Changeset 90c3b1c for doc/refrat


Ignore:
Timestamp:
Mar 2, 2016, 4:59:19 PM (6 years ago)
Author:
Peter A. Buhr <pabuhr@…>
Branches:
aaron-thesis, arm-eh, cleanup-dtors, ctor, deferred_resn, demangler, gc_noraii, jacob/cs343-translation, jenkins-sandbox, master, memory, new-ast, new-ast-unique-expr, new-env, no_list, persistent-indexer, resolv-new, string, with_gc
Children:
bdad1679
Parents:
ac1ed49
Message:

compile CFA with C++11, further update refrat with lstlisting macros, support varags, enumeration initialization, add implicit separators to output streams, update example programs that print

Location:
doc/refrat
Files:
2 edited

Legend:

Unmodified
Added
Removed
  • doc/refrat/Makefile

    rac1ed49 r90c3b1c  
    11## Define the appropriate configuration variables.
    22
    3 TeXLIB = .::
     3Macros =
     4TeXLIB = .:${Macros}:
    45LaTeX  = TEXINPUTS=${TeXLIB} && export TEXINPUTS && latex
    56BibTeX = BSTINPUTS=${TeXLIB} && export BSTINPUTS && bibtex
  • doc/refrat/refrat.tex

    rac1ed49 r90c3b1c  
    3333
    3434\makeatletter
    35 % index macros
     35\renewcommand{\labelitemi}{{\raisebox{0.25ex}{\footnotesize$\bullet$}}}
     36\renewenvironment{itemize}{\begin{list}{\labelitemi}{\topsep=5pt\itemsep=5pt\parsep=0pt}}{\end{list}}
     37
     38%  Reduce size of chapter/section titles
     39\def\@makechapterhead#1{%
     40  \vspace*{50\p@}%
     41  {\parindent \z@ \raggedright \normalfont
     42    \ifnum \c@secnumdepth >\m@ne
     43        \large\bfseries \@chapapp\space \thechapter
     44        \par\nobreak
     45        \vskip 5\p@
     46    \fi
     47    \interlinepenalty\@M
     48    \Large \bfseries #1\par\nobreak
     49    \vskip 50\p@
     50  }}
     51\def\@makeschapterhead#1{%
     52  \vspace*{50\p@}%
     53  {\parindent \z@ \raggedright
     54    \normalfont
     55    \interlinepenalty\@M
     56    \Large \bfseries  #1\par\nobreak
     57    \vskip 50\p@
     58  }}
     59\renewcommand\section{\@startsection{section}{1}{\z@}{-3.0ex \@plus -1ex \@minus -.2ex}{1.0ex \@plus .2ex}{\normalfont\large\bfseries}}
     60\renewcommand\subsection{\@startsection{subsection}{2}{\z@}{-2.5ex \@plus -1ex \@minus -.2ex}{1.0ex \@plus .2ex}{\normalfont\normalsize\bfseries}}
     61\renewcommand\subsubsection{\@startsection{subsubsection}{3}{\z@}{-2.0ex \@plus -1ex \@minus -.2ex}{1.0ex \@plus .2ex}{\normalfont\normalsize\bfseries}}
     62\renewcommand\paragraph{\@startsection{paragraph}{4}{\z@}{-2.0ex \@plus -1ex \@minus -.2ex}{-1em}{\normalfont\normalsize\bfseries}}
     63
    3664\newcommand{\italic}[1]{\emph{\hyperpage{#1}}}
    3765\newcommand{\definition}[1]{\textbf{\hyperpage{#1}}}
     
    6088%\newcommand{\impl}[1]{\index{\protect#1@{\lstinline$\protect#1$}|definition}}
    6189
    62 % text inline and lowercase index: \Index{Inline and index text}
    63 % text inline and as-in index: \Index{Inline and Index text}
    64 % text inline but index with different as-is text: \Index[index text]{inline text}
     90% inline text and lowercase index: \Index{inline and lowercase index text}
     91% inline text and as-in index: \Index[as-is index text]{inline text}
     92% inline text but index with different as-is text: \Index[index text]{inline text}
    6593\newcommand{\Index}{\@ifstar\@sIndex\@Index}
    6694\newcommand{\@Index}[2][\@empty]{\lowercase{\def\temp{#2}}#2\ifx#1\@empty\index{\temp}\else\index{#1@{\protect#2}}\fi}
     
    145173\linenumbers                                    % comment out to turn off line numbering
    146174
    147 \title{\CFA (\CFAA) Reference Manual and Rationale}
    148 \author{Glen Ditchfield \and Peter A. Buhr}
    149 \date{DRAFT\\\today}
     175\title{\Huge
     176\CFA (\CFAA) Reference Manual and Rationale
     177}% title
     178\author{\huge
     179Glen Ditchfield and Peter A. Buhr
     180}% author
     181\date{
     182DRAFT\\\today
     183}% date
    150184
    151185\pagenumbering{roman}
     
    159193\copyright\,2015 Glen Ditchfield \\ \\
    160194\noindent
    161 This work is licensed under the Creative Commons Attribution 4.0 International License. To view a
    162 copy of this license, visit {\small\url{http://creativecommons.org/licenses/by/4.0}}.
     195This work is licensed under the Creative Commons Attribution 4.0 International License.
     196To view a copy of this license, visit {\small\url{http://creativecommons.org/licenses/by/4.0}}.
    163197\vspace*{1in}
    164198
     
    173207\chapter*{Introduction}\addcontentsline{toc}{chapter}{Introduction}
    174208
    175 This document is a reference manual and rationale for \CFA, a polymorphic extension of the C
    176 programming language. It makes frequent reference to the {\c11} standard \cite{ANS:C11}, and
    177 occasionally compares \CFA to {\CC} \cite{c++}.
    178 
    179 The manual deliberately imitates the ordering of the {\c11} standard (although the section numbering
    180 differs). Unfortunately, this means the manual contains more ``forward references'' than usual,
    181 making it harder to follow if the reader does not have a copy of the {\c11} standard. For a simple
    182 introduction to \CFA, see the companion document ``An Overview of \CFA''
     209This document is a reference manual and rationale for \CFA, a polymorphic extension of the C programming language.
     210It makes frequent reference to the {\c11} standard \cite{ANS:C11}, and occasionally compares \CFA to {\CC} \cite{c++}.
     211
     212The manual deliberately imitates the ordering of the {\c11} standard (although the section numbering differs).
     213Unfortunately, this means the manual contains more ``forward references'' than usual, making it harder to follow if the reader does not have a copy of the {\c11} standard.
     214For a simple introduction to \CFA, see the companion document ``An Overview of \CFA''
    183215\cite{Ditchfield96:Overview}.
    184216
    185217\begin{rationale}
    186 Commentary (like this) is quoted with quads. Commentary usually deals with subtle points, the
    187 rationale behind a rule, and design decisions.
     218Commentary (like this) is quoted with quads.
     219Commentary usually deals with subtle points, the rationale behind a rule, and design decisions.
    188220\end{rationale}
    189221
     
    194226\chapter{Terms, definitions, and symbols}
    195227
    196 Terms from the {\c11} standard used in this document have the same meaning as in the {\c11}
    197 standard.
     228Terms from the {\c11} standard used in this document have the same meaning as in the {\c11} standard.
    198229
    199230% No ``Conformance'' or ``Environment'' chapters yet.
     
    205236
    206237\section{Notation}
    207 The syntax notation used in this document is the same as in the {\c11} standard, with one exception:
    208 ellipsis in the definition of a nonterminal, as in ``\emph{declaration:} \ldots'', indicates that
    209 these rules extend a previous definition, which occurs in this document or in the {\c11} standard.
     238The syntax notation used in this document is the same as in the {\c11} standard, with one exception: ellipsis in the definition of a nonterminal, as in ``\emph{declaration:} \ldots'', indicates that these rules extend a previous definition, which occurs in this document or in the {\c11} standard.
    210239
    211240
     
    215244\subsection{Scopes of identifiers}\index{scopes}
    216245
    217 \CFA's scope rules differ from C's in one major respect: a declaration of an identifier may
    218 overload\index{overloading} outer declarations of lexically identical identifiers in the same
    219 \Index{name space}, instead of hiding them. The outer declaration is hidden if the two declarations
    220 have \Index{compatible type}, or if one declares an array type and the other declares a pointer type
    221 and the element type and pointed-at type are compatible, or if one has function type and the other
    222 is a pointer to a compatible function type, or if one declaration is a \lstinline$type$\use{type} or
     246\CFA's scope rules differ from C's in one major respect: a declaration of an identifier may overload\index{overloading} outer declarations of lexically identical identifiers in the same
     247\Index{name space}, instead of hiding them.
     248The outer declaration is hidden if the two declarations have \Index{compatible type}, or if one declares an array type and the other declares a pointer type and the element type and pointed-at type are compatible, or if one has function type and the other is a pointer to a compatible function type, or if one declaration is a \lstinline$type$\use{type} or
    223249\lstinline$typedef$\use{typedef} declaration and the other is not.  The outer declaration becomes
    224250\Index{visible} when the scope of the inner declaration terminates.
    225251\begin{rationale}
    226 Hence, a \CFA program can declare an \lstinline$int v$ and a \lstinline$float v$ in the same
    227 scope; a {\CC} program can not.
     252Hence, a \CFA program can declare an \lstinline$int v$ and a \lstinline$float v$ in the same scope;
     253a {\CC} program can not.
    228254\end{rationale}
    229255
     
    232258\index{linkage}
    233259
    234 \CFA's linkage rules differ from C's in only one respect: instances of a particular identifier with
    235 external or internal linkage do not necessarily denote the same object or function. Instead, in the
    236 set of translation units and libraries that constitutes an entire program, any two instances of a
    237 particular identifier with \Index{external linkage} denote the same object or function if they have
    238 \Index{compatible type}s, or if one declares an array type and the other declares a pointer type and
    239 the element type and pointed-at type are compatible, or if one has function type and the other is a
    240 pointer to a compatible function type. Within one translation unit, each instance of an identifier
    241 with \Index{internal linkage} denotes the same object or function in the same circumstances.
     260\CFA's linkage rules differ from C's in only one respect: instances of a particular identifier with external or internal linkage do not necessarily denote the same object or function.
     261Instead, in the set of translation units and libraries that constitutes an entire program, any two instances of a particular identifier with \Index{external linkage} denote the same object or function if they have
     262\Index{compatible type}s, or if one declares an array type and the other declares a pointer type and the element type and pointed-at type are compatible, or if one has function type and the other is a pointer to a compatible function type.
     263Within one translation unit, each instance of an identifier with \Index{internal linkage} denotes the same object or function in the same circumstances.
    242264Identifiers with \Index{no linkage} always denote unique entities.
    243265\begin{rationale}
    244 A \CFA program can declare an \lstinline$extern int v$ and an \lstinline$extern float v$; a C
    245 program cannot.
     266A \CFA program can declare an \lstinline$extern int v$ and an \lstinline$extern float v$;
     267a C program cannot.
    246268\end{rationale}
    247269
     
    253275\subsubsection{Semantics}
    254276
    255 \CFA provides a capability for generic types; using this capability a single "generic type
    256 generator" can be written that can represent multiple concrete type instantiations by substitution
    257 of the "type parameters" of the generic type for concrete types. Syntactically a generic type
    258 generator is represented by putting a forall specifier on a struct or union declaration, as defined
    259 in \VRef{forall}. An instantiation of the generic type is written by specifying the type parameters
    260 in parentheses after the name of the generic type generator:
     277\CFA provides a capability for generic types;
     278using this capability a single "generic type generator" can be written that can represent multiple concrete type instantiations by substitution of the "type parameters" of the generic type for concrete types.
     279Syntactically a generic type generator is represented by putting a forall specifier on a struct or union declaration, as defined in \VRef{forall}.
     280An instantiation of the generic type is written by specifying the type parameters in parentheses after the name of the generic type generator:
    261281\begin{lstlisting}
    262282forall( type T | sumable( T ) ) struct pair {
     
    267287\end{lstlisting}
    268288
    269 The type parameters in an instantiation of a generic type must satisfy any constraints in the forall
    270 specifier on the type generator declaration, e.g., \lstinline$sumable$. The instantiation then has
    271 the semantics that would result if the type parameters were substituted into the type generator
    272 declaration by macro substitution.
    273 
    274 Polymorphic functions may have generic types as parameters, and those generic types may use type
    275 parameters of the polymorphic function as type parameters of the generic type:
     289The type parameters in an instantiation of a generic type must satisfy any constraints in the forall specifier on the type generator declaration, e.g., \lstinline$sumable$.
     290The instantiation then has the semantics that would result if the type parameters were substituted into the type generator declaration by macro substitution.
     291
     292Polymorphic functions may have generic types as parameters, and those generic types may use type parameters of the polymorphic function as type parameters of the generic type:
    276293\begin{lstlisting}
    277294forall( type T ) void swap( pair(T) *p ) {
     
    285302\subsubsection{Constraints}
    286303
    287 To avoid unduly constraining implementors, the generic type generator definition must be visible at
    288 any point where it is instantiated.  Forward declarations of generic type generators are not
    289 forbidden, but the definition must be visible to instantiate the generic type.  Equivalently,
    290 instantiations of generic types are not allowed to be incomplete types.
     304To avoid unduly constraining implementors, the generic type generator definition must be visible at any point where it is instantiated.  Forward declarations of generic type generators are not forbidden, but the definition must be visible to instantiate the generic type.  Equivalently, instantiations of generic types are not allowed to be incomplete types.
    291305
    292306\examples
     
    295309
    296310forall( type T ) struct B {
    297         A(T) *a;  // legal, but cannot instantiate B(T)
     311        A(T) *a;                        // legal, but cannot instantiate B(T)
    298312};
    299313
    300 B(T) x; // illegal, *x.a is of an incomplete generic type
    301 
     314B(T) x;                                 // illegal, *x.a is of an incomplete generic type
     315 
    302316forall( type T ) struct A {
    303317        B( T ) *b;
    304318};
    305319
    306 B( T ) y; // legal, *x.a is now of a complete generic type
    307 
     320B( T ) y;                               // legal, *x.a is now of a complete generic type
    308321
    309322// box.h:
     
    313326       
    314327// main.c:
    315         box( int ) *b = make_box( 42 ); // illegal, def'n of box not visible
    316         use_box( b ); // illegal
     328        box( int ) *b = make_box( 42 ); // illegal, definition of box not visible
     329        use_box( b );           // illegal
    317330\end{lstlisting}
    318331
     
    320333\section{Conversions}
    321334\CFA defines situations where values of one type are automatically converted to another type.
    322 These conversions are called \define{implicit conversion}s. The programmer can request
     335These conversions are called \define{implicit conversion}s.
     336The programmer can request
    323337\define{explicit conversion}s using cast expressions.
    324338
     
    330344\subsubsection{Safe arithmetic conversions}
    331345
    332 In C, a pattern of conversions known as the \define{usual arithmetic conversion}s is used with most
    333 binary arithmetic operators to convert the operands to a common type and determine the type of the
    334 operator's result. In \CFA, these conversions play a role in overload resolution, and
    335 collectively are called the \define{safe arithmetic conversion}s.
    336 
    337 Let \(int_r\) and \(unsigned_r\) be the signed and unsigned integer types with integer conversion
    338 rank\index{integer conversion rank}\index{rank|see{integer conversion rank}} $r$. Let
    339 \(unsigned_{mr}\) be the unsigned integer type with maximal rank.
     346In C, a pattern of conversions known as the \define{usual arithmetic conversion}s is used with most binary arithmetic operators to convert the operands to a common type and determine the type of the operator's result.
     347In \CFA, these conversions play a role in overload resolution, and collectively are called the \define{safe arithmetic conversion}s.
     348
     349Let \(int_r\) and \(unsigned_r\) be the signed and unsigned integer types with integer conversion rank\index{integer conversion rank}\index{rank|see{integer conversion rank}} $r$.
     350Let \(unsigned_{mr}\) be the unsigned integer type with maximal rank.
    340351
    341352The following conversions are \emph{direct} safe arithmetic conversions.
     
    343354\item
    344355The \Index{integer promotion}s.
    345 
    346 \item
    347 For every rank $r$ greater than or equal to the rank of \lstinline$int$, conversion from \(int_r\)
    348 to \(unsigned_r\).
    349 
    350 \item
    351 For every rank $r$ greater than or equal to the rank of \lstinline$int$, where \(int_{r+1}\) exists
    352 and can represent all values of \(unsigned_r\), conversion from \(unsigned_r\) to \(int_{r+1}\).
    353 
     356\item
     357For every rank $r$ greater than or equal to the rank of \lstinline$int$, conversion from \(int_r\) to \(unsigned_r\).
     358\item
     359For every rank $r$ greater than or equal to the rank of \lstinline$int$, where \(int_{r+1}\) exists and can represent all values of \(unsigned_r\), conversion from \(unsigned_r\) to \(int_{r+1}\).
    354360\item
    355361Conversion from \(unsigned_{mr}\) to \lstinline$float$.
    356 
    357362\item
    358363Conversion from an enumerated type to its compatible integer type.
    359 
    360 \item
    361 Conversion from \lstinline$float$ to \lstinline$double$, and from \lstinline$double$ to
    362 \lstinline$long double$.
    363 
    364 \item
    365 Conversion from \lstinline$float _Complex$ to \lstinline$double _Complex$,
    366 and from \lstinline$double _Complex$ to \lstinline$long double _Complex$.
    367 
     364\item
     365Conversion from \lstinline$float$ to \lstinline$double$, and from \lstinline$double$ to \lstinline$long double$.
     366\item
     367Conversion from \lstinline$float _Complex$ to \lstinline$double _Complex$, and from \lstinline$double _Complex$ to \lstinline$long double _Complex$.
    368368\begin{sloppypar}
    369369\item
    370 Conversion from \lstinline$float _Imaginary$ to \lstinline$double _Imaginary$, and from
    371 \lstinline$double _Imaginary$ to \lstinline$long double$ \lstinline$_Imaginary$, if the
    372 implementation supports imaginary types.
     370Conversion from \lstinline$float _Imaginary$ to \lstinline$double _Imaginary$, and from \lstinline$double _Imaginary$ to \lstinline$long double$ \lstinline$_Imaginary$, if the implementation supports imaginary types.
    373371\end{sloppypar}
    374372\end{itemize}
    375373
    376 If type \lstinline$T$ can be converted to type \lstinline$U$ by a safe direct arithmetic conversion
    377 and type \lstinline$U$ can be converted to type \lstinline$V$ by a safe arithmetic conversion, then
    378 the conversion from \lstinline$T$ to type \lstinline$V$ is an \emph{indirect} safe arithmetic
    379 conversion.
    380 
    381 \begin{rationale}
    382 Note that {\c11} does not include conversion from \Index{real type}s to \Index{complex type}s in the
    383 usual arithmetic conversions, and \CFA does not include them as safe conversions.
     374If type \lstinline$T$ can be converted to type \lstinline$U$ by a safe direct arithmetic conversion and type \lstinline$U$ can be converted to type \lstinline$V$ by a safe arithmetic conversion, then the conversion from \lstinline$T$ to type \lstinline$V$ is an \emph{indirect} safe arithmetic conversion.
     375
     376\begin{rationale}
     377Note that {\c11} does not include conversion from \Index{real type}s to \Index{complex type}s in the usual arithmetic conversions, and \CFA does not include them as safe conversions.
    384378\end{rationale}
    385379
     
    393387
    394388If an expression's type is a pointer to a structure or union type that has a member that is an
    395 \Index{anonymous structure} or an \Index{anonymous union}, it can be implicitly
    396 converted\index{implicit conversion} to a pointer to the anonymous structure's or anonymous union's
    397 type. The result of the conversion is a pointer to the member.
     389\Index{anonymous structure} or an \Index{anonymous union}, it can be implicitly converted\index{implicit conversion} to a pointer to the anonymous structure's or anonymous union's type.
     390The result of the conversion is a pointer to the member.
    398391
    399392\examples
     
    402395        int x, y;
    403396};
    404 void move_by(struct point * p1, struct point * p2) {@\impl{move_by}@
     397void move_by( struct point * p1, struct point * p2 ) {@\impl{move_by}@
    405398        p1->x += p2.x;
    406399        p1->y += p2.y;
    407400}
    408 
    409401struct color_point {
    410402        enum { RED, BLUE, GREEN } color;
    411403        struct point;
    412404} cp1, cp2;
    413 move_to(&cp1, &cp2);
     405move_to( &cp1, &cp2 );
    414406\end{lstlisting}
    415407Thanks to implicit conversion, the two arguments that \lstinline$move_by()$ receives are pointers to
     
    419411\subsubsection{Specialization}
    420412A function or value whose type is polymorphic may be implicitly converted to one whose type is
    421 \Index{less polymorphic} by binding values to one or more of its \Index{inferred parameter}. Any
    422 value that is legal for the inferred parameter may be used, including other inferred parameters.
    423 
    424 If, after the inferred parameter binding, an \Index{assertion parameter} has no inferred parameters
    425 in its type, then an object or function must be visible at the point of the specialization that has
    426 the same identifier as the assertion parameter and has a type that is compatible\index{compatible
    427   type} with or can be specialized to the type of the assertion parameter.  The assertion parameter
    428 is bound to that object or function.
    429 
    430 The type of the specialization is the type of the original with the bound inferred parameters and
    431 the bound assertion parameters replaced by their bound values.
     413\Index{less polymorphic} by binding values to one or more of its \Index{inferred parameter}.
     414Any value that is legal for the inferred parameter may be used, including other inferred parameters.
     415
     416If, after the inferred parameter binding, an \Index{assertion parameter} has no inferred parameters in its type, then an object or function must be visible at the point of the specialization that has the same identifier as the assertion parameter and has a type that is compatible\index{compatible
     417  type} with or can be specialized to the type of the assertion parameter.  The assertion parameter is bound to that object or function.
     418
     419The type of the specialization is the type of the original with the bound inferred parameters and the bound assertion parameters replaced by their bound values.
    432420
    433421\examples
     
    438426can be specialized to (among other things)
    439427\begin{lstlisting}
    440 forall( type T ) void (*)( T, T );              // U bound to T 
    441 forall( type T ) void (*)( T, real );   // U bound to real 
    442 forall( type U ) void (*)( real, U );   // T bound to real 
     428forall( type T ) void (*)( T, T );              // U bound to T
     429forall( type T ) void (*)( T, real );   // U bound to real
     430forall( type U ) void (*)( real, U );   // T bound to real
    443431void f( real, real );                                   // both bound to real
    444432\end{lstlisting}
     
    446434The type
    447435\begin{lstlisting}
    448 forall( type T | T ?+?( T, T )) T (*)( T );
     436forall( type T | T ?+?( T, T ) ) T (*)( T );
    449437\end{lstlisting}
    450438can be specialized to (among other things)
    451439\begin{lstlisting}
    452 int (*)( int );                                         // T bound to int, and T ?+?(T, T ) bound to int ?+?( int, int )
     440int (*)( int );         // T bound to int, and T ?+?(T, T ) bound to int ?+?( int, int )
    453441\end{lstlisting}
    454442
     
    465453from a pointer to any non-\lstinline$void$ type to a pointer to \lstinline$void$;
    466454\item
    467 from a pointer to any type to a pointer to a more qualified version of the type\index{qualified
    468 type};
    469 \item
    470 from a pointer to a structure or union type to a pointer to the type of a member of the structure or
    471 union that is an \Index{anonymous structure} or an \Index{anonymous union};
    472 \item
    473 within the scope of an initialized \Index{type declaration}, conversions between a type and its
    474 implementation or between a pointer to a type and a pointer to its implementation.
     455from a pointer to any type to a pointer to a more qualified version of the type\index{qualified type};
     456\item
     457from a pointer to a structure or union type to a pointer to the type of a member of the structure or union that is an \Index{anonymous structure} or an \Index{anonymous union};
     458\item
     459within the scope of an initialized \Index{type declaration}, conversions between a type and its implementation or between a pointer to a type and a pointer to its implementation.
    475460\end{itemize}
    476461
    477462Conversions that are not safe conversions are \define{unsafe conversion}s.
    478463\begin{rationale}
    479 As in C, there is an implicit conversion from \lstinline$void *$ to any pointer type. This is
    480 clearly dangerous, and {\CC} does not have this implicit conversion.
    481 \CFA\index{deficiencies!void * conversion} keeps it, in the interest of remaining as pure a
    482 superset of C as possible, but discourages it by making it unsafe.
     464As in C, there is an implicit conversion from \lstinline$void *$ to any pointer type.
     465This is clearly dangerous, and {\CC} does not have this implicit conversion.
     466\CFA\index{deficiencies!void * conversion} keeps it, in the interest of remaining as pure a superset of C as possible, but discourages it by making it unsafe.
    483467\end{rationale}
    484468
     
    486470\subsection{Conversion cost}
    487471
    488 The \define{conversion cost} of a safe\index{safe conversion}
    489 conversion\footnote{Unsafe\index{unsafe conversion} conversions do not have defined conversion
    490 costs.} is a measure of how desirable or undesirable it is. It is defined as follows.
     472The \define{conversion cost} of a safe\index{safe conversion} conversion\footnote{Unsafe\index{unsafe conversion} conversions do not have defined conversion costs.} is a measure of how desirable or undesirable it is.
     473It is defined as follows.
    491474\begin{itemize}
    492475\item
     
    497480
    498481\item
    499 The cost of an indirect safe arithmetic conversion is the smallest number of direct conversions
    500 needed to make up the conversion.
     482The cost of an indirect safe arithmetic conversion is the smallest number of direct conversions needed to make up the conversion.
    501483\end{itemize}
    502484
     
    506488\begin{itemize}
    507489\item
    508 The cost of an implicit conversion from \lstinline$int$ to \lstinline$long$ is 1. The cost of an
    509 implicit conversion from \lstinline$long$ to \lstinline$double$ is 3, because it is defined in terms
    510 of conversions from \lstinline$long$ to \lstinline$unsigned long$, then to \lstinline$float$, and
    511 then to \lstinline$double$.
    512 
    513 \item
    514 If \lstinline$int$ can represent all the values of \lstinline$unsigned short$, then the cost of an
    515 implicit conversion from \lstinline$unsigned short$ to \lstinline$unsigned$ is 2:
    516 \lstinline$unsigned short$ to \lstinline$int$ to \lstinline$unsigned$. Otherwise,
     490The cost of an implicit conversion from \lstinline$int$ to \lstinline$long$ is 1.
     491The cost of an implicit conversion from \lstinline$long$ to \lstinline$double$ is 3, because it is defined in terms of conversions from \lstinline$long$ to \lstinline$unsigned long$, then to \lstinline$float$, and then to \lstinline$double$.
     492
     493\item
     494If \lstinline$int$ can represent all the values of \lstinline$unsigned short$, then the cost of an implicit conversion from \lstinline$unsigned short$ to \lstinline$unsigned$ is 2:
     495\lstinline$unsigned short$ to \lstinline$int$ to \lstinline$unsigned$.
     496Otherwise,
    517497\lstinline$unsigned short$ is converted directly to \lstinline$unsigned$, and the cost is 1.
    518498
    519499\item
    520 If \lstinline$long$ can represent all the values of \lstinline$unsigned$, then the conversion cost
    521 of \lstinline$unsigned$ to \lstinline$long$ is 1. Otherwise, the conversion is an unsafe
    522 conversion, and its conversion cost is undefined.
     500If \lstinline$long$ can represent all the values of \lstinline$unsigned$, then the conversion cost of \lstinline$unsigned$ to \lstinline$long$ is 1.
     501Otherwise, the conversion is an unsafe conversion, and its conversion cost is undefined.
    523502\end{itemize}
    524503
     
    538517\subsection{Identifiers}
    539518
    540 \CFA allows operator \Index{overloading} by associating operators with special function
    541 identifiers. Furthermore, the constants ``\lstinline$0$'' and ``\lstinline$1$'' have special status
    542 for many of C's data types (and for many programmer-defined data types as well), so \CFA treats them
    543 as overloadable identifiers. Programmers can use these identifiers to declare functions and objects
    544 that implement operators and constants for their own types.
     519\CFA allows operator \Index{overloading} by associating operators with special function identifiers.
     520Furthermore, the constants ``\lstinline$0$'' and ``\lstinline$1$'' have special status for many of C's data types (and for many programmer-defined data types as well), so \CFA treats them as overloadable identifiers.
     521Programmers can use these identifiers to declare functions and objects that implement operators and constants for their own types.
    545522
    546523
     
    554531\end{syntax}
    555532
    556 \index{constant identifiers}\index{identifiers!for constants} The tokens ``\lstinline$0$''\impl{0}
    557 and ``\lstinline$1$''\impl{1} are identifiers. No other tokens defined by the rules for integer
    558 constants are considered to be identifiers.
    559 \begin{rationale}
    560 Why ``\lstinline$0$'' and ``\lstinline$1$''? Those integers have special status in C. All scalar
    561 types can be incremented and decremented, which is defined in terms of adding or subtracting 1. The
    562 operations ``\lstinline$&&$'', ``\lstinline$||$'', and ``\lstinline$!$'' can be applied to any
    563 scalar arguments, and are defined in terms of comparison against 0. A \nonterm{constant-expression}
    564 that evaluates to 0 is effectively compatible with every pointer type.
    565 
    566 In C, the integer constants 0 and 1 suffice because the integer promotion rules can convert them to
    567 any arithmetic type, and the rules for pointer expressions treat constant expressions evaluating to
    568 0 as a special case. However, user-defined arithmetic types often need the equivalent of a 1 or 0
    569 for their functions or operators, polymorphic functions often need 0 and 1 constants of a type
    570 matching their polymorphic parameters, and user-defined pointer-like types may need a null value.
    571 Defining special constants for a user-defined type is more efficient than defining a conversion to
    572 the type from \lstinline$_Bool$.
    573 
    574 Why \emph{just} ``\lstinline$0$'' and ``\lstinline$1$''? Why not other integers? No other integers
    575 have special status in C. A facility that let programmers declare specific
    576 constants---``\lstinline$const Rational 12$'', for instance---would not be much of an improvement.
    577 Some facility for defining the creation of values of programmer-defined types from arbitrary integer
    578 tokens would be needed. The complexity of such a feature doesn't seem worth the gain.
     533\index{constant identifiers}\index{identifiers!for constants} The tokens ``\lstinline$0$''\impl{0} and ``\lstinline$1$''\impl{1} are identifiers.
     534No other tokens defined by the rules for integer constants are considered to be identifiers.
     535\begin{rationale}
     536Why ``\lstinline$0$'' and ``\lstinline$1$''? Those integers have special status in C.
     537All scalar types can be incremented and decremented, which is defined in terms of adding or subtracting 1.
     538The operations ``\lstinline$&&$'', ``\lstinline$||$'', and ``\lstinline$!$'' can be applied to any scalar arguments, and are defined in terms of comparison against 0.
     539A \nonterm{constant-expression} that evaluates to 0 is effectively compatible with every pointer type.
     540
     541In C, the integer constants 0 and 1 suffice because the integer promotion rules can convert them to any arithmetic type, and the rules for pointer expressions treat constant expressions evaluating to
     5420 as a special case.
     543However, user-defined arithmetic types often need the equivalent of a 1 or 0 for their functions or operators, polymorphic functions often need 0 and 1 constants of a type matching their polymorphic parameters, and user-defined pointer-like types may need a null value.
     544Defining special constants for a user-defined type is more efficient than defining a conversion to the type from \lstinline$_Bool$.
     545
     546Why \emph{just} ``\lstinline$0$'' and ``\lstinline$1$''? Why not other integers? No other integers have special status in C.
     547A facility that let programmers declare specific constants---``\lstinline$const Rational 12$'', for instance---would not be much of an improvement.
     548Some facility for defining the creation of values of programmer-defined types from arbitrary integer tokens would be needed.
     549The complexity of such a feature doesn't seem worth the gain.
    579550\end{rationale}
    580551
     
    582553\subsubsection{Operator identifiers}
    583554
    584 \index{operator identifiers}\index{identifiers!for operators} Table \ref{opids} lists the
    585 programmer-definable operator identifiers and the operations they are associated with. Functions
    586 that are declared with (or pointed at by function pointers that are declared with) these identifiers
    587 can be called by expressions that use the operator tokens and syntax, or the operator identifiers
    588 and ``function call'' syntax. The relationships between operators and function calls are discussed
    589 in descriptions of the operators.
     555\index{operator identifiers}\index{identifiers!for operators} Table \ref{opids} lists the programmer-definable operator identifiers and the operations they are associated with.
     556Functions that are declared with (or pointed at by function pointers that are declared with) these identifiers can be called by expressions that use the operator tokens and syntax, or the operator identifiers and ``function call'' syntax.
     557The relationships between operators and function calls are discussed in descriptions of the operators.
    590558
    591559\begin{table}[hbt]
     
    644612
    645613\begin{rationale}
    646 Operator identifiers are made up of the characters of the operator token, with question marks added
    647 to mark the positions of the arguments of operators. The question marks serve as mnemonic devices;
    648 programmers can not create new operators by arbitrarily mixing question marks and other
    649 non-alphabetic characters. Note that prefix and postfix versions of the increment and decrement
    650 operators are distinguished by the position of the question mark.
    651 \end{rationale}
    652 
    653 \begin{rationale}
    654 The use of ``\lstinline$?$'' in identifiers means that some C programs are not \CFA programs.  For
    655 instance, the sequence of characters ``\lstinline$(i < 0)?--i:i$'' is legal in a C program, but a
    656 \CFA compiler detects a syntax error because it treats ``\lstinline$?--$'' as an identifier, not
    657 as the two tokens ``\lstinline$?$'' and ``\lstinline$--$''.
     614Operator identifiers are made up of the characters of the operator token, with question marks added to mark the positions of the arguments of operators.
     615The question marks serve as mnemonic devices;
     616programmers can not create new operators by arbitrarily mixing question marks and other non-alphabetic characters.
     617Note that prefix and postfix versions of the increment and decrement operators are distinguished by the position of the question mark.
     618\end{rationale}
     619
     620\begin{rationale}
     621The use of ``\lstinline$?$'' in identifiers means that some C programs are not \CFA programs.  For instance, the sequence of characters ``\lstinline$(i < 0)?--i:i$'' is legal in a C program, but a
     622\CFA compiler detects a syntax error because it treats ``\lstinline$?--$'' as an identifier, not as the two tokens ``\lstinline$?$'' and ``\lstinline$--$''.
    658623\end{rationale}
    659624
     
