source: doc/refrat/refrat.tex @ 5ff188f

aaron-thesisarm-ehcleanup-dtorsdeferred_resndemanglerjacob/cs343-translationjenkins-sandboxnew-astnew-ast-unique-exprnew-envno_listpersistent-indexerresolv-newwith_gc
Last change on this file since 5ff188f was 5ff188f, checked in by Peter A. Buhr <pabuhr@…>, 4 years ago

further changes to document Makefiles

  • Property mode set to 100644
File size: 186.4 KB
Line 
1%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -*- Mode: Latex -*- %%%%%%%%%%%%%%%%%%%%%%%%%%%%
2%%
3%% Cforall Version 1.0.0 Copyright (C) 2016 University of Waterloo
4%%
5%% The contents of this file are covered under the licence agreement in the
6%% file "LICENCE" distributed with Cforall.
7%%
8%% refrat.tex --
9%%
10%% Author           : Peter A. Buhr
11%% Created On       : Wed Apr  6 14:52:25 2016
12%% Last Modified By : Peter A. Buhr
13%% Last Modified On : Wed Jan 31 17:30:23 2018
14%% Update Count     : 108
15%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
16
17% requires tex packages: texlive-base texlive-latex-base tex-common texlive-humanities texlive-latex-extra texlive-fonts-recommended
18
19\documentclass[openright,twoside,11pt]{report}
20
21%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
22
23% Latex packages used in the document.
24\usepackage[T1]{fontenc}                                % allow Latin1 (extended ASCII) characters
25\usepackage{textcomp}
26\usepackage[latin1]{inputenc}
27
28\usepackage{fullpage,times,comment}
29\usepackage{epic,eepic}
30\usepackage{upquote}                                                                    % switch curled `'" to straight
31\usepackage{calc}
32\usepackage{xspace}
33\usepackage{varioref}                                                                   % extended references
34\usepackage{listings}                                                                   % format program code
35\usepackage[flushmargin]{footmisc}                                              % support label/reference in footnote
36\usepackage{latexsym}                                   % \Box glyph
37\usepackage{mathptmx}                                   % better math font with "times"
38\usepackage[usenames]{color}
39\input{common}                                          % common CFA document macros
40\usepackage[dvips,plainpages=false,pdfpagelabels,pdfpagemode=UseNone,colorlinks=true,pagebackref=true,linkcolor=blue,citecolor=blue,urlcolor=blue,pagebackref=true,breaklinks=true]{hyperref}
41\usepackage{breakurl}
42\renewcommand{\UrlFont}{\small\sf}
43
44\usepackage[pagewise]{lineno}
45\renewcommand{\linenumberfont}{\scriptsize\sffamily}
46\usepackage[firstpage]{draftwatermark}
47\SetWatermarkLightness{0.9}
48
49% Default underscore is too low and wide. Cannot use lstlisting "literate" as replacing underscore
50% removes it as a variable-name character so keywords in variables are highlighted. MUST APPEAR
51% AFTER HYPERREF.
52\renewcommand{\textunderscore}{\leavevmode\makebox[1.2ex][c]{\rule{1ex}{0.075ex}}}
53
54\setlength{\topmargin}{-0.45in}                                                 % move running title into header
55\setlength{\headsep}{0.25in}
56
57%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
58
59\CFAStyle                                                                                               % use default CFA format-style
60\lstnewenvironment{C++}[1][]                            % use C++ style
61{\lstset{language=C++,moredelim=**[is][\protect\color{red}]{®}{®}#1}}
62{}
63
64% inline code ©...© (copyright symbol) emacs: C-q M-)
65% red highlighting ®...® (registered trademark symbol) emacs: C-q M-.
66% blue highlighting ß...ß (sharp s symbol) emacs: C-q M-_
67% green highlighting ¢...¢ (cent symbol) emacs: C-q M-"
68% LaTex escape §...§ (section symbol) emacs: C-q M-'
69% keyword escape ¶...¶ (pilcrow symbol) emacs: C-q M-^
70% math escape $...$ (dollar symbol)
71
72%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
73
74% Names used in the document.
75\newcommand{\Version}{\input{../../version}}
76\newcommand{\Textbf}[2][red]{{\color{#1}{\textbf{#2}}}}
77\newcommand{\Emph}[2][red]{{\color{#1}\textbf{\emph{#2}}}}
78\newcommand{\R}[1]{\Textbf{#1}}
79\newcommand{\B}[1]{{\Textbf[blue]{#1}}}
80\newcommand{\G}[1]{{\Textbf[OliveGreen]{#1}}}
81
82%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
83
84\setcounter{secnumdepth}{3}                             % number subsubsections
85\setcounter{tocdepth}{3}                                % subsubsections in table of contents
86\makeindex
87
88%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
89
90\title{\Huge
91\vspace*{1in}
92\CFA (\CFL) Reference Manual and Rationale
93}% title
94
95\author{\huge
96Glen Ditchfield and Peter A. Buhr
97}% author
98
99\date{
100\today
101}% date
102
103%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
104
105\begin{document}
106\pagestyle{headings}
107% changed after setting pagestyle
108\renewcommand{\chaptermark}[1]{\markboth{\thechapter\quad #1}{\thechapter\quad #1}}
109\renewcommand{\sectionmark}[1]{\markboth{\thesection\quad #1}{\thesection\quad #1}}
110\renewcommand{\subsectionmark}[1]{\markboth{\thesubsection\quad #1}{\thesubsection\quad #1}}
111\pagenumbering{roman}
112\linenumbers                                            % comment out to turn off line numbering
113
114\maketitle
115\thispagestyle{empty}
