,               
     51%    numbers=left,                   
     52%    numbersep=5pt,                 
     53%    numberstyle=\tiny\color{mGray},
     54%    showspaces=false,               
    6255    showstringspaces=false,
    63     showtabs=false,                 
    64     tabsize=2,
    65     language=C
    66 }
    67 
    68 %%
    69 %% \BibTeX command to typeset BibTeX logo in the docs
    70 \AtBeginDocument{%
    71   \providecommand\BibTeX{{%
    72     \normalfont B\kern-0.5em{\scshape i\kern-0.25em b}\kern-0.8em\TeX}}}
    73 
    74 
    75 %%
    76 %% end of the preamble, start of the body of the document source.
     56%    showtabs=false,                 
     57        showlines=true,                                                 % show blank lines at end of code
     58    tabsize=5,
     59    language=C,
     60        aboveskip=4pt,                                                  % spacing above/below code block
     61        belowskip=2pt,
     62        xleftmargin=\parindent,                 % indent code to paragraph indentation
     63}
     64\lstset{style=CStyle,moredelim=**[is][\color{red}]{@}{@}}
     65\lstMakeShortInline@                            % single-character for \lstinline
     66
    7767\begin{document}
    7868
    79 %%
    80 %% The "title" command has an optional parameter,
    81 %% allowing the author to define a "short title" to be used in page headers.
    82 \title{Enumeration in Cforall}
    83 
    84 %%
    85 %% The "author" command and its associated commands are used to define
    86 %% the authors and their affiliations.
    87 %% Of note is the shared affiliation of the first two authors, and the
    88 %% "authornote" and "authornotemark" commands
    89 %% used to denote shared contribution to the research.
     69\title{\vspace*{-0.5in}Enumeration in \CFA}
    9070\author{Jiada Liang}
    9171
    92 
    93 %%
    94 %% The abstract is a short summary of the work to be presented in the
    95 %% article.
     72\maketitle
     73
    9674\begin{abstract}
    97     An enumeration, or enum in short, is a type that defines a list of named constant values in C. C uses integral type as the underlying representation of enum. Cforall extends C enum to allow more types, including custom types, to be used as enumeration inner representation.
     75An enumeration is a type that defines a list of named constant values in C (and other languages).
     76C uses an integral type as the underlying representation of an enumeration.
     77\CFA extends C enumerations to allow all basic and custom types for the inner representation.
    9878\end{abstract}
    9979
    100 %%
    101 %% The code below is generated by the tool at http://dl.acm.org/ccs.cfm.
    102 %% Please copy and paste the code instead of the example below.
    103 %%
    104 
    105 
    106 %%
    107 %% This command processes the author and affiliation and title
    108 %% information and builds the first part of the formatted document.
    109 \maketitle
    110 
    11180\section{C-Style Enum}
    112 \begin{lstlisting}[style=CStyle, label{lst:weekday}]
     81
     82\CFA supports the C-Style enumeration using the same syntax and semantics.
     83\begin{lstlisting}[label=lst:weekday]
    11384enum Weekday { Monday, Tuesday, Wednesday, Thursday=10, Friday, Saturday, Sunday };
    11485\end{lstlisting}
    115 Cforall supports the C-Style enumeration (C-enum for short). It has the same syntax as C and resembles the same language semantics. In code~\ref{lst:weekday} example, the syntax defines an enum class $Weekday$ with enumerators $Monday$, $Tuesday$, $Wednesday$, $Thursday$, $Friday$, $Saturday$ and $Sunday$ in order. The successor of $Tuesday$ is $Monday$ and the predecessor of $Tuesday$ is $Wednesday$. Enumerators have an integral type, either being explicitly initialized by an initializer or being assigned a value by the compiler. For example, $Thursday$ has been assigned with value $10$. If not explicitly initialized, the first value of an enum, $Monday$ in the $Weekday$ example, has the integer value 0. Other uninitialized enum value has a value that is equal to their successor $+ 1$. The enum value $Tuesday$, $Wednesday$, $Friday$, $Saturday$, and $Sunday$ have value 1, 2, 11, 12, and 13 respectively.
    116 
    117 \begin{lstlisting}[label{lst:enum_scope}, style=CStyle]
    118 {
    119     {
    120         enum RGB {R, G, B};
    121         int i = R  // i == 0
    122     }
    123     int j = G; // ERROR! G is not declared in this scope
    124 }
    125 \end{lstlisting}
    126 C-enums are unscoped: enumerators declared inside of an enum are visible in the enclosing scope of the enum class.
    127 
    128 \section{Cforall-Style Enum}
    129 \begin{lstlisting}[style=CStyle, label{lst:color}]
    130 enum Color(char *) { Red="R", Green="G", Blue="B"  };
    131 \end{lstlisting}
    132 A Cforall enumeration is parameterized by a type declared. Cforall allows any oType in the enum declaration, and values assigned to enumerators must be in the declared type.