    663628\item
    664629The logical operators ``\lstinline$&&$'' and ``\lstinline$||$'', and the conditional operator
    665 ``\lstinline$?:$''. These operators do not always evaluate their operands, and hence can not be
    666 properly defined by functions unless some mechanism like call-by-name is added to the language.
    667 Note that the definitions of ``\lstinline$&&$'' and ``\lstinline$||$'' say that they work by
    668 checking that their arguments are unequal to 0, so defining ``\lstinline$!=$'' and ``\lstinline$0$''
    669 for user-defined types is enough to allow them to be used in logical expressions.
    670 
    671 \item
    672 The comma operator\index{comma expression}. It is a control-flow operator like those above.
     630``\lstinline$?:$''.
     631These operators do not always evaluate their operands, and hence can not be properly defined by functions unless some mechanism like call-by-name is added to the language.
     632Note that the definitions of ``\lstinline$&&$'' and ``\lstinline$||$'' say that they work by checking that their arguments are unequal to 0, so defining ``\lstinline$!=$'' and ``\lstinline$0$'' for user-defined types is enough to allow them to be used in logical expressions.
     633
     634\item
     635The comma operator\index{comma expression}.
     636It is a control-flow operator like those above.
    673637Changing its meaning seems pointless and confusing.
    674638
    675639\item
    676 The ``address of'' operator. It would seem useful to define a unary ``\lstinline$&$'' operator that
    677 returns values of some programmer-defined pointer-like type. The problem lies with the type of the
    678 operator. Consider the expression ``\lstinline$p = &x$'', where \lstinline$x$ is of type
    679 \lstinline$T$ and \lstinline$p$ has the programmer-defined type \lstinline$T_ptr$. The expression
    680 might be treated as a call to the unary function ``\lstinline$&?$''. Now what is the type of the
    681 function's parameter? It can not be \lstinline$T$, because then \lstinline$x$ would be passed by
    682 value, and there is no way to create a useful pointer-like result from a value. Hence the parameter
    683 must have type \lstinline$T *$. But then the expression must be rewritten as ``\lstinline$p = &?( &x )$''
     640The ``address of'' operator.
     641It would seem useful to define a unary ``\lstinline$&$'' operator that returns values of some programmer-defined pointer-like type.
     642The problem lies with the type of the operator.
     643Consider the expression ``\lstinline$p = &x$'', where \lstinline$x$ is of type
     644\lstinline$T$ and \lstinline$p$ has the programmer-defined type \lstinline$T_ptr$.
     645The expression might be treated as a call to the unary function ``\lstinline$&?$''.
     646Now what is the type of the function's parameter? It can not be \lstinline$T$, because then \lstinline$x$ would be passed by value, and there is no way to create a useful pointer-like result from a value.
     647Hence the parameter must have type \lstinline$T *$.
     648But then the expression must be rewritten as ``\lstinline$p = &?( &x )$''
    684649---which doesn't seem like progress!
    685650
    686 The rule for address-of expressions would have to be something like ``keep applying address-of
    687 functions until you get one that takes a pointer argument, then use the built-in operator and
    688 stop''. It seems simpler to define a conversion function from \lstinline$T *$ to \lstinline$T_ptr$.
    689 
    690 \item
    691 The \lstinline$sizeof$ operator. It is already defined for every object type, and intimately tied
    692 into the language's storage allocation model. Redefining it seems pointless.
    693 
    694 \item
    695 The ``member of'' operators ``\lstinline$.$'' and ``\lstinline$->$''. These are not really infix
    696 operators, since their right ``operand'' is not a value or object.
    697 
    698 \item
    699 Cast operators\index{cast expression}. Anything that can be done with an explicit cast can be done
    700 with a function call. The difference in syntax is small.
     651The rule for address-of expressions would have to be something like ``keep applying address-of functions until you get one that takes a pointer argument, then use the built-in operator and stop''.
     652It seems simpler to define a conversion function from \lstinline$T *$ to \lstinline$T_ptr$.
     653
     654\item
     655The \lstinline$sizeof$ operator.
     656It is already defined for every object type, and intimately tied into the language's storage allocation model.
     657Redefining it seems pointless.
     658
     659\item
     660The ``member of'' operators ``\lstinline$.$'' and ``\lstinline$->$''.
     661These are not really infix operators, since their right ``operand'' is not a value or object.
     662
     663\item
     664Cast operators\index{cast expression}.
     665Anything that can be done with an explicit cast can be done with a function call.
     666The difference in syntax is small.
    701667\end{itemize}
    702668\end{rationale}
     
    705671\section{Expressions}
    706672
    707 \CFA allows operators and identifiers to be overloaded. Hence, each expression can have a number
    708 of \define{interpretation}s, each of which has a different type. The interpretations that are
    709 potentially executable are called \define{valid interpretation}s. The set of interpretations
    710 depends on the kind of expression and on the interpretations of the subexpressions that it contains.
    711 The rules for determining the valid interpretations of an expression are discussed below for each
    712 kind of expression. Eventually the context of the outermost expression chooses one interpretation
    713 of that expression.
    714 
    715 An \define{ambiguous interpretation} is an interpretation which does not specify the exact object or
    716 function denoted by every identifier in the expression. An expression can have some interpretations
    717 that are ambiguous and others that are unambiguous. An expression that is chosen to be executed
    718 shall not be ambiguous.
    719 
    720 The \define{best valid interpretations} are the valid interpretations that use the fewest
    721 unsafe\index{unsafe conversion} conversions. Of these, the best are those where the functions and
    722 objects involved are the least polymorphic\index{less polymorphic}. Of these, the best have the
    723 lowest total \Index{conversion cost}, including all implicit conversions in the argument
    724 expressions. Of these, the best have the highest total conversion cost for the implicit conversions
    725 (if any) applied to the argument expressions. If there is no single best valid interpretation, or if
    726 the best valid interpretation is ambiguous, then the resulting interpretation is
    727 ambiguous\index{ambiguous interpretation}.
    728 
    729 \begin{rationale}
    730 \CFA's rules for selecting the best interpretation are designed to allow overload resolution to
    731 mimic C's operator semantics. In C, the ``usual arithmetic conversions'' are applied to the
    732 operands of binary operators if necessary to convert the operands to types with a common real type.
    733 In \CFA, those conversions are ``safe''. The ``fewest unsafe conversions'' rule ensures that the
    734 usual conversions are done, if possible. The ``lowest total expression cost'' rule chooses the
    735 proper common type. The odd-looking ``highest argument conversion cost'' rule ensures that, when
    736 unary expressions must be converted, conversions of function results are preferred to conversion of
    737 function arguments: \lstinline$(double)-i$ will be preferred to \lstinline$-(double)i$.
    738 
    739 The ``least polymorphic'' rule reduces the number of polymorphic function calls, since such
    740 functions are presumably more expensive than monomorphic functions and since the more specific
    741 function is presumably more appropriate. It also gives preference to monomorphic values (such as the
     673\CFA allows operators and identifiers to be overloaded.
     674Hence, each expression can have a number of \define{interpretation}s, each of which has a different type.
     675The interpretations that are potentially executable are called \define{valid interpretation}s.
     676The set of interpretations depends on the kind of expression and on the interpretations of the subexpressions that it contains.
     677The rules for determining the valid interpretations of an expression are discussed below for each kind of expression.
     678Eventually the context of the outermost expression chooses one interpretation of that expression.
     679
     680An \define{ambiguous interpretation} is an interpretation which does not specify the exact object or function denoted by every identifier in the expression.
     681An expression can have some interpretations that are ambiguous and others that are unambiguous.
     682An expression that is chosen to be executed shall not be ambiguous.
     683
     684The \define{best valid interpretations} are the valid interpretations that use the fewest unsafe\index{unsafe conversion} conversions.
     685Of these, the best are those where the functions and objects involved are the least polymorphic\index{less polymorphic}.
     686Of these, the best have the lowest total \Index{conversion cost}, including all implicit conversions in the argument expressions.
     687Of these, the best have the highest total conversion cost for the implicit conversions
     688(if any) applied to the argument expressions.
     689If there is no single best valid interpretation, or if the best valid interpretation is ambiguous, then the resulting interpretation is ambiguous\index{ambiguous interpretation}.
     690
     691\begin{rationale}
     692\CFA's rules for selecting the best interpretation are designed to allow overload resolution to mimic C's operator semantics.
     693In C, the ``usual arithmetic conversions'' are applied to the operands of binary operators if necessary to convert the operands to types with a common real type.
     694In \CFA, those conversions are ``safe''.
     695The ``fewest unsafe conversions'' rule ensures that the usual conversions are done, if possible.
     696The ``lowest total expression cost'' rule chooses the proper common type.
     697The odd-looking ``highest argument conversion cost'' rule ensures that, when unary expressions must be converted, conversions of function results are preferred to conversion of function arguments: \lstinline$(double)-i$ will be preferred to \lstinline$-(double)i$.
     698
     699The ``least polymorphic'' rule reduces the number of polymorphic function calls, since such functions are presumably more expensive than monomorphic functions and since the more specific function is presumably more appropriate.
     700It also gives preference to monomorphic values (such as the
    742701\lstinline$int$ \lstinline$0$) over polymorphic values (such as the \Index{null pointer}
    743 \lstinline$0$\use{0}). However, interpretations that call polymorphic functions are preferred to
    744 interpretations that perform unsafe conversions, because those conversions potentially lose accuracy
    745 or violate strong typing.
     702\lstinline$0$\use{0}).
     703However, interpretations that call polymorphic functions are preferred to interpretations that perform unsafe conversions, because those conversions potentially lose accuracy or violate strong typing.
    746704
    747705There are two notable differences between \CFA's overload resolution rules and the rules for
    748 {\CC} defined in \cite{c++}. First, the result type of a function plays a role. In {\CC}, a
    749 function call must be completely resolved based on the arguments to the call in most circumstances.
    750 In \CFA, a function call may have several interpretations, each with a different result type, and
    751 the interpretations of the containing context choose among them. Second, safe conversions are used
    752 to choose among interpretations of all sorts of functions; in {\CC}, the ``usual arithmetic
    753 conversions'' are a separate set of rules that apply only to the built-in operators.
    754 \end{rationale}
    755 
    756 Expressions involving certain operators\index{operator identifiers} are considered to be equivalent
    757 to function calls. A transformation from ``operator'' syntax to ``function call'' syntax is defined
    758 by \define{rewrite rules}. Each operator has a set of predefined functions that overload its
    759 identifier. Overload resolution determines which member of the set is executed in a given
    760 expression. The functions have \Index{internal linkage} and are implicitly declared with \Index{file
    761 scope}. The predefined functions and rewrite rules are discussed below for each of these
    762 operators.
    763 \begin{rationale}
    764 Predefined functions and constants have internal linkage because that simplifies optimization in
    765 traditional compile-and-link environments. For instance, ``\lstinline$an_int + an_int$'' is
    766 equivalent to ``\lstinline$?+?(an_int, an_int)$''. If integer addition has not been redefined in
    767 the current scope, a compiler can generate code to perform the addition directly. If predefined
    768 functions had external linkage, this optimization would be difficult.
    769 \end{rationale}
    770 
    771 \begin{rationale}
    772 Since each subsection describes the interpretations of an expression in terms of the interpretations
    773 of its subexpressions, this chapter can be taken as describing an overload resolution algorithm that
    774 uses one bottom-up pass over an expression tree. Such an algorithm was first described (for Ada) by
    775 Baker~\cite{Bak:overload}. It is extended here to handle polymorphic functions and arithmetic
    776 conversions. The overload resolution rules and the predefined functions have been chosen so that, in
    777 programs that do not introduce overloaded declarations, expressions will have the same meaning in C
    778 and in \CFA.
    779 \end{rationale}
    780 
    781 \begin{rationale}
    782 Expression syntax is quoted from the {\c11} standard. The syntax itself defines the precedence and
    783 associativity of operators. The sections are arranged in decreasing order of precedence, with all
    784 operators in a section having the same precedence.
     706{\CC} defined in \cite{c++}.
     707First, the result type of a function plays a role.
     708In {\CC}, a function call must be completely resolved based on the arguments to the call in most circumstances.
     709In \CFA, a function call may have several interpretations, each with a different result type, and the interpretations of the containing context choose among them.
     710Second, safe conversions are used to choose among interpretations of all sorts of functions;
     711in {\CC}, the ``usual arithmetic conversions'' are a separate set of rules that apply only to the built-in operators.
     712\end{rationale}
     713
     714Expressions involving certain operators\index{operator identifiers} are considered to be equivalent to function calls.
     715A transformation from ``operator'' syntax to ``function call'' syntax is defined by \define{rewrite rules}.
     716Each operator has a set of predefined functions that overload its identifier.
     717Overload resolution determines which member of the set is executed in a given expression.
     718The functions have \Index{internal linkage} and are implicitly declared with \Index{file scope}.
     719The predefined functions and rewrite rules are discussed below for each of these operators.
     720\begin{rationale}
     721Predefined functions and constants have internal linkage because that simplifies optimization in traditional compile-and-link environments.
     722For instance, ``\lstinline$an_int + an_int$'' is equivalent to ``\lstinline$?+?(an_int, an_int)$''.
     723If integer addition has not been redefined in the current scope, a compiler can generate code to perform the addition directly.
     724If predefined functions had external linkage, this optimization would be difficult.
     725\end{rationale}
     726
     727\begin{rationale}
     728Since each subsection describes the interpretations of an expression in terms of the interpretations of its subexpressions, this chapter can be taken as describing an overload resolution algorithm that uses one bottom-up pass over an expression tree.
     729Such an algorithm was first described (for Ada) by Baker~\cite{Bak:overload}.
     730It is extended here to handle polymorphic functions and arithmetic conversions.
     731The overload resolution rules and the predefined functions have been chosen so that, in programs that do not introduce overloaded declarations, expressions will have the same meaning in C and in \CFA.
     732\end{rationale}
     733
     734\begin{rationale}
     735Expression syntax is quoted from the {\c11} standard.
     736The syntax itself defines the precedence and associativity of operators.
     737The sections are arranged in decreasing order of precedence, with all operators in a section having the same precedence.
    785738\end{rationale}
    786739
     
    801754const int 1;@\use{1}@
    802755const int 0;@\use{0}@
    803 forall( dtype DT ) DT *const 0;
    804 forall( ftype FT ) FT *const 0;
     756forall( dtype DT ) DT * const 0;
     757forall( ftype FT ) FT * const 0;
    805758\end{lstlisting}
    806759
    807760\semantics
    808 The \Index{valid interpretation} of an \nonterm{identifier} are given by the visible\index{visible}
    809 declarations of the identifier.
    810 
    811 A \nonterm{constant} or \nonterm{string-literal} has one valid interpretation, which has the type
    812 and value defined by {\c11}. The predefined integer identifiers ``\lstinline$1$'' and
    813 ``\lstinline$0$'' have the integer values 1 and 0, respectively. The other two predefined
    814 ``\lstinline$0$'' identifiers are bound to polymorphic pointer values that, when
    815 specialized\index{specialization} with a data type or function type respectively, produce a null
    816 pointer of that type.
     761The \Index{valid interpretation} of an \nonterm{identifier} are given by the visible\index{visible} declarations of the identifier.
     762
     763A \nonterm{constant} or \nonterm{string-literal} has one valid interpretation, which has the type and value defined by {\c11}.
     764The predefined integer identifiers ``\lstinline$1$'' and ``\lstinline$0$'' have the integer values 1 and 0, respectively.
     765The other two predefined ``\lstinline$0$'' identifiers are bound to polymorphic pointer values that, when specialized\index{specialization} with a data type or function type respectively, produce a null pointer of that type.
    817766
    818767A parenthesised expression has the same interpretations as the contained \nonterm{expression}.
    819768
    820769\examples
    821 The expression \lstinline$(void *)0$\use{0} specializes the (polymorphic) null pointer to a null
    822 pointer to \lstinline$void$. \lstinline$(const void *)0$ does the same, and also uses a safe
    823 conversion from \lstinline$void *$ to \lstinline$const void *$. In each case, the null pointer
    824 conversion is better\index{best valid interpretations} than the unsafe conversion of the integer
     770The expression \lstinline$(void *)0$\use{0} specializes the (polymorphic) null pointer to a null pointer to \lstinline$void$. \lstinline$(const void *)0$ does the same, and also uses a safe conversion from \lstinline$void *$ to \lstinline$const void *$.
     771In each case, the null pointer conversion is better\index{best valid interpretations} than the unsafe conversion of the integer
    825772\lstinline$0$ to a pointer.
    826773
     
    828775Note that the predefined identifiers have addresses.
    829776
    830 \CFA does not have C's concept of ``null pointer constants'', which are not typed values but
    831 special strings of tokens. The C token ``\lstinline$0$'' is an expression of type \lstinline$int$
    832 with the value ``zero'', and it \emph{also} is a null pointer constant. Similarly,
    833 ``\lstinline$(void *)0$ is an expression of type \lstinline$(void *)$ whose value is a null pointer,
    834 and it also is a null pointer constant. However, in C, ``\lstinline$(void *)(void *)0$'' is
    835 \emph{not} a null pointer constant, even though it is null-valued, a pointer, and constant! The
    836 semantics of C expressions contain many special cases to deal with subexpressions that are null
    837 pointer constants.
    838 
    839 \CFA handles these cases through overload resolution. The declaration
    840 \begin{lstlisting}
    841 forall( dtype DT ) DT *const 0;
    842 \end{lstlisting}
    843 means that \lstinline$0$ is a polymorphic object, and contains a value that can have \emph{any}
    844 pointer-to-object type or pointer-to-incomplete type. The only such value is the null pointer.
    845 Therefore the type \emph{alone} is enough to identify a null pointer. Where C defines an operator
    846 with a special case for the null pointer constant, \CFA defines predefined functions with a
    847 polymorphic object parameter.
     777\CFA does not have C's concept of ``null pointer constants'', which are not typed values but special strings of tokens.
     778The C token ``\lstinline$0$'' is an expression of type \lstinline$int$ with the value ``zero'', and it \emph{also} is a null pointer constant.
     779Similarly,
     780``\lstinline$(void *)0$ is an expression of type \lstinline$(void *)$ whose value is a null pointer, and it also is a null pointer constant.
     781However, in C, ``\lstinline$(void *)(void *)0$'' is
     782\emph{not} a null pointer constant, even though it is null-valued, a pointer, and constant! The semantics of C expressions contain many special cases to deal with subexpressions that are null pointer constants.
     783
     784\CFA handles these cases through overload resolution.
     785The declaration
     786\begin{lstlisting}
     787forall( dtype DT ) DT * const 0;
     788\end{lstlisting} means that \lstinline$0$ is a polymorphic object, and contains a value that can have \emph{any} pointer-to-object type or pointer-to-incomplete type.
     789The only such value is the null pointer.
     790Therefore the type \emph{alone} is enough to identify a null pointer.
     791Where C defines an operator with a special case for the null pointer constant, \CFA defines predefined functions with a polymorphic object parameter.
    848792\end{rationale}
    849793
     
    851795\subsubsection{Generic selection}
    852796
    853 \constraints The best interpretation of the controlling expression shall be
    854 unambiguous\index{ambiguous interpretation}, and shall have type compatible with at most one of the
    855 types named in its generic association list. If a generic selection has no \lstinline$default$
    856 generic association, the best interpretation of its controlling expression shall have type
    857 compatible with exactly one of the types named in its generic association list.
     797\constraints The best interpretation of the controlling expression shall be unambiguous\index{ambiguous interpretation}, and shall have type compatible with at most one of the types named in its generic association list.
     798If a generic selection has no \lstinline$default$ generic association, the best interpretation of its controlling expression shall have type compatible with exactly one of the types named in its generic association list.
    858799
    859800\semantics
     
    883824\rewriterules
    884825\begin{lstlisting}
    885 a[b] @\rewrite@ ?[?]( b, a ) // if a has integer type */@\use{?[?]}@
     826a[b] @\rewrite@ ?[?]( b, a ) // if a has integer type@\use{?[?]}@
    886827a[b] @\rewrite@ ?[?]( a, b ) // otherwise
    887 a( ${\em arguments }$ ) @\rewrite@ ?()( a, ${\em arguments} )$@\use{?()}@
     828a( @\emph{arguments}@ ) @\rewrite@ ?()( a, @\emph{arguments}@ )@\use{?()}@
    888829a++ @\rewrite@ ?++(&( a ))@\use{?++}@
    889830a-- @\rewrite@ ?--(&( a ))@\use{?--}@
     
    913854\end{lstlisting}
    914855\semantics
    915 The interpretations of subscript expressions are the interpretations of the corresponding function
    916 call expressions.
     856The interpretations of subscript expressions are the interpretations of the corresponding function call expressions.
    917857\begin{rationale}
    918858C defines subscripting as pointer arithmetic in a way that makes \lstinline$a[i]$ and
    919 \lstinline$i[a]$ equivalent. \CFA provides the equivalence through a rewrite rule to reduce the
    920 number of overloadings of \lstinline$?[?]$.
    921 
    922 Subscript expressions are rewritten as function calls that pass the first parameter by value. This
    923 is somewhat unfortunate, since array-like types tend to be large. The alternative is to use the
    924 rewrite rule ``\lstinline$a[b]$ \rewrite \lstinline$?[?](&(a), b)$''. However, C semantics forbid
    925 this approach: the \lstinline$a$ in ``\lstinline$a[b]$'' can be an arbitrary pointer value, which
    926 does not have an address.
     859\lstinline$i[a]$ equivalent. \CFA provides the equivalence through a rewrite rule to reduce the number of overloadings of \lstinline$?[?]$.
     860
     861Subscript expressions are rewritten as function calls that pass the first parameter by value.
     862This is somewhat unfortunate, since array-like types tend to be large.
     863The alternative is to use the rewrite rule ``\lstinline$a[b]$ \rewrite \lstinline$?[?](&(a), b)$''.
     864However, C semantics forbid this approach: the \lstinline$a$ in ``\lstinline$a[b]$'' can be an arbitrary pointer value, which does not have an address.
    927865
    928866The repetitive form of the predefined identifiers shows up a deficiency\index{deficiencies!pointers
    929  to qualified types} of \CFA's type system. Type qualifiers are not included in type values, so
    930 polymorphic functions that take pointers to arbitrary types often come in one flavor for each
    931 possible qualification of the pointed-at type.
     867 to qualified types} of \CFA's type system.
     868Type qualifiers are not included in type values, so polymorphic functions that take pointers to arbitrary types often come in one flavor for each possible qualification of the pointed-at type.
    932869\end{rationale}
    933870
     
    936873
    937874\semantics
    938 A \define{function designator} is an interpretation of an expression that has function type. The
    939 \nonterm{postfix-expression} in a function call may have some interpretations that are function
    940 designators and some that are not.
    941 
    942 For those interpretations of the \nonterm{postfix-expression} that are not function designators, the
    943 expression is rewritten and becomes a call of a function named ``\lstinline$?()$''. The valid
    944 interpretations of the rewritten expression are determined in the manner described below.
    945 
    946 Each combination of function designators and argument interpretations is considered. For those
    947 interpretations of the \nonterm{postfix-expression} that are \Index{monomorphic function}
    948 designators, the combination has a \Index{valid interpretation} if the function designator accepts
    949 the number of arguments given, and each argument interpretation matches the corresponding explicit
    950 parameter:
     875A \define{function designator} is an interpretation of an expression that has function type.
     876The
     877\nonterm{postfix-expression} in a function call may have some interpretations that are function designators and some that are not.
     878
     879For those interpretations of the \nonterm{postfix-expression} that are not function designators, the expression is rewritten and becomes a call of a function named ``\lstinline$?()$''.
     880The valid interpretations of the rewritten expression are determined in the manner described below.
     881
     882Each combination of function designators and argument interpretations is considered.
     883For those interpretations of the \nonterm{postfix-expression} that are \Index{monomorphic function} designators, the combination has a \Index{valid interpretation} if the function designator accepts the number of arguments given, and each argument interpretation matches the corresponding explicit parameter:
    951884\begin{itemize}
    952 \item
    953 if the argument corresponds to a parameter in the function designator's prototype, the argument
    954 interpretation must have the same type as the corresponding parameter, or be implicitly convertible
    955 to the parameter's type
    956 \item
    957 if the function designator's type does not include a prototype or if the argument corresponds to
     885\item if the argument corresponds to a parameter in the function designator's prototype, the argument interpretation must have the same type as the corresponding parameter, or be implicitly convertible to the parameter's type
     886\item if the function designator's type does not include a prototype or if the argument corresponds to
    958887``\lstinline$...$'' in a prototype, a \Index{default argument promotion} is applied to it.
    959888\end{itemize}
     
    961890
    962891For those combinations where the interpretation of the \nonterm{postfix-expression} is a
    963 \Index{polymorphic function} designator and the function designator accepts the number of arguments
    964 given, there shall be at least one set of \define{implicit argument}s for the implicit parameters
    965 such that
     892\Index{polymorphic function} designator and the function designator accepts the number of arguments given, there shall be at least one set of \define{implicit argument}s for the implicit parameters such that
    966893\begin{itemize}
    967894\item
    968 If the declaration of the implicit parameter uses \Index{type-class} \lstinline$type$\use{type}, the
    969 implicit argument must be an object type; if it uses \lstinline$dtype$, the implicit argument must
    970 be an object type or an incomplete type; and if it uses \lstinline$ftype$, the implicit argument
    971 must be a function type.
    972 
    973 \item
    974 if an explicit parameter's type uses any implicit parameters, then the corresponding explicit
    975 argument must have a type that is (or can be safely converted\index{safe conversion} to) the type
    976 produced by substituting the implicit arguments for the implicit parameters in the explicit
    977 parameter type.
    978 
    979 \item
    980 the remaining explicit arguments must match the remaining explicit parameters, as described for
    981 monomorphic function designators.
    982 
    983 \item
    984 for each \Index{assertion parameter} in the function designator's type, there must be an object or
    985 function with the same identifier that is visible at the call site and whose type is compatible with
    986 or can be specialized to the type of the assertion declaration.
     895If the declaration of the implicit parameter uses \Index{type-class} \lstinline$type$\use{type}, the implicit argument must be an object type;
     896if it uses \lstinline$dtype$, the implicit argument must be an object type or an incomplete type;
     897and if it uses \lstinline$ftype$, the implicit argument must be a function type.
     898
     899\item if an explicit parameter's type uses any implicit parameters, then the corresponding explicit argument must have a type that is (or can be safely converted\index{safe conversion} to) the type produced by substituting the implicit arguments for the implicit parameters in the explicit parameter type.
     900
     901\item the remaining explicit arguments must match the remaining explicit parameters, as described for monomorphic function designators.
     902
     903\item for each \Index{assertion parameter} in the function designator's type, there must be an object or function with the same identifier that is visible at the call site and whose type is compatible with or can be specialized to the type of the assertion declaration.
    987904\end{itemize}
    988 There is a valid interpretation for each such set of implicit parameters. The type of each valid
    989 interpretation is the return type of the function designator with implicit parameter values
    990 substituted for the implicit arguments.
    991 
    992 A valid interpretation is ambiguous\index{ambiguous interpretation} if the function designator or
    993 any of the argument interpretations is ambiguous.
    994 
    995 Every valid interpretation whose return type is not compatible with any other valid interpretation's
    996 return type is an interpretation of the function call expression.
    997 
    998 Every set of valid interpretations that have mutually compatible\index{compatible type} result types
    999 also produces an interpretation of the function call expression. The type of the interpretation is
    1000 the \Index{composite type} of the types of the valid interpretations, and the value of the
    1001 interpretation is that of the \Index{best valid interpretation}.
    1002 \begin{rationale}
    1003 One desirable property of a polymorphic programming language is \define{generalizability}: the
    1004 ability to replace an abstraction with a more general but equivalent abstraction without requiring
    1005 changes in any of the uses of the original\cite{Cormack90}. For instance, it should be possible to
    1006 replace a function ``\lstinline$int f( int );$'' with ``\lstinline$forall( type T ) T f( T );$''
    1007 without affecting any calls of \lstinline$f$.
     905There is a valid interpretation for each such set of implicit parameters.
     906The type of each valid interpretation is the return type of the function designator with implicit parameter values substituted for the implicit arguments.
     907
     908A valid interpretation is ambiguous\index{ambiguous interpretation} if the function designator or any of the argument interpretations is ambiguous.
     909
     910Every valid interpretation whose return type is not compatible with any other valid interpretation's return type is an interpretation of the function call expression.
     911
     912Every set of valid interpretations that have mutually compatible\index{compatible type} result types also produces an interpretation of the function call expression.
     913The type of the interpretation is the \Index{composite type} of the types of the valid interpretations, and the value of the interpretation is that of the \Index{best valid interpretation}.
     914\begin{rationale}
     915One desirable property of a polymorphic programming language is \define{generalizability}: the ability to replace an abstraction with a more general but equivalent abstraction without requiring changes in any of the uses of the original\cite{Cormack90}.
     916For instance, it should be possible to replace a function ``\lstinline$int f( int );$'' with ``\lstinline$forall( type T ) T f( T );$'' without affecting any calls of \lstinline$f$.
    1008917
    1009918\CFA\index{deficiencies!generalizability} does not fully possess this property, because
     
    1015924float f;
    1016925double d;
    1017 f = g( f, f );  // (1)
    1018 f = g( i, f );  // (2) (safe conversion to float)
    1019 f = g( d, f );  // (3) (unsafe conversion to float)
    1020 \end{lstlisting}
    1021 If \lstinline$g$ was replaced by ``\lstinline$forall( type T ) T g( T, T );$'', the first and second
    1022 calls would be unaffected, but the third would change: \lstinline$f$ would be converted to
     926f = g( f, f );          // (1)
     927f = g( i, f );          // (2) (safe conversion to float)
     928f = g( d, f );          // (3) (unsafe conversion to float)
     929\end{lstlisting}
     930If \lstinline$g$ was replaced by ``\lstinline$forall( type T ) T g( T, T );$'', the first and second calls would be unaffected, but the third would change: \lstinline$f$ would be converted to
    1023931\lstinline$double$, and the result would be a \lstinline$double$.
    1024932
    1025 Another example is the function ``\lstinline$void h( int *);$''. This function can be passed a
    1026 \lstinline$void *$ argument, but the generalization ``\lstinline$forall( type T ) void h( T *);$''
    1027 can not. In this case, \lstinline$void$ is not a valid value for \lstinline$T$ because it is not an
    1028 object type. If unsafe conversions were allowed, \lstinline$T$ could be inferred to be \emph{any}
    1029 object type, which is undesirable.
     933Another example is the function ``\lstinline$void h( int *);$''.
     934This function can be passed a
     935\lstinline$void *$ argument, but the generalization ``\lstinline$forall( type T ) void h( T *);$'' can not.
     936In this case, \lstinline$void$ is not a valid value for \lstinline$T$ because it is not an object type.
     937If unsafe conversions were allowed, \lstinline$T$ could be inferred to be \emph{any} object type, which is undesirable.
    1030938\end{rationale}
    1031939
     
    1045953For that interpretation, the function call is treated as ``\lstinline$?()( sin_dx, 12.9 )$''.
    1046954\begin{lstlisting}
    1047 int f( long );          // (1) 
    1048 int f( int, int );      // (2) 
     955int f( long );          // (1)
     956int f( int, int );      // (2)
    1049957int f( int *);          // (3)
    1050 
    1051958int i = f( 5 );         // calls (1)
    1052959\end{lstlisting}
    1053 Function (1) provides a valid interpretation of ``\lstinline$f( 5 )$'', using an implicit
    1054 \lstinline$int$ to \lstinline$long$ conversion. The other functions do not, since the second
    1055 requires two arguments, and since there is no implicit conversion from \lstinline$int$ to
    1056 \lstinline$int *$ that could be used with the third function.
     960Function (1) provides a valid interpretation of ``\lstinline$f( 5 )$'', using an implicit \lstinline$int$ to \lstinline$long$ conversion.
     961The other functions do not, since the second requires two arguments, and since there is no implicit conversion from \lstinline$int$ to \lstinline$int *$ that could be used with the third function.
    1057962
    1058963\begin{lstlisting}
     