    133 
    134 \section{Enumerable Type Traits}
    135 A trait is a collection of constraints in Cforall, which can be used to describe types. Cforall standard library defines traits to categorize types that are related enumeration features.
    136 \subsection{Enumerable}
    137 A type is enumerable if it can map an integer to a value.
    138 \begin{lstlisting}[style=CStyle]
    139 forall(T)
    140 trait Enumerable {
    141     T value( *class_name* , int );
    142 };
    143 \end{lstlisting}
    144 The parameter class name stands for the name of an enumeration class, Weekday, for example.
    145 
    146 \subsection{AutoInitializable}
    147 \begin{lstlisting}[style=CStyle]
     86The example defines an @enum@ type @Weekday@ with ordered enumerators @Monday@, @Tuesday@, @Wednesday@, @Thursday@, @Friday@, @Saturday@ and @Sunday@.
     87The successor of @Tuesday@ is @Monday@ and the predecessor of @Tuesday@ is @Wednesday@.
     88A C enumeration has an integral type, with consecutive enumerator values assigned by the compiler starting at zero or explicitly initialized by the programmer.
     89For example, @Monday@ to @Wednesday@ have values 0--2, @Thursday@ is set to @10@, and after it, @Friday@ to @Sunday@ have values 11--13.
     90
     91There are 3 attributes for an enumeration: position, label, and value:
     92\begin{cquote}
     93\small\sf
     94\begin{tabular}{rccccccccccc}
     95enum Weekday \{ & Monday,       & Tuesday,      & Wednesday,    & Thursday=10,  & Friday,       & Saturday,     & Sunday \}; \\
     96position                & 0                     & 1                     & 2                             & 3                             & 4                     & 5                     & 6                     \\
     97label                   & Monday        & Tuesday       & Wednesday             & Thursday              & Friday        & Saturday      & Sunday        \\
     98value                   & 0                     & 1                     & 2                             & 10                    & 11            & 12            & 13
     99\end{tabular}
     100\end{cquote}
     101
     102The enumerators of an enum are unscoped, i.e., enumerators declared inside of an enum are visible in the enclosing scope of the enum class.
     103\begin{lstlisting}[label=lst:enum_scope]
     104{
     105        enum RGB { R, G, B };
     106        int i = R  // i == 0
     107}
     108int j = G; // ERROR! G is not declared in this scope
     109\end{lstlisting}
     110
     111\section{\CFA-Style Enum}
     112
     113A \CFA enumeration is parameterized by a type, which specifies the type for each enumerator.
     114\CFA allows any object type for the enumerators, and values assigned to enumerators must be in the declared type.
     115\begin{lstlisting}[label=lst:color]
     116enum Colour( @char *@ ) { Red = "R", Green = "G", Blue = "B"  };
     117\end{lstlisting}
     118The type of @Colour@ is @char *@ and each enumerator is initialized with a C string.
     119Only types have define an ordering can be automatically initialized (see Section~\ref{s:AutoInitializable}).
     120
     121
     122% An instance of \CFA-enum (denoted as @<enum_instance>@) is a label for the defined enum name.
     123% The label can be retrieved by calling the function @label( <enum_instance> )@.
     124% Similarly, the @value()@ function returns the value used to initialize the \CFA-enum.
     125
     126A \CFA-enum is scoped: enumeration constants are not automatically exposed to the global scope. Enumeration constant can be referenced using qualified expressions like an aggregate that supports qualified references to its fields. The syntax of $qualified_expression$ for \CFA-enum is the following:
     127$$<qualified\_expression> := <enum\_type>.<enumerator>$$
     128
     129
     130\subsection{enumeration instance}
     131\begin{lstlisting}[label=lst:sample_cforall_enum_usage]
     132Colour green = Colour.Green;
     133\end{lstlisting}
     134The ~\ref{lst:sample_cforall_enum_usage} example declares a $enumeration\ instance$ named \textit{red} and initializes it with $enumeration\ constant$ \textit{Color.Red}. An enumeration instance is a data structure that captures attributes of an enumeration constant, which can be retrieved by functions $position( enumeration\ instance )$, $value( enumeration\ instance )$, and $label( enumeration\ instance )$.
     135
     136\begin{lstlisting}
     137int green_pos = position( green ); // 1
     138char * green_value = value( green ); // "G"
     139char * green_label = label( green ); // "Green"
     140\end{lstlisting}
     141
     142An enumeration instance can be assigned to a variable or used as its position with type integer, its value with declared type T, or its label with type char *, and the compiler will resolve the usage as a type fits the context.
     143
     144\begin{lstlisting}[label=lst:enum_inst_assign_int]
     145int green_pos = green; // equivalent to position( green );
     146\end{lstlisting}
     147
     148A resolution of an enumeration constant is $unambigious$ if only one of the attributes has the resolvable type. In the example~\ref{lst:enum_inst_assign_int }, the right-hand side of the assignment expression expects integer type. The position of an enumeration is int, while the other two cannot be resolved as integers. The expression unambiguously returns the position of green.