    1064969
    1065970\begin{lstlisting}
    1066 forall( type T, type U ) void g( T, U );        // (4) 
    1067 forall( type T ) void g( T, T );                        // (5) 
    1068 forall( type T ) void g( T, long );                     // (6) 
    1069 void g( long, long );                                           // (7) 
     971forall( type T, type U ) void g( T, U );        // (4)
     972forall( type T ) void g( T, T );                        // (5)
     973forall( type T ) void g( T, long );                     // (6)
     974void g( long, long );                                           // (7)
    1070975double d;
    1071976int i;
    1072977int *p;
    1073 
    1074 g( d, d );                      // calls (5)
    1075 g( d, i );                      // calls (6)
    1076 g( i, i );                      // calls (7)
     978g( d, d );                      // calls (5)
     979g( d, i );                      // calls (6)
     980g( i, i );                      // calls (7)
    1077981g( i, p );                      // calls (4)
    1078982\end{lstlisting}
    1079 The first call has valid interpretations for all four versions of \lstinline$g$. (6) and (7) are
    1080 discarded because they involve unsafe \lstinline$double$-to-\lstinline$long$ conversions. (5) is
    1081 chosen because it is less polymorphic than (4).
    1082 
    1083 For the second call, (7) is again discarded. Of the remaining interpretations for (4), (5), and (6)
    1084 (with \lstinline$i$ converted to \lstinline$long$), (6) is chosen because it is the least
    1085 polymorphic.
    1086 
    1087 The third call has valid interpretations for all of the functions; (7) is chosen since it is not
    1088 polymorphic at all.
    1089 
    1090 The fourth call has no interpretation for (5), because its arguments must have compatible type. (4)
    1091 is chosen because it does not involve unsafe conversions.
     983The first call has valid interpretations for all four versions of \lstinline$g$. (6) and (7) are discarded because they involve unsafe \lstinline$double$-to-\lstinline$long$ conversions. (5) is chosen because it is less polymorphic than (4).
     984
     985For the second call, (7) is again discarded.
     986Of the remaining interpretations for (4), (5), and (6) (with \lstinline$i$ converted to \lstinline$long$), (6) is chosen because it is the least polymorphic.
     987
     988The third call has valid interpretations for all of the functions;
     989(7) is chosen since it is not polymorphic at all.
     990
     991The fourth call has no interpretation for (5), because its arguments must have compatible type. (4) is chosen because it does not involve unsafe conversions.
    1092992\begin{lstlisting}
    1093993forall( type T ) T min( T, T );
     
    1098998}
    1099999forall( type U | min_max( U ) ) void shuffle( U, U );
    1100 shuffle(9, 10);
    1101 \end{lstlisting}
    1102 The only possibility for \lstinline$U$ is \lstinline$double$, because that is the type used in the
    1103 only visible \lstinline$max$ function. 9 and 10 must be converted to \lstinline$double$, and
     1000shuffle( 9, 10 );
     1001\end{lstlisting}
     1002The only possibility for \lstinline$U$ is \lstinline$double$, because that is the type used in the only visible \lstinline$max$ function. 9 and 10 must be converted to \lstinline$double$, and
    11041003\lstinline$min$ must be specialized with \lstinline$T$ bound to \lstinline$double$.
    11051004\begin{lstlisting}
    1106 extern void q( int );           // (8) 
    1107 extern void q( void * );        // (9) 
     1005extern void q( int );           // (8)
     1006extern void q( void * );        // (9)
    11081007extern void r();
    11091008q( 0 );
    11101009r( 0 );
    11111010\end{lstlisting}
    1112 The \lstinline$int 0$ could be passed to (8), or the \lstinline$(void *)$ \Index{specialization} of
    1113 the null pointer\index{null pointer} \lstinline$0$\use{0} could be passed to (9). The former is
    1114 chosen because the \lstinline$int$ \lstinline$0$ is \Index{less polymorphic}. For
    1115 the same reason, \lstinline$int$ \lstinline$0$ is passed to \lstinline$r()$, even though it has
    1116 \emph{no} declared parameter types.
     1011The \lstinline$int 0$ could be passed to (8), or the \lstinline$(void *)$ \Index{specialization} of the null pointer\index{null pointer} \lstinline$0$\use{0} could be passed to (9).
     1012The former is chosen because the \lstinline$int$ \lstinline$0$ is \Index{less polymorphic}.
     1013For the same reason, \lstinline$int$ \lstinline$0$ is passed to \lstinline$r()$, even though it has \emph{no} declared parameter types.
    11171014
    11181015
    11191016\subsubsection{Structure and union members}
    11201017
    1121 \semantics In the member selection expression ``\lstinline$s$.\lstinline$m$'', there shall be at
    1122 least one interpretation of \lstinline$s$ whose type is a structure type or union type containing a
    1123 member named \lstinline$m$. If two or more interpretations of \lstinline$s$ have members named
    1124 \lstinline$m$ with mutually compatible types, then the expression has an \Index{ambiguous
    1125 interpretation} whose type is the composite type of the types of the members. If an interpretation
    1126 of \lstinline$s$ has a member \lstinline$m$ whose type is not compatible with any other
    1127 \lstinline$s$'s \lstinline$m$, then the expression has an interpretation with the member's type. The
    1128 expression has no other interpretations.
     1018\semantics In the member selection expression ``\lstinline$s$.\lstinline$m$'', there shall be at least one interpretation of \lstinline$s$ whose type is a structure type or union type containing a member named \lstinline$m$.
     1019If two or more interpretations of \lstinline$s$ have members named
     1020\lstinline$m$ with mutually compatible types, then the expression has an \Index{ambiguous interpretation} whose type is the composite type of the types of the members.
     1021If an interpretation of \lstinline$s$ has a member \lstinline$m$ whose type is not compatible with any other
     1022\lstinline$s$'s \lstinline$m$, then the expression has an interpretation with the member's type.
     1023The expression has no other interpretations.
    11291024
    11301025The expression ``\lstinline$p->m$'' has the same interpretations as the expression
     
    11361031\predefined
    11371032\begin{lstlisting}
    1138 _Bool ?++( volatile _Bool * ),
    1139         ?++( _Atomic volatile _Bool * );
    1140 char ?++( volatile char * ),
    1141         ?++( _Atomic volatile char * );
    1142 signed char ?++( volatile signed char * ),
    1143         ?++( _Atomic volatile signed char * );
    1144 unsigned char ?++( volatile signed char * ),
    1145         ?++( _Atomic volatile signed char * );
    1146 short int ?++( volatile short int * ),
    1147         ?++( _Atomic volatile short int * );
    1148 unsigned short int ?++( volatile unsigned short int * ),
    1149         ?++( _Atomic volatile unsigned short int * );
    1150 int ?++( volatile int * ),
    1151         ?++( _Atomic volatile int * );
    1152 unsigned int ?++( volatile unsigned int * ),
    1153         ?++( _Atomic volatile unsigned int * );
    1154 long int ?++( volatile long int * ),
    1155         ?++( _Atomic volatile long int * );
    1156 long unsigned int ?++( volatile long unsigned int * ),
    1157         ?++( _Atomic volatile long unsigned int * );
    1158 long long int ?++( volatile long long int * ),
    1159         ?++( _Atomic volatile long long int * );
    1160 long long unsigned ?++( volatile long long unsigned int * ),
    1161         ?++( _Atomic volatile long long unsigned int * );
    1162 float ?++( volatile float * ),
    1163         ?++( _Atomic volatile float * );
    1164 double ?++( volatile double * ),
    1165         ?++( _Atomic volatile double * );
    1166 long double ?++( volatile long double * ),
    1167         ?++( _Atomic volatile long double * );
    1168 
    1169 forall( type T ) T * ?++( T * restrict volatile * ),
    1170         * ?++( T * _Atomic restrict volatile * );
    1171 
    1172 forall( type T ) _Atomic T * ?++( _Atomic T * restrict volatile * ),
    1173         * ?++( _Atomic T * _Atomic restrict volatile * );
    1174 
    1175 forall( type T ) const T * ?++( const T * restrict volatile * ),
    1176         * ?++( const T * _Atomic restrict volatile * );
    1177 
    1178 forall( type T ) volatile T * ?++( volatile T * restrict volatile * ),
    1179         * ?++( volatile T * _Atomic restrict volatile * );
    1180 
    1181 forall( type T ) restrict T * ?++( restrict T * restrict volatile * ),
    1182         * ?++( restrict T * _Atomic restrict volatile * );
    1183 
     1033_Bool ?++( volatile _Bool * ), ?++( _Atomic volatile _Bool * );
     1034char ?++( volatile char * ), ?++( _Atomic volatile char * );
     1035signed char ?++( volatile signed char * ), ?++( _Atomic volatile signed char * );
     1036unsigned char ?++( volatile signed char * ), ?++( _Atomic volatile signed char * );
     1037short int ?++( volatile short int * ), ?++( _Atomic volatile short int * );
     1038unsigned short int ?++( volatile unsigned short int * ), ?++( _Atomic volatile unsigned short int * );
     1039int ?++( volatile int * ), ?++( _Atomic volatile int * );
     1040unsigned int ?++( volatile unsigned int * ), ?++( _Atomic volatile unsigned int * );
     1041long int ?++( volatile long int * ), ?++( _Atomic volatile long int * );
     1042long unsigned int ?++( volatile long unsigned int * ), ?++( _Atomic volatile long unsigned int * );
     1043long long int ?++( volatile long long int * ), ?++( _Atomic volatile long long int * );
     1044long long unsigned ?++( volatile long long unsigned int * ), ?++( _Atomic volatile long long unsigned int * );
     1045float ?++( volatile float * ), ?++( _Atomic volatile float * );
     1046double ?++( volatile double * ), ?++( _Atomic volatile double * );
     1047long double ?++( volatile long double * ), ?++( _Atomic volatile long double * );
     1048
     1049forall( type T ) T * ?++( T * restrict volatile * ), * ?++( T * _Atomic restrict volatile * );
     1050forall( type T ) _Atomic T * ?++( _Atomic T * restrict volatile * ), * ?++( _Atomic T * _Atomic restrict volatile * );
     1051forall( type T ) const T * ?++( const T * restrict volatile * ), * ?++( const T * _Atomic restrict volatile * );
     1052forall( type T ) volatile T * ?++( volatile T * restrict volatile * ), * ?++( volatile T * _Atomic restrict volatile * );
     1053forall( type T ) restrict T * ?++( restrict T * restrict volatile * ), * ?++( restrict T * _Atomic restrict volatile * );
    11841054forall( type T ) _Atomic const T * ?++( _Atomic const T * restrict volatile * ),
    11851055        * ?++( _Atomic const T * _Atomic restrict volatile * );
    1186 
    11871056forall( type T ) _Atomic restrict T * ?++( _Atomic restrict T * restrict volatile * ),
    11881057        * ?++( _Atomic restrict T * _Atomic restrict volatile * );
    1189 
    11901058forall( type T ) _Atomic volatile T * ?++( _Atomic volatile T * restrict volatile * ),
    11911059        * ?++( _Atomic volatile T * _Atomic restrict volatile * );
    1192 
    11931060forall( type T ) const restrict T * ?++( const restrict T * restrict volatile * ),
    11941061        * ?++( const restrict T * _Atomic restrict volatile * );
    1195 
    11961062forall( type T ) const volatile T * ?++( const volatile T * restrict volatile * ),
    11971063        * ?++( const volatile T * _Atomic restrict volatile * );
    1198 
    11991064forall( type T ) restrict volatile T * ?++( restrict volatile T * restrict volatile * ),
    12001065        * ?++( restrict volatile T * _Atomic restrict volatile * );
    1201 
    12021066forall( type T ) _Atomic const restrict T * ?++( _Atomic const restrict T * restrict volatile * ),
    12031067        * ?++( _Atomic const restrict T * _Atomic restrict volatile * );
    1204 
    12051068forall( type T ) _Atomic const volatile T * ?++( _Atomic const volatile T * restrict volatile * ),
    12061069        * ?++( _Atomic const volatile T * _Atomic restrict volatile * );
    1207 
    12081070forall( type T ) _Atomic restrict volatile T * ?++( _Atomic restrict volatile T * restrict volatile * ),
    12091071        * ?++( _Atomic restrict volatile T * _Atomic restrict volatile * );
    1210 
    12111072forall( type T ) const restrict volatile T * ?++( const restrict volatile T * restrict volatile * ),
    12121073        * ?++( const restrict volatile T * _Atomic restrict volatile * );
    1213 
    12141074forall( type T ) _Atomic const restrict volatile T * ?++( _Atomic const restrict volatile T * restrict volatile * ),
    12151075        * ?++( _Atomic const restrict volatile T * _Atomic restrict volatile * );
    12161076
    1217 _Bool ?--( volatile _Bool * ),
    1218         ?--( _Atomic volatile _Bool * );
    1219 char ?--( volatile char * ),
    1220         ?--( _Atomic volatile char * );
    1221 signed char ?--( volatile signed char * ),
    1222         ?--( _Atomic volatile signed char * );
    1223 unsigned char ?--( volatile signed char * ),
    1224         ?--( _Atomic volatile signed char * );
    1225 short int ?--( volatile short int * ),
    1226         ?--( _Atomic volatile short int * );
    1227 unsigned short int ?--( volatile unsigned short int * ),
    1228         ?--( _Atomic volatile unsigned short int * );
    1229 int ?--( volatile int * ),
    1230         ?--( _Atomic volatile int * );
    1231 unsigned int ?--( volatile unsigned int * ),
    1232         ?--( _Atomic volatile unsigned int * );
    1233 long int ?--( volatile long int * ),
    1234         ?--( _Atomic volatile long int * );
    1235 long unsigned int ?--( volatile long unsigned int * ),
    1236         ?--( _Atomic volatile long unsigned int * );
    1237 long long int ?--( volatile long long int * ),
    1238         ?--( _Atomic volatile long long int * );
    1239 long long unsigned ?--( volatile long long unsigned int * ),
    1240         ?--( _Atomic volatile long long unsigned int * );
    1241 float ?--( volatile float * ),
    1242         ?--( _Atomic volatile float * );
    1243 double ?--( volatile double * ),
    1244         ?--( _Atomic volatile double * );
    1245 long double ?--( volatile long double * ),
    1246         ?--( _Atomic volatile long double * );
    1247 
    1248 forall( type T ) T * ?--( T * restrict volatile * ),
    1249         * ?--( T * _Atomic restrict volatile * );
    1250 
    1251 forall( type T ) _Atomic T * ?--( _Atomic T * restrict volatile * ),
    1252         * ?--( _Atomic T * _Atomic restrict volatile * );
    1253 
    1254 forall( type T ) const T * ?--( const T * restrict volatile * ),
    1255         * ?--( const T * _Atomic restrict volatile * );
    1256 
    1257 forall( type T ) volatile T * ?--( volatile T * restrict volatile * ),
    1258         * ?--( volatile T * _Atomic restrict volatile * );
    1259 
    1260 forall( type T ) restrict T * ?--( restrict T * restrict volatile * ),
    1261         * ?--( restrict T * _Atomic restrict volatile * );
    1262 
     1077_Bool ?--( volatile _Bool * ), ?--( _Atomic volatile _Bool * );
     1078char ?--( volatile char * ), ?--( _Atomic volatile char * );
     1079signed char ?--( volatile signed char * ), ?--( _Atomic volatile signed char * );
     1080unsigned char ?--( volatile signed char * ), ?--( _Atomic volatile signed char * );
     1081short int ?--( volatile short int * ), ?--( _Atomic volatile short int * );
     1082unsigned short int ?--( volatile unsigned short int * ), ?--( _Atomic volatile unsigned short int * );
     1083int ?--( volatile int * ), ?--( _Atomic volatile int * );
     1084unsigned int ?--( volatile unsigned int * ), ?--( _Atomic volatile unsigned int * );
     1085long int ?--( volatile long int * ), ?--( _Atomic volatile long int * );
     1086long unsigned int ?--( volatile long unsigned int * ), ?--( _Atomic volatile long unsigned int * );
     1087long long int ?--( volatile long long int * ), ?--( _Atomic volatile long long int * );
     1088long long unsigned ?--( volatile long long unsigned int * ), ?--( _Atomic volatile long long unsigned int * );
     1089float ?--( volatile float * ), ?--( _Atomic volatile float * );
     1090double ?--( volatile double * ), ?--( _Atomic volatile double * );
     1091long double ?--( volatile long double * ), ?--( _Atomic volatile long double * );
     1092
     1093forall( type T ) T * ?--( T * restrict volatile * ), * ?--( T * _Atomic restrict volatile * );
     1094forall( type T ) _Atomic T * ?--( _Atomic T * restrict volatile * ), * ?--( _Atomic T * _Atomic restrict volatile * );
     1095forall( type T ) const T * ?--( const T * restrict volatile * ), * ?--( const T * _Atomic restrict volatile * );
     1096forall( type T ) volatile T * ?--( volatile T * restrict volatile * ), * ?--( volatile T * _Atomic restrict volatile * );
     1097forall( type T ) restrict T * ?--( restrict T * restrict volatile * ), * ?--( restrict T * _Atomic restrict volatile * );
    12631098forall( type T ) _Atomic const T * ?--( _Atomic const T * restrict volatile * ),
    12641099        * ?--( _Atomic const T * _Atomic restrict volatile * );
    1265 
    12661100forall( type T ) _Atomic restrict T * ?--( _Atomic restrict T * restrict volatile * ),
    12671101        * ?--( _Atomic restrict T * _Atomic restrict volatile * );
    1268 
    12691102forall( type T ) _Atomic volatile T * ?--( _Atomic volatile T * restrict volatile * ),
    12701103        * ?--( _Atomic volatile T * _Atomic restrict volatile * );
    1271 
    12721104forall( type T ) const restrict T * ?--( const restrict T * restrict volatile * ),
    12731105        * ?--( const restrict T * _Atomic restrict volatile * );
    1274 
    12751106forall( type T ) const volatile T * ?--( const volatile T * restrict volatile * ),
    12761107        * ?--( const volatile T * _Atomic restrict volatile * );
    1277 
    12781108forall( type T ) restrict volatile T * ?--( restrict volatile T * restrict volatile * ),
    12791109        * ?--( restrict volatile T * _Atomic restrict volatile * );
    1280 
    12811110forall( type T ) _Atomic const restrict T * ?--( _Atomic const restrict T * restrict volatile * ),
    12821111        * ?--( _Atomic const restrict T * _Atomic restrict volatile * );
    1283 
    12841112forall( type T ) _Atomic const volatile T * ?--( _Atomic const volatile T * restrict volatile * ),
    12851113        * ?--( _Atomic const volatile T * _Atomic restrict volatile * );
    1286 
    12871114forall( type T ) _Atomic restrict volatile T * ?--( _Atomic restrict volatile T * restrict volatile * ),
    12881115        * ?--( _Atomic restrict volatile T * _Atomic restrict volatile * );
    1289 
    12901116forall( type T ) const restrict volatile T * ?--( const restrict volatile T * restrict volatile * ),
    12911117        * ?--( const restrict volatile T * _Atomic restrict volatile * );
    1292 
    12931118forall( type T ) _Atomic const restrict volatile T * ?--( _Atomic const restrict volatile T * restrict volatile * ),
    12941119        * ?--( _Atomic const restrict volatile T * _Atomic restrict volatile * );
     
    13081133
    13091134\begin{rationale}
    1310 Note that ``\lstinline$++$'' and ``\lstinline$--$'' are rewritten as function calls that are given a
    1311 pointer to that operand. (This is true of all operators that modify an operand.) As Hamish Macdonald
    1312 has pointed out, this forces the modified operand of such expressions to be an lvalue. This
    1313 partially enforces the C semantic rule that such operands must be \emph{modifiable} lvalues.
    1314 \end{rationale}
    1315 
    1316 \begin{rationale}
    1317 In C, a semantic rule requires that pointer operands of increment and decrement be pointers to
    1318 object types. Hence, \lstinline$void *$ objects cannot be incremented. In \CFA, the restriction
    1319 follows from the use of a \lstinline$type$ parameter in the predefined function definitions, as
    1320 opposed to \lstinline$dtype$, since only object types can be inferred arguments corresponding to the
    1321 type parameter \lstinline$T$.
     1135Note that ``\lstinline$++$'' and ``\lstinline$--$'' are rewritten as function calls that are given a pointer to that operand. (This is true of all operators that modify an operand.) As Hamish Macdonald has pointed out, this forces the modified operand of such expressions to be an lvalue.
     1136This partially enforces the C semantic rule that such operands must be \emph{modifiable} lvalues.
     1137\end{rationale}
     1138
     1139\begin{rationale}
     1140In C, a semantic rule requires that pointer operands of increment and decrement be pointers to object types.
     1141Hence, \lstinline$void *$ objects cannot be incremented.
     1142In \CFA, the restriction follows from the use of a \lstinline$type$ parameter in the predefined function definitions, as opposed to \lstinline$dtype$, since only object types can be inferred arguments corresponding to the type parameter \lstinline$T$.
    13221143\end{rationale}
    13231144
    13241145\semantics
    1325 First, each interpretation of the operand of an increment or decrement expression is considered
    1326 separately. For each interpretation that is a bit-field or is declared with the
    1327 \lstinline$register$\index{register@{\lstinline$register$}} \index{Itorage-class specifier}, the
    1328 expression has one valid interpretation, with the type of the operand, and the expression is
    1329 ambiguous if the operand is.
    1330 
    1331 For the remaining interpretations, the expression is rewritten, and the interpretations of the
    1332 expression are the interpretations of the corresponding function call. Finally, all interpretations
    1333 of the expression produced for the different interpretations of the operand are combined to produce
    1334 the interpretations of the expression as a whole; where interpretations have compatible result
    1335 types, the best interpretations are selected in the manner described for function call expressions.
     1146First, each interpretation of the operand of an increment or decrement expression is considered separately.
     1147For each interpretation that is a bit-field or is declared with the
     1148\lstinline$register$\index{register@{\lstinline$register$}} \index{Itorage-class specifier}, the expression has one valid interpretation, with the type of the operand, and the expression is ambiguous if the operand is.
     1149
     1150For the remaining interpretations, the expression is rewritten, and the interpretations of the expression are the interpretations of the corresponding function call.
     1151Finally, all interpretations of the expression produced for the different interpretations of the operand are combined to produce the interpretations of the expression as a whole; where interpretations have compatible result types, the best interpretations are selected in the manner described for function call expressions.
    13361152
    13371153\examples
     
    13461162\lstinline$vs++$ calls the \lstinline$?++$ function with the \lstinline$volatile short *$ parameter.
    13471163\lstinline$s++$ does the same, applying the safe conversion from \lstinline$short int *$ to
    1348 \lstinline$volatile short int *$. Note that there is no conversion that adds an \lstinline$_Atomic$
    1349 qualifier, so the \lstinline$_Atomic volatile short int$ overloading does not provide a valid
    1350 interpretation.
     1164\lstinline$volatile short int *$.
     1165Note that there is no conversion that adds an \lstinline$_Atomic$ qualifier, so the \lstinline$_Atomic volatile short int$ overloading does not provide a valid interpretation.
    13511166\end{sloppypar}
    13521167
    1353 There is no safe conversion from \lstinline$const short int *$ to \lstinline$volatile short int *$,
    1354 and no \lstinline$?++$ function that accepts a \lstinline$const *$ parameter, so \lstinline$cs++$
    1355 has no valid interpretations.
    1356 
    1357 The best valid interpretation of \lstinline$as++$ calls the \lstinline$short ?++$ function with the
    1358 \lstinline$_Atomic volatile short int *$ parameter, applying a safe conversion to add the
    1359 \lstinline$volatile$ qualifier.
    1360 
    1361 \begin{lstlisting}
    1362 char * const restrict volatile * restrict volatile pqpc; pqpc++
    1363 char * * restrict volatile ppc; ppc++;
    1364 \end{lstlisting}
    1365 Since \lstinline$&(pqpc)$ has type \lstinline$char * const restrict volatile * restrict volatile *$,
    1366 the best valid interpretation of \lstinline$pqpc++$ calls the polymorphic \lstinline$?++$ function
    1367 with the \lstinline$const restrict volatile T * restrict volatile *$ parameter, inferring
    1368 \lstinline$T$ to be \lstinline$char *$.
    1369 
    1370 \begin{sloppypar}
    1371 \lstinline$ppc++$ calls the same function, again inferring \lstinline$T$ to be \lstinline$char *$,
    1372 and using the safe conversions from \lstinline$T$ to \lstinline$T const restrict volatile$.
    1373 \end{sloppypar}
    1374 
    1375 \begin{rationale}
    1376 Increment and decrement expressions show up a deficiency of \CFA's type system. There is no such
    1377 thing as a pointer to a register object or bit-field\index{deficiencies!pointers to bit-fields}.
    1378 Therefore, there is no way to define a function that alters them, and hence no way to define
    1379 increment and decrement functions for them. As a result, the semantics of increment and decrement
    1380 expressions must treat them specially. This holds true for all of the operators that may modify
    1381 such objects.
    1382 \end{rationale}
    1383 
    1384 \begin{rationale}
    1385 The polymorphic overloadings for pointer increment and decrement can be understood by considering
    1386 increasingly complex types.
     1168There is no safe conversion from \lstinline$const short int *$ to \lstinline$volatile short int *$, and no \lstinline$?++$ function that accepts a \lstinline$const *$ parameter, so \lstinline$cs++$ has no valid interpretations.
     1169
     1170The best valid interpretation of \lstinline$as++$ calls the \lstinline$short ?++$ function with the \lstinline$_Atomic volatile short int *$ parameter, applying a safe conversion to add the \lstinline$volatile$ qualifier.
     1171\begin{lstlisting}
     1172char * const restrict volatile * restrict volatile pqpc;
     1173pqpc++
     1174char * * restrict volatile ppc;
     1175ppc++;
     1176\end{lstlisting}
     1177Since \lstinline$&(pqpc)$ has type \lstinline$char * const restrict volatile * restrict volatile *$, the best valid interpretation of \lstinline$pqpc++$ calls the polymorphic \lstinline$?++$ function with the \lstinline$const restrict volatile T * restrict volatile *$ parameter, inferring \lstinline$T$ to be \lstinline$char *$.
     1178
     1179\lstinline$ppc++$ calls the same function, again inferring \lstinline$T$ to be \lstinline$char *$, and using the safe conversions from \lstinline$T$ to \lstinline$T const$ \lstinline$restrict volatile$.
     1180
     1181\begin{rationale}
     1182Increment and decrement expressions show up a deficiency of \CFA's type system.
     1183There is no such thing as a pointer to a register object or bit-field\index{deficiencies!pointers to bit-fields}.
     1184Therefore, there is no way to define a function that alters them, and hence no way to define increment and decrement functions for them.
     1185As a result, the semantics of increment and decrement expressions must treat them specially.
     1186This holds true for all of the operators that may modify such objects.
     1187\end{rationale}
     1188
     1189\begin{rationale}
     1190The polymorphic overloadings for pointer increment and decrement can be understood by considering increasingly complex types.
    13871191\begin{enumerate}
    13881192\item
    1389 ``\lstinline$char * p; p++;$''. The argument to \lstinline$?++$ has type \lstinline$char * *$, and
    1390 the result has type \lstinline$char *$. The expression would be valid if \lstinline$?++$ were
    1391 declared by
     1193``\lstinline$char * p; p++;$''.
     1194The argument to \lstinline$?++$ has type \lstinline$char * *$, and the result has type \lstinline$char *$.
     1195The expression would be valid if \lstinline$?++$ were declared by
    13921196\begin{lstlisting}
    13931197forall( type T ) T * ?++( T * * );
    1394 \end{lstlisting}
    1395 with \lstinline$T$ inferred to be \lstinline$char$.
    1396 
    1397 \item
    1398 ``\lstinline$char *restrict volatile qp; qp++$''. The result again has type \lstinline$char *$, but
    1399 the argument now has type \lstinline$char *restrict volatile *$, so it cannot be passed to the
    1400 hypothetical function declared in point 1. Hence the actual predefined function is
     1198\end{lstlisting} with \lstinline$T$ inferred to be \lstinline$char$.
     1199
     1200\item
     1201``\lstinline$char *restrict volatile qp; qp++$''.
     1202The result again has type \lstinline$char *$, but the argument now has type \lstinline$char *restrict volatile *$, so it cannot be passed to the hypothetical function declared in point 1.
     1203Hence the actual predefined function is
    14011204\begin{lstlisting}
    14021205forall( type T ) T * ?++( T * restrict volatile * );
    1403 \end{lstlisting}
    1404 which also accepts a \lstinline$char * *$ argument, because of the safe conversions that add
    1405 \lstinline$volatile$ and \lstinline$restrict$ qualifiers. (The parameter is not const-qualified, so
    1406 constant pointers cannot be incremented.)
    1407 
    1408 \item
    1409 ``\lstinline$char *_Atomic ap; ap++$''. The result again has type \lstinline$char *$, but no safe
    1410 conversion adds an \lstinline$_Atomic$ qualifier, so the function in point 2 is not applicable. A
    1411 separate overloading of \lstinline$?++$ is required.
    1412 
    1413 \item
    1414 ``\lstinline$char const volatile * pq; pq++$''. Here the result has type
     1206\end{lstlisting} which also accepts a \lstinline$char * *$ argument, because of the safe conversions that add
     1207\lstinline$volatile$ and \lstinline$restrict$ qualifiers. (The parameter is not const-qualified, so constant pointers cannot be incremented.)
     1208
     1209\item
     1210``\lstinline$char *_Atomic ap; ap++$''.
     1211The result again has type \lstinline$char *$, but no safe conversion adds an \lstinline$_Atomic$ qualifier, so the function in point 2 is not applicable.
     1212A separate overloading of \lstinline$?++$ is required.
     1213
     1214\item
     1215``\lstinline$char const volatile * pq; pq++$''.
     1216Here the result has type
    14151217\lstinline$char const volatile *$, so a new overloading is needed:
    14161218\begin{lstlisting}
    14171219forall( type T ) T const volatile * ?++( T const volatile *restrict volatile * );
    14181220\end{lstlisting}
    1419 One overloading is needed for each combination of qualifiers in the pointed-at
    1420 type\index{deficiencies!pointers to qualified types}.
     1221One overloading is needed for each combination of qualifiers in the pointed-at type\index{deficiencies!pointers to qualified types}.
    14211222 
    14221223\item
    1423 ``\lstinline$float *restrict * prp; prp++$''. The \lstinline$restrict$ qualifier is handled just
    1424 like \lstinline$const$ and \lstinline$volatile$ in the previous case:
     1224``\lstinline$float *restrict * prp; prp++$''.
     1225The \lstinline$restrict$ qualifier is handled just like \lstinline$const$ and \lstinline$volatile$ in the previous case:
    14251226\begin{lstlisting}
    14261227forall( type T ) T restrict * ?++( T restrict *restrict volatile * );
    1427 \end{lstlisting}
    1428 with \lstinline$T$ inferred to be \lstinline$float *$. This looks odd, because {\c11} contains a
    1429 constraint that requires restrict-qualified types to be pointer-to-object types, and \lstinline$T$
    1430 is not syntactically a pointer type. \CFA loosens the constraint.
     1228\end{lstlisting} with \lstinline$T$ inferred to be \lstinline$float *$.
     1229This looks odd, because {\c11} contains a constraint that requires restrict-qualified types to be pointer-to-object types, and \lstinline$T$ is not syntactically a pointer type. \CFA loosens the constraint.
    14311230\end{enumerate}
    14321231\end{rationale}
     
    14361235
    14371236\semantics
    1438 A compound literal has one interpretation, with the type given by the \nonterm{type-name} of the
    1439 compound literal.
     1237A compound literal has one interpretation, with the type given by the \nonterm{type-name} of the compound literal.
    14401238
    14411239
     
    14551253\rewriterules
    14561254\begin{lstlisting}
    1457 *a      @\rewrite@ *?(a) @\use{*?}@
    1458 +a      @\rewrite@ +?(a) @\use{+?}@
    1459 -a      @\rewrite@ -?(a) @\use{-?}@
    1460 ~a      @\rewrite@ ~?(a) @\use{~?}@
    1461 !a      @\rewrite@ !?(a) @\use{"!?}@
    1462 ++a     @\rewrite@ ++?(&(a)) @\use{++?}@
    1463 --a     @\rewrite@ --?(&(a)) @\use{--?}@
     1255*a      @\rewrite@ *?( a ) @\use{*?}@
     1256+a      @\rewrite@ +?( a ) @\use{+?}@
     1257-a      @\rewrite@ -?( a ) @\use{-?}@
     1258~a      @\rewrite@ ~?( a ) @\use{~?}@
     1259!a      @\rewrite@ !?( a ) @\use{"!?}@
     1260++a     @\rewrite@ ++?(&( a )) @\use{++?}@
     1261--a     @\rewrite@ --?(&( a )) @\use{--?}@
    14641262\end{lstlisting}
    14651263
     