     149
     150\begin{lstlisting}[label=lst:enum_inst_assign_string]
     151char * green_value = green; // equivalent to value( green );
     152\end{lstlisting}
     153On the other hand, the resolution of an enumeration constant is $ambigious$ if multiple attributes have the expected type. In the example~\ref{lst:enum_inst_assign_string}, both value and label have the expected type char *. When a resolution is ambiguous, a \textit{resolution precedence} applies:
     154$$value > position > label$$
     155\CFA uses resolution distance to describe if one type can be used as another. While \CFA calculates the resolution distance between the expected type and types of all three attributes, it would not choose the attribute with the closest distance. Instead, when resolving an enumeration constant, \CFA always chooses value whenever it is a possible resolution (resolution distance is not infinite), followed by position, then label.
     156
     157\begin{lstlisting}[label=lst:enum_inst_precedence]
     158enum(double) Foo { Bar };
     159int tee = Foo.Bar; // value( Bar );
     160\end{lstlisting}
     161In the example~\ref{lst:enum_inst_precedence}, while $position( Bar )$ has the closest resolution among the three attributes, $Foo.Bar$ is resolved as $value( Bar )$ because of the resolution precedence.
     162
     163Although \CFA enumeration captures three different attributes, an instance of enumeration does not occupy extra memory. The $sizeof$ \CFA enumeration instance is always 4 bytes, the same amount of memory to store a C enumeration instance. It comes from the fact that: 1. a \CFA enumeration is always statically typed; 2. it is always resolved as one of its attributes in terms of real usage.
     164
     165When creating the enumeration instance green and assigns it with the enumeration constant $Color.Green$, the compilers essentially allocate an integer variables and store the position 1. The invocations of $positions()$, $value()$, and $label()$ turn into calls to special functions defined in the prelude:
     166\begin{lstlisting}[label=lst:companion_call]
     167position( green );
     168>>> position( Colour, 1 ) -> int
     169value( green );
     170>>> value( Colour, 1 ) -> T
     171label( green );
     172>>> label( Colour, 1) -> char *
     173\end{lstlisting}
     174T represents the type declared in the \CFA enumeration defined and char * in the example.
     175These generated functions are $Companion Functions$, they take an $companion$ object and the position as parameters.
     176
     177\subsection{Companion Object and Companion Function}
     178\begin{lstlisting}[caption={Enum Type Functions}, label=lst:cforall_enum_functions]
     179forall( T )  {
     180        struct Companion {
     181                const T * const values;
     182                const char** const labels;
     183            int length;
     184        };
     185}
     186\end{lstlisting}
     187\CFA creates an object of Companion for every \CFA-enumeration. A companion object has the same name as the enumeration is defined for. A companion object stores values and labels of enumeration constants, in the order of the constants defined in the enumeration.
     188
     189\CFA generates the definition of companion functions. Because \CFA implicitly stores enumeration instance as its position, the companion function $position$ does nothing but returns the position it passes it. Companions function $value$ and $label$ return the array item at the given position of $values$ and $labels$, respectively.
     190
     191\begin{lstlisting}[label=lst:companion_definition]
     192int position( Companion o, int pos ) { return pos; }
     193T value( Companion o, int pos ) { return o.values[ pos ]; }
     194char * label( Companion o, int pos ) { return o.labels[ pos ]; }
     195\end{lstlisting}
     196
     197Notably, the Companion structure definition, and all companion objects, are visible to the users. A user can retrieve values and labels defined in an enumeration by accessing the values and labels directly, or indirectly by calling Companion functions $values$ and $labels$
     198\begin{lstlisting}[label=lst:companion_definition_values_labels]
     199Colour.values; // read the Companion's values
     200values( Colour ); // Same as Colour.values
     201\end{lstlisting}
     202
     203\subsection{User Define Enumeration Functions}
     204The Companion objects make extending features for \CFA enumeration easy.
     205
     206\begin{lstlisting}[label=lst:companion_user_definition]
     207char * charastic_string( Companion o, int position ) {
     208    return sprintf("Label: %s; Value: %s", label( o, position ), value( o, position) );
     209}
     210printf( charactic_string ( Color, 1 ) );
     211>>> Label: G; Value: G
     212\end{lstlisting}
     213Defining a function takes a Companion object effectively defines functions for all \CFA enumeration.
     214
     215The \CFA compiler turns a function call that takes an enumeration instance as a parameter into a function call with a companion object plus a position. Therefore, a user can use the syntax with a user-defined enumeration function call:
     216\begin{lstlisting}[label=lst:companion_user_definition]
     217charactic_string ( Color.Green ); // equivalent to charactic_string ( Color, 1 )
     218>>> Label: G; Value: G
     219\end{lstlisting}
     220
     221Similarly, the user can work with the enumeration type itself: (see section ref...)