    14691267\predefined
    14701268\begin{lstlisting}
    1471 _Bool ++?( volatile _Bool * ),
    1472         ++?( _Atomic volatile _Bool * );
    1473 char ++?( volatile char * ),
    1474         ++?( _Atomic volatile char * );
    1475 signed char ++?( volatile signed char * ),
    1476         ++?( _Atomic volatile signed char * );
    1477 unsigned char ++?( volatile signed char * ),
    1478         ++?( _Atomic volatile signed char * );
    1479 short int ++?( volatile short int * ),
    1480         ++?( _Atomic volatile short int * );
    1481 unsigned short int ++?( volatile unsigned short int * ),
    1482         ++?( _Atomic volatile unsigned short int * );
    1483 int ++?( volatile int * ),
    1484         ++?( _Atomic volatile int * );
    1485 unsigned int ++?( volatile unsigned int * ),
    1486         ++?( _Atomic volatile unsigned int * );
    1487 long int ++?( volatile long int * ),
    1488         ++?( _Atomic volatile long int * );
    1489 long unsigned int ++?( volatile long unsigned int * ),
    1490         ++?( _Atomic volatile long unsigned int * );
    1491 long long int ++?( volatile long long int * ),
    1492         ++?( _Atomic volatile long long int * );
    1493 long long unsigned ++?( volatile long long unsigned int * ),
    1494         ++?( _Atomic volatile long long unsigned int * );
    1495 float ++?( volatile float * ),
    1496         ++?( _Atomic volatile float * );
    1497 double ++?( volatile double * ),
    1498         ++?( _Atomic volatile double * );
    1499 long double ++?( volatile long double * ),
    1500         ++?( _Atomic volatile long double * );
    1501 
    1502 forall( type T ) T * ++?( T * restrict volatile * ),
    1503         * ++?( T * _Atomic restrict volatile * );
    1504 
    1505 forall( type T ) _Atomic T * ++?( _Atomic T * restrict volatile * ),
    1506         * ++?( _Atomic T * _Atomic restrict volatile * );
    1507 
    1508 forall( type T ) const T * ++?( const T * restrict volatile * ),
    1509         * ++?( const T * _Atomic restrict volatile * );
    1510 
    1511 forall( type T ) volatile T * ++?( volatile T * restrict volatile * ),
    1512         * ++?( volatile T * _Atomic restrict volatile * );
    1513 
    1514 forall( type T ) restrict T * ++?( restrict T * restrict volatile * ),
    1515         * ++?( restrict T * _Atomic restrict volatile * );
    1516 
     1269_Bool ++?( volatile _Bool * ), ++?( _Atomic volatile _Bool * );
     1270char ++?( volatile char * ), ++?( _Atomic volatile char * );
     1271signed char ++?( volatile signed char * ), ++?( _Atomic volatile signed char * );
     1272unsigned char ++?( volatile signed char * ), ++?( _Atomic volatile signed char * );
     1273short int ++?( volatile short int * ), ++?( _Atomic volatile short int * );
     1274unsigned short int ++?( volatile unsigned short int * ), ++?( _Atomic volatile unsigned short int * );
     1275int ++?( volatile int * ), ++?( _Atomic volatile int * );
     1276unsigned int ++?( volatile unsigned int * ), ++?( _Atomic volatile unsigned int * );
     1277long int ++?( volatile long int * ), ++?( _Atomic volatile long int * );
     1278long unsigned int ++?( volatile long unsigned int * ), ++?( _Atomic volatile long unsigned int * );
     1279long long int ++?( volatile long long int * ), ++?( _Atomic volatile long long int * );
     1280long long unsigned ++?( volatile long long unsigned int * ), ++?( _Atomic volatile long long unsigned int * );
     1281float ++?( volatile float * ), ++?( _Atomic volatile float * );
     1282double ++?( volatile double * ), ++?( _Atomic volatile double * );
     1283long double ++?( volatile long double * ), ++?( _Atomic volatile long double * );
     1284
     1285forall( type T ) T * ++?( T * restrict volatile * ), * ++?( T * _Atomic restrict volatile * );
     1286forall( type T ) _Atomic T * ++?( _Atomic T * restrict volatile * ), * ++?( _Atomic T * _Atomic restrict volatile * );
     1287forall( type T ) const T * ++?( const T * restrict volatile * ), * ++?( const T * _Atomic restrict volatile * );
     1288forall( type T ) volatile T * ++?( volatile T * restrict volatile * ), * ++?( volatile T * _Atomic restrict volatile * );
     1289forall( type T ) restrict T * ++?( restrict T * restrict volatile * ), * ++?( restrict T * _Atomic restrict volatile * );
    15171290forall( type T ) _Atomic const T * ++?( _Atomic const T * restrict volatile * ),
    15181291        * ++?( _Atomic const T * _Atomic restrict volatile * );
    1519 
    15201292forall( type T ) _Atomic volatile T * ++?( _Atomic volatile T * restrict volatile * ),
    15211293        * ++?( _Atomic volatile T * _Atomic restrict volatile * );
    1522 
    15231294forall( type T ) _Atomic restrict T * ++?( _Atomic restrict T * restrict volatile * ),
    15241295        * ++?( _Atomic restrict T * _Atomic restrict volatile * );
    1525 
    15261296forall( type T ) const volatile T * ++?( const volatile T * restrict volatile * ),
    15271297        * ++?( const volatile T * _Atomic restrict volatile * );
    1528 
    15291298forall( type T ) const restrict T * ++?( const restrict T * restrict volatile * ),
    15301299        * ++?( const restrict T * _Atomic restrict volatile * );
    1531 
    15321300forall( type T ) restrict volatile T * ++?( restrict volatile T * restrict volatile * ),
    15331301        * ++?( restrict volatile T * _Atomic restrict volatile * );
    1534 
    15351302forall( type T ) _Atomic const volatile T * ++?( _Atomic const volatile T * restrict volatile * ),
    15361303        * ++?( _Atomic const volatile T * _Atomic restrict volatile * );
    1537 
    15381304forall( type T ) _Atomic const restrict T * ++?( _Atomic const restrict T * restrict volatile * ),
    15391305        * ++?( _Atomic const restrict T * _Atomic restrict volatile * );
    1540 
    15411306forall( type T ) _Atomic restrict volatile T * ++?( _Atomic restrict volatile T * restrict volatile * ),
    15421307        * ++?( _Atomic restrict volatile T * _Atomic restrict volatile * );
    1543 
    15441308forall( type T ) const restrict volatile T * ++?( const restrict volatile T * restrict volatile * ),
    15451309        * ++?( const restrict volatile T * _Atomic restrict volatile * );
    1546 
    15471310forall( type T ) _Atomic const restrict volatile T * ++?( _Atomic const restrict volatile T * restrict volatile * ),
    15481311        * ++?( _Atomic const restrict volatile T * _Atomic restrict volatile * );
    15491312
    1550 _Bool --?( volatile _Bool * ),
    1551         --?( _Atomic volatile _Bool * );
    1552 char --?( volatile char * ),
    1553         --?( _Atomic volatile char * );
    1554 signed char --?( volatile signed char * ),
    1555         --?( _Atomic volatile signed char * );
    1556 unsigned char --?( volatile signed char * ),
    1557         --?( _Atomic volatile signed char * );
    1558 short int --?( volatile short int * ),
    1559         --?( _Atomic volatile short int * );
    1560 unsigned short int --?( volatile unsigned short int * ),
    1561         --?( _Atomic volatile unsigned short int * );
    1562 int --?( volatile int * ),
    1563         --?( _Atomic volatile int * );
    1564 unsigned int --?( volatile unsigned int * ),
    1565         --?( _Atomic volatile unsigned int * );
    1566 long int --?( volatile long int * ),
    1567         --?( _Atomic volatile long int * );
    1568 long unsigned int --?( volatile long unsigned int * ),
    1569         --?( _Atomic volatile long unsigned int * );
    1570 long long int --?( volatile long long int * ),
    1571         --?( _Atomic volatile long long int * );
    1572 long long unsigned --?( volatile long long unsigned int * ),
    1573         --?( _Atomic volatile long long unsigned int * );
    1574 float --?( volatile float * ),
    1575         --?( _Atomic volatile float * );
    1576 double --?( volatile double * ),
    1577         --?( _Atomic volatile double * );
    1578 long double --?( volatile long double * ),
    1579         --?( _Atomic volatile long double * );
    1580 
    1581 forall( type T ) T * --?( T * restrict volatile * ),
    1582         * --?( T * _Atomic restrict volatile * );
    1583 
    1584 forall( type T ) _Atomic T * --?( _Atomic T * restrict volatile * ),
    1585         * --?( _Atomic T * _Atomic restrict volatile * );
    1586 
    1587 forall( type T ) const T * --?( const T * restrict volatile * ),
    1588         * --?( const T * _Atomic restrict volatile * );
    1589 
    1590 forall( type T ) volatile T * --?( volatile T * restrict volatile * ),
    1591         * --?( volatile T * _Atomic restrict volatile * );
    1592 
    1593 forall( type T ) restrict T * --?( restrict T * restrict volatile * ),
    1594         * --?( restrict T * _Atomic restrict volatile * );
    1595 
     1313_Bool --?( volatile _Bool * ), --?( _Atomic volatile _Bool * );
     1314char --?( volatile char * ), --?( _Atomic volatile char * );
     1315signed char --?( volatile signed char * ), --?( _Atomic volatile signed char * );
     1316unsigned char --?( volatile signed char * ), --?( _Atomic volatile signed char * );
     1317short int --?( volatile short int * ), --?( _Atomic volatile short int * );
     1318unsigned short int --?( volatile unsigned short int * ), --?( _Atomic volatile unsigned short int * );
     1319int --?( volatile int * ), --?( _Atomic volatile int * );
     1320unsigned int --?( volatile unsigned int * ), --?( _Atomic volatile unsigned int * );
     1321long int --?( volatile long int * ), --?( _Atomic volatile long int * );
     1322long unsigned int --?( volatile long unsigned int * ), --?( _Atomic volatile long unsigned int * );
     1323long long int --?( volatile long long int * ), --?( _Atomic volatile long long int * );
     1324long long unsigned --?( volatile long long unsigned int * ), --?( _Atomic volatile long long unsigned int * );
     1325float --?( volatile float * ), --?( _Atomic volatile float * );
     1326double --?( volatile double * ), --?( _Atomic volatile double * );
     1327long double --?( volatile long double * ), --?( _Atomic volatile long double * );
     1328
     1329forall( type T ) T * --?( T * restrict volatile * ), * --?( T * _Atomic restrict volatile * );
     1330forall( type T ) _Atomic T * --?( _Atomic T * restrict volatile * ), * --?( _Atomic T * _Atomic restrict volatile * );
     1331forall( type T ) const T * --?( const T * restrict volatile * ), * --?( const T * _Atomic restrict volatile * );
     1332forall( type T ) volatile T * --?( volatile T * restrict volatile * ), * --?( volatile T * _Atomic restrict volatile * );
     1333forall( type T ) restrict T * --?( restrict T * restrict volatile * ), * --?( restrict T * _Atomic restrict volatile * );
    15961334forall( type T ) _Atomic const T * --?( _Atomic const T * restrict volatile * ),
    15971335        * --?( _Atomic const T * _Atomic restrict volatile * );
    1598 
    15991336forall( type T ) _Atomic volatile T * --?( _Atomic volatile T * restrict volatile * ),
    16001337        * --?( _Atomic volatile T * _Atomic restrict volatile * );
    1601 
    16021338forall( type T ) _Atomic restrict T * --?( _Atomic restrict T * restrict volatile * ),
    16031339        * --?( _Atomic restrict T * _Atomic restrict volatile * );
    1604 
    16051340forall( type T ) const volatile T * --?( const volatile T * restrict volatile * ),
    16061341        * --?( const volatile T * _Atomic restrict volatile * );
    1607 
    16081342forall( type T ) const restrict T * --?( const restrict T * restrict volatile * ),
    16091343        * --?( const restrict T * _Atomic restrict volatile * );
    1610 
    16111344forall( type T ) restrict volatile T * --?( restrict volatile T * restrict volatile * ),
    16121345        * --?( restrict volatile T * _Atomic restrict volatile * );
    1613 
    16141346forall( type T ) _Atomic const volatile T * --?( _Atomic const volatile T * restrict volatile * ),
    16151347        * --?( _Atomic const volatile T * _Atomic restrict volatile * );
    1616 
    16171348forall( type T ) _Atomic const restrict T * --?( _Atomic const restrict T * restrict volatile * ),
    16181349        * --?( _Atomic const restrict T * _Atomic restrict volatile * );
    1619 
    16201350forall( type T ) _Atomic restrict volatile T * --?( _Atomic restrict volatile T * restrict volatile * ),
    16211351        * --?( _Atomic restrict volatile T * _Atomic restrict volatile * );
    1622 
    16231352forall( type T ) const restrict volatile T * --?( const restrict volatile T * restrict volatile * ),
    16241353        * --?( const restrict volatile T * _Atomic restrict volatile * );
    1625 
    16261354forall( type T ) _Atomic const restrict volatile T * --?( _Atomic const restrict volatile T * restrict volatile * ),
    16271355        * --?( _Atomic const restrict volatile T * _Atomic restrict volatile * );
     
    16451373
    16461374\semantics
    1647 The interpretations of prefix increment and decrement expressions are
    1648 determined in the same way as the interpretations of postfix increment and
    1649 decrement expressions.
     1375The interpretations of prefix increment and decrement expressions are determined in the same way as the interpretations of postfix increment and decrement expressions.
    16501376
    16511377
     
    16701396forall( type T ) const restrict volatile lvalue T *?( const restrict volatile T * );
    16711397forall( type T ) _Atomic const restrict volatile lvalue T *?( _Atomic const restrict volatile T * );
    1672 
    16731398forall( ftype FT ) FT *?( FT * );
    16741399\end{lstlisting}
     
    16821407\lstinline$T$ is the type of the operand.
    16831408
    1684 The interpretations of an indirection expression are the interpretations of the corresponding
    1685 function call.
     1409The interpretations of an indirection expression are the interpretations of the corresponding function call.
    16861410
    16871411
     
    16901414\predefined
    16911415\begin{lstlisting}
    1692 int
    1693         +?( int ),
    1694         -?( int ),
    1695         ~?( int );
    1696 unsigned int
    1697         +?( unsigned int ),
    1698         -?( unsigned int ),
    1699          ~?( unsigned int );
    1700 long int
    1701         +?( long int ),
    1702         -?( long int ),
    1703         ~?( long int );
    1704 long unsigned int
    1705         +?( long unsigned int ),
    1706         -?( long unsigned int ),
    1707         ~?( long unsigned int );
    1708 long long int
    1709         +?( long long int ),
    1710         -?( long long int ),
    1711         ~?( long long int );
    1712 long long unsigned int
    1713         +?( long long unsigned int ),
    1714         -?( long long unsigned int ),
    1715         ~?( long long unsigned int );
    1716 float
    1717         +?( float ),
    1718         -?( float );
    1719 double
    1720         +?( double ),
    1721         -?( double );
    1722 long double
    1723         +?( long double ),
    1724         -?( long double );
    1725 _Complex float
    1726         +?( _Complex float ),
    1727         -?( _Complex float );
    1728 _Complex double
    1729         +?( _Complex double ),
    1730         -?( _Complex double );
    1731 _Complex long double
    1732         +?( _Complex long double ),
    1733         -?( _Complex long double );
    1734 
    1735 int !?( int ),
    1736         !?( unsigned int ),
    1737         !?( long ),
    1738         !?( long unsigned int ),
    1739         !?( long long int ),
    1740         !?( long long unsigned int ),
    1741         !?( float ),
    1742         !?( double ),
    1743         !?( long double ),
    1744         !?( _Complex float ),
    1745         !?( _Complex double ),
    1746         !?( _Complex long double );
    1747 
     1416int     +?( int ), -?( int ), ~?( int );
     1417unsigned int +?( unsigned int ), -?( unsigned int ), ~?( unsigned int );
     1418long int +?( long int ), -?( long int ), ~?( long int );
     1419long unsigned int +?( long unsigned int ), -?( long unsigned int ), ~?( long unsigned int );
     1420long long int +?( long long int ), -?( long long int ), ~?( long long int );
     1421long long unsigned int +?( long long unsigned int ), -?( long long unsigned int ), ~?( long long unsigned int );
     1422float +?( float ), -?( float );
     1423double +?( double ), -?( double );
     1424long double +?( long double ), -?( long double );
     1425_Complex float +?( _Complex float ), -?( _Complex float );
     1426_Complex double +?( _Complex double ), -?( _Complex double );
     1427_Complex long double +?( _Complex long double ), -?( _Complex long double );
     1428int !?( int ), !?( unsigned int ), !?( long ), !?( long unsigned int ),
     1429        !?( long long int ), !?( long long unsigned int ),
     1430        !?( float ), !?( double ), !?( long double ),
     1431        !?( _Complex float ), !?( _Complex double ), !?( _Complex long double );
    17481432forall( dtype DT ) int !?( const restrict volatile DT * );
    17491433forall( dtype DT ) int !?( _Atomic const restrict volatile DT * );
    17501434forall( ftype FT ) int !?( FT * );
    17511435\end{lstlisting}
    1752 For every extended integer type \lstinline$X$ with \Index{integer conversion rank} greater than the
    1753 rank of \lstinline$int$ there exist
     1436For every extended integer type \lstinline$X$ with \Index{integer conversion rank} greater than the rank of \lstinline$int$ there exist
    17541437% Don't use predefined: keep this out of prelude.cf.
    17551438\begin{lstlisting}
     
    17591442
    17601443\semantics
    1761 The interpretations of a unary arithmetic expression are the interpretations of the corresponding
    1762 function call.
     1444The interpretations of a unary arithmetic expression are the interpretations of the corresponding function call.
    17631445
    17641446\examples
     
    17661448long int li;
    17671449void eat_double( double );@\use{eat_double}@
    1768 
    1769 eat_double(-li ); // @\rewrite@ eat_double( -?( li ) );
     1450eat_double(-li ); // @\rewrite@ eat_double( -?( li ) );
    17701451\end{lstlisting}
    17711452The valid interpretations of ``\lstinline$-li$'' (assuming no extended integer types exist) are
    17721453\begin{center}
    1773 \begin{tabular}{llc}
    1774 interpretation & result type & expression conversion cost \\
     1454\begin{tabular}{llc} interpretation & result type & expression conversion cost \\
    17751455\hline
    17761456\lstinline$-?( (int)li )$                                       & \lstinline$int$                                       & (unsafe) \\
     
    17881468\end{tabular}
    17891469\end{center}
    1790 The valid interpretations of the \lstinline$eat_double$ call, with the cost of the argument
    1791 conversion and the cost of the entire expression, are
     1470The valid interpretations of the \lstinline$eat_double$ call, with the cost of the argument conversion and the cost of the entire expression, are
    17921471\begin{center}
    1793 \begin{tabular}{lcc}
    1794 interpretation & argument cost & expression cost \\
     1472\begin{tabular}{lcc} interpretation & argument cost & expression cost \\
    17951473\hline
    17961474\lstinline$eat_double( (double)-?( (int)li) )$                                  & 7                     & (unsafe) \\
     
    18081486\end{tabular}
    18091487\end{center}
    1810 Each has result type \lstinline$void$, so the best must be selected. The interpretations involving
    1811 unsafe conversions are discarded. The remainder have equal expression conversion costs, so the
     1488Each has result type \lstinline$void$, so the best must be selected.
     1489The interpretations involving unsafe conversions are discarded.
     1490The remainder have equal expression conversion costs, so the
    18121491``highest argument conversion cost'' rule is invoked, and the chosen interpretation is
    18131492\lstinline$eat_double( (double)-?(li) )$.
     
    18201499\lstinline$dtype$, or \lstinline$ftype$.
    18211500
    1822 When the \lstinline$sizeof$\use{sizeof} operator is applied to an expression, the expression shall
    1823 have exactly one \Index{interpretation}\index{ambiguous interpretation}, which shall
    1824 be unambiguous. \semantics A \lstinline$sizeof$ or \lstinline$_Alignof$ expression has one
    1825 interpretation, of type \lstinline$size_t$.
     1501When the \lstinline$sizeof$\use{sizeof} operator is applied to an expression, the expression shall have exactly one \Index{interpretation}\index{ambiguous interpretation}, which shall be unambiguous. \semantics A \lstinline$sizeof$ or \lstinline$_Alignof$ expression has one interpretation, of type \lstinline$size_t$.
    18261502
    18271503When \lstinline$sizeof$ is applied to an identifier declared by a \nonterm{type-declaration} or a
    1828 \nonterm{type-parameter}, it yields the size in bytes of the type that implements the operand. When
    1829 the operand is an opaque type or an inferred type parameter\index{inferred parameter}, the
    1830 expression is not a constant expression.
     1504\nonterm{type-parameter}, it yields the size in bytes of the type that implements the operand.
     1505When the operand is an opaque type or an inferred type parameter\index{inferred parameter}, the expression is not a constant expression.
    18311506
    18321507When \lstinline$_Alignof$ is applied to an identifier declared by a \nonterm{type-declaration} or a
    1833 \nonterm{type-parameter}, it yields the alignment requirement of the type that implements the
    1834 operand. When the operand is an opaque type or an inferred type parameter\index{inferred
    1835 parameter}, the expression is not a constant expression.
     1508\nonterm{type-parameter}, it yields the alignment requirement of the type that implements the operand.
     1509When the operand is an opaque type or an inferred type parameter\index{inferred parameter}, the expression is not a constant expression.
    18361510\begin{rationale}
    18371511\begin{lstlisting}
    18381512type Pair = struct { int first, second; };
    18391513size_t p_size = sizeof(Pair);           // constant expression
    1840 
    18411514extern type Rational;@\use{Rational}@
    18421515size_t c_size = sizeof(Rational);       // non-constant expression
    1843 
    18441516forall(type T) T f(T p1, T p2) {
    18451517        size_t t_size = sizeof(T);              // non-constant expression
     
    18471519}
    18481520\end{lstlisting}
    1849 ``\lstinline$sizeof Rational$'', although not statically known, is fixed. Within \lstinline$f()$,
     1521``\lstinline$sizeof Rational$'', although not statically known, is fixed.
     1522Within \lstinline$f()$,
    18501523``\lstinline$sizeof(T)$'' is fixed for each call of \lstinline$f()$, but may vary from call to call.
    18511524\end{rationale}
     
    18671540
    18681541In a \Index{cast expression} ``\lstinline$($\nonterm{type-name}\lstinline$)e$'', if
    1869 \nonterm{type-name} is the type of an interpretation of \lstinline$e$, then that interpretation is
    1870 the only interpretation of the cast expression; otherwise, \lstinline$e$ shall have some
    1871 interpretation that can be converted to \nonterm{type-name}, and the interpretation of the cast
    1872 expression is the cast of the interpretation that can be converted at the lowest cost. The cast
    1873 expression's interpretation is ambiguous\index{ambiguous interpretation} if more than one
    1874 interpretation can be converted at the lowest cost or if the selected interpretation is ambiguous.
    1875 
    1876 \begin{rationale}
    1877 Casts can be used to eliminate ambiguity in expressions by selecting interpretations of
    1878 subexpressions, and to specialize polymorphic functions and values.
     1542\nonterm{type-name} is the type of an interpretation of \lstinline$e$, then that interpretation is the only interpretation of the cast expression;
     1543otherwise, \lstinline$e$ shall have some interpretation that can be converted to \nonterm{type-name}, and the interpretation of the cast expression is the cast of the interpretation that can be converted at the lowest cost.
     1544The cast expression's interpretation is ambiguous\index{ambiguous interpretation} if more than one interpretation can be converted at the lowest cost or if the selected interpretation is ambiguous.
     1545
     1546\begin{rationale}
     1547Casts can be used to eliminate ambiguity in expressions by selecting interpretations of subexpressions, and to specialize polymorphic functions and values.
    18791548\end{rationale}
    18801549
     
    18991568\predefined
    19001569\begin{lstlisting}
    1901 int?*?( int, int ),
    1902         ?/?( int, int ),
    1903         ?%?( int, int );
    1904 unsigned int?*?( unsigned int, unsigned int ),
    1905         ?/?( unsigned int, unsigned int ),
    1906         ?%?( unsigned int, unsigned int );
    1907 long int?*?( long int, long int ),
    1908         ?/?( long, long ),
    1909         ?%?( long, long );
     1570int?*?( int, int ), ?/?( int, int ), ?%?( int, int );
     1571unsigned int?*?( unsigned int, unsigned int ), ?/?( unsigned int, unsigned int ), ?%?( unsigned int, unsigned int );
     1572long int?*?( long int, long int ), ?/?( long, long ), ?%?( long, long );
    19101573long unsigned int?*?( long unsigned int, long unsigned int ),
    1911         ?/?( long unsigned int, long unsigned int ),
    1912         ?%?( long unsigned int, long unsigned int );
    1913 long long int?*?( long long int, long long int ),
    1914         ?/?( long long int, long long int ),
     1574        ?/?( long unsigned int, long unsigned int ), ?%?( long unsigned int, long unsigned int );
     1575long long int?*?( long long int, long long int ), ?/?( long long int, long long int ),
    19151576        ?%?( long long int, long long int );
    19161577long long unsigned int ?*?( long long unsigned int, long long unsigned int ),
    1917         ?/?( long long unsigned int, long long unsigned int ),
    1918         ?%?( long long unsigned int, long long unsigned int );
    1919 float?*?( float, float ),
    1920         ?/?( float, float );
    1921 double?*?( double, double ),
    1922         ?/?( double, double );
    1923 long double?*?( long double, long double ),
    1924         ?/?( long double, long double );
    1925 _Complex float?*?( float, _Complex float ),
    1926         ?/?( float, _Complex float ),
    1927         ?*?( _Complex float, float ),
    1928         ?/?( _Complex float, float ),
    1929         ?*?( _Complex float, _Complex float ),
    1930         ?/?( _Complex float, _Complex float );
    1931 _Complex double?*?( double, _Complex double ),
    1932         ?/?( double, _Complex double ),
    1933         ?*?( _Complex double, double ),
    1934         ?/?( _Complex double, double ),
    1935         ?*?( _Complex double, _Complex double ),
    1936         ?/?( _Complex double, _Complex double );
    1937 _Complex long double?*?( long double, _Complex long double ),
    1938         ?/?( long double, _Complex long double ),
    1939         ?*?( _Complex long double, long double ),
    1940         ?/?( _Complex long double, long double ),
    1941         ?*?( _Complex long double, _Complex long double ),
    1942         ?/?( _Complex long double, _Complex long double );
    1943 \end{lstlisting}
    1944 For every extended integer type \lstinline$X$ with \Index{integer conversion rank} greater than the
    1945 rank of \lstinline$int$ there exist
     1578        ?/?( long long unsigned int, long long unsigned int ), ?%?( long long unsigned int, long long unsigned int );
     1579float?*?( float, float ), ?/?( float, float );
     1580double?*?( double, double ), ?/?( double, double );
     1581long double?*?( long double, long double ), ?/?( long double, long double );
     1582_Complex float?*?( float, _Complex float ), ?/?( float, _Complex float ),
     1583        ?*?( _Complex float, float ), ?/?( _Complex float, float ),
     1584        ?*?( _Complex float, _Complex float ), ?/?( _Complex float, _Complex float );
     1585_Complex double?*?( double, _Complex double ), ?/?( double, _Complex double ),
     1586        ?*?( _Complex double, double ), ?/?( _Complex double, double ),
     1587        ?*?( _Complex double, _Complex double ), ?/?( _Complex double, _Complex double );
     1588_Complex long double?*?( long double, _Complex long double ), ?/?( long double, _Complex long double ),
     1589        ?*?( _Complex long double, long double ), ?/?( _Complex long double, long double ),
     1590        ?*?( _Complex long double, _Complex long double ), ?/?( _Complex long double, _Complex long double );
     1591\end{lstlisting}
     1592For every extended integer type \lstinline$X$ with \Index{integer conversion rank} greater than the rank of \lstinline$int$ there exist
    19461593% Don't use predefined: keep this out of prelude.cf.
    19471594\begin{lstlisting}
     
    19511598\begin{rationale}
    19521599{\c11} does not include conversions from the \Index{real type}s to \Index{complex type}s in the
    1953 \Index{usual arithmetic conversion}s.  Instead it specifies conversion of the result of binary
    1954 operations on arguments from mixed type domains. \CFA's predefined operators match that pattern.
     1600\Index{usual arithmetic conversion}s.  Instead it specifies conversion of the result of binary operations on arguments from mixed type domains. \CFA's predefined operators match that pattern.
    19551601\end{rationale}
    19561602
    19571603\semantics
    1958 The interpretations of multiplicative expressions are the interpretations of the corresponding
    1959 function call.
     1604The interpretations of multiplicative expressions are the interpretations of the corresponding function call.
    19601605
    19611606\examples
     
    19661611eat_double( li % i );
    19671612\end{lstlisting}
    1968 ``\lstinline$li % i$'' is rewritten as ``\lstinline$?%?(li, i )$''. The valid interpretations
    1969 of \lstinline$?%?(li, i )$, the cost\index{conversion cost} of converting their arguments, and
    1970 the cost of converting the result to \lstinline$double$ (assuming no extended integer types are
    1971 present ) are
     1613``\lstinline$li % i$'' is rewritten as ``\lstinline$?%?(li, i )$''.
     1614The valid interpretations of \lstinline$?%?(li, i )$, the cost\index{conversion cost} of converting their arguments, and the cost of converting the result to \lstinline$double$ (assuming no extended integer types are present ) are
    19721615\begin{center}
    1973 \begin{tabular}{lcc}
    1974 interpretation & argument cost & result cost \\
     1616\begin{tabular}{lcc} interpretation & argument cost & result cost \\
    19751617\hline
    19761618\lstinline$ ?%?( (int)li, i )$                                                                          & (unsafe)      & 6     \\
    19771619\lstinline$ ?%?( (unsigned)li,(unsigned)i )$                                            & (unsafe)      & 5     \\
    1978 \lstinline$ ?%?(li,(long)i )$                                                                           & 1                     & 4     \\
     1620\lstinline$ ?%?( li, (long)i )$                                                                         & 1                     & 4     \\
    19791621\lstinline$ ?%?( (long unsigned)li,(long unsigned)i )$                          & 3                     & 3     \\
    19801622\lstinline$ ?%?( (long long)li,(long long)i )$                                          & 5                     & 2     \\
     
    19831625\end{center}
    19841626The best interpretation of \lstinline$eat_double( li, i )$ is
    1985 \lstinline$eat_double( (double)?%?(li, (long)i ))$, which has no unsafe conversions and the
    1986 lowest total cost.
    1987 
    1988 \begin{rationale}
    1989 {\c11} defines most arithmetic operations to apply an \Index{integer promotion} to any argument that
    1990 belongs to a type that has an \Index{integer conversion rank} less than that of \lstinline$int$.If
     1627\lstinline$eat_double( (double)?%?(li, (long)i ))$, which has no unsafe conversions and the lowest total cost.
     1628
     1629\begin{rationale}
     1630{\c11} defines most arithmetic operations to apply an \Index{integer promotion} to any argument that belongs to a type that has an \Index{integer conversion rank} less than that of \lstinline$int$.If
    19911631\lstinline$s$ is a \lstinline$short int$, ``\lstinline$s *s$'' does not have type \lstinline$short int$;
    1992 it is treated as ``\lstinline$( (int)s ) * ( (int)s )$'', and has type \lstinline$int$. \CFA matches
    1993 that pattern; it does not predefine ``\lstinline$short ?*?( short, short )$''.
    1994 
    1995 These ``missing'' operators limit polymorphism. Consider
     1632it is treated as ``\lstinline$( (int)s ) * ( (int)s )$'', and has type \lstinline$int$. \CFA matches that pattern;
     1633it does not predefine ``\lstinline$short ?*?( short, short )$''.
     1634
     1635These ``missing'' operators limit polymorphism.
     1636Consider
    19961637\begin{lstlisting}
    19971638forall( type T | T ?*?( T, T ) ) T square( T );
     
    20011642Since \CFA does not define a multiplication operator for \lstinline$short int$,
    20021643\lstinline$square( s )$ is treated as \lstinline$square( (int)s )$, and the result has type
    2003 \lstinline$int$. This is mildly surprising, but it follows the {\c11} operator pattern.
     1644\lstinline$int$.
     1645This is mildly surprising, but it follows the {\c11} operator pattern.
    20041646
    20051647A more troubling example is
     
    20101652\end{lstlisting}
    20111653This has no valid interpretations, because \CFA has no conversion from ``array of
    2012 \lstinline$short int$'' to ``array of \lstinline$int$''. The alternatives in such situations
    2013 include
     1654\lstinline$short int$'' to ``array of \lstinline$int$''.
     1655The alternatives in such situations include
    20141656\begin{itemize}
    20151657\item
     
    20201662\lstinline$product$.
    20211663\item
    2022 Defining \lstinline$product$ to take as an argument a conversion function from the ``small'' type to
    2023 the operator's argument type.
     1664Defining \lstinline$product$ to take as an argument a conversion function from the ``small'' type to the operator's argument type.
    20241665\end{itemize}
    20251666\end{rationale}
     
    20431684\predefined
    20441685\begin{lstlisting}
    2045 int?+?( int, int ),
    2046         ?-?( int, int );
    2047 unsigned int?+?( unsigned int, unsigned int ),
    2048         ?-?( unsigned int, unsigned int );
    2049 long int?+?( long int, long int ),
    2050         ?-?( long int, long int );
    2051 long unsigned int?+?( long unsigned int, long unsigned int ),
    2052         ?-?( long unsigned int, long unsigned int );
    2053 long long int?+?( long long int, long long int ),
    2054         ?-?( long long int, long long int );
     1686int?+?( int, int ), ?-?( int, int );
     1687unsigned int?+?( unsigned int, unsigned int ), ?-?( unsigned int, unsigned int );
     1688long int?+?( long int, long int ), ?-?( long int, long int );
     1689long unsigned int?+?( long unsigned int, long unsigned int ), ?-?( long unsigned int, long unsigned int );
     1690long long int?+?( long long int, long long int ), ?-?( long long int, long long int );
    20551691long long unsigned int ?+?( long long unsigned int, long long unsigned int ),
    20561692        ?-?( long long unsigned int, long long unsigned int );
    2057 float?+?( float, float ),
    2058         ?-?( float, float );
    2059 double?+?( double, double ),
    2060         ?-?( double, double );
    2061 long double?+?( long double, long double ),
    2062         ?-?( long double, long double );
    2063 _Complex float?+?( _Complex float, float ),
    2064         ?-?( _Complex float, float ),
    2065         ?+?( float, _Complex float ),
    2066         ?-?( float, _Complex float ),
    2067         ?+?( _Complex float, _Complex float ),
    2068         ?-?( _Complex float, _Complex float );
    2069 _Complex double?+?( _Complex double, double ),
    2070         ?-?( _Complex double, double ),
    2071         ?+?( double, _Complex double ),
    2072         ?-?( double, _Complex double ),
    2073         ?+?( _Complex double, _Complex double ),
    2074         ?-?( _Complex double, _Complex double );
    2075 _Complex long double?+?( _Complex long double, long double ),
    2076         ?-?( _Complex long double, long double ),
    2077         ?+?( long double, _Complex long double ),
    2078         ?-?( long double, _Complex long double ),
    2079         ?+?( _Complex long double, _Complex long double ),
    2080         ?-?( _Complex long double, _Complex long double );
    2081 
    2082 forall( type T ) T
    2083         * ?+?( T *, ptrdiff_t ),
    2084         * ?+?( ptrdiff_t, T * ),
    2085         * ?-?( T *, ptrdiff_t );
    2086 
    2087 forall( type T ) _Atomic T
    2088         * ?+?( _Atomic T *, ptrdiff_t ),
    2089         * ?+?( ptrdiff_t, _Atomic T * ),
     1693float?+?( float, float ), ?-?( float, float );
     1694double?+?( double, double ), ?-?( double, double );
     1695long double?+?( long double, long double ), ?-?( long double, long double );
     1696_Complex float?+?( _Complex float, float ), ?-?( _Complex float, float ),
     1697        ?+?( float, _Complex float ), ?-?( float, _Complex float ),
     1698        ?+?( _Complex float, _Complex float ), ?-?( _Complex float, _Complex float );
     1699_Complex double?+?( _Complex double, double ), ?-?( _Complex double, double ),
     1700        ?+?( double, _Complex double ), ?-?( double, _Complex double ),
     1701        ?+?( _Complex double, _Complex double ), ?-?( _Complex double, _Complex double );
     1702_Complex long double?+?( _Complex long double, long double ), ?-?( _Complex long double, long double ),
     1703        ?+?( long double, _Complex long double ), ?-?( long double, _Complex long double ),
     1704        ?+?( _Complex long double, _Complex long double ), ?-?( _Complex long double, _Complex long double );
     1705
     1706forall( type T ) T * ?+?( T *, ptrdiff_t ), * ?+?( ptrdiff_t, T * ), * ?-?( T *, ptrdiff_t );
     1707forall( type T ) _Atomic T * ?+?( _Atomic T *, ptrdiff_t ), * ?+?( ptrdiff_t, _Atomic T * ),
    20901708        * ?-?( _Atomic T *, ptrdiff_t );
    2091 
    2092 forall( type T ) const T
    2093         * ?+?( const T *, ptrdiff_t ),
    2094         * ?+?( ptrdiff_t, const T * ),
     1709forall( type T ) const T * ?+?( const T *, ptrdiff_t ), * ?+?( ptrdiff_t, const T * ),
    20951710        * ?-?( const T *, ptrdiff_t );
    2096 
    2097 forall( type T ) restrict T
    2098         * ?+?( restrict T *, ptrdiff_t ),
    2099         * ?+?( ptrdiff_t, restrict T * ),
     1711forall( type T ) restrict T * ?+?( restrict T *, ptrdiff_t ), * ?+?( ptrdiff_t, restrict T * ),
    21001712        * ?-?( restrict T *, ptrdiff_t );
    2101 
    2102 forall( type T ) volatile T
    2103         * ?+?( volatile T *, ptrdiff_t ),
    2104         * ?+?( ptrdiff_t, volatile T * ),
     1713forall( type T ) volatile T * ?+?( volatile T *, ptrdiff_t ), * ?+?( ptrdiff_t, volatile T * ),
    21051714        * ?-?( volatile T *, ptrdiff_t );
    2106 
    2107 forall( type T ) _Atomic const T
    2108         * ?+?( _Atomic const T *, ptrdiff_t ),
    2109         * ?+?( ptrdiff_t, _Atomic const T * ),
     1715forall( type T ) _Atomic const T * ?+?( _Atomic const T *, ptrdiff_t ), * ?+?( ptrdiff_t, _Atomic const T * ),
    21101716        * ?-?( _Atomic const T *, ptrdiff_t );
    2111 
    2112 forall( type T ) _Atomic restrict T
    2113         * ?+?( _Atomic restrict T *, ptrdiff_t ),
    2114         * ?+?( ptrdiff_t, _Atomic restrict T * ),
     1717forall( type T ) _Atomic restrict T * ?+?( _Atomic restrict T *, ptrdiff_t ), * ?+?( ptrdiff_t, _Atomic restrict T * ),
    21151718        * ?-?( _Atomic restrict T *, ptrdiff_t );
    2116 
    2117 forall( type T ) _Atomic volatile T
    2118         * ?+?( _Atomic volatile T *, ptrdiff_t ),
    2119         * ?+?( ptrdiff_t, _Atomic volatile T * ),
     1719forall( type T ) _Atomic volatile T * ?+?( _Atomic volatile T *, ptrdiff_t ), * ?+?( ptrdiff_t, _Atomic volatile T * ),
    21201720        * ?-?( _Atomic volatile T *, ptrdiff_t );
    2121 
    2122 forall( type T ) const restrict T
    2123         * ?+?( const restrict T *, ptrdiff_t ),
    2124         * ?+?( ptrdiff_t, const restrict T * ),
     1721forall( type T ) const restrict T * ?+?( const restrict T *, ptrdiff_t ), * ?+?( ptrdiff_t, const restrict T * ),
    21251722        * ?-?( const restrict T *, ptrdiff_t );
    2126 
    2127 forall( type T ) const volatile T
    2128         * ?+?( const volatile T *, ptrdiff_t ),
    2129         * ?+?( ptrdiff_t, const volatile T * ),
     1723forall( type T ) const volatile T * ?+?( const volatile T *, ptrdiff_t ), * ?+?( ptrdiff_t, const volatile T * ),
    21301724        * ?-?( const volatile T *, ptrdiff_t );
    2131 
    2132 forall( type T ) restrict volatile T
    2133         * ?+?( restrict volatile T *, ptrdiff_t ),
    2134         * ?+?( ptrdiff_t, restrict volatile T * ),
     1725forall( type T ) restrict volatile T * ?+?( restrict volatile T *, ptrdiff_t ), * ?+?( ptrdiff_t, restrict volatile T * ),
    21351726        * ?-?( restrict volatile T *, ptrdiff_t );
    2136 
    2137 forall( type T ) _Atomic const restrict T
    2138         * ?+?( _Atomic const restrict T *, ptrdiff_t ),
     1727forall( type T ) _Atomic const restrict T * ?+?( _Atomic const restrict T *, ptrdiff_t ),
    21391728        * ?+?( ptrdiff_t, _Atomic const restrict T * ),
    21401729        * ?-?( _Atomic const restrict T *, ptrdiff_t );
    2141 
    21421730forall( type T ) ptrdiff_t
    21431731        * ?-?( const restrict volatile T *, const restrict volatile T * ),
    21441732        * ?-?( _Atomic const restrict volatile T *, _Atomic const restrict volatile T * );
    21451733\end{lstlisting}
    2146 For every extended integer type \lstinline$X$ with \Index{integer conversion rank} greater than the
    2147 rank of \lstinline$int$ there exist
     1734For every extended integer type \lstinline$X$ with \Index{integer conversion rank} greater than the rank of \lstinline$int$ there exist
    21481735% Don't use predefined: keep this out of prelude.cf.
    21491736\begin{lstlisting}
     
    21521739
    21531740\semantics
    2154 The interpretations of additive expressions are the interpretations of the corresponding function
    2155 calls.
    2156 
    2157 \begin{rationale}
    2158 \lstinline$ptrdiff_t$ is an implementation-defined identifier defined in \lstinline$<stddef.h>$ that
    2159 is synonymous with a signed integral type that is large enough to hold the difference between two
    2160 pointers. It seems reasonable to use it for pointer addition as well. (This is technically a
    2161 difference between \CFA and C, which only specifies that pointer addition uses an \emph{integral}
    2162 argument.) Hence it is also used for subscripting, which is defined in terms of pointer addition.
    2163 The {\c11} standard uses \lstinline$size_t$ in several cases where a library function takes an
    2164 argument that is used as a subscript, but \lstinline$size_t$ is unsuitable here because it is an
    2165 unsigned type.
     1741The interpretations of additive expressions are the interpretations of the corresponding function calls.
     1742
     1743\begin{rationale}
     1744\lstinline$ptrdiff_t$ is an implementation-defined identifier defined in \lstinline$<stddef.h>$ that is synonymous with a signed integral type that is large enough to hold the difference between two pointers.
     1745It seems reasonable to use it for pointer addition as well. (This is technically a difference between \CFA and C, which only specifies that pointer addition uses an \emph{integral} argument.) Hence it is also used for subscripting, which is defined in terms of pointer addition.
     1746The {\c11} standard uses \lstinline$size_t$ in several cases where a library function takes an argument that is used as a subscript, but \lstinline$size_t$ is unsuitable here because it is an unsigned type.
    21661747\end{rationale}
    21671748
     
    21841765\predefined
    21851766\begin{lstlisting}
    2186 int ?<<?( int, int ),
    2187          ?>>?( int, int );
    2188 unsigned int ?<<?( unsigned int, int ),
    2189          ?>>?( unsigned int, int );
    2190 long int ?<<?( long int, int ),
    2191          ?>>?( long int, int );
    2192 long unsigned int ?<<?( long unsigned int, int ),
    2193          ?>>?( long unsigned int, int );
    2194 long long int ?<<?( long long int, int ),
    2195          ?>>?( long long int, int );
    2196 long long unsigned int ?<<?( long long unsigned int, int ),
    2197          ?>>?( long long unsigned int, int);
    2198 \end{lstlisting}
    2199 For every extended integer type \lstinline$X$ with \Index{integer conversion rank} greater than the
    2200 rank of \lstinline$int$ there exist
     1767int ?<<?( int, int ), ?>>?( int, int );
     1768unsigned int ?<<?( unsigned int, int ), ?>>?( unsigned int, int );
     1769long int ?<<?( long int, int ), ?>>?( long int, int );
     1770long unsigned int ?<<?( long unsigned int, int ), ?>>?( long unsigned int, int );
     1771long long int ?<<?( long long int, int ), ?>>?( long long int, int );
     1772long long unsigned int ?<<?( long long unsigned int, int ), ?>>?( long long unsigned int, int);
     1773\end{lstlisting}
     1774For every extended integer type \lstinline$X$ with \Index{integer conversion rank} greater than the rank of \lstinline$int$ there exist
    22011775% Don't use predefined: keep this out of prelude.cf.
    22021776\begin{lstlisting}
     
    22051779
    22061780\begin{rationale}
    2207 The bitwise shift operators break the usual pattern: they do not convert both operands to a common
    2208 type. The right operand only undergoes \Index{integer promotion}.
     1781The bitwise shift operators break the usual pattern: they do not convert both operands to a common type.
     1782The right operand only undergoes \Index{integer promotion}.
    22091783\end{rationale}
    22101784
    22111785\semantics
    2212 The interpretations of a bitwise shift expression are the interpretations of the corresponding
    2213 function calls.
     1786The interpretations of a bitwise shift expression are the interpretations of the corresponding function calls.
    22141787
    22151788
     
    22351808\predefined
    22361809\begin{lstlisting}
    2237 int ?<?( int, int ),
    2238         ?<=?( int, int ),
    2239         ?>?( int, int ),
    2240         ?>=?( int, int );
    2241 int ?<?( unsigned int, unsigned int ),
    2242         ?<=?( unsigned int, unsigned int ),
    2243         ?>?( unsigned int, unsigned int ),
    2244         ?>=?( unsigned int, unsigned int );
    2245 int ?<?( long int, long int ),
    2246         ?<=?( long int, long int ),
    2247         ?>?( long int, long int ),
    2248         ?>=?( long int, long int );
    2249 int ?<?( long unsigned int, long unsigned ),
    2250         ?<=?( long unsigned int, long unsigned ),
    2251         ?>?( long unsigned int, long unsigned ),
    2252         ?>=?( long unsigned int, long unsigned );
    2253 int ?<?( long long int, long long int ),
    2254         ?<=?( long long int, long long int ),
    2255         ?>?( long long int, long long int ),
    2256         ?>=?( long long int, long long int );
    2257 int ?<?( long long unsigned int, long long unsigned ),
    2258         ?<=?( long long unsigned int, long long unsigned ),
    2259         ?>?( long long unsigned int, long long unsigned ),
    2260         ?>=?( long long unsigned int, long long unsigned );
    2261 int ?<?( float, float ),
    2262         ?<=?( float, float ),
    2263         ?>?( float, float ),
    2264         ?>=?( float, float );
    2265 int ?<?( double, double ),
    2266         ?<=?( double, double ),
    2267         ?>?( double, double ),
    2268         ?>=?( double, double );
    2269 int ?<?( long double, long double ),
    2270         ?<=?( long double, long double ),
    2271         ?>?( long double, long double ),
    2272         ?>=?( long double, long double );
    2273 
    2274 forall( dtype DT ) int
    2275         ?<?( const restrict volatile DT *, const restrict volatile DT * ),
     1810int ?<?( int, int ), ?<=?( int, int ),
     1811        ?>?( int, int ), ?>=?( int, int );
     1812int ?<?( unsigned int, unsigned int ), ?<=?( unsigned int, unsigned int ),
     1813        ?>?( unsigned int, unsigned int ), ?>=?( unsigned int, unsigned int );
     1814int ?<?( long int, long int ), ?<=?( long int, long int ),
     1815        ?>?( long int, long int ), ?>=?( long int, long int );
     1816int ?<?( long unsigned int, long unsigned ), ?<=?( long unsigned int, long unsigned ),
     1817        ?>?( long unsigned int, long unsigned ), ?>=?( long unsigned int, long unsigned );
     1818int ?<?( long long int, long long int ), ?<=?( long long int, long long int ),
     1819        ?>?( long long int, long long int ), ?>=?( long long int, long long int );
     1820int ?<?( long long unsigned int, long long unsigned ), ?<=?( long long unsigned int, long long unsigned ),
     1821        ?>?( long long unsigned int, long long unsigned ), ?>=?( long long unsigned int, long long unsigned );
     1822int ?<?( float, float ), ?<=?( float, float ),
     1823        ?>?( float, float ), ?>=?( float, float );
     1824int ?<?( double, double ), ?<=?( double, double ),
     1825        ?>?( double, double ), ?>=?( double, double );
     1826int ?<?( long double, long double ), ?<=?( long double, long double ),
     1827        ?>?( long double, long double ), ?>=?( long double, long double );
     1828forall( dtype DT ) int ?<?( const restrict volatile DT *, const restrict volatile DT * ),
    22761829        ?<?( _Atomic const restrict volatile DT *, _Atomic const restrict volatile DT * ),
    22771830        ?<=?( const restrict volatile DT *, const restrict volatile DT * ),
     
    22821835        ?>=?( _Atomic const restrict volatile DT *, _Atomic const restrict volatile DT * );
    22831836\end{lstlisting}
    2284 For every extended integer type \lstinline$X$ with \Index{integer conversion rank} greater than the
    2285 rank of \lstinline$int$ there exist
     1837For every extended integer type \lstinline$X$ with \Index{integer conversion rank} greater than the rank of \lstinline$int$ there exist
    22861838% Don't use predefined: keep this out of prelude.cf.
    22871839\begin{lstlisting}
     
    22931845
    22941846\semantics
    2295 The interpretations of a relational expression are the interpretations of the corresponding function
    2296 call.
     1847The interpretations of a relational expression are the interpretations of the corresponding function call.
    22971848
    22981849
     
    23141865\predefined
    23151866\begin{lstlisting}
    2316 int ?==?( int, int ),
    2317         ?!=?( int, int ),
    2318         ?==?( unsigned int, unsigned int ),
    2319         ?!=?( unsigned int, unsigned int ),
    2320         ?==?( long int, long int ),
    2321         ?!=?( long int, long int ),
    2322         ?==?( long unsigned int, long unsigned int ),
    2323         ?!=?( long unsigned int, long unsigned int ),
    2324         ?==?( long long int, long long int ),
    2325         ?!=?( long long int, long long int ),
    2326         ?==?( long long unsigned int, long long unsigned int ),
    2327         ?!=?( long long unsigned int, long long unsigned int ),
    2328         ?==?( float, float ),
    2329         ?!=?( float, float ),
    2330         ?==?( _Complex float, float ),
    2331         ?!=?( _Complex float, float ),
    2332         ?==?( float, _Complex float ),
    2333         ?!=?( float, _Complex float ),
    2334         ?==?( _Complex float, _Complex float ),
    2335         ?!=?( _Complex float, _Complex float ),
    2336         ?==?( double, double ),
    2337         ?!=?( double, double ),
    2338         ?==?( _Complex double, double ),
    2339         ?!=?( _Complex double, double ),
    2340         ?==?( double, _Complex double ),
    2341         ?!=?( double, _Complex double ),
    2342         ?==?( _Complex double, _Complex double ),
    2343         ?!=?( _Complex double, _Complex double ),
    2344         ?==?( long double, long double ),
    2345         ?!=?( long double, long double ),
    2346         ?==?( _Complex long double, long double ),
    2347         ?!=?( _Complex long double, long double ),
    2348         ?==?( long double, _Complex long double ),
    2349         ?!=?( long double, _Complex long double ),
    2350         ?==?( _Complex long double, _Complex long double ),
    2351         ?!=?( _Complex long double, _Complex long double );
    2352 
     1867int ?==?( int, int ), ?!=?( int, int ),
     1868        ?==?( unsigned int, unsigned int ), ?!=?( unsigned int, unsigned int ),
     1869        ?==?( long int, long int ), ?!=?( long int, long int ),
     1870        ?==?( long unsigned int, long unsigned int ), ?!=?( long unsigned int, long unsigned int ),
     1871        ?==?( long long int, long long int ), ?!=?( long long int, long long int ),
     1872        ?==?( long long unsigned int, long long unsigned int ), ?!=?( long long unsigned int, long long unsigned int ),
     1873        ?==?( float, float ), ?!=?( float, float ),
     1874        ?==?( _Complex float, float ), ?!=?( _Complex float, float ),
     1875        ?==?( float, _Complex float ), ?!=?( float, _Complex float ),
     1876        ?==?( _Complex float, _Complex float ), ?!=?( _Complex float, _Complex float ),
     1877        ?==?( double, double ), ?!=?( double, double ),
     1878        ?==?( _Complex double, double ), ?!=?( _Complex double, double ),
     1879        ?==?( double, _Complex double ), ?!=?( double, _Complex double ),
     1880        ?==?( _Complex double, _Complex double ), ?!=?( _Complex double, _Complex double ),
     1881        ?==?( long double, long double ), ?!=?( long double, long double ),
     1882        ?==?( _Complex long double, long double ), ?!=?( _Complex long double, long double ),
     1883        ?==?( long double, _Complex long double ), ?!=?( long double, _Complex long double ),
     1884        ?==?( _Complex long double, _Complex long double ), ?!=?( _Complex long double, _Complex long double );
    23531885forall( dtype DT ) int
    23541886        ?==?( const restrict volatile DT *, const restrict volatile DT * ),
     
    23751907        ?==?( forall( dtype DT2) const DT2*, _Atomic const restrict volatile DT * ),
    23761908        ?!=?( forall( dtype DT2) const DT2*, _Atomic const restrict volatile DT * );
    2377 
    23781909forall( ftype FT ) int
    2379         ?==?( FT *, FT * ),
    2380         ?!=?( FT *, FT * ),
    2381         ?==?( FT *, forall( ftype FT2) FT2 * ),
    2382         ?!=?( FT *, forall( ftype FT2) FT2 * ),
    2383         ?==?( forall( ftype FT2) FT2*, FT * ),
    2384         ?!=?( forall( ftype FT2) FT2*, FT * ),
    2385         ?==?( forall( ftype FT2) FT2*, forall( ftype FT3) FT3 * ),
    2386         ?!=?( forall( ftype FT2) FT2*, forall( ftype FT3) FT3 * );
    2387 \end{lstlisting}
    2388 For every extended integer type \lstinline$X$ with \Index{integer conversion rank} greater than the
    2389 rank of \lstinline$int$ there exist
     1910        ?==?( FT *, FT * ), ?!=?( FT *, FT * ),
     1911        ?==?( FT *, forall( ftype FT2) FT2 * ), ?!=?( FT *, forall( ftype FT2) FT2 * ),
     1912        ?==?( forall( ftype FT2) FT2*, FT * ), ?!=?( forall( ftype FT2) FT2*, FT * ),
     1913        ?==?( forall( ftype FT2) FT2*, forall( ftype FT3) FT3 * ), ?!=?( forall( ftype FT2) FT2*, forall( ftype FT3) FT3 * );
     1914\end{lstlisting}
     1915For every extended integer type \lstinline$X$ with \Index{integer conversion rank} greater than the rank of \lstinline$int$ there exist
    23901916% Don't use predefined: keep this out of prelude.cf.
    23911917\begin{lstlisting}
     
    23951921
    23961922\begin{rationale}
    2397 The polymorphic equality operations come in three styles: comparisons between pointers of compatible
    2398 types, between pointers to \lstinline$void$ and pointers to object types or incomplete types, and
    2399 between the \Index{null pointer} constant and pointers to any type. In the last case, a special
    2400 constraint rule for null pointer constant operands has been replaced by a consequence of the \CFA
    2401 type system.
     1923The polymorphic equality operations come in three styles: comparisons between pointers of compatible types, between pointers to \lstinline$void$ and pointers to object types or incomplete types, and between the \Index{null pointer} constant and pointers to any type.
     1924In the last case, a special constraint rule for null pointer constant operands has been replaced by a consequence of the \CFA type system.
    24021925\end{rationale}
    24031926
    24041927\semantics
    2405 The interpretations of an equality expression are the interpretations of the corresponding function
    2406 call.
     1928The interpretations of an equality expression are the interpretations of the corresponding function call.
    24071929
    24081930\begin{sloppypar}
    2409 The result of an equality comparison between two pointers to predefined functions or predefined
    2410 values is implementation-defined.
     1931The result of an equality comparison between two pointers to predefined functions or predefined values is implementation-defined.
    24111932\end{sloppypar}
    24121933\begin{rationale}
    2413 The implementation-defined status of equality comparisons allows implementations to use one library
    2414 routine to implement many predefined functions. These optimization are particularly important when
    2415 the predefined functions are polymorphic, as is the case for most pointer operations
     1934The implementation-defined status of equality comparisons allows implementations to use one library routine to implement many predefined functions.
     1935These optimization are particularly important when the predefined functions are polymorphic, as is the case for most pointer operations
    24161936\end{rationale}
    24171937
     
    24391959long long unsigned int ?&?( long long unsigned int, long long unsigned int );
    24401960\end{lstlisting}
    2441 For every extended integer type \lstinline$X$ with \Index{integer conversion rank} greater than the
    2442 rank of \lstinline$int$ there exist
     1961For every extended integer type \lstinline$X$ with \Index{integer conversion rank} greater than the rank of \lstinline$int$ there exist
    24431962% Don't use predefined: keep this out of prelude.cf.
    24441963\begin{lstlisting}
     
    24471966
    24481967\semantics
    2449 The interpretations of a bitwise AND expression are the interpretations of the corresponding
    2450 function call.
     1968The interpretations of a bitwise AND expression are the interpretations of the corresponding function call.
    24511969
    24521970
     
    24731991long long unsigned int ?^?( long long unsigned int, long long unsigned int );
    24741992\end{lstlisting}
    2475 For every extended integer type \lstinline$X$ with \Index{integer conversion rank} greater than the
    2476 rank of \lstinline$int$ there exist
     1993For every extended integer type \lstinline$X$ with \Index{integer conversion rank} greater than the rank of \lstinline$int$ there exist
    24771994% Don't use predefined: keep this out of prelude.cf.
    24781995\begin{lstlisting}
     
    24811998
    24821999\semantics
    2483 The interpretations of a bitwise exclusive OR expression are the interpretations of the
    2484 corresponding function call.
     2000The interpretations of a bitwise exclusive OR expression are the interpretations of the corresponding function call.
    24852001
    24862002
     
    25072023long long unsigned int ?|?( long long unsigned int, long long unsigned int );
    25082024\end{lstlisting}
    2509 For every extended integer type \lstinline$X$ with \Index{integer conversion rank} greater than the
    2510 rank of \lstinline$int$ there exist
     2025For every extended integer type \lstinline$X$ with \Index{integer conversion rank} greater than the rank of \lstinline$int$ there exist
    25112026% Don't use predefined: keep this out of prelude.cf.
    25122027\begin{lstlisting}
     
    25152030
    25162031\semantics
    2517 The interpretations of a bitwise inclusive OR expression are the interpretations of the
    2518 corresponding function call.
     2032The interpretations of a bitwise inclusive OR expression are the interpretations of the corresponding function call.
    25192033
    25202034
     
    25282042
    25292043\semantics The operands of the expression ``\lstinline$a && b$'' are treated as
    2530 ``\lstinline$(int)((a)!=0)$'' and ``\lstinline$(int)((b)!=0)$'', which shall both be
    2531 unambiguous. The expression has only one interpretation, which is of type \lstinline$int$.
    2532 \begin{rationale}
    2533 When the operands of a logical expression are values of built-in types, and ``\lstinline$!=$'' has
    2534 not been redefined for those types, the compiler can optimize away the function calls.
     2044``\lstinline$(int)((a)!=0)$'' and ``\lstinline$(int)((b)!=0)$'', which shall both be unambiguous.
     2045The expression has only one interpretation, which is of type \lstinline$int$.
     2046\begin{rationale}
     2047When the operands of a logical expression are values of built-in types, and ``\lstinline$!=$'' has not been redefined for those types, the compiler can optimize away the function calls.
    25352048
    25362049A common C idiom omits comparisons to \lstinline$0$ in the controlling expressions of loops and
    2537 \lstinline$if$ statements. For instance, the loop below iterates as long as \lstinline$rp$ points
    2538 at a \lstinline$Rational$ value that is non-zero.
     2050\lstinline$if$ statements.
     2051For instance, the loop below iterates as long as \lstinline$rp$ points at a \lstinline$Rational$ value that is non-zero.
    25392052
    25402053\begin{lstlisting}
     
    25432056extern int ?!=?( Rational, Rational );
    25442057Rational *rp;
    2545 
    25462058while ( rp && *rp ) { ... }
    25472059\end{lstlisting}
    2548 The logical expression calls the \lstinline$Rational$ inequality operator, passing
    2549 it \lstinline$*rp$ and the \lstinline$Rational 0$, and getting a 1 or 0 as a result. In
    2550 contrast, {\CC} would apply a programmer-defined \lstinline$Rational$-to-\lstinline$int$
    2551 conversion to \lstinline$*rp$ in the equivalent situation. The conversion to \lstinline$int$ would
    2552 produce a general integer value, which is unfortunate, and possibly dangerous if the conversion was
    2553 not written with this situation in mind.
     2060The logical expression calls the \lstinline$Rational$ inequality operator, passing it \lstinline$*rp$ and the \lstinline$Rational 0$, and getting a 1 or 0 as a result.
     2061In contrast, {\CC} would apply a programmer-defined \lstinline$Rational$-to-\lstinline$int$ conversion to \lstinline$*rp$ in the equivalent situation.
     2062The conversion to \lstinline$int$ would produce a general integer value, which is unfortunate, and possibly dangerous if the conversion was not written with this situation in mind.
    25542063\end{rationale}
    25552064
     
    25652074\semantics
    25662075
    2567 The operands of the expression ``\lstinline$a || b$'' are treated as ``\lstinline$(int)((a)!=0)$''
    2568 and ``\lstinline$(int)((b))!=0)$'', which shall both be unambiguous. The expression has only one
    2569 interpretation, which is of type \lstinline$int$.
     2076The operands of the expression ``\lstinline$a || b$'' are treated as ``\lstinline$(int)((a)!=0)$'' and ``\lstinline$(int)((b))!=0)$'', which shall both be unambiguous.
     2077The expression has only one interpretation, which is of type \lstinline$int$.
    25702078
    25712079
     
    25802088
    25812089\semantics
    2582 In the conditional expression\use{?:} ``\lstinline$a?b:c$'', if the second and
    2583 third operands both have an interpretation with \lstinline$void$ type, then the expression has an
    2584 interpretation with type \lstinline$void$, equivalent to
     2090In the conditional expression\use{?:} ``\lstinline$a?b:c$'', if the second and third operands both have an interpretation with \lstinline$void$ type, then the expression has an interpretation with type \lstinline$void$, equivalent to
    25852091\begin{lstlisting}
    25862092( int)(( a)!=0) ? ( void)( b) : ( void)( c)
    25872093\end{lstlisting}
    25882094
    2589 If the second and third operands both have interpretations with non-\lstinline$void$ types, the
    2590 expression is treated as if it were the call ``\lstinline$cond((a)!=0, b, c)$'',
    2591 with \lstinline$cond$ declared as
     2095If the second and third operands both have interpretations with non-\lstinline$void$ types, the expression is treated as if it were the call ``\lstinline$cond((a)!=0, b, c)$'', with \lstinline$cond$ declared as
    25922096\begin{lstlisting}
    25932097forall( type T ) T cond( int, T, T );
    2594  
    2595 forall( dtype D ) void
    2596         * cond( int, D *, void * ),
    2597         * cond( int, void *, D * );
    2598        
    2599 forall( dtype D ) _atomic void
    2600         * cond( int, _Atomic D *, _Atomic void * ),
    2601         * cond( int, _Atomic void *, _Atomic D * );
    2602 
    2603 forall( dtype D ) const void
    2604         * cond( int, const D *, const void * ),
    2605         * cond( int, const void *, const D * );
    2606 
    2607 forall( dtype D ) restrict void
    2608         * cond( int, restrict D *, restrict void * ),
    2609         * cond( int, restrict void *, restrict D * );
    2610 
    2611 forall( dtype D ) volatile void
    2612         * cond( int, volatile D *, volatile void * ),
    2613         * cond( int, volatile void *, volatile D * );
    2614 
    2615 forall( dtype D ) _Atomic const void
    2616         * cond( int, _Atomic const D *, _Atomic const void * ),
    2617         * cond( int, _Atomic const void *, _Atomic const D * );
    2618 
    2619 forall( dtype D ) _Atomic restrict void
    2620         * cond( int, _Atomic restrict D *, _Atomic restrict void * ),
    2621         * cond( int, _Atomic restrict void *, _Atomic restrict D * );
    2622 
    2623 forall( dtype D ) _Atomic volatile void
    2624         * cond( int, _Atomic volatile D *, _Atomic volatile void * ),
    2625         * cond( int, _Atomic volatile void *, _Atomic volatile D * );
    2626 
    2627 forall( dtype D ) const restrict void
    2628         * cond( int, const restrict D *, const restrict void * ),
    2629         * cond( int, const restrict void *, const restrict D * );
    2630 
    2631 forall( dtype D ) const volatile void
    2632         * cond( int, const volatile D *, const volatile void * ),
    2633         * cond( int, const volatile void *, const volatile D * );
    2634 
    2635 forall( dtype D ) restrict volatile void
    2636         * cond( int, restrict volatile D *, restrict volatile void * ),
    2637         * cond( int, restrict volatile void *, restrict volatile D * );
    2638 
    2639 forall( dtype D ) _Atomic const restrict void
    2640         * cond( int, _Atomic const restrict D *, _Atomic const restrict void * ),
     2098forall( dtype D ) void * cond( int, D *, void * ), * cond( int, void *, D * );
     2099forall( dtype D ) _atomic void * cond(
     2100        int, _Atomic D *, _Atomic void * ), * cond( int, _Atomic void *, _Atomic D * );
     2101forall( dtype D ) const void * cond(
     2102        int, const D *, const void * ), * cond( int, const void *, const D * );
     2103forall( dtype D ) restrict void * cond(
     2104        int, restrict D *, restrict void * ), * cond( int, restrict void *, restrict D * );
     2105forall( dtype D ) volatile void * cond(
     2106        int, volatile D *, volatile void * ), * cond( int, volatile void *, volatile D * );
     2107forall( dtype D ) _Atomic const void * cond(
     2108        int, _Atomic const D *, _Atomic const void * ), * cond( int, _Atomic const void *, _Atomic const D * );
     2109forall( dtype D ) _Atomic restrict void * cond(
     2110        int, _Atomic restrict D *, _Atomic restrict void * ), * cond( int, _Atomic restrict void *, _Atomic restrict D * );
     2111forall( dtype D ) _Atomic volatile void * cond(
     2112        int, _Atomic volatile D *, _Atomic volatile void * ), * cond( int, _Atomic volatile void *, _Atomic volatile D * );
     2113forall( dtype D ) const restrict void * cond(
     2114        int, const restrict D *, const restrict void * ), * cond( int, const restrict void *, const restrict D * );
     2115forall( dtype D ) const volatile void * cond(
     2116        int, const volatile D *, const volatile void * ), * cond( int, const volatile void *, const volatile D * );
     2117forall( dtype D ) restrict volatile void * cond(
     2118        int, restrict volatile D *, restrict volatile void * ), * cond( int, restrict volatile void *, restrict volatile D * );
     2119forall( dtype D ) _Atomic const restrict void * cond(
     2120        int, _Atomic const restrict D *, _Atomic const restrict void * ),
    26412121        * cond( int, _Atomic const restrict void *, _Atomic const restrict D * );
    2642 
    2643 forall( dtype D ) _Atomic const volatile void
    2644         * cond( int, _Atomic const volatile D *, _Atomic const volatile void * ),
     2122forall( dtype D ) _Atomic const volatile void * cond(
     2123        int, _Atomic const volatile D *, _Atomic const volatile void * ),
    26452124        * cond( int, _Atomic const volatile void *, _Atomic const volatile D * );
    2646 
    2647 forall( dtype D ) _Atomic restrict volatile void
    2648         * cond( int, _Atomic restrict volatile D *,
    2649          _Atomic restrict volatile void * ),
    2650         * cond( int, _Atomic restrict volatile void *,
    2651          _Atomic restrict volatile D * );
    2652 
    2653 forall( dtype D ) const restrict volatile void
    2654         * cond( int, const restrict volatile D *,
    2655          const restrict volatile void * ),
    2656         * cond( int, const restrict volatile void *,
    2657          const restrict volatile D * );
    2658 
    2659 forall( dtype D ) _Atomic const restrict volatile void
    2660         * cond( int, _Atomic const restrict volatile D *,
    2661          _Atomic const restrict volatile void * ),
    2662         * cond( int, _Atomic const restrict volatile void *,
    2663          _Atomic const restrict volatile D * );
    2664 \end{lstlisting}
    2665 
    2666 \begin{rationale}
    2667 The object of the above is to apply the \Index{usual arithmetic conversion}s when the second and
    2668 third operands have arithmetic type, and to combine the qualifiers of the second and third operands
    2669 if they are pointers.
     2125forall( dtype D ) _Atomic restrict volatile void * cond(
     2126        int, _Atomic restrict volatile D *, _Atomic restrict volatile void * ),
     2127        * cond( int, _Atomic restrict volatile void *, _Atomic restrict volatile D * );
     2128forall( dtype D ) const restrict volatile void * cond(
     2129        int, const restrict volatile D *, const restrict volatile void * ),
     2130        * cond( int, const restrict volatile void *, const restrict volatile D * );
     2131forall( dtype D ) _Atomic const restrict volatile void * cond(
     2132        int, _Atomic const restrict volatile D *, _Atomic const restrict volatile void * ),
     2133        * cond( int, _Atomic const restrict volatile void *, _Atomic const restrict volatile D * );
     2134\end{lstlisting}
     2135
     2136\begin{rationale}
     2137The object of the above is to apply the \Index{usual arithmetic conversion}s when the second and third operands have arithmetic type, and to combine the qualifiers of the second and third operands if they are pointers.
    26702138\end{rationale}
    26712139
     