     222\begin{lstlisting}[ label=lst:companion_user_definition]
     223void print_enumerators ( Companion o ) {
     224    for ( c : Companion o ) {
     225        sout | label (c) | value( c ) ;
     226    }
     227}
     228print_enumerators( Colour );
     229\end{lstlisting}
     230
     231\subsection{Runtime Enumeration}
     232The Companion structure definition is visible to users, and users can create an instance of Companion object themselves, which effectively constructs a \textit{Runtime Enumeration}.
     233\begin{lstlisting}[ label=lst:runtime_enum ]
     234const char values[] = { "Hello", "World" };
     235const char labels[] = { "First", "Second" };
     236Companion (char *) MyEnum = { .values: values, .labels: labels, .length: 2 };
     237\end{lstlisting}
     238A runtime enumeration can be used to call enumeration functions.
     239\begin{lstlisting}[ label=lst:runtime_enum_usage ]
     240sout | charatstic_string( MyEnum, 1 );
     241>>> Label: Second; Value: World
     242\end{lstlisting}
     243However, a runtime enumeration cannot create an enumeration instance, and it does not support enum-qualified syntax.
     244\begin{lstlisting}[ label=lst:runtime_enum_usage ]
     245MyEnum e = MyEnum.First; // Does not work: cannot create an enumeration instance e,
     246                        // and MyEnum.First is not recognizable
     247\end{lstlisting}
     248During the compilation, \CFA adds enumeration declarations to an enumeration symbol table and creates specialized function definitions for \CFA enumeration. \CFA does not recognize runtime enumeration during compilation and would not add them to the enumeration symbol table, resulting in a lack of supports for runtime enumeration.
     249
     250\section{Enumeration Features}
     251A trait is a collection of constraints in \CFA, which can be used to describe types.
     252The \CFA standard library defines traits to categorize types with related enumeration features.
     253
     254
     255\subsection{Auto Initializable}
     256\label{s:AutoInitializable}
     257TODO: make the initialization rule a separate section.
     258
     259If no explicit initializer is given to an enumeration constant, C initializes the first enumeration constant with value 0, and the other enumeration constant has a value equal to its $predecessor+1$. \CFA enumerations have the same rule in enumeration constant initialization. However, not all types can be automatically initialized by \CFA because the meaning of $zero$, $one$, and addition operator may not be well-defined.
     260
     261A type is auto-initializable if it has defined $zero\_t$, $one\_t$, and an addition operator.
     262\begin{lstlisting}
    148263forall(T)
    149264trait AutoInitializable {
    150   void ?()( T & t, zero_t );
    151   void ?()( T & t, one_t );
    152   S& ?+=?( T & t, one_t );
    153   void ?{}( T &, T );
    154   T ?{}( T &, T );
    155 };
    156 \end{lstlisting}
    157 
    158 \subsection{AutoInitializable}
    159 \begin{lstlisting}[style=CStyle]
    160 forall(T)
    161 trait AutoInitializable {
    162   void ?()( T & t, zero_t );
    163   void ?()( T & t, one_t );
    164   S& ?+=?( T & t, one_t );
    165   void ?{}( T &, T );
    166   T ?{}( T &, T );
    167 };
    168 \end{lstlisting}
    169 A type is AutoInitializable if it has defined a zero\_t constructor, a one\_t constructor, an addition assignment operator, a copy constructor, and a copy assignment operator.
    170 
    171 \subsection{Enumerable Type}
    172 \begin{lstlisting}[style=CStyle]
    173 forall(T)
    174 trait enumerable {
    175   void ?()( T & t, zero_t );
    176   void ?()( T & t, one_t );
    177   S& ?+=?( T & t, one_t );
    178   void ?{}( T &, T );
    179   T ?{}( T &, T );
    180 };
    181 \end{lstlisting}
    182 
    183 
    184 
    185 
    186 
    187 (Should change the definition of enumerable to something else. Maybe auto-constructible. If a type is not auto-constructible, all enumeration must be explicitly initialized)
    188 \begin{lstlisting}[caption={An example enumerable type}, label{lst:sample_enumerable}, style=CStyle]
    189 struct Type { int i; };
    190 void ?()( Type & t, zero_t ) { t.i = 0; };
    191 void ?()( Type & t, one_t ) { t.i = 1; };
    192 int ?!=?( Type t, zero_t ) { return t.i != 0; };
    193 S& ?+=?( Type & t, one_t ) { t.i += 1; return t; };
    194 void ?()( Type & t, Type rhs ) { t.i = rhs.i; };
    195 Type ?()( Type & t, Type rhs ) { t.i = rhs.i; return t; };
    196 \end{lstlisting}
    197 
    198 A Cforall-enum is a C-enum parameterized by an enumerable type. For example,  $enum(int)$ turns a C-enum into a Cforall-enum.