    26852153rand() ? cip : vip;
    26862154\end{lstlisting}
    2687 The expression has type \lstinline$const volatile int *$, with safe conversions applied to the second
    2688 and third operands to add \lstinline$volatile$ and \lstinline$const$ qualifiers, respectively.
     2155The expression has type \lstinline$const volatile int *$, with safe conversions applied to the second and third operands to add \lstinline$volatile$ and \lstinline$const$ qualifiers, respectively.
    26892156
    26902157\begin{lstlisting}
     
    27082175
    27092176\rewriterules
    2710 Let ``\(\leftarrow\)'' be any of the assignment operators. Then
     2177Let ``\(\leftarrow\)'' be any of the assignment operators.
     2178Then
    27112179\use{?=?}\use{?*=?}\use{?/=?}\use{?%=?}\use{?+=?}\use{?-=?}
    27122180\use{?>>=?}\use{?&=?}\use{?^=?}\use{?"|=?}%use{?<<=?}
     
    27162184
    27172185\semantics
    2718 Each interpretation of the left operand of an assignment expression is considered separately. For
    2719 each interpretation that is a bit-field or is declared with the \lstinline$register$ storage class
    2720 specifier, the expression has one valid interpretation, with the type of the left operand. The
    2721 right operand is cast to that type, and the assignment expression is ambiguous if either operand is.
    2722 For the remaining interpretations, the expression is rewritten, and the interpretations of the
    2723 assignment expression are the interpretations of the corresponding function call. Finally, all
    2724 interpretations of the expression produced for the different interpretations of the left operand are
    2725 combined to produce the interpretations of the expression as a whole; where interpretations have
    2726 compatible result types, the best interpretations are selected in the manner described for function
    2727 call expressions.
     2186Each interpretation of the left operand of an assignment expression is considered separately.
     2187For each interpretation that is a bit-field or is declared with the \lstinline$register$ storage class specifier, the expression has one valid interpretation, with the type of the left operand.
     2188The right operand is cast to that type, and the assignment expression is ambiguous if either operand is.
     2189For the remaining interpretations, the expression is rewritten, and the interpretations of the assignment expression are the interpretations of the corresponding function call.
     2190Finally, all interpretations of the expression produced for the different interpretations of the left operand are combined to produce the interpretations of the expression as a whole;
     2191where interpretations have compatible result types, the best interpretations are selected in the manner described for function call expressions.
    27282192
    27292193
     
    27902254        ?=?( volatile _Complex long double *, _Complex long double ),
    27912255        ?=?( _Atomic volatile _Complex long double *, _Atomic _Complex long double );
    2792 
    27932256forall( ftype FT ) FT
    27942257        * ?=?( FT * volatile *, FT * ),
    27952258        * ?=?( FT * volatile *, forall( ftype F ) F * );
    2796 
    27972259forall( ftype FT ) FT const
    27982260        * ?=?( FT const * volatile *, FT const * ),
    27992261        * ?=?( FT const * volatile *, forall( ftype F ) F * );
    2800 
    28012262forall( ftype FT ) FT volatile
    28022263        * ?=?( FT volatile * volatile *, FT * ),
    28032264        * ?=?( FT volatile * volatile *, forall( ftype F ) F * );
    2804 
    28052265forall( ftype FT ) FT const
    28062266        * ?=?( FT const volatile * volatile *, FT const * ),
    28072267        * ?=?( FT const volatile * volatile *, forall( ftype F ) F * );
    2808 
    28092268forall( dtype DT ) DT
    28102269        * ?=?( DT * restrict volatile *, DT * ),
     
    28142273        * ?=?( DT * _Atomic restrict volatile *, void * ),
    28152274        * ?=?( DT * _Atomic restrict volatile *, forall( dtype D ) D * );
    2816 
    28172275forall( dtype DT ) DT _Atomic
    28182276        * ?=?( _Atomic DT * restrict volatile *, DT _Atomic * ),
     
    28222280        * ?=?( _Atomic DT * _Atomic restrict volatile *, void * ),
    28232281        * ?=?( _Atomic DT * _Atomic restrict volatile *, forall( dtype D ) D * );
    2824 
    28252282forall( dtype DT ) DT const
    28262283        * ?=?( DT const * restrict volatile *, DT const * ),
     
    28302287        * ?=?( DT const * _Atomic restrict volatile *, void const * ),
    28312288        * ?=?( DT const * _Atomic restrict volatile *, forall( dtype D ) D * );
    2832 
    28332289forall( dtype DT ) DT restrict
    28342290        * ?=?( restrict DT * restrict volatile *, DT restrict * ),
     
    28382294        * ?=?( restrict DT * _Atomic restrict volatile *, void * ),
    28392295        * ?=?( restrict DT * _Atomic restrict volatile *, forall( dtype D ) D * );
    2840 
    28412296forall( dtype DT ) DT volatile
    28422297        * ?=?( DT volatile * restrict volatile *, DT volatile * ),
     
    28462301        * ?=?( DT volatile * _Atomic restrict volatile *, void volatile * ),
    28472302        * ?=?( DT volatile * _Atomic restrict volatile *, forall( dtype D ) D * );
    2848 
    28492303forall( dtype DT ) DT _Atomic const
    28502304        * ?=?( DT _Atomic const * restrict volatile *, DT _Atomic const * ),
     
    28542308        * ?=?( DT _Atomic const * _Atomic restrict volatile *, void const * ),
    28552309        * ?=?( DT _Atomic const * _Atomic restrict volatile *, forall( dtype D ) D * );
    2856 
    28572310forall( dtype DT ) DT _Atomic restrict
    28582311        * ?=?( _Atomic restrict DT * restrict volatile *, DT _Atomic restrict * ),
     
    28622315        * ?=?( _Atomic restrict DT * _Atomic restrict volatile *, void * ),
    28632316        * ?=?( _Atomic restrict DT * _Atomic restrict volatile *, forall( dtype D ) D * );
    2864 
    28652317forall( dtype DT ) DT _Atomic volatile
    28662318        * ?=?( DT _Atomic volatile * restrict volatile *, DT _Atomic volatile * ),
     
    28702322        * ?=?( DT _Atomic volatile * _Atomic restrict volatile *, void volatile * ),
    28712323        * ?=?( DT _Atomic volatile * _Atomic restrict volatile *, forall( dtype D ) D * );
    2872 
    28732324forall( dtype DT ) DT const restrict
    28742325        * ?=?( DT const restrict * restrict volatile *, DT const restrict * ),
     
    28782329        * ?=?( DT const restrict * _Atomic restrict volatile *, void const * ),
    28792330        * ?=?( DT const restrict * _Atomic restrict volatile *, forall( dtype D ) D * );
    2880 
    28812331forall( dtype DT ) DT const volatile
    28822332        * ?=?( DT const volatile * restrict volatile *, DT const volatile * ),
     
    28862336        * ?=?( DT const volatile * _Atomic restrict volatile *, void const volatile * ),
    28872337        * ?=?( DT const volatile * _Atomic restrict volatile *, forall( dtype D ) D * );
    2888 
    28892338forall( dtype DT ) DT restrict volatile
    28902339        * ?=?( DT restrict volatile * restrict volatile *, DT restrict volatile * ),
     
    28942343        * ?=?( DT restrict volatile * _Atomic restrict volatile *, void volatile * ),
    28952344        * ?=?( DT restrict volatile * _Atomic restrict volatile *, forall( dtype D ) D * );
    2896 
    28972345forall( dtype DT ) DT _Atomic const restrict
    28982346        * ?=?( DT _Atomic const restrict * restrict volatile *,
     
    29082356        * ?=?( DT _Atomic const restrict * _Atomic restrict volatile *,
    29092357         forall( dtype D ) D * );
    2910 
    29112358forall( dtype DT ) DT _Atomic const volatile
    29122359        * ?=?( DT _Atomic const volatile * restrict volatile *,
     
    29222369        * ?=?( DT _Atomic const volatile * _Atomic restrict volatile *,
    29232370         forall( dtype D ) D * );
    2924 
    29252371forall( dtype DT ) DT _Atomic restrict volatile
    29262372        * ?=?( DT _Atomic restrict volatile * restrict volatile *,
     
    29362382        * ?=?( DT _Atomic restrict volatile * _Atomic restrict volatile *,
    29372383         forall( dtype D ) D * );
    2938 
    29392384forall( dtype DT ) DT const restrict volatile
    29402385        * ?=?( DT const restrict volatile * restrict volatile *,
     
    29502395        * ?=?( DT const restrict volatile * _Atomic restrict volatile *,
    29512396         forall( dtype D ) D * );
    2952 
    29532397forall( dtype DT ) DT _Atomic const restrict volatile
    29542398        * ?=?( DT _Atomic const restrict volatile * restrict volatile *,
     
    29642408        * ?=?( DT _Atomic const restrict volatile * _Atomic restrict volatile *,
    29652409         forall( dtype D ) D * );
    2966 
    29672410forall( dtype DT ) void
    29682411        * ?=?( void * restrict volatile *, DT * );
    2969 
    29702412forall( dtype DT ) void const
    29712413        * ?=?( void const * restrict volatile *, DT const * );
    2972 
    29732414forall( dtype DT ) void volatile
    29742415        * ?=?( void volatile * restrict volatile *, DT volatile * );
    2975 
    29762416forall( dtype DT ) void const volatile
    29772417        * ?=?( void const volatile * restrict volatile *, DT const volatile * );
    29782418\end{lstlisting}
    29792419\begin{rationale}
    2980 The pattern of overloadings for simple assignment resembles that of pointer increment and decrement,
    2981 except that the polymorphic pointer assignment functions declare a \lstinline$dtype$ parameter,
    2982 instead of a \lstinline$type$ parameter, because the left operand may be a pointer to an incomplete
    2983 type.
     2420The pattern of overloadings for simple assignment resembles that of pointer increment and decrement, except that the polymorphic pointer assignment functions declare a \lstinline$dtype$ parameter, instead of a \lstinline$type$ parameter, because the left operand may be a pointer to an incomplete type.
    29842421\end{rationale}
    29852422
     
    30062443
    30072444\semantics
    3008 The structure assignment functions provide member-wise assignment; each non-array member and each
    3009 element of each array member of the right argument is assigned to the corresponding member or
    3010 element of the left argument using the assignment function defined for its type. All other
    3011 assignment functions have the same effect as the corresponding C assignment expression.
    3012 \begin{rationale}
    3013 Note that, by default, union assignment\index{deficiencies!union assignment} uses C semantics---that
    3014 is, bitwise copy---even if some of the union members have programmer-defined assignment functions.
     2445The structure assignment functions provide member-wise assignment;
     2446each non-array member and each element of each array member of the right argument is assigned to the corresponding member or element of the left argument using the assignment function defined for its type.
     2447All other assignment functions have the same effect as the corresponding C assignment expression.
     2448\begin{rationale}
     2449Note that, by default, union assignment\index{deficiencies!union assignment} uses C semantics---that is, bitwise copy---even if some of the union members have programmer-defined assignment functions.
    30152450\end{rationale}
    30162451
     
    30252460        * ?+=?( T * _Atomic restrict volatile *, ptrdiff_t ),
    30262461        * ?-=?( T * _Atomic restrict volatile *, ptrdiff_t );
    3027 
    30282462forall( type T ) T _Atomic
    30292463        * ?+=?( T _Atomic * restrict volatile *, ptrdiff_t ),
     
    30312465        * ?+=?( T _Atomic * _Atomic restrict volatile *, ptrdiff_t ),
    30322466        * ?-=?( T _Atomic * _Atomic restrict volatile *, ptrdiff_t );
    3033 
    30342467forall( type T ) T const
    30352468        * ?+=?( T const * restrict volatile *, ptrdiff_t ),
     
    30372470        * ?+=?( T const * _Atomic restrict volatile *, ptrdiff_t ),
    30382471        * ?-=?( T const * _Atomic restrict volatile *, ptrdiff_t );
    3039 
    30402472forall( type T ) T restrict
    30412473        * ?+=?( T restrict * restrict volatile *, ptrdiff_t ),
     
    30432475        * ?+=?( T restrict * _Atomic restrict volatile *, ptrdiff_t ),
    30442476        * ?-=?( T restrict * _Atomic restrict volatile *, ptrdiff_t );
    3045 
    30462477forall( type T ) T volatile
    30472478        * ?+=?( T volatile * restrict volatile *, ptrdiff_t ),
     
    30492480        * ?+=?( T volatile * _Atomic restrict volatile *, ptrdiff_t ),
    30502481        * ?-=?( T volatile * _Atomic restrict volatile *, ptrdiff_t );
    3051 
    30522482forall( type T ) T _Atomic const
    30532483        * ?+=?( T _Atomic const restrict volatile *, ptrdiff_t ),
     
    30552485        * ?+=?( T _Atomic const _Atomic restrict volatile *, ptrdiff_t ),
    30562486        * ?-=?( T _Atomic const _Atomic restrict volatile *, ptrdiff_t );
    3057 
    30582487forall( type T ) T _Atomic restrict
    30592488        * ?+=?( T _Atomic restrict * restrict volatile *, ptrdiff_t ),
     
    30612490        * ?+=?( T _Atomic restrict * _Atomic restrict volatile *, ptrdiff_t ),
    30622491        * ?-=?( T _Atomic restrict * _Atomic restrict volatile *, ptrdiff_t );
    3063 
    30642492forall( type T ) T _Atomic volatile
    30652493        * ?+=?( T _Atomic volatile * restrict volatile *, ptrdiff_t ),
     
    30672495        * ?+=?( T _Atomic volatile * _Atomic restrict volatile *, ptrdiff_t ),
    30682496        * ?-=?( T _Atomic volatile * _Atomic restrict volatile *, ptrdiff_t );
    3069 
    30702497forall( type T ) T const restrict
    30712498        * ?+=?( T const restrict * restrict volatile *, ptrdiff_t ),
     
    30732500        * ?+=?( T const restrict * _Atomic restrict volatile *, ptrdiff_t ),
    30742501        * ?-=?( T const restrict * _Atomic restrict volatile *, ptrdiff_t );
    3075 
    30762502forall( type T ) T const volatile
    30772503        * ?+=?( T const volatile * restrict volatile *, ptrdiff_t ),
     
    30792505        * ?+=?( T const volatile * _Atomic restrict volatile *, ptrdiff_t ),
    30802506        * ?-=?( T const volatile * _Atomic restrict volatile *, ptrdiff_t );
    3081 
    30822507forall( type T ) T restrict volatile
    30832508        * ?+=?( T restrict volatile * restrict volatile *, ptrdiff_t ),
     
    30852510        * ?+=?( T restrict volatile * _Atomic restrict volatile *, ptrdiff_t ),
    30862511        * ?-=?( T restrict volatile * _Atomic restrict volatile *, ptrdiff_t );
    3087 
    30882512forall( type T ) T _Atomic const restrict
    30892513        * ?+=?( T _Atomic const restrict * restrict volatile *, ptrdiff_t ),
     
    30912515        * ?+=?( T _Atomic const restrict * _Atomic restrict volatile *, ptrdiff_t ),
    30922516        * ?-=?( T _Atomic const restrict * _Atomic restrict volatile *, ptrdiff_t );
    3093 
    30942517forall( type T ) T _Atomic const volatile
    30952518        * ?+=?( T _Atomic const volatile * restrict volatile *, ptrdiff_t ),
     
    30972520        * ?+=?( T _Atomic const volatile * _Atomic restrict volatile *, ptrdiff_t ),
    30982521        * ?-=?( T _Atomic const volatile * _Atomic restrict volatile *, ptrdiff_t );
    3099 
    31002522forall( type T ) T _Atomic restrict volatile
    31012523        * ?+=?( T _Atomic restrict volatile * restrict volatile *, ptrdiff_t ),
     
    31032525        * ?+=?( T _Atomic restrict volatile * _Atomic restrict volatile *, ptrdiff_t ),
    31042526        * ?-=?( T _Atomic restrict volatile * _Atomic restrict volatile *, ptrdiff_t );
    3105 
    31062527forall( type T ) T const restrict volatile
    31072528        * ?+=?( T const restrict volatile * restrict volatile *, ptrdiff_t ),
     
    31092530        * ?+=?( T const restrict volatile * _Atomic restrict volatile *, ptrdiff_t ),
    31102531        * ?-=?( T const restrict volatile * _Atomic restrict volatile *, ptrdiff_t );
    3111 
    31122532forall( type T ) T _Atomic const restrict volatile
    31132533        * ?+=?( T _Atomic const restrict volatile * restrict volatile *, ptrdiff_t ),
     
    33212741\semantics
    33222742In the comma expression ``\lstinline$a, b$'', the first operand is interpreted as
    3323 ``\lstinline$( void )(a)$'', which shall be unambiguous\index{ambiguous interpretation}. The
    3324 interpretations of the expression are the interpretations of the second operand.
     2743``\lstinline$( void )(a)$'', which shall be unambiguous\index{ambiguous interpretation}.
     2744The interpretations of the expression are the interpretations of the second operand.
    33252745
    33262746
     
    33372757
    33382758\constraints
    3339 If an identifier has \Index{no linkage}, there shall be no more than one declaration of the
    3340 identifier ( in a declarator or type specifier ) with compatible types in the same scope and in the
    3341 same name space, except that:
     2759If an identifier has \Index{no linkage}, there shall be no more than one declaration of the identifier ( in a declarator or type specifier ) with compatible types in the same scope and in the same name space, except that:
    33422760\begin{itemize}
    3343 \item
    3344 a typedef name may be redefined to denote the same type as it currently does, provided that type is
    3345 not a variably modified type;
    3346 \item
    3347 tags may be redeclared as specified in section 6.7.2.3 of the {\c11} standard.
     2761\item a typedef name may be redefined to denote the same type as it currently does, provided that type is not a variably modified type;
     2762\item tags may be redeclared as specified in section 6.7.2.3 of the {\c11} standard.
    33482763\end{itemize}
    33492764\begin{rationale}
    3350 This constraint adds the phrase ``with compatible types'' to the {\c11} constraint, to allow
    3351 overloading.
    3352 \end{rationale}
    3353 
    3354 An identifier declared by a type declaration shall not be redeclared as a parameter in a function
    3355 definition whose declarator includes an identifier list.
    3356 \begin{rationale}
    3357 This restriction echos {\c11}'s ban on the redeclaration of typedef names as parameters. This
    3358 avoids an ambiguity between old-style function declarations and new-style function prototypes:
     2765This constraint adds the phrase ``with compatible types'' to the {\c11} constraint, to allow overloading.
     2766\end{rationale}
     2767
     2768An identifier declared by a type declaration shall not be redeclared as a parameter in a function definition whose declarator includes an identifier list.
     2769\begin{rationale}
     2770This restriction echos {\c11}'s ban on the redeclaration of typedef names as parameters.
     2771This avoids an ambiguity between old-style function declarations and new-style function prototypes:
    33592772\begin{lstlisting}
    33602773void f( Complex,        // ... 3000 characters ...
    33612774void g( Complex,        // ... 3000 characters ...
    3362 int Complex; { ... }
    3363 \end{lstlisting}
    3364 Without the rule, \lstinline$Complex$ would be a type in the first case, and a parameter name in the
    3365 second.
     2775int Complex;
     2776{ ... }
     2777\end{lstlisting}
     2778Without the rule, \lstinline$Complex$ would be a type in the first case, and a parameter name in the second.
    33662779\end{rationale}
    33672780
     
    33822795
    33832796\semantics
    3384 \CFA extends the {\c11} definition of \define{anonymous structure} to include structure
    3385 specifiers with tags, and extends the {\c11} definition of \define{anonymous union} to include union
    3386 specifiers with tags.
     2797\CFA extends the {\c11} definition of \define{anonymous structure} to include structure specifiers with tags, and extends the {\c11} definition of \define{anonymous union} to include union specifiers with tags.
    33872798\begin{rationale}
    33882799This extension imitates an extension in the Plan 9 C compiler \cite{Thompson90new}.
     
    34012812cp.x = 0;
    34022813cp.color = RED;
    3403 
    34042814struct literal {@\impl{literal}@
    34052815        enum { NUMBER, STRING } tag;
    34062816        union {
    3407          double n;
    3408          char *s;
     2817                double n;
     2818                char *s;
    34092819        };
    34102820};
     
    34282838\begin{comment}
    34292839\constraints
    3430 If the \nonterm{declaration-specifiers} of a declaration that contains a \nonterm{forall-specifier}
    3431 declares a structure or union tag, the types of the members of the structure or union shall not use
    3432 any of the type identifiers declared by the \nonterm{type-parameter-list}.
    3433 \begin{rationale}
    3434 This sort of declaration is illegal because the scope of the type identifiers ends at the end of the
    3435 declaration, but the scope of the structure tag does not.
    3436 \begin{lstlisting}
    3437 forall( type T ) struct Pair { T a, b; } mkPair( T, T ); // illegal
    3438 \end{lstlisting}
    3439 If an instance of \lstinline$struct Pair$ was declared later in the current scope, what would the
    3440 members' type be?
     2840If the \nonterm{declaration-specifiers} of a declaration that contains a \nonterm{forall-specifier} declares a structure or union tag, the types of the members of the structure or union shall not use any of the type identifiers declared by the \nonterm{type-parameter-list}.
     2841\begin{rationale}
     2842This sort of declaration is illegal because the scope of the type identifiers ends at the end of the declaration, but the scope of the structure tag does not.
     2843\begin{lstlisting}
     2844forall( type T ) struct Pair { T a, b;
     2845} mkPair( T, T ); // illegal
     2846\end{lstlisting}
     2847If an instance of \lstinline$struct Pair$ was declared later in the current scope, what would the members' type be?
    34412848\end{rationale}
    34422849\end{comment}
    34432850
    34442851\semantics
    3445 The \nonterm{type-parameter-list}s and assertions of the \nonterm{forall-specifier}s declare type
    3446 identifiers, function and object identifiers with \Index{no linkage}.
     2852The \nonterm{type-parameter-list}s and assertions of the \nonterm{forall-specifier}s declare type identifiers, function and object identifiers with \Index{no linkage}.
    34472853
    34482854If, in the declaration ``\lstinline$T D$'', \lstinline$T$ contains \nonterm{forall-specifier}s and
     
    34502856\begin{lstlisting}
    34512857D( @\normalsize\nonterm{parameter-type-list}@ )
    3452 \end{lstlisting}
    3453 then a type identifier declared by one of the \nonterm{forall-specifier}s is an \define{inferred
    3454 parameter} of the function declarator if and only if it is not an inferred parameter of a function
    3455 declarator in \lstinline$D$, and it is used in the type of a parameter in the following
     2858\end{lstlisting} then a type identifier declared by one of the \nonterm{forall-specifier}s is an \define{inferred parameter} of the function declarator if and only if it is not an inferred parameter of a function declarator in \lstinline$D$, and it is used in the type of a parameter in the following
    34562859\nonterm{type-parameter-list} or it and an inferred parameter are used as arguments of a
    3457 \Index{specification} in one of the \nonterm{forall-specifier}s. The identifiers declared by
    3458 assertions that use an inferred parameter of a function declarator are \Index{assertion parameter}s
    3459 of that function declarator.
     2860\Index{specification} in one of the \nonterm{forall-specifier}s.
     2861The identifiers declared by assertions that use an inferred parameter of a function declarator are \Index{assertion parameter}s of that function declarator.
    34602862
    34612863\begin{comment}
    34622864\begin{rationale}
    3463 Since every inferred parameter is used by some parameter, inference can be understood as a single
    3464 bottom-up pass over the expression tree, that only needs to apply local reasoning at each node.
     2865Since every inferred parameter is used by some parameter, inference can be understood as a single bottom-up pass over the expression tree, that only needs to apply local reasoning at each node.
    34652866
    34662867If this restriction were lifted, it would be possible to write
    34672868\begin{lstlisting}
    3468 forall( type T ) T * alloc( void );@\use{alloc}@
    3469 int *p = alloc();
     2869forall( type T ) T * alloc( void );@\use{alloc}@ int *p = alloc();
    34702870\end{lstlisting}
    34712871Here \lstinline$alloc()$ would receive \lstinline$int$ as an inferred argument, and return an
    3472 \lstinline$int *$. In general, if a call to \lstinline$alloc()$ is a subexpression of an expression
    3473 involving polymorphic functions and overloaded identifiers, there could be considerable distance
    3474 between the call and the subexpression that causes \lstinline$T$ to be bound.
     2872\lstinline$int *$.
     2873In general, if a call to \lstinline$alloc()$ is a subexpression of an expression involving polymorphic functions and overloaded identifiers, there could be considerable distance between the call and the subexpression that causes \lstinline$T$ to be bound.
    34752874
    34762875With the current restriction, \lstinline$alloc()$ must be given an argument that determines
     
    34822881\end{comment}
    34832882
    3484 If a function declarator is part of a function definition, its inferred parameters and assertion
    3485 parameters have \Index{block scope}; otherwise, identifiers declared by assertions have a
     2883If a function declarator is part of a function definition, its inferred parameters and assertion parameters have \Index{block scope};
     2884otherwise, identifiers declared by assertions have a
    34862885\define{declaration scope}, which terminates at the end of the \nonterm{declaration}.
    34872886
    34882887A function type that has at least one inferred parameter is a \define{polymorphic function} type.
    3489 Function types with no inferred parameters are \define{monomorphic function} types. One function
    3490 type is \define{less polymorphic} than another if it has fewer inferred parameters, or if it has the
    3491 same number of inferred parameters and fewer of its explicit parameters have types that depend on an
    3492 inferred parameter.
    3493 
    3494 The names of inferred parameters and the order of identifiers in forall specifiers are not relevant
    3495 to polymorphic function type compatibility. Let $f$ and $g$ be two polymorphic function types with
    3496 the same number of inferred parameters, and let $f_i$ and $g_i$ be the inferred parameters of $f$
    3497 and $g$ in their order of occurance in the function types' \nonterm{parameter-type-list}s. Let $f'$
    3498 be $f$ with every occurrence of $f_i$ replaced by $g_i$, for all $i$. Then $f$ and $g$ are
    3499 \Index{compatible type}s if $f'$'s and $g$'s return types and parameter lists are compatible, and if
    3500 for every assertion parameter of $f'$ there is an assertion parameter in $g$ with the same
    3501 identifier and compatible type, and vice versa.
     2888Function types with no inferred parameters are \define{monomorphic function} types.
     2889One function type is \define{less polymorphic} than another if it has fewer inferred parameters, or if it has the same number of inferred parameters and fewer of its explicit parameters have types that depend on an inferred parameter.
     2890
     2891The names of inferred parameters and the order of identifiers in forall specifiers are not relevant to polymorphic function type compatibility.
     2892Let $f$ and $g$ be two polymorphic function types with the same number of inferred parameters, and let $f_i$ and $g_i$ be the inferred parameters of $f$ and $g$ in their order of occurance in the function types' \nonterm{parameter-type-list}s.
     2893Let $f'$ be $f$ with every occurrence of $f_i$ replaced by $g_i$, for all $i$.
     2894Then $f$ and $g$ are
     2895\Index{compatible type}s if $f'$'s and $g$'s return types and parameter lists are compatible, and if for every assertion parameter of $f'$ there is an assertion parameter in $g$ with the same identifier and compatible type, and vice versa.
    35022896
    35032897\examples
     
    35132907forall( type T ) T (*pfT )( T ) = fT;
    35142908\end{lstlisting}
    3515 \lstinline$pfi$ and \lstinline$pfT$ are pointers to functions. \lstinline$pfT$ is not
    3516 polymorphic, but the function it points at is.
     2909\lstinline$pfi$ and \lstinline$pfT$ are pointers to functions. \lstinline$pfT$ is not polymorphic, but the function it points at is.
    35172910\begin{lstlisting}
    35182911int (*fvpfi( void ))( int ) {
     
    35232916}
    35242917\end{lstlisting}
    3525 \lstinline$fvpfi()$ and \lstinline$fvpfT()$ are functions taking no arguments and returning pointers
    3526 to functions. \lstinline$fvpfT()$ is monomorphic, but the function that its return value points
    3527 at is polymorphic.
     2918\lstinline$fvpfi()$ and \lstinline$fvpfT()$ are functions taking no arguments and returning pointers to functions. \lstinline$fvpfT()$ is monomorphic, but the function that its return value points at is polymorphic.
    35282919\begin{lstlisting}
    35292920forall( type T ) int ( *fTpfi( T ) )( int );
     
    35312922forall( type T, type U ) U ( *fTpfU( T ) )( U );
    35322923\end{lstlisting}
    3533 \lstinline$fTpfi()$ is a polymorphic function that returns a pointer to a monomorphic function
    3534 taking an integer and returning an integer. It could return \lstinline$pfi$. \lstinline$fTpfT()$
    3535 is subtle: it is a polymorphic function returning a \emph{monomorphic} function taking and returning
    3536 \lstinline$T$, where \lstinline$T$ is an inferred parameter of \lstinline$fTpfT()$. For instance,
    3537 in the expression ``\lstinline$fTpfT(17)$'', \lstinline$T$ is inferred to be \lstinline$int$, and
    3538 the returned value would have type \lstinline$int ( * )( int )$. ``\lstinline$fTpfT(17)(13)$'' and
     2924\lstinline$fTpfi()$ is a polymorphic function that returns a pointer to a monomorphic function taking an integer and returning an integer.
     2925It could return \lstinline$pfi$. \lstinline$fTpfT()$ is subtle: it is a polymorphic function returning a \emph{monomorphic} function taking and returning
     2926\lstinline$T$, where \lstinline$T$ is an inferred parameter of \lstinline$fTpfT()$.
     2927For instance, in the expression ``\lstinline$fTpfT(17)$'', \lstinline$T$ is inferred to be \lstinline$int$, and the returned value would have type \lstinline$int ( * )( int )$. ``\lstinline$fTpfT(17)(13)$'' and
    35392928``\lstinline$fTpfT("yes")("no")$'' are legal, but ``\lstinline$fTpfT(17)("no")$'' is illegal.
    3540 \lstinline$fTpfU()$ is polymorphic ( in type \lstinline$T$), and returns a pointer to a function that
    3541 is polymorphic ( in type \lstinline$U$). ``\lstinline$f5(17)("no")$'' is a legal expression of type
     2929\lstinline$fTpfU()$ is polymorphic ( in type \lstinline$T$), and returns a pointer to a function that is polymorphic ( in type \lstinline$U$). ``\lstinline$f5(17)("no")$'' is a legal expression of type
    35422930\lstinline$char *$.
    35432931\begin{lstlisting}
     
    35452933forall( type U, type V, type W ) U * g( V *, U, W * const );
    35462934\end{lstlisting}
    3547 The functions \lstinline$f()$ and \lstinline$g()$ have compatible types. Let \(f\) and \(g\) be
    3548 their types; then \(f_1\) = \lstinline$T$, \(f_2\) = \lstinline$U$, \(f_3\) = \lstinline$V$, \(g_1\)
    3549 = \lstinline$V$, \(g_2\) = \lstinline$U$, and \(g_3\) = \lstinline$W$. Replacing every \(f_i\)
    3550 by \(g_i\) in \(f\) gives
     2935The functions \lstinline$f()$ and \lstinline$g()$ have compatible types.
     2936Let \(f\) and \(g\) be their types;
     2937then \(f_1\) = \lstinline$T$, \(f_2\) = \lstinline$U$, \(f_3\) = \lstinline$V$, \(g_1\)
     2938= \lstinline$V$, \(g_2\) = \lstinline$U$, and \(g_3\) = \lstinline$W$.
     2939Replacing every \(f_i\) by \(g_i\) in \(f\) gives
    35512940\begin{lstlisting}
    35522941forall( type V, type U, type W ) U * f( V *, U, W * const );
    3553 \end{lstlisting}
    3554 which has a return type and parameter list that is compatible with \(g\).
    3555 \begin{rationale}
    3556 The word ``\lstinline$type$'' in a forall specifier is redundant at the moment, but I want to leave
    3557 room for inferred parameters of ordinary types in case parameterized types get added one day.
     2942\end{lstlisting} which has a return type and parameter list that is compatible with \(g\).
     2943\begin{rationale}
     2944The word ``\lstinline$type$'' in a forall specifier is redundant at the moment, but I want to leave room for inferred parameters of ordinary types in case parameterized types get added one day.
    35582945
    35592946Even without parameterized types, I might try to allow
    35602947\begin{lstlisting}
    35612948forall( int n ) int sum( int vector[n] );
    3562 \end{lstlisting}
    3563 but C currently rewrites array parameters as pointer parameters, so the effects of such a change
    3564 require more thought.
    3565 \end{rationale}
    3566 
    3567 \begin{rationale}
    3568 A polymorphic declaration must do two things: it must introduce type parameters, and it must apply
    3569 assertions to those types. Adding this to existing C declaration syntax and semantics was delicate,
    3570 and not entirely successful.
    3571 
    3572 C depends on declaration-before-use, so a forall specifier must introduce type names before they can
    3573 be used in the declaration specifiers. This could be done by making the forall specifier part of
    3574 the declaration specifiers, or by making it a new introductory clause of declarations.
    3575 
    3576 Assertions are also part of polymorphic function types, because it must be clear which functions
    3577 have access to the assertion parameters declared by the assertions. All attempts to put assertions
    3578 inside an introductory clause produced complex semantics and confusing code. Building them into the
    3579 declaration specifiers could be done by placing them in the function's parameter list, or in a
    3580 forall specifier that is a declaration specifier. Assertions are also used with type parameters of
    3581 specifications, and by type declarations. For consistency's sake it seems best to attach assertions
    3582 to the type declarations in forall specifiers, which means that forall specifiers must be
    3583 declaration specifiers.
     2949\end{lstlisting} but C currently rewrites array parameters as pointer parameters, so the effects of such a change require more thought.
     2950\end{rationale}
     2951
     2952\begin{rationale}
     2953A polymorphic declaration must do two things: it must introduce type parameters, and it must apply assertions to those types.
     2954Adding this to existing C declaration syntax and semantics was delicate, and not entirely successful.
     2955
     2956C depends on declaration-before-use, so a forall specifier must introduce type names before they can be used in the declaration specifiers.
     2957This could be done by making the forall specifier part of the declaration specifiers, or by making it a new introductory clause of declarations.
     2958
     2959Assertions are also part of polymorphic function types, because it must be clear which functions have access to the assertion parameters declared by the assertions.
     2960All attempts to put assertions inside an introductory clause produced complex semantics and confusing code.
     2961Building them into the declaration specifiers could be done by placing them in the function's parameter list, or in a forall specifier that is a declaration specifier.
     2962Assertions are also used with type parameters of specifications, and by type declarations.
     2963For consistency's sake it seems best to attach assertions to the type declarations in forall specifiers, which means that forall specifiers must be declaration specifiers.
    35842964\end{rationale}
    35852965%HERE
     
    35952975
    35962976\constraints
    3597 \lstinline$restrict$\index{register@{\lstinline$restrict$}} Types other than type parameters and
    3598 pointer types whose referenced type is an object type shall not be restrict-qualified.
     2977\lstinline$restrict$\index{register@{\lstinline$restrict$}} Types other than type parameters and pointer types whose referenced type is an object type shall not be restrict-qualified.
    35992978
    36002979\semantics
    3601 An object's type may be a restrict-qualified type parameter. \lstinline$restrict$ does not
    3602 establish any special semantics in that case.
    3603 
    3604 \begin{rationale}
    3605 \CFA loosens the constraint on the restrict qualifier so that restrict-qualified pointers may be
    3606 passed to polymorphic functions.
    3607 \end{rationale}
    3608 
    3609 \lstinline$lvalue$ may be used to qualify the return type of a function type. Let \lstinline$T$ be
    3610 an unqualified version of a type; then the result of calling a function with return type
     2980An object's type may be a restrict-qualified type parameter. \lstinline$restrict$ does not establish any special semantics in that case.
     2981
     2982\begin{rationale}
     2983\CFA loosens the constraint on the restrict qualifier so that restrict-qualified pointers may be passed to polymorphic functions.
     2984\end{rationale}
     2985
     2986\lstinline$lvalue$ may be used to qualify the return type of a function type.
     2987Let \lstinline$T$ be an unqualified version of a type;
     2988then the result of calling a function with return type
    36112989\lstinline$lvalue T$ is a \Index{modifiable lvalue} of type \lstinline$T$.
    3612 \lstinline$const$\use{const} and \lstinline$volatile$\use{volatile} qualifiers may also be added to
    3613 indicate that the function result is a constant or volatile lvalue.
    3614 \begin{rationale}
    3615 The \lstinline$const$ and \lstinline$volatile$ qualifiers can only be sensibly used to qualify the
    3616 return type of a function if the \lstinline$lvalue$ qualifier is also used.
    3617 \end{rationale}
    3618 
    3619 An {lvalue}-qualified type may be used in a \Index{cast expression} if the operand is an lvalue; the
    3620 result of the expression is an lvalue.
    3621 
    3622 \begin{rationale}
    3623 \lstinline$lvalue$ provides some of the functionality of {\CC}'s ``\lstinline$T&$'' ( reference to
    3624 object of type \lstinline$T$) type. Reference types have four uses in {\CC}.
     2990\lstinline$const$\use{const} and \lstinline$volatile$\use{volatile} qualifiers may also be added to indicate that the function result is a constant or volatile lvalue.
     2991\begin{rationale}
     2992The \lstinline$const$ and \lstinline$volatile$ qualifiers can only be sensibly used to qualify the return type of a function if the \lstinline$lvalue$ qualifier is also used.
     2993\end{rationale}
     2994
     2995An {lvalue}-qualified type may be used in a \Index{cast expression} if the operand is an lvalue;
     2996the result of the expression is an lvalue.
     2997
     2998\begin{rationale}
     2999\lstinline$lvalue$ provides some of the functionality of {\CC}'s ``\lstinline$T&$'' ( reference to object of type \lstinline$T$) type.
     3000Reference types have four uses in {\CC}.
    36253001\begin{itemize}
    36263002\item
     
    36293005
    36303006\item
    3631 A reference can be used to define an alias for a complicated lvalue expression, as a way of getting
    3632 some of the functionality of the Pascal \lstinline$with$ statement. The following {\CC} code gives
    3633 an example.
     3007A reference can be used to define an alias for a complicated lvalue expression, as a way of getting some of the functionality of the Pascal \lstinline$with$ statement.
     3008The following {\CC} code gives an example.
    36343009\begin{lstlisting}
    36353010{
     
    36413016
    36423017\item
    3643 A reference parameter can be used to allow a function to modify an argument without forcing the
    3644 caller to pass the address of the argument. This is most useful for user-defined assignment
    3645 operators. In {\CC}, plain assignment is done by a function called ``\lstinline$operator=$'', and
    3646 the two expressions
     3018A reference parameter can be used to allow a function to modify an argument without forcing the caller to pass the address of the argument.
     3019This is most useful for user-defined assignment operators.
     3020In {\CC}, plain assignment is done by a function called ``\lstinline$operator=$'', and the two expressions
    36473021\begin{lstlisting}
    36483022a = b;
    36493023operator=( a, b );
    3650 \end{lstlisting}
    3651 are equivalent. If \lstinline$a$ and \lstinline$b$ are of type \lstinline$T$, then the first
    3652 parameter of \lstinline$operator=$ must have type ``\lstinline$T&$''. It cannot have type
     3024\end{lstlisting} are equivalent.
     3025If \lstinline$a$ and \lstinline$b$ are of type \lstinline$T$, then the first parameter of \lstinline$operator=$ must have type ``\lstinline$T&$''.
     3026It cannot have type
    36533027\lstinline$T$, because then assignment couldn't alter the variable, and it can't have type
    36543028``\lstinline$T *$'', because the assignment would have to be written ``\lstinline$&a = b;$''.
    36553029
    3656 In the case of user-defined operators, this could just as well be handled by using pointer types and
    3657 by changing the rewrite rules so that ``\lstinline$a = b;$'' is equivalent to
    3658 ``\lstinline$operator=(&( a), b )$''. Reference parameters of ``normal'' functions are Bad Things,
    3659 because they remove a useful property of C function calls: an argument can only be modified by a
    3660 function if it is preceded by ``\lstinline$&$''.
     3030In the case of user-defined operators, this could just as well be handled by using pointer types and by changing the rewrite rules so that ``\lstinline$a = b;$'' is equivalent to
     3031``\lstinline$operator=(&( a), b )$''.
     3032Reference parameters of ``normal'' functions are Bad Things, because they remove a useful property of C function calls: an argument can only be modified by a function if it is preceded by ``\lstinline$&$''.
    36613033
    36623034\item
     
    36683040void fiddle( const Thing & );
    36693041\end{lstlisting}
    3670 If the second form is used, then constructors and destructors are not invoked to create a temporary
    3671 variable at the call site ( and it is bad style for the caller to make any assumptions about such
    3672 things), and within \lstinline$fiddle$ the parameter is subject to the usual problems caused by
    3673 aliases. The reference form might be chosen for efficiency's sake if \lstinline$Thing$s are too
    3674 large or their constructors or destructors are too expensive. An implementation may switch between
    3675 them without causing trouble for well-behaved clients. This leaves the implementor to define ``too
    3676 large'' and ``too expensive''.
     3042If the second form is used, then constructors and destructors are not invoked to create a temporary variable at the call site ( and it is bad style for the caller to make any assumptions about such things), and within \lstinline$fiddle$ the parameter is subject to the usual problems caused by aliases.
     3043The reference form might be chosen for efficiency's sake if \lstinline$Thing$s are too large or their constructors or destructors are too expensive.
     3044An implementation may switch between them without causing trouble for well-behaved clients.
     3045This leaves the implementor to define ``too large'' and ``too expensive''.
    36773046
    36783047I propose to push this job onto the compiler by allowing it to implement
    36793048\begin{lstlisting}
    36803049void fiddle( const volatile Thing );
    3681 \end{lstlisting}
    3682 with call-by-reference. Since it knows all about the size of \lstinline$Thing$s and the parameter
    3683 passing mechanism, it should be able to come up with a better definition of ``too large'', and may
    3684 be able to make a good guess at ``too expensive''.
     3050\end{lstlisting} with call-by-reference.
     3051Since it knows all about the size of \lstinline$Thing$s and the parameter passing mechanism, it should be able to come up with a better definition of ``too large'', and may be able to make a good guess at ``too expensive''.
    36853052\end{itemize}
    36863053
    3687 In summary, since references are only really necessary for returning lvalues, I'll only provide
    3688 lvalue functions.
     3054In summary, since references are only really necessary for returning lvalues, I'll only provide lvalue functions.
    36893055\end{rationale}
    36903056
     
    36933059\subsection{Initialization}
    36943060
    3695 An expression that is used as an \nonterm{initializer} is treated as being cast to the type of the
    3696 object being initialized. An expression used in an \nonterm{initializer-list} is treated as being
    3697 cast to the type of the aggregate member that it initializes. In either case the cast must have a
    3698 single unambiguous \Index{interpretation}.
     3061An expression that is used as an \nonterm{initializer} is treated as being cast to the type of the object being initialized.
     3062An expression used in an \nonterm{initializer-list} is treated as being cast to the type of the aggregate member that it initializes.
     3063In either case the cast must have a single unambiguous \Index{interpretation}.
    36993064
    37003065
     
    37173082\end{syntax}
    37183083\begin{rationale}
    3719 The declarations allowed in a specification are much the same as those allowed in a structure,
    3720 except that bit fields are not allowed, and \Index{incomplete type}s and function types are allowed.
     3084The declarations allowed in a specification are much the same as those allowed in a structure, except that bit fields are not allowed, and \Index{incomplete type}s and function types are allowed.
    37213085\end{rationale}
    37223086
    37233087\semantics
    3724 A \define{specification definition} defines a name for a \define{specification}: a parameterized
    3725 collection of object and function declarations.
     3088A \define{specification definition} defines a name for a \define{specification}: a parameterized collection of object and function declarations.
    37263089
    37273090The declarations in a specification consist of the declarations in the
    37283091\nonterm{spec-declaration-list} and declarations produced by any assertions in the
    3729 \nonterm{spec-parameter-list}. If the collection contains two declarations that declare the same
    3730 identifier and have compatible types, they are combined into one declaration with the composite type
    3731 constructed from the two types.
     3092\nonterm{spec-parameter-list}.
     3093If the collection contains two declarations that declare the same identifier and have compatible types, they are combined into one declaration with the composite type constructed from the two types.
    37323094
    37333095
     
    37473109
    37483110\constraints
    3749 The \nonterm{identifier} in an assertion that is not a \nonterm{spec-declaration} shall be the name
    3750 of a specification. The \nonterm{type-name-list} shall contain one \nonterm{type-name} argument for
    3751 each \nonterm{type-parameter} in that specification's \nonterm{spec-parameter-list}. If the
    3752 \nonterm{type-parameter} uses type-class \lstinline$type$\use{type}, the argument shall be the type
    3753 name of an \Index{object type}; if it uses \lstinline$dtype$, the argument shall be the type name of
    3754 an object type or an \Index{incomplete type}; and if it uses \lstinline$ftype$, the argument shall
    3755 be the type name of a \Index{function type}.
     3111The \nonterm{identifier} in an assertion that is not a \nonterm{spec-declaration} shall be the name of a specification.
     3112The \nonterm{type-name-list} shall contain one \nonterm{type-name} argument for each \nonterm{type-parameter} in that specification's \nonterm{spec-parameter-list}.
     3113If the
     3114\nonterm{type-parameter} uses type-class \lstinline$type$\use{type}, the argument shall be the type name of an \Index{object type};
     3115if it uses \lstinline$dtype$, the argument shall be the type name of an object type or an \Index{incomplete type};
     3116and if it uses \lstinline$ftype$, the argument shall be the type name of a \Index{function type}.
    37563117
    37573118\semantics
     
    37593120\define{assertion parameters}.
    37603121
    3761 The assertion parameters produced by an assertion that applies the name of a specification to type
    3762 arguments are found by taking the declarations specified in the specification and treating each of
    3763 the specification's parameters as a synonym for the corresponding \nonterm{type-name} argument.
    3764 
    3765 The collection of assertion parameters produced by the \nonterm{assertion-list} are found by
    3766 combining the declarations produced by each assertion. If the collection contains two declarations
    3767 that declare the same identifier and have compatible types, they are combined into one declaration
    3768 with the \Index{composite type} constructed from the two types.
     3122The assertion parameters produced by an assertion that applies the name of a specification to type arguments are found by taking the declarations specified in the specification and treating each of the specification's parameters as a synonym for the corresponding \nonterm{type-name} argument.
     3123
     3124The collection of assertion parameters produced by the \nonterm{assertion-list} are found by combining the declarations produced by each assertion.
     3125If the collection contains two declarations that declare the same identifier and have compatible types, they are combined into one declaration with the \Index{composite type} constructed from the two types.
    37693126
    37703127\examples
     
    37743131        return val + val;
    37753132}
    3776 
    37773133context summable( type T ) {@\impl{summable}@
    37783134        T ?+=?( T *, T );@\use{?+=?}@
     
    37883144context sum_list( type List, type Element | summable( Element ) | list_of( List, Element ) ) {};
    37893145\end{lstlisting}
    3790 \lstinline$sum_list$ contains seven declarations, which describe a list whose elements can be added
    3791 up. The assertion ``\lstinline$|sum_list( i_list, int )$''\use{sum_list} produces the assertion
    3792 parameters
     3146\lstinline$sum_list$ contains seven declarations, which describe a list whose elements can be added up.
     3147The assertion ``\lstinline$|sum_list( i_list, int )$''\use{sum_list} produces the assertion parameters
    37933148\begin{lstlisting}
    37943149int ?+=?( int *, int );
     
    38253180
    38263181\constraints
    3827 If a type declaration has block scope, and the declared identifier has external or internal linkage,
    3828 the declaration shall have no initializer for the identifier.
     3182If a type declaration has block scope, and the declared identifier has external or internal linkage, the declaration shall have no initializer for the identifier.
    38293183
    38303184\semantics
    3831 A \nonterm{type-parameter} or a \nonterm{type-declarator} declares an identifier to be a \Index{type
    3832 name} for a type incompatible with all other types.
    3833 
    3834 An identifier declared by a \nonterm{type-parameter} has \Index{no linkage}. Identifiers declared
    3835 with type-class \lstinline$type$\use{type} are \Index{object type}s; those declared with type-class
    3836 \lstinline$dtype$\use{dtype} are \Index{incomplete type}s; and those declared with type-class
    3837 \lstinline$ftype$\use{ftype} are \Index{function type}s. The identifier has \Index{block scope} that
    3838 terminates at the end of the \nonterm{spec-declaration-list} or polymorphic function that contains
    3839 the \nonterm{type-parameter}.
    3840 
    3841 A \nonterm{type-declarator} with an \Index{initializer} is a \define{type definition}.  The declared
    3842 identifier is an \Index{incomplete type} within the initializer, and an \Index{object type} after
    3843 the end of the initializer. The type in the initializer is called the \define{implementation
    3844   type}. Within the scope of the declaration, \Index{implicit conversion}s can be performed between
    3845 the defined type and the implementation type, and between pointers to the defined type and pointers
    3846 to the implementation type.
    3847 
    3848 A type declaration without an \Index{initializer} and without a \Index{storage-class specifier} or
    3849 with storage-class specifier \lstinline$static$\use{static} defines an \Index{incomplete type}. If a
    3850 \Index{translation unit} or \Index{block} contains one or more such declarations for an identifier,
    3851 it must contain exactly one definition of the identifier ( but not in an enclosed block, which would
    3852 define a new type known only within that block).
     3185A \nonterm{type-parameter} or a \nonterm{type-declarator} declares an identifier to be a \Index{type name} for a type incompatible with all other types.
     3186
     3187An identifier declared by a \nonterm{type-parameter} has \Index{no linkage}.
     3188Identifiers declared with type-class \lstinline$type$\use{type} are \Index{object type}s;
     3189those declared with type-class
     3190\lstinline$dtype$\use{dtype} are \Index{incomplete type}s;
     3191and those declared with type-class
     3192\lstinline$ftype$\use{ftype} are \Index{function type}s.
     3193The identifier has \Index{block scope} that terminates at the end of the \nonterm{spec-declaration-list} or polymorphic function that contains the \nonterm{type-parameter}.
     3194
     3195A \nonterm{type-declarator} with an \Index{initializer} is a \define{type definition}.  The declared identifier is an \Index{incomplete type} within the initializer, and an \Index{object type} after the end of the initializer.
     3196The type in the initializer is called the \define{implementation
     3197  type}.
     3198Within the scope of the declaration, \Index{implicit conversion}s can be performed between the defined type and the implementation type, and between pointers to the defined type and pointers to the implementation type.
     3199
     3200A type declaration without an \Index{initializer} and without a \Index{storage-class specifier} or with storage-class specifier \lstinline$static$\use{static} defines an \Index{incomplete type}.
     3201If a
     3202\Index{translation unit} or \Index{block} contains one or more such declarations for an identifier, it must contain exactly one definition of the identifier ( but not in an enclosed block, which would define a new type known only within that block).
    38533203\begin{rationale}
    38543204Incomplete type declarations allow compact mutually-recursive types.
    38553205\begin{lstlisting}
    3856 type t1; // Incomplete type declaration.
     3206type t1; // incomplete type declaration
    38573207type t2 = struct { t1 * p; ... };
    38583208type t1 = struct { t2 * p; ... };
    38593209\end{lstlisting}
    3860 Without them, mutual recursion could be handled by declaring mutually recursive structures, then
    3861 initializing the types to those structures.
     3210Without them, mutual recursion could be handled by declaring mutually recursive structures, then initializing the types to those structures.
    38623211\begin{lstlisting}
    38633212struct s1;
     
    38653214type t1 = struct s1 { struct s2 * p; ... };
    38663215\end{lstlisting}
    3867 This introduces extra names, and may force the programmer to cast between the types and their
    3868 implementations.
     3216This introduces extra names, and may force the programmer to cast between the types and their implementations.
    38693217\end{rationale}
    38703218
    38713219A type declaration without an initializer and with \Index{storage-class specifier}
    3872 \lstinline$extern$\use{extern} is an \define{opaque type declaration}. Opaque types are
    3873 \Index{object type}s. An opaque type is not a \nonterm{constant-expression}; neither is a structure
    3874 or union that has a member whose type is not a \nonterm{constant-expression}.  Every other
    3875 \Index{object type} is a \nonterm{constant-expression}. Objects with static storage duration shall
    3876 be declared with a type that is a \nonterm{constant-expression}.
    3877 \begin{rationale}
    3878 Type declarations can declare identifiers with external linkage, whereas typedef declarations
    3879 declare identifiers that only exist within a translation unit. These opaque types can be used in
    3880 declarations, but the implementation of the type is not visible.
    3881 
    3882 Static objects can not have opaque types because space for them would have to be allocated at
    3883 program start-up. This is a deficiency\index{deficiencies!static opaque objects}, but I don't want
    3884 to deal with ``module initialization'' code just now.
    3885 \end{rationale}
    3886 
    3887 An \Index{incomplete type} which is not a qualified version\index{qualified type} of a type is a
    3888 value of \Index{type-class} \lstinline$dtype$. An object type\index{object types} which is not a
    3889 qualified version of a type is a value of type-classes \lstinline$type$ and \lstinline$dtype$. A
     3220\lstinline$extern$\use{extern} is an \define{opaque type declaration}.
     3221Opaque types are
     3222\Index{object type}s.
     3223An opaque type is not a \nonterm{constant-expression};
     3224neither is a structure or union that has a member whose type is not a \nonterm{constant-expression}.  Every other
     3225\Index{object type} is a \nonterm{constant-expression}.
     3226Objects with static storage duration shall be declared with a type that is a \nonterm{constant-expression}.
     3227\begin{rationale}
     3228Type declarations can declare identifiers with external linkage, whereas typedef declarations declare identifiers that only exist within a translation unit.
     3229These opaque types can be used in declarations, but the implementation of the type is not visible.
     3230
     3231Static objects can not have opaque types because space for them would have to be allocated at program start-up.
     3232This is a deficiency\index{deficiencies!static opaque objects}, but I don't want to deal with ``module initialization'' code just now.
     3233\end{rationale}
     3234
     3235An \Index{incomplete type} which is not a qualified version\index{qualified type} of a type is a value of \Index{type-class} \lstinline$dtype$.
     3236An object type\index{object types} which is not a qualified version of a type is a value of type-classes \lstinline$type$ and \lstinline$dtype$.
     3237A
    38903238\Index{function type} is a value of type-class \lstinline$ftype$.
    38913239\begin{rationale}
    3892 Syntactically, a type value is a \nonterm{type-name}, which is a declaration for an object which
    3893 omits the identifier being declared.
    3894 
    3895 Object types are precisely the types that can be instantiated. Type qualifiers are not included in
    3896 type values because the compiler needs the information they provide at compile time to detect
    3897 illegal statements or to produce efficient machine instructions. For instance, the code that a
    3898 compiler must generate to manipulate an object that has volatile-qualified type may be different
    3899 from the code to manipulate an ordinary object.
    3900 
    3901 Type qualifiers are a weak point of C's type system. Consider the standard library function
    3902 \lstinline$strchr()$ which, given a string and a character, returns a pointer to the first
    3903 occurrence of the character in the string.
     3240Syntactically, a type value is a \nonterm{type-name}, which is a declaration for an object which omits the identifier being declared.
     3241
     3242Object types are precisely the types that can be instantiated.
     3243Type qualifiers are not included in type values because the compiler needs the information they provide at compile time to detect illegal statements or to produce efficient machine instructions.
     3244For instance, the code that a compiler must generate to manipulate an object that has volatile-qualified type may be different from the code to manipulate an ordinary object.
     3245
     3246Type qualifiers are a weak point of C's type system.
     3247Consider the standard library function
     3248\lstinline$strchr()$ which, given a string and a character, returns a pointer to the first occurrence of the character in the string.
    39043249\begin{lstlisting}
    39053250char *strchr( const char *s, int c ) {@\impl{strchr}@
    39063251        char real_c = c; // done because c was declared as int.
    39073252        for ( ; *s != real_c; s++ )
    3908          if ( *s == '\0' ) return NULL;
     3253                if ( *s == '\0' ) return NULL;
    39093254        return ( char * )s;
    39103255}
    39113256\end{lstlisting}
    3912 The parameter \lstinline$s$ must be \lstinline$const char *$, because \lstinline$strchr()$ might be
    3913 used to search a constant string, but the return type must be \lstinline$char *$, because the result
    3914 might be used to modify a non-constant string. Hence the body must perform a cast, and ( even worse)
    3915 \lstinline$strchr()$ provides a type-safe way to attempt to modify constant strings. What is needed
    3916 is some way to say that \lstinline$s$'s type might contain qualifiers, and the result type has
    3917 exactly the same qualifiers. Polymorphic functions do not provide a fix for this
    3918 deficiency\index{deficiencies!pointers to qualified types}, because type qualifiers are not part of
    3919 type values. Instead, overloading can be used to define \lstinline$strchr()$ for each combination
    3920 of qualifiers.
    3921 \end{rationale}
    3922 
    3923 \begin{rationale}
    3924 Since \Index{incomplete type}s are not type values, they can not be used as the initializer in a
    3925 type declaration, or as the type of a structure or union member. This prevents the declaration of
    3926 types that contain each other.
     3257The parameter \lstinline$s$ must be \lstinline$const char *$, because \lstinline$strchr()$ might be used to search a constant string, but the return type must be \lstinline$char *$, because the result might be used to modify a non-constant string.
     3258Hence the body must perform a cast, and ( even worse)
     3259\lstinline$strchr()$ provides a type-safe way to attempt to modify constant strings.
     3260What is needed is some way to say that \lstinline$s$'s type might contain qualifiers, and the result type has exactly the same qualifiers.
     3261Polymorphic functions do not provide a fix for this deficiency\index{deficiencies!pointers to qualified types}, because type qualifiers are not part of type values.
     3262Instead, overloading can be used to define \lstinline$strchr()$ for each combination of qualifiers.
     3263\end{rationale}
     3264
     3265\begin{rationale}
     3266Since \Index{incomplete type}s are not type values, they can not be used as the initializer in a type declaration, or as the type of a structure or union member.
     3267This prevents the declaration of types that contain each other.
    39273268\begin{lstlisting}
    39283269type t1;
    3929 type t2 = t1; // illegal: incomplete type t1.
     3270type t2 = t1; // illegal: incomplete type t1
    39303271type t1 = t2;
    39313272\end{lstlisting}
    39323273
    3933 The initializer in a file-scope declaration must be a constant expression. This means type
    3934 declarations can not build on opaque types, which is a deficiency\index{deficiencies!nesting opaque
     3274The initializer in a file-scope declaration must be a constant expression.
     3275This means type declarations can not build on opaque types, which is a deficiency\index{deficiencies!nesting opaque
    39353276 types}.
    39363277\begin{lstlisting}
    3937 extern type Huge; // extended-precision integer type.
     3278extern type Huge; // extended-precision integer type
    39383279type Rational = struct {
    39393280        Huge numerator, denominator;    // illegal
     
    39443285\end{lstlisting}
    39453286Without this restriction, \CFA might require ``module initialization'' code ( since
    3946 \lstinline$Rational$ has external linkage, it must be created before any other translation unit
    3947 instantiates it), and would force an ordering on the initialization of the translation unit that
    3948 defines \lstinline$Huge$ and the translation that declares \lstinline$Rational$.
    3949 
    3950 A benefit of the restriction is that it prevents the declaration in separate translation units of
    3951 types that contain each other, which would be hard to prevent otherwise.
     3287\lstinline$Rational$ has external linkage, it must be created before any other translation unit instantiates it), and would force an ordering on the initialization of the translation unit that defines \lstinline$Huge$ and the translation that declares \lstinline$Rational$.
     3288
     3289A benefit of the restriction is that it prevents the declaration in separate translation units of types that contain each other, which would be hard to prevent otherwise.
    39523290\begin{lstlisting}
    39533291//  File a.c:
     
    39623300\begin{rationale}
    39633301Since a \nonterm{type-declaration} is a \nonterm{declaration} and not a
    3964 \nonterm{struct-declaration}, type declarations can not be structure members. The form of
     3302\nonterm{struct-declaration}, type declarations can not be structure members.
     3303The form of
    39653304\nonterm{type-declaration} forbids arrays of, pointers to, and functions returning \lstinline$type$.
    3966 Hence the syntax of \nonterm{type-specifier} does not have to be extended to allow type-valued
    3967 expressions. It also side-steps the problem of type-valued expressions producing different values
    3968 in different declarations.
    3969 
    3970 Since a type declaration is not a \nonterm{parameter-declaration}, functions can not have explicit
    3971 type parameters. This may be too restrictive, but it attempts to make compilation simpler. Recall
    3972 that when traditional C scanners read in an identifier, they look it up in the symbol table to
    3973 determine whether or not it is a typedef name, and return a ``type'' or ``identifier'' token
    3974 depending on what they find. A type parameter would add a type name to the current scope. The
    3975 scope manipulations involved in parsing the declaration of a function that takes function pointer
    3976 parameters and returns a function pointer may just be too complicated.
    3977 
    3978 Explicit type parameters don't seem to be very useful, anyway, because their scope would not include
    3979 the return type of the function. Consider the following attempt to define a type-safe memory
    3980 allocation function.
     3305Hence the syntax of \nonterm{type-specifier} does not have to be extended to allow type-valued expressions.
     3306It also side-steps the problem of type-valued expressions producing different values in different declarations.
     3307
     3308Since a type declaration is not a \nonterm{parameter-declaration}, functions can not have explicit type parameters.
     3309This may be too restrictive, but it attempts to make compilation simpler.
     3310Recall that when traditional C scanners read in an identifier, they look it up in the symbol table to determine whether or not it is a typedef name, and return a ``type'' or ``identifier'' token depending on what they find.
     3311A type parameter would add a type name to the current scope.
     3312The scope manipulations involved in parsing the declaration of a function that takes function pointer parameters and returns a function pointer may just be too complicated.
     3313
     3314Explicit type parameters don't seem to be very useful, anyway, because their scope would not include the return type of the function.
     3315Consider the following attempt to define a type-safe memory allocation function.
    39813316\begin{lstlisting}
    39823317#include <stdlib.h>
    39833318T * new( type T ) { return ( T * )malloc( sizeof( T) ); };
    3984 @\ldots@
    3985 int * ip = new( int );
    3986 \end{lstlisting}
    3987 This looks sensible, but \CFA's declaration-before-use rules mean that ``\lstinline$T$'' in the
    3988 function body refers to the parameter, but the ``\lstinline$T$'' in the return type refers to the
    3989 meaning of \lstinline$T$ in the scope that contains \lstinline$new$; it could be undefined, or a
    3990 type name, or a function or variable name. Nothing good can result from such a situation.
     3319@\ldots@ int * ip = new( int );
     3320\end{lstlisting}
     3321This looks sensible, but \CFA's declaration-before-use rules mean that ``\lstinline$T$'' in the function body refers to the parameter, but the ``\lstinline$T$'' in the return type refers to the meaning of \lstinline$T$ in the scope that contains \lstinline$new$;
     3322it could be undefined, or a type name, or a function or variable name.
     3323Nothing good can result from such a situation.
    39913324\end{rationale}
    39923325
     
    40033336f2( v2 );
    40043337\end{lstlisting}
    4005 \lstinline$V1$ is passed by value, so \lstinline$f1()$'s assignment to \lstinline$a[0]$ does not
    4006 modify v1.  \lstinline$V2$ is converted to a pointer, so \lstinline$f2()$ modifies
    4007 \lstinline$v2[0]$.
     3338\lstinline$V1$ is passed by value, so \lstinline$f1()$'s assignment to \lstinline$a[0]$ does not modify v1.  \lstinline$V2$ is converted to a pointer, so \lstinline$f2()$ modifies \lstinline$v2[0]$.
    40083339
    40093340A translation unit containing the declarations
    40103341\begin{lstlisting}
    4011 extern type Complex;@\use{Complex}@ // opaque type declaration.
     3342extern type Complex;@\use{Complex}@ // opaque type declaration
    40123343extern float abs( Complex );@\use{abs}@
    4013 \end{lstlisting}
    4014 can contain declarations of complex numbers, which can be passed to \lstinline$abs$. Some other
    4015 translation unit must implement \lstinline$Complex$ and \lstinline$abs$. That unit might contain
    4016 the declarations
     3344\end{lstlisting} can contain declarations of complex numbers, which can be passed to \lstinline$abs$.
     3345Some other translation unit must implement \lstinline$Complex$ and \lstinline$abs$.
     3346That unit might contain the declarations
    40173347\begin{lstlisting}
    40183348type Complex = struct { float re, im; };@\impl{Complex}@
     
    40223352}
    40233353\end{lstlisting}
    4024 Note that \lstinline$c$ is implicitly converted to a \lstinline$struct$ so that its components can
    4025 be retrieved.
     3354Note that \lstinline$c$ is implicitly converted to a \lstinline$struct$ so that its components can be retrieved.
    40263355
    40273356\begin{lstlisting}
     