    199 \begin{lstlisting}[caption={An example Cforall enum}, label{lst:sample_cforall_enum}, style=CStyle]
    200 enum Color(Type) { Red, Green, Blue };
    201 
    202 > Type Color.values[] = { 0, values[0]++, values[1]++ };
    203 > enum Color.Label { Red_Label, Green_Label, Blue_Label };
    204 \end{lstlisting}
    205 Declaring a Cforall-enum, the compiler defines a C-enum names every element in the Cforall-enum, and an array that stores Cforall enumeration values.
    206 
    207 \subsection{Cforall Enumerations Behaviour}
    208 An instance of Cforall-enum (denoted as $<enum\_instance>$) has a label, the defined enum name. The label can be retrieved by calling the function $label()$ on a $<enum\_instance>$. The $value()$ function on the other hand returns the value used to initialize the Cforall-enum.
    209 
    210 Cforall-enum supports a qualified expression. The syntax of the qualified expression for Cforall-enum is $$<enum\_type\_name>.<enum\_instance\_name>$$. In the $Color$ example, $Color$ is a $<enum\_type\_name>$ and $Red$, $Green$, $Blue$ are $<enum\_instance\_name>$.
    211 
    212 \begin{lstlisting}[caption={An example Cforall enum}, label{lst:sample_cforall_enum_usage}, style=CStyle]
    213 enum Color red = Color.Red;
    214 > enum Color.Label red = = Color.Label.Red_Label;
    215 Type instance = Color.Red;
    216 > Type instance = Color.values[ Color.Label.Red_Label ];
    217 \end{lstlisting}
    218 
    219 The expression $Color.Red$ is overloaded to represent both $value(Color.Red)$ and $label(Color.Red)$. The expression returns the $label(Color.Red)$ by default but returns $value()$ whenever the $value()$ is a closer candidate in the context. [more explanation] In \ref{lst:sample_cforall_enum_usage}, when assigned to an enum variable, $Color.Red$ returns the label. This is to reduce the memory to store a Cforall-enum variable. In an assignment expression when the left-hand-side expects a $Type$, the resolution finds $value(Color.Red)$ is a better candidate than $label(Color.Red)$, and returns the value instead.
    220 
    221 \subsection{Enum Type Functions}
    222 \begin{lstlisting}[caption={Enum Type Functions}, label{lst:cforall_enum_functions}, style=CStyle]
    223 enum Color(string) { // assume String has been defined as an enumerable type
    224     R = "Red", G = "Green", B = "Blue"
    225 };
    226 values( Color );
    227 > [ String("Red"), String("Green"), String("Blue") ];
    228 label_strings( Color );
    229 > [ "R", "G", "B" ];
    230 enum Color green = Color.G;
    231 
    232 label_string( Color, green );
    233 > "G"
    234 label( Color, green );
    235 > 1
    236 value( Color, green ) ;
    237 > "Green"
    238 value( Color, "G" );
    239 > "Green"
    240 label( Color, "G" );
    241 > 1
    242 value( Color, "DNE" );
    243 > (null)
    244 value( Color, 1 ); // "1" is the label "G"
    245 > "Green"
    246 \end{lstlisting}
    247 Names of labels are distinct in an enum declaration. Cforall therefore allows indexing an enum value with its string representation of a label.
     265        void ?()( T & t, zero_t );
     266        void ?()( T & t, one_t );
     267        S ?+?( T & t, one_t );
     268};
     269\end{lstlisting}
     270
     271An example of user-defined @AutoInitializable@ would look like the following:
     272\begin{lstlisting}[label=lst:sample_auto_initializable]
     273struct Odd { int i; };
     274void ?()( Odd & t, zero_t ) { t.i = 1; };
     275void ?()( Odd & t, one_t ) { t.i = 2; };
     276Odd ?+?( Odd t1, Odd t2 )
     277    { return Odd( t1.i + t2.i); };
     278\end{lstlisting}
     279
     280When an enumeration declares an AutoInitializable as its type, no explicit initialization is necessary.
     281\begin{lstlisting}[label=lst:sample_auto_initializable_usage]
     282enum AutoInitUsage(Odd) {
     283    A, B, C = 6, D
     284};
     285\end{lstlisting}
     286
     287In the example~\ref{lst:sample_auto_initializable_usage}, because no initializer is specified for the first enumeration constant @A@, \CFA initializes it with the value of $zero_t$, which is 1. B and D have the values of their $predecessor + one_t$, while $one_t$ has the value 2. Therefore, the enumeration is initialized as the following:
     288
     289\begin{lstlisting}[label=lst:sample_auto_initializable_usage_gen]
     290enum AutoInitUsage(Odd) {
     291    A=1, B=3, C = 6, D=8
     292};
     293\end{lstlisting}
     294
     295In \CFA, integral types, float types, and imaginary numbers are example types that are AutoInitialiable.
     296\begin{lstlisting}[label=lst:letter]
     297enum Alphabet(int) {
     298    A='A', B, C, D, E, F, G, H, I, J, K, L, M,
     299    N, O, P, Q, R, S, T, U, V, W, X, Y, Z,
     300    a='a', b, c, d, e, f, g, h, i, j, k, l, m,
     301    n, o, p, q, r, s, t, u, v, w, x, y, z
     302};
     303print( "%c, %c, %c", Alphabet.F, Alphabet.o, Alphabet.o );
     304>>> F, o, o
     305\end{lstlisting}
    248306
    249307\subsection{Iteration and Range}
    250 A Cforall enum is iterable and supports range function.
    251 \begin{lstlisting}[caption={Range Functions}, label{lst:range_functions}, style=CStyle]
    252 struct string;
    253 enum(string) Weekday(
    254     Monday = "M", Tuesday = "Tu", ...
    255 };
    256 for ( i; Weekday ) { sout | i; }
    257 >> M Tu W Th F Sat Sun
    258 for ( Monday ~= Tuesday )
    259 >> M Tu
     308
     309It is convenient to iterate over a \CFA enumeration. Here is the basic usage:
     310\begin{lstlisting}[label=lst:range_functions]
     311for ( Alphabet ch; Alphabet; ) {
     312    printf( "%d ", ch );
     313}
     314>>> A B C (...omit the rest)
     315
     316\end{lstlisting}
     317The for-loop uses the enumeration type @Alphabet@ as range. When that happens, \CFA iterates all enumerators in the order they defined in the enumeration. 'ch' is the iterating enumerator, and it returns the value of an Alphabet in this context according to the precedence rule.
     318
     319\CFA offers a shorthand for iterating all enumeration constants:
     320\begin{lstlisting}[label=lst:range_functions]
     321for ( Alphabet ch ) {
     322    printf( "%d ", ch );
     323}
     324>>> A B C (...omit the rest)
     325\end{lstlisting}
     326
     327Enumeration supports the \CFA loop control syntax for for-loop.
     328\begin{lstlisting}[label=lst:range_functions]
     329for ( Alphabet.D )
     330for ( ch; Alphabet.g ~ Alphabet.z )
     331for ( Alphabet ch; Alphabet.R ~ Alphabet.X ~ 2 )
     332\end{lstlisting}
     333
     334Notably, the meaning of "step" of iteration has changed for enumeration. Consider the following example:
     335\begin{lstlisting}[label=lst:range_functions]
     336enum(int) Sequence {
     337    A = 10, B = 12, C = 14; 
     338}
     339for ( s; Sequence.A ~ Sequence.C ) {
     340    printf( "%d ", s );
     341}
     342
     343>>> 10 12 14
     344
     345for ( s; Sequence.A ~ Sequence.A ~ 2 ) {
     346    printf( "%d ", s );
     347}
     348>>> 10 14
     349\end{lstlisting}
     350The range iteration of enumeration does not return the $current\_value++$ until it reaches the upper bound. The semantics is to return the next enumeration constant. If a stepping is specified, 2 for example, it returns the 2 enumeration constant after the current one, rather than the $current+2$
     351
     352It is also possible to iterate over an enumeration's labels, implicitly or explicitly:
     353\begin{lstlisting}[label=lst:range_functions_label_implicit]
     354for ( char * ch; Alphabet )
     355\end{lstlisting}
     356This for-loop implicitly iterates every label of the enumeration, because a label is the only valid resolution to the ch with type $char *$ in this case. If the value can also be resolved as the char *, you might iterate the labels explicitly with the array iteration.
     357\begin{lstlisting}[label=lst:range_functions_label_implicit]
     358for ( char * ch; labels( Alphabet ) )
    260359\end{lstlisting}
    261360
    262361\section{Implementation}
    263 
    264 \subsection{Companion Object}
    265 The intuition to create a companion object is that functions that support enumeration features need static information of an enumeration class. For example, values() returns an array of values defined for the enumeration. $label( Color, "G" )$ needs information about enum names defined for the enum class $Color$. Theoretically, enum-type functions can be defined as functions that take $TypeName$ expression as the first parameter. An alternative approach is to define that "companion object".
    266 
    267 \begin{lstlisting}[caption={Enum Type Functions}, label{lst:cforall_enum_functions}, style=CStyle]
    268 struct string;
    269 enum Color( string ) {
    270     R = "Red", G = "Green", B = "Blue"
    271 };
    272 
    273 forall( T | enumerable(T) )  {
    274     struct Companion {
    275         T* values;
    276         char** labels;
    277     };
    278 }
    279 >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
    280 enum Color.Label;
    281 Companion( string ) Color = {
    282     .values = [ "Red", "Green", "Blue" ],
    283     .labels = [ "R", "G", "B" ]
    284 };
    285 >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
    286 forall( T | enumerable(T) )
    287 T value( Companion companion, int index ) { return companion.values[ index ]; }
    288 T value( Companion, enum Color.Label );
    289 char* label( Companion companion, int index ) { return companion.values[ index ]; }
    290 char* label( Companion, enum Color.Label );
    291 
    292 \end{lstlisting}
    293 
    294 
    295 \subsection{Companion Trait}
    296 Users can define the companion object themselves. A companion object should define an array of any type called values and an array of strings representing a label. Defining a companion object effectively creates a new enumerable type.