    40343363
    40353364\begin{rationale}
    4036 Within the scope of a type definition, an instance of the type can be viewed as having that type or
    4037 as having the implementation type. In the \lstinline$Time_of_day$ example, the difference is
    4038 important. Different languages have treated the distinction between the abstraction and the
    4039 implementation in different ways.
     3365Within the scope of a type definition, an instance of the type can be viewed as having that type or as having the implementation type.
     3366In the \lstinline$Time_of_day$ example, the difference is important.
     3367Different languages have treated the distinction between the abstraction and the implementation in different ways.
    40403368\begin{itemize}
    40413369\item
    4042 Inside a Clu cluster \cite{clu}, the declaration of an instance states which view applies. Two
    4043 primitives called \lstinline$up$ and \lstinline$down$ can be used to convert between the views.
    4044 \item
    4045 The Simula class \cite{Simula87} is essentially a record type. Since the only operations on a
    4046 record are member selection and assignment, which can not be overloaded, there is never any
    4047 ambiguity as to whether the abstraction or the implementation view is being used. In {\CC}
    4048 \cite{c++}, operations on class instances include assignment and ``\lstinline$&$'', which can be
    4049 overloaded. A ``scope resolution'' operator can be used inside the class to specify whether the
    4050 abstract or implementation version of the operation should be used.
    4051 \item
    4052 An Ada derived type definition \cite{ada} creates a new type from an old type, and also implicitly
    4053 declares derived subprograms that correspond to the existing subprograms that use the old type as a
    4054 parameter type or result type. The derived subprograms are clones of the existing subprograms with
    4055 the old type replaced by the derived type. Literals and aggregates of the old type are also cloned.
     3370Inside a Clu cluster \cite{clu}, the declaration of an instance states which view applies.
     3371Two primitives called \lstinline$up$ and \lstinline$down$ can be used to convert between the views.
     3372\item
     3373The Simula class \cite{Simula87} is essentially a record type.
     3374Since the only operations on a record are member selection and assignment, which can not be overloaded, there is never any ambiguity as to whether the abstraction or the implementation view is being used.
     3375In {\CC}
     3376\cite{c++}, operations on class instances include assignment and ``\lstinline$&$'', which can be overloaded.
     3377A ``scope resolution'' operator can be used inside the class to specify whether the abstract or implementation version of the operation should be used.
     3378\item
     3379An Ada derived type definition \cite{ada} creates a new type from an old type, and also implicitly declares derived subprograms that correspond to the existing subprograms that use the old type as a parameter type or result type.
     3380The derived subprograms are clones of the existing subprograms with the old type replaced by the derived type.
     3381Literals and aggregates of the old type are also cloned.
    40563382In other words, the abstract view provides exactly the same operations as the implementation view.
    40573383This allows the abstract view to be used in all cases.
    40583384
    4059 The derived subprograms can be replaced by programmer-specified subprograms. This is an exception
    4060 to the normal scope rules, which forbid duplicate definitions of a subprogram in a scope. In this
    4061 case, explicit conversions between the derived type and the old type can be used.
     3385The derived subprograms can be replaced by programmer-specified subprograms.
     3386This is an exception to the normal scope rules, which forbid duplicate definitions of a subprogram in a scope.
     3387In this case, explicit conversions between the derived type and the old type can be used.
    40623388\end{itemize}
    4063 \CFA's rules are like Clu's, except that implicit conversions and
    4064 conversion costs allow it to do away with most uses of \lstinline$up$ and \lstinline$down$.
     3389\CFA's rules are like Clu's, except that implicit conversions and conversion costs allow it to do away with most uses of \lstinline$up$ and \lstinline$down$.
    40653390\end{rationale}
    40663391
     
    40703395A declaration\index{type declaration} of a type identifier \lstinline$T$ with type-class
    40713396\lstinline$type$ implicitly declares a \define{default assignment} function
    4072 \lstinline$T ?=?( T *, T )$\use{?=?}, with the same \Index{scope} and \Index{linkage} as the
    4073 identifier \lstinline$T$.
    4074 \begin{rationale}
    4075 Assignment is central to C's imperative programming style, and every existing C object type has
    4076 assignment defined for it ( except for array types, which are treated as pointer types for purposes
    4077 of assignment). Without this rule, nearly every inferred type parameter would need an accompanying
    4078 assignment assertion parameter. If a type parameter should not have an assignment operation,
    4079 \lstinline$dtype$ should be used. If a type should not have assignment defined, the user can define
    4080 an assignment function that causes a run-time error, or provide an external declaration but no
    4081 definition and thus cause a link-time error.
    4082 \end{rationale}
    4083 
    4084 A definition\index{type definition} of a type identifier \lstinline$T$ with \Index{implementation
    4085 type} \lstinline$I$ and type-class \lstinline$type$ implicitly defines a default assignment
    4086 function. A definition\index{type definition} of a type identifier \lstinline$T$ with implementation
    4087 type \lstinline$I$ and an assertion list implicitly defines \define{default function}s and
    4088 \define{default object}s as declared by the assertion declarations. The default objects and
    4089 functions have the same \Index{scope} and \Index{linkage} as the identifier \lstinline$T$. Their
    4090 values are determined as follows:
     3397\lstinline$T ?=?( T *, T )$\use{?=?}, with the same \Index{scope} and \Index{linkage} as the identifier \lstinline$T$.
     3398\begin{rationale}
     3399Assignment is central to C's imperative programming style, and every existing C object type has assignment defined for it ( except for array types, which are treated as pointer types for purposes of assignment).
     3400Without this rule, nearly every inferred type parameter would need an accompanying assignment assertion parameter.
     3401If a type parameter should not have an assignment operation,
     3402\lstinline$dtype$ should be used.
     3403If a type should not have assignment defined, the user can define an assignment function that causes a run-time error, or provide an external declaration but no definition and thus cause a link-time error.
     3404\end{rationale}
     3405
     3406A definition\index{type definition} of a type identifier \lstinline$T$ with \Index{implementation type} \lstinline$I$ and type-class \lstinline$type$ implicitly defines a default assignment function.
     3407A definition\index{type definition} of a type identifier \lstinline$T$ with implementation type \lstinline$I$ and an assertion list implicitly defines \define{default function}s and
     3408\define{default object}s as declared by the assertion declarations.
     3409The default objects and functions have the same \Index{scope} and \Index{linkage} as the identifier \lstinline$T$.
     3410Their values are determined as follows:
    40913411\begin{itemize}
    40923412\item
    4093 If at the definition of \lstinline$T$ there is visible a declaration of an object with the same name
    4094 as the default object, and if the type of that object with all occurrence of \lstinline$I$ replaced
    4095 by \lstinline$T$ is compatible with the type of the default object, then the default object is
    4096 initialized with that object. Otherwise the scope of the declaration of \lstinline$T$ must contain
    4097 a definition of the default object.
     3413If at the definition of \lstinline$T$ there is visible a declaration of an object with the same name as the default object, and if the type of that object with all occurrence of \lstinline$I$ replaced by \lstinline$T$ is compatible with the type of the default object, then the default object is initialized with that object.
     3414Otherwise the scope of the declaration of \lstinline$T$ must contain a definition of the default object.
    40983415
    40993416\item
    4100 If at the definition of \lstinline$T$ there is visible a declaration of a function with the same
    4101 name as the default function, and if the type of that function with all occurrence of \lstinline$I$
    4102 replaced by \lstinline$T$ is compatible with the type of the default function, then the default
    4103 function calls that function after converting its arguments and returns the converted result.
    4104 
    4105 Otherwise, if \lstinline$I$ contains exactly one anonymous member\index{anonymous member} such that
    4106 at the definition of \lstinline$T$ there is visible a declaration of a function with the same name
    4107 as the default function, and the type of that function with all occurrences of the anonymous
    4108 member's type in its parameter list replaced by \lstinline$T$ is compatible with the type of the
    4109 default function, then the default function calls that function after converting its arguments and
    4110 returns the result.
    4111 
    4112 Otherwise the scope of the declaration of \lstinline$T$ must contain a definition of the default
    4113 function.
     3417If at the definition of \lstinline$T$ there is visible a declaration of a function with the same name as the default function, and if the type of that function with all occurrence of \lstinline$I$ replaced by \lstinline$T$ is compatible with the type of the default function, then the default function calls that function after converting its arguments and returns the converted result.
     3418
     3419Otherwise, if \lstinline$I$ contains exactly one anonymous member\index{anonymous member} such that at the definition of \lstinline$T$ there is visible a declaration of a function with the same name as the default function, and the type of that function with all occurrences of the anonymous member's type in its parameter list replaced by \lstinline$T$ is compatible with the type of the default function, then the default function calls that function after converting its arguments and returns the result.
     3420
     3421Otherwise the scope of the declaration of \lstinline$T$ must contain a definition of the default function.
    41143422\end{itemize}
    41153423\begin{rationale}
    4116 Note that a pointer to a default function will not compare as equal to a pointer to the inherited
    4117 function.
    4118 \end{rationale}
    4119 
    4120 A function or object with the same type and name as a default function or object that is declared
    4121 within the scope of the definition of \lstinline$T$ replaces the default function or object.
     3424Note that a pointer to a default function will not compare as equal to a pointer to the inherited function.
     3425\end{rationale}
     3426
     3427A function or object with the same type and name as a default function or object that is declared within the scope of the definition of \lstinline$T$ replaces the default function or object.
    41223428
    41233429\examples
     
    41253431context s( type T ) {
    41263432        T a, b;
    4127 }
    4128 struct impl { int left, right; } a = { 0, 0 };
     3433} struct impl { int left, right; } a = { 0, 0 };
    41293434type Pair | s( Pair ) = struct impl;
    41303435Pair b = { 1, 1 };
    41313436\end{lstlisting}
    41323437The definition of \lstinline$Pair$ implicitly defines two objects \lstinline$a$ and \lstinline$b$.
    4133 \lstinline$Pair a$ inherits its value from the \lstinline$struct impl a$. The definition of
    4134 \lstinline$Pair b$ is compulsory because there is no \lstinline$struct impl b$ to construct a value
    4135 from.
     3438\lstinline$Pair a$ inherits its value from the \lstinline$struct impl a$.
     3439The definition of
     3440\lstinline$Pair b$ is compulsory because there is no \lstinline$struct impl b$ to construct a value from.
    41363441\begin{lstlisting}
    41373442context ss( type T ) {
     
    41523457void munge( Doodad * );
    41533458\end{lstlisting}
    4154 The assignment function inherits \lstinline$struct doodad$'s assignment function because the types
    4155 match when \lstinline$struct doodad$ is replaced by \lstinline$Doodad$ throughout.
     3459The assignment function inherits \lstinline$struct doodad$'s assignment function because the types match when \lstinline$struct doodad$ is replaced by \lstinline$Doodad$ throughout.
    41563460\lstinline$munge()$ inherits \lstinline$Whatsit$'s \lstinline$munge()$ because the types match when
    4157 \lstinline$Whatsit$ is replaced by \lstinline$Doodad$ in the parameter list. \lstinline$clone()$
    4158 does \emph{not} inherit \lstinline$Whatsit$'s \lstinline$clone()$: replacement in the parameter
    4159 list yields ``\lstinline$Whatsit clone( Doodad )$'', which is not compatible with
    4160 \lstinline$Doodad$'s \lstinline$clone()$'s type. Hence the definition of
     3461\lstinline$Whatsit$ is replaced by \lstinline$Doodad$ in the parameter list. \lstinline$clone()$ does \emph{not} inherit \lstinline$Whatsit$'s \lstinline$clone()$: replacement in the parameter list yields ``\lstinline$Whatsit clone( Doodad )$'', which is not compatible with
     3462\lstinline$Doodad$'s \lstinline$clone()$'s type.
     3463Hence the definition of
    41613464``\lstinline$Doodad clone( Doodad )$'' is necessary.
    41623465
     
    41733476
    41743477\begin{rationale}
    4175 The \emph{class} construct of object-oriented programming languages performs three independent
    4176 functions. It \emph{encapsulates} a data structure; it defines a \emph{subtype} relationship, whereby
    4177 instances of one class may be used in contexts that require instances of another; and it allows one
    4178 class to \emph{inherit} the implementation of another.
    4179 
    4180 In \CFA, encapsulation is provided by opaque types and the scope rules, and subtyping is provided
    4181 by specifications and assertions. Inheritance is provided by default functions and objects.
     3478The \emph{class} construct of object-oriented programming languages performs three independent functions.
     3479It \emph{encapsulates} a data structure;
     3480it defines a \emph{subtype} relationship, whereby instances of one class may be used in contexts that require instances of another;
     3481and it allows one class to \emph{inherit} the implementation of another.
     3482
     3483In \CFA, encapsulation is provided by opaque types and the scope rules, and subtyping is provided by specifications and assertions.
     3484Inheritance is provided by default functions and objects.
    41823485\end{rationale}
    41833486
     
    41903493\end{syntax}
    41913494
    4192 Many statements contain expressions, which may have more than one interpretation. The following
    4193 sections describe how the \CFA translator selects an interpretation. In all cases the result of the
    4194 selection shall be a single unambiguous \Index{interpretation}.
     3495Many statements contain expressions, which may have more than one interpretation.
     3496The following sections describe how the \CFA translator selects an interpretation.
     3497In all cases the result of the selection shall be a single unambiguous \Index{interpretation}.
    41953498
    41963499
     
    42393542switch ( E ) ...
    42403543choose ( E ) ...
    4241 \end{lstlisting}
    4242 may have more than one interpretation, but it shall have only one interpretation with an integral type.
     3544\end{lstlisting} may have more than one interpretation, but it shall have only one interpretation with an integral type.
    42433545An \Index{integer promotion} is performed on the expression if necessary.
    42443546The constant expressions in \lstinline$case$ statements with the switch are converted to the promoted type.
     
    42843586while ( E ) ...
    42853587do ... while ( E );
    4286 \end{lstlisting}
    4287 is treated as ``\lstinline$( int )((E)!=0)$''.
     3588\end{lstlisting} is treated as ``\lstinline$( int )((E)!=0)$''.
    42883589
    42893590The statement
    42903591\begin{lstlisting}
    42913592for ( a; b; c ) @\ldots@
    4292 \end{lstlisting}
    4293 is treated as
     3593\end{lstlisting} is treated as
    42943594\begin{lstlisting}
    42953595for ( ( void )( a ); ( int )(( b )!=0); ( void )( c ) ) ...
     
    44133713
    44143714The implementation shall define the macro names \lstinline$__LINE__$, \lstinline$__FILE__$,
    4415 \lstinline$__DATE__$, and \lstinline$__TIME__$, as in the {\c11} standard. It shall not define the
    4416 macro name \lstinline$__STDC__$.
    4417 
    4418 In addition, the implementation shall define the macro name \lstinline$__CFORALL__$ to be the
    4419 decimal constant 1.
     3715\lstinline$__DATE__$, and \lstinline$__TIME__$, as in the {\c11} standard.
     3716It shall not define the macro name \lstinline$__STDC__$.
     3717
     3718In addition, the implementation shall define the macro name \lstinline$__CFORALL__$ to be the decimal constant 1.
    44203719
    44213720
     
    44273726
    44283727\section{C types}
    4429 This section gives example specifications for some groups of types that are important in the C
    4430 language, in terms of the predefined operations that can be applied to those types.
     3728This section gives example specifications for some groups of types that are important in the C language, in terms of the predefined operations that can be applied to those types.
    44313729
    44323730
    44333731\subsection{Scalar, arithmetic, and integral types}
    44343732
    4435 The pointer, integral, and floating-point types are all \define{scalar types}. All of these types
    4436 can be logically negated and compared. The assertion ``\lstinline$scalar( Complex )$'' should be read
    4437 as ``type \lstinline$Complex$ is scalar''.
     3733The pointer, integral, and floating-point types are all \define{scalar types}.
     3734All of these types can be logically negated and compared.
     3735The assertion ``\lstinline$scalar( Complex )$'' should be read as ``type \lstinline$Complex$ is scalar''.
    44383736\begin{lstlisting}
    44393737context scalar( type T ) {@\impl{scalar}@
     
    44433741\end{lstlisting}
    44443742
    4445 The integral and floating-point types are \define{arithmetic types}, which support the basic
    4446 arithmetic operators. The use of an assertion in the \nonterm{spec-parameter-list} declares that,
    4447 in order to be arithmetic, a type must also be scalar ( and hence that scalar operations are
    4448 available ). This is equivalent to inheritance of specifications.
     3743The integral and floating-point types are \define{arithmetic types}, which support the basic arithmetic operators.
     3744The use of an assertion in the \nonterm{spec-parameter-list} declares that, in order to be arithmetic, a type must also be scalar ( and hence that scalar operations are available ).
     3745This is equivalent to inheritance of specifications.
    44493746\begin{lstlisting}
    44503747context arithmetic( type T | scalar( T ) ) {@\impl{arithmetic}@@\use{scalar}@
     
    44773774
    44783775Modifiable scalar lvalues are scalars and are modifiable lvalues, and assertions in the
    4479 \nonterm{spec-parameter-list} reflect those relationships. This is equivalent to multiple
    4480 inheritance of specifications. Scalars can also be incremented and decremented.
     3776\nonterm{spec-parameter-list} reflect those relationships.
     3777This is equivalent to multiple inheritance of specifications.
     3778Scalars can also be incremented and decremented.
    44813779\begin{lstlisting}
    44823780context m_l_scalar( type T | scalar( T ) | m_lvalue( T ) ) {@\impl{m_l_scalar}@
     
    44863784\end{lstlisting}
    44873785
    4488 Modifiable arithmetic lvalues are both modifiable scalar lvalues and arithmetic. Note that this
    4489 results in the ``inheritance'' of \lstinline$scalar$ along both paths.
     3786Modifiable arithmetic lvalues are both modifiable scalar lvalues and arithmetic.
     3787Note that this results in the ``inheritance'' of \lstinline$scalar$ along both paths.
    44903788\begin{lstlisting}
    44913789context m_l_arithmetic( type T | m_l_scalar( T ) | arithmetic( T ) ) {@\impl{m_l_arithmetic}@
     
    44933791        T ?+=?( T *, T ), ?-=?( T *, T );
    44943792};
    4495 
    44963793context m_l_integral( type T | m_l_arithmetic( T ) | integral( T ) ) {@\impl{m_l_integral}@
    44973794        T ?&=?( T *, T ), ?|=?( T *, T ), ?^=?( T *, T );@\use{m_l_arithmetic}@
     
    45033800\subsection{Pointer and array types}
    45043801
    4505 Array types can barely be said to exist in {\c11}, since in most cases an array name is treated as a
    4506 constant pointer to the first element of the array, and the subscript expression
     3802Array types can barely be said to exist in {\c11}, since in most cases an array name is treated as a constant pointer to the first element of the array, and the subscript expression
    45073803``\lstinline$a[i]$'' is equivalent to the dereferencing expression ``\lstinline$(*( a+( i )))$''.
    45083804Technically, pointer arithmetic and pointer comparisons other than ``\lstinline$==$'' and
    4509 ``\lstinline$!=$'' are only defined for pointers to array elements, but the type system does not
    4510 enforce those restrictions. Consequently, there is no need for a separate ``array type''
    4511 specification.
    4512 
    4513 Pointer types are scalar types. Like other scalar types, they have ``\lstinline$+$'' and
     3805``\lstinline$!=$'' are only defined for pointers to array elements, but the type system does not enforce those restrictions.
     3806Consequently, there is no need for a separate ``array type'' specification.
     3807
     3808Pointer types are scalar types.
     3809Like other scalar types, they have ``\lstinline$+$'' and
    45143810``\lstinline$-$'' operators, but the types do not match the types of the operations in
    45153811\lstinline$arithmetic$, so these operators cannot be consolidated in \lstinline$scalar$.
     
    45193815        ptrdiff_t ?-?( P, P );
    45203816};
    4521 
    45223817context m_l_pointer( type P | pointer( P ) | m_l_scalar( P ) ) {@\impl{m_l_pointer}@
    45233818        P ?+=?( P *, long int ), ?-=?( P *, long int );
     
    45273822\end{lstlisting}
    45283823
    4529 Specifications that define the dereference operator ( or subscript operator ) require two
    4530 parameters, one for the pointer type and one for the pointed-at ( or element ) type. Different
    4531 specifications are needed for each set of \Index{type qualifier}s, because qualifiers are not
    4532 included in types. The assertion ``\lstinline$|ptr_to( Safe_pointer, int )$'' should be read as
     3824Specifications that define the dereference operator ( or subscript operator ) require two parameters, one for the pointer type and one for the pointed-at ( or element ) type.
     3825Different specifications are needed for each set of \Index{type qualifier}s, because qualifiers are not included in types.
     3826The assertion ``\lstinline$|ptr_to( Safe_pointer, int )$'' should be read as
    45333827``\lstinline$Safe_pointer$ acts like a pointer to \lstinline$int$''.
    45343828\begin{lstlisting}
    45353829context ptr_to( type P | pointer( P ), type T ) {@\impl{ptr_to}@@\use{pointer}@
    4536         lvalue T *?( P ); lvalue T ?[?]( P, long int );
     3830        lvalue T *?( P );
     3831        lvalue T ?[?]( P, long int );
    45373832};
    4538 
    45393833context ptr_to_const( type P | pointer( P ), type T ) {@\impl{ptr_to_const}@
    4540         const lvalue T *?( P ); const lvalue T ?[?]( P, long int );@\use{pointer}@
     3834        const lvalue T *?( P );
     3835        const lvalue T ?[?]( P, long int );@\use{pointer}@
    45413836};
    4542 
    45433837context ptr_to_volatile( type P | pointer( P ), type T ) }@\impl{ptr_to_volatile}@
    4544         volatile lvalue T *?( P ); volatile lvalue T ?[?]( P, long int );@\use{pointer}@
     3838        volatile lvalue T *?( P );
     3839        volatile lvalue T ?[?]( P, long int );@\use{pointer}@
    45453840};
    4546 \end{lstlisting}
    4547 \begin{lstlisting}
    45483841context ptr_to_const_volatile( type P | pointer( P ), type T ) }@\impl{ptr_to_const_volatile}@
    45493842        const volatile lvalue T *?( P );@\use{pointer}@
     
    45523845\end{lstlisting}
    45533846
    4554 Assignment to pointers is more complicated than is the case with other types, because the target's
    4555 type can have extra type qualifiers in the pointed-at type: a ``\lstinline$T *$'' can be assigned to
    4556 a ``\lstinline$const T *$'', a ``\lstinline$volatile T *$'', and a ``\lstinline$const volatile T *$''.
     3847Assignment to pointers is more complicated than is the case with other types, because the target's type can have extra type qualifiers in the pointed-at type: a ``\lstinline$T *$'' can be assigned to a ``\lstinline$const T *$'', a ``\lstinline$volatile T *$'', and a ``\lstinline$const volatile T *$''.
    45573848Again, the pointed-at type is passed in, so that assertions can connect these specifications to the
    45583849``\lstinline$ptr_to$'' specifications.
     
    45623853        T * ?=?( T **, P );
    45633854};
    4564 
    45653855context m_l_ptr_to_const( type P | m_l_pointer( P ),@\use{m_l_pointer}@@\impl{m_l_ptr_to_const}@ type T | ptr_to_const( P, T )@\use{ptr_to_const}@) {
    45663856        P ?=?( P *, const T * );
    45673857        const T * ?=?( const T **, P );
    45683858};
    4569 
    45703859context m_l_ptr_to_volatile( type P | m_l_pointer( P ),@\use{m_l_pointer}@@\impl{m_l_ptr_to_volatile}@ type T | ptr_to_volatile( P, T )) {@\use{ptr_to_volatile}@
    45713860        P ?=?( P *, volatile T * );
    45723861        volatile T * ?=?( volatile T **, P );
    45733862};
    4574 
    45753863context m_l_ptr_to_const_volatile( type P | ptr_to_const_volatile( P ),@\use{ptr_to_const_volatile}@@\impl{m_l_ptr_to_const_volatile}@
    45763864                type T | m_l_ptr_to_volatile( P, T ) | m_l_ptr_to_const( P )) {@\use{m_l_ptr_to_const}@@\use{m_l_ptr_to_volatile}@
     
    45803868\end{lstlisting}
    45813869
    4582 Note the regular manner in which type qualifiers appear in those specifications. An alternative
    4583 specification can make use of the fact that qualification of the pointed-at type is part of a
    4584 pointer type to capture that regularity.
     3870Note the regular manner in which type qualifiers appear in those specifications.
     3871An alternative specification can make use of the fact that qualification of the pointed-at type is part of a pointer type to capture that regularity.
    45853872\begin{lstlisting}
    45863873context m_l_ptr_like( type MyP | m_l_pointer( MyP ),@\use{m_l_pointer}@@\impl{m_l_ptr_like}@ type CP | m_l_pointer( CP ) ) {
     
    45903877\end{lstlisting}
    45913878The assertion ``\lstinline$| m_l_ptr_like( Safe_ptr, const int * )$'' should be read as
    4592 ``\lstinline$Safe_ptr$ is a pointer type like \lstinline$const int *$''. This specification has two
    4593 defects, compared to the original four: there is no automatic assertion that dereferencing a
     3879``\lstinline$Safe_ptr$ is a pointer type like \lstinline$const int *$''.
     3880This specification has two defects, compared to the original four: there is no automatic assertion that dereferencing a
    45943881\lstinline$MyP$ produces an lvalue of the type that \lstinline$CP$ points at, and the
    4595 ``\lstinline$|m_l_pointer( CP )$'' assertion provides only a weak assurance that the argument passed
    4596 to \lstinline$CP$ really is a pointer type.
     3882``\lstinline$|m_l_pointer( CP )$'' assertion provides only a weak assurance that the argument passed to \lstinline$CP$ really is a pointer type.
    45973883
    45983884
    45993885\section{Relationships between operations}
    46003886
    4601 Different operators often have related meanings; for instance, in C, ``\lstinline$+$'',
     3887Different operators often have related meanings;
     3888for instance, in C, ``\lstinline$+$'',
    46023889``\lstinline$+=$'', and the two versions of ``\lstinline$++$'' perform variations of addition.
    4603 Languages like {\CC} and Ada allow programmers to define operators for new types, but do not
    4604 require that these relationships be preserved, or even that all of the operators be implemented.
    4605 Completeness and consistency is left to the good taste and discretion of the programmer. It is
    4606 possible to encourage these attributes by providing generic operator functions, or member functions
    4607 of abstract classes, that are defined in terms of other, related operators.
    4608 
    4609 In \CFA, polymorphic functions provide the equivalent of these generic operators, and
    4610 specifications explicitly define the minimal implementation that a programmer should provide. This
    4611 section shows a few examples.
     3890Languages like {\CC} and Ada allow programmers to define operators for new types, but do not require that these relationships be preserved, or even that all of the operators be implemented.
     3891Completeness and consistency is left to the good taste and discretion of the programmer.
     3892It is possible to encourage these attributes by providing generic operator functions, or member functions of abstract classes, that are defined in terms of other, related operators.
     3893
     3894In \CFA, polymorphic functions provide the equivalent of these generic operators, and specifications explicitly define the minimal implementation that a programmer should provide.
     3895This section shows a few examples.
    46123896
    46133897
    46143898\subsection{Relational and equality operators}
    46153899
    4616 The different comparison operators have obvious relationships, but there is no obvious subset of the
    4617 operations to use in the implementation of the others. However, it is usually convenient to
    4618 implement a single comparison function that returns a negative integer, 0, or a positive integer if
    4619 its first argument is respectively less than, equal to, or greater than its second argument; the
    4620 library function \lstinline$strcmp$ is an example.
    4621 
    4622 C and \CFA have an extra, non-obvious comparison operator: ``\lstinline$!$'', logical negation,
    4623 returns 1 if its operand compares equal to 0, and 0 otherwise.
     3900The different comparison operators have obvious relationships, but there is no obvious subset of the operations to use in the implementation of the others.
     3901However, it is usually convenient to implement a single comparison function that returns a negative integer, 0, or a positive integer if its first argument is respectively less than, equal to, or greater than its second argument;
     3902the library function \lstinline$strcmp$ is an example.
     3903
     3904C and \CFA have an extra, non-obvious comparison operator: ``\lstinline$!$'', logical negation, returns 1 if its operand compares equal to 0, and 0 otherwise.
    46243905\begin{lstlisting}
    46253906context comparable( type T ) {
     
    46273908        int compare( T, T );
    46283909}
    4629 
    46303910forall( type T | comparable( T ) ) int ?<?( T l, T r ) {
    46313911        return compare( l, r ) < 0;
    46323912}
    46333913// ... similarly for <=, ==, >=, >, and !=.
    4634 
    46353914forall( type T | comparable( T ) ) int !?( T operand ) {
    46363915        return !compare( operand, 0 );
     
    46413920\subsection{Arithmetic and integer operations}
    46423921
    4643 A complete arithmetic type would provide the arithmetic operators and the corresponding assignment
    4644 operators. Of these, the assignment operators are more likely to be implemented directly, because
    4645 it is usually more efficient to alter the contents of an existing object than to create and return a
    4646 new one. Similarly, a complete integral type would provide integral operations based on integral
    4647 assignment operations.
     3922A complete arithmetic type would provide the arithmetic operators and the corresponding assignment operators.
     3923Of these, the assignment operators are more likely to be implemented directly, because it is usually more efficient to alter the contents of an existing object than to create and return a new one.
     3924Similarly, a complete integral type would provide integral operations based on integral assignment operations.
    46483925\begin{lstlisting}
    46493926context arith_base( type T ) {
     
    46513928        T ?+=?( T *, T ), ?-=?( T *, T ), ?*=?( T *, T ), ?/=?( T *, T );
    46523929}
    4653 
    46543930forall( type T | arith_base( T ) ) T ?+?( T l, T r ) {
    46553931        return l += r;
    46563932}
    4657 
    46583933forall( type T | arith_base( T ) ) T ?++( T * operand ) {
    46593934        T temporary = *operand;
     
    46613936        return temporary;
    46623937}
    4663 
    46643938forall( type T | arith_base( T ) ) T ++?( T * operand ) {
    46653939        return *operand += 1;
    46663940}
    46673941// ... similarly for -, --, *, and /.
    4668 
    46693942context int_base( type T ) {
    46703943        T ?&=?( T *, T ), ?|=?( T *, T ), ?^=?( T *, T );
    46713944        T ?%=?( T *, T ), ?<<=?( T *, T ), ?>>=?( T *, T );
    46723945}
    4673 
    46743946forall( type T | int_base( T ) ) T ?&?( T l, T r ) {
    46753947        return l &= r;
     
    46783950\end{lstlisting}
    46793951
    4680 Note that, although an arithmetic type would certainly provide comparison functions, and an integral
    4681 type would provide arithmetic operations, there does not have to be any relationship among
    4682 \lstinline$int_base$, \lstinline$arith_base$ and \lstinline$comparable$. Note also that these
    4683 declarations provide guidance and assistance, but they do not define an absolutely minimal set of
    4684 requirements. A truly minimal implementation of an arithmetic type might only provide
     3952Note that, although an arithmetic type would certainly provide comparison functions, and an integral type would provide arithmetic operations, there does not have to be any relationship among
     3953\lstinline$int_base$, \lstinline$arith_base$ and \lstinline$comparable$.
     3954Note also that these declarations provide guidance and assistance, but they do not define an absolutely minimal set of requirements.
     3955A truly minimal implementation of an arithmetic type might only provide
    46853956\lstinline$0$, \lstinline$1$, and \lstinline$?-=?$, which would be used by polymorphic
    46863957\lstinline$?+=?$, \lstinline$?*=?$, and \lstinline$?/=?$ functions.
     
    46923963Review index entries.
    46933964
    4694 Restrict allowed to qualify anything, or type/dtype parameters, but only affects pointers. This gets
    4695 into \lstinline$noalias$ territory. Qualifying anything (``\lstinline$short restrict rs$'') means
    4696 pointer parameters of \lstinline$?++$, etc, would need restrict qualifiers.
    4697 
    4698 Enumerated types. Constants are not ints. Overloading. Definition should be ``representable as an
    4699 integer type'', not ``as an int''. C11 usual conversions freely convert to and from ordinary
    4700 integer types via assignment, which works between any integer types. Does enum Color ?*?( enum
     3965Restrict allowed to qualify anything, or type/dtype parameters, but only affects pointers.
     3966This gets into \lstinline$noalias$ territory.
     3967Qualifying anything (``\lstinline$short restrict rs$'') means pointer parameters of \lstinline$?++$, etc, would need restrict qualifiers.
     3968
     3969Enumerated types.
     3970Constants are not ints.
     3971Overloading.
     3972Definition should be ``representable as an integer type'', not ``as an int''.
     3973C11 usual conversions freely convert to and from ordinary integer types via assignment, which works between any integer types.
     3974Does enum Color ?*?( enum
    47013975Color, enum Color ) really make sense? ?++ does, but it adds (int)1.
    47023976
    4703 Operators on {,signed,unsigned} char and other small types. ?<? harmless; ?*? questionable for
    4704 chars. Generic selections make these choices visible. Safe conversion operators? Predefined
     3977Operators on {,signed,unsigned} char and other small types. ?<? harmless;
     3978?*? questionable for chars.
     3979Generic selections make these choices visible.
     3980Safe conversion operators? Predefined
    47053981``promotion'' function?
    47063982
    4707 \lstinline$register$ assignment might be handled as assignment to a temporary with copying back and
    4708 forth, but copying must not be done by assignment.
     3983\lstinline$register$ assignment might be handled as assignment to a temporary with copying back and forth, but copying must not be done by assignment.
    47093984
    47103985Don't use ptrdiff\_t by name in the predefineds.
    47113986
    4712 Polymorphic objects. Polymorphic typedefs and type declarations.
     3987Polymorphic objects.
     3988Polymorphic typedefs and type declarations.
    47133989
    47143990
     
    47193995\addcontentsline{toc}{chapter}{\indexname} % add index name to table of contents
    47203996\begin{theindex}
    4721 Italic page numbers give the location of the main entry for the referenced term. Plain page numbers
    4722 denote uses of the indexed term. Entries for grammar non-terminals are italicized. A typewriter
    4723 font is used for grammar terminals and program identifiers.
     3997Italic page numbers give the location of the main entry for the referenced term.
     3998Plain page numbers denote uses of the indexed term.
     3999Entries for grammar non-terminals are italicized.
     4000A typewriter font is used for grammar terminals and program identifiers.
    47244001\indexspace
    47254002\input{refrat.ind}
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