    297 
    298 \subsection{Companion Mapping}
    299 
    300 
    301 
    302 \begin{lstlisting}[caption={Enum Type Functions}, label{lst:cforall_enum_functions}, style=CStyle]
    303 
    304 \end{lstlisting}
    305 %%
    306 %% If your work has an appendix, this is the place to put it.
    307 \appendix
    308 
     362\CFA places the definition of Companion structure and non-parameterized Companion functions in the prelude, visible globally.
     363
     364\subsection{declaration}
     365The qualified enumeration syntax is dedicated to \CFA enumeration.
     366\begin{lstlisting}[label=lst:range_functions]
     367enum (type_declaration) name { enumerator = const_expr, enumerator = const_expr, ... }
     368\end{lstlisting}
     369A compiler stores the name, the underlying type, and all enumerators in an @enumeration table@. During the $Validation$ pass, the compiler links the type declaration to the type's definition. It ensures that the name of an enumerator is unique within the enumeration body, and checks if all values of the enumerator have the declaration type. If the declared type is not @Auto Initializable@, \CFA rejects the enumeration definition. Otherwise, it attempts to initialize enumerators with the enumeration initialization pattern. (a reference to a future initialization pattern section)
     370
     371\begin{lstlisting}[label=lst:init]
     372struct T { ... };
     373void ?{}( T & t, zero_t ) { ... };
     374void ?{}( T & t, one_t ) { ... };
     375T ?+?( T & lhs, T & rhs ) { ... };
     376
     377enum (T) Sample {
     378    Zero: 0 /* zero_t */,
     379    One: Zero + 1 /* ?+?( Zero, one_t ) */ , ...
     380};
     381\end{lstlisting}
     382
     383Challenge:
     384The value of an enumerator, or the initializer, requires $const\_expr$. While previously getting around the issue by pushing it to the C compiler, it might not work anymore because of the user-defined types, user-defined $zero\_t$, $one\_t$, and addition operation. Might not be able to implement a *Correct* static check.
     385
     386\CFA $autogens$ a Companion object for the declared enumeration.
     387\begin{lstlisting}[label=lst:companion]
     388Companion( T ) Sample {
     389    .values: { 0, 0+1, 0+1+1, 0+1+1+1, ... }, /* 0: zero_t, 1: one_t, +: ?+?{} */
     390    .labels: { "Zero", "One", "Two", "Three", ...},
     391    .length: /* number of enumerators */
     392};
     393\end{lstlisting}
     394\CFA stores values as intermediate expressions because the result of the function call to the function $?+?{}(T\&, T\&)$ is statically unknown to \CFA. But the result will be computed in run time, and the compiler ensures the $values$ will not be changed.
     395
     396\subsection{qualified expression}
     397\CFA uses qualified expression to address the scoping of \CFA-enumeration.
     398\begin{lstlisting}[label=lst:qualified_expression]
     399aggregation_name.field;
     400\end{lstlisting}
     401The qualified expression is not dedicated to \CFA enumeration. It is a feature that is supported by other aggregation in \CFA as well, including a C enumeration. When C enumerations are unscoped, the qualified expression syntax still helps to disambiguate names in the context. \CFA recognizes if the expression references a \CFA aggregation by searching the presence of $aggregation\_name$ in the \CFA enumeration table. If the $aggregation\_name$ is identified as a \CFA enumeration, the compiler checks if $field$ presents in the declared \CFA enumeration.
     402
     403\subsection{with statement/statement}
     404@Working in Progress@
     405Instead of qualifying an enumeration expression every time, one can use the $with$ to expose enumerators to the current scope so that they are directly accessible.
     406
     407\subsection{instance declaration}
     408@Working in Progress@
     409\begin{lstlisting}[label=lst:declaration]
     410enum Sample s1;
     411Sample s2;
     412\end{lstlisting}
     413A declaration of \CFA enumeration instance that has no difference than a C enumeration or other \CFA aggregation. The compiler recognizes the type of a variable declaration by searching the name in all possible types. The \textit{enum} keyword is not necessary but helps to disambiguate types (questionable). The generated code for a \CFA enumeration declaration is utterly an integer, which is meant to store the position.
     414\begin{lstlisting}[label=lst:declaration]
     415int s1;
     416int s2;
     417\end{lstlisting}
     418
     419\subsection{Compiler Representation}
     420@Working in Progress@
     421
     422The internal representation of an enumeration constant is \textit{EnumInstType}. The minimum information an \textit{EnumInstType} stores is a reference to the \CFA-enumeration declaration and the position of the enumeration constant.
     423\begin{lstlisting}[label=lst:EnumInstType]
     424class EnumInstType {
     425    EnumDecl enumDecl;
     426    int position;
     427};
     428\end{lstlisting}
     429
     430
     431\subsection{unification and resolution }
     432@Working in Progress@
     433
     434\begin{lstlisting}
     435enum Colour( char * ) { Red = "R", Green = "G", Blue = "B"  };
     436\end{lstlisting}
     437The EnumInstType is convertible to other types. A \CFA enumeration expression is implicitly "overloaded" with its three different attributes: value, position, and label. The \CFA compilers need to resolve an EnumInstType as one of its attributes based on the current context.
     438
     439\begin{lstlisting}[caption={Null Context}, label=lst:null_context]
     440{
     441    Colour.Green;
     442}
     443\end{lstlisting}
     444In the example~\ref{lst:null_context}, the environment gives no information to help with the resolution of $Colour.Green$. In this case, any of the attributes is resolvable. According to the \textit{precedence rule}, the expression with EnumInstType will be resolved as $value( Colour.Green )$. The EnumInstType is converted to the type of the value, which is statically known to the compiler as char *. When the compilation reaches the code generation, the compiler outputs code for type char * with the value "G".
     445\begin{lstlisting}[caption={Null Context Generated Code}, label=lst:null_context]
     446{
     447    "G";
     448}
     449\end{lstlisting}
     450
     451 
     452\begin{lstlisting}[caption={int Context}, label=lst:int_context]
     453{
     454    int g = Colour.Green;
     455}
     456\end{lstlisting}
     457
     458The assignment expression gives a context for the EnumInstType resolution. The EnumInstType is used as an int, and \CFA needs to determine which of the attributes can be resolved as an int type.
     459The functions $Unify( T1, T2 ): bool$ take two types as parameters and determine if one type can be used as another. In the example\ref{lst:int_context} example, the compiler is trying to unify int and EnumInstType of Colour.
     460$$Unification( int, EnumInstType<Colour> )$$
     461which turns into three Unification call
     462\begin{lstlisting}[label=lst:attr_resolution_1]
     463{
     464    Unify( int, char * ); // unify with the type of value
     465    Unify( int, int ); // unify with the type of position
     466    Unify( int, char * ); // unify with the type of label
     467}
     468\end{lstlisting}
     469
     470\begin{lstlisting}[label=lst:attr_resolution_precedence]
     471{
     472    Unification( T1, EnumInstType<T2> ) {
     473        if ( Unify( T1, T2 ) ) return T2;
     474        if ( Unify( T1, int ) ) return int;
     475        if ( Unify( T1, char * ) ) return char *;
     476        Error: Cannot Unify T1 with EnumInstType<T2>;
     477    }
     478}
     479\end{lstlisting}
     480After the unification, EnumInstType will be replaced by its attributes.
     481
     482\begin{lstlisting}[caption={Unification Functions}, label=lst:unification_func_call]
     483{
     484    T2 foo ( T1 ); // function take variable with T1 as a parameter
     485    foo( EnumInstType<T3> ); // Call foo with a variable has type EnumInstType<T3>
     486    >>>> Unification( T1, EnumInstType<T3> )
     487}
     488\end{lstlisting}
     489
     490% The conversion can work backward: in restrictive cases, attributes of can be implicitly converted back to the EnumInstType.
     491Backward conversion:
     492\begin{lstlisting}[caption={Unification Functions}, label=lst:unification_func_call]
     493{
     494    enum Colour colour = 1;
     495}
     496\end{lstlisting}
     497
     498\begin{lstlisting}[caption={Unification Functions}, label=lst:unification_func_call]
     499{
     500   Unification( EnumInstType<Colour>, int ) >>> label
     501}
     502\end{lstlisting}
     503int can be unified with the label of Colour. "5" is a constant expression -> Compiler knows the value during the compilation -> turns it into
     504\begin{lstlisting}
     505{
     506   enum Colour colour = Colour.Green;
     507}
     508\end{lstlisting}
     509Steps:
     5101: identify "1" as a constant expression with type int, and the value is statically known as 1
     5112. unification( EnumInstType<Colour>, int ): position( EnumInstType< Colour > )
     5123. return the enumeration constant at the position 1
     513
     514\begin{lstlisting}
     515{
     516    enum T (int) { ... } // Declaration
     517    enum T t = 1;
     518}
     519\end{lstlisting}
     520Steps:
     5211: identify "1" as a constant expression with type int, and the value is statically known as 1
     5222. unification( EnumInstType<Colour>, int ): value( EnumInstType< Colour > )
     5233. return the FIRST enumeration constant that has the value 1, by searching through the values array
     524
     525The downside of the precedence rule: EnumInstType -> int ( value ) -> EnumInstType may return a different EnumInstType because the value can be repeated and there is no way to know which one is expected -> want uniqueness
    309526
    310527\end{document}
    311 \endinput
    312 %%
    313 %% End of file `sample-manuscript.tex'.
     528
     529% Local Variables: %
     530% tab-width: 4 %
     531% compile-command: "pdflatex enum.tex" %
     532% End: %
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