116\vspace*{\fill}
117\noindent
118\copyright\,2015 Glen Ditchfield \\ \\
119\noindent
120This work is licensed under the Creative Commons Attribution 4.0 International License.
121To view a copy of this license, visit {\small\url{http://creativecommons.org/licenses/by/4.0}}.
122\vspace*{1in}
123
124\clearpage
125\thispagestyle{plain}
126\pdfbookmark[1]{Contents}{section}
127\tableofcontents
128
129\clearpage
130\thispagestyle{plain}
131\pagenumbering{arabic}
132
133
134\chapter*{Introduction}\addcontentsline{toc}{chapter}{Introduction}
135
136This document is a reference manual and rationale for \CFA, a polymorphic extension of the C programming language.
137It covers low-level syntactic and semantic details of the language to address complex language issues for programmers, and provide language implementers with a precise language description.
138It makes frequent reference to the \Celeven standard~\cite{C11}, and occasionally compares \CFA to \CC~\cite{C++}.
139Changes to the syntax and additional features are expected to be included in later revisions.
140
141The manual deliberately imitates the ordering of the \Celeven standard (although the section numbering differs).
142Unfortunately, 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 \Celeven standard.
143For a simple introduction to \CFA, see~\cite{Cforall}.
144
145\begin{rationale}
146Commentary (like this) is quoted with quads.
147Commentary usually deals with subtle points, the rationale behind a rule, and design decisions.
148\end{rationale}
149
150% No ``Scope'' or ``Normative references'' chapters yet.
151
152
153\setcounter{chapter}{2}
154\chapter{Terms, definitions, and symbols}
155
156Terms from the \Celeven standard used in this document have the same meaning as in the \Celeven standard.
157
158% No ``Conformance'' or ``Environment'' chapters yet.
159
160
161\setcounter{chapter}{5}
162\chapter{Language}
163
164
165\section{Notation}
166The syntax notation used in this document is the same as in the \Celeven 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 \Celeven standard.
167
168
169\section{Concepts}
170
171
172\subsection{Scopes of identifiers}\index{scopes}
173
174\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 \Index{name space}, instead of hiding them.
175The 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 ©type©\use{type} or ©typedef©\use{typedef} declaration and the other is not.
176The outer declaration becomes \Index{visible} when the scope of the inner declaration terminates.
177\begin{rationale}
178Hence, a \CFA program can declare an ©int v© and a ©float v© in the same scope;
179a \CC program can not.
180\end{rationale}
181
182
183\subsection{Linkage of identifiers}
184\index{linkage}
185
186\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.
187Instead, 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 \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.
188Within one translation unit, each instance of an identifier with \Index{internal linkage} denotes the same object or function in the same circumstances.
189Identifiers with \Index{no linkage} always denote unique entities.
190\begin{rationale}
191A \CFA program can declare an ©extern int v© and an ©extern float v©;
192a C program cannot.
193\end{rationale}
194
195
196\setcounter{subsection}{8}
197\subsection{Generic Types}
198
199
200\subsubsection{Semantics}
201
202\CFA provides a capability for generic types;
203using 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.
204Syntactically a generic type generator is represented by putting a forall specifier on a struct or union declaration, as defined in \VRef{forall}.
205An instantiation of the generic type is written by specifying the type parameters in parentheses after the name of the generic type generator:
206\begin{lstlisting}
207forall( otype T | sumable( T ) ) struct pair {
208        T x;
209        T y;
210};
211pair( int ) p = { 3, 14 };
212\end{lstlisting}
213
214The type parameters in an instantiation of a generic type must satisfy any constraints in the forall specifier on the type generator declaration, e.g., ©sumable©.
215The instantiation then has the semantics that would result if the type parameters were substituted into the type generator declaration by macro substitution.
216
217Polymorphic 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:
218\begin{lstlisting}
219forall( otype T ) void swap( pair(T) *p ) {
220        T z = p->x;
221        p->x = p->y;
222        p->y = z;
223}
224\end{lstlisting}
225
226
227\subsubsection{Constraints}
228
229To avoid unduly constraining implementors, the generic type generator definition must be visible at any point where it is instantiated.
230Forward 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.
231
232\examples
233\begin{lstlisting}
234forall( otype T ) struct A;
235
236forall( otype T ) struct B {
237        A(T) *a;                        // legal, but cannot instantiate B(T)
238};
239
240B(T) x;                                 // illegal, *x.a is of an incomplete generic type
241 
242forall( otype T ) struct A {
243        B( T ) *b;
244};
245
246B( T ) y;                               // legal, *x.a is now of a complete generic type
247
248// box.h:
249        forall( otype T ) struct box;
250        forall( otype T ) box( T ) *make_box( T );
251        forall( otype T ) void use_box( box( T ) *b );
252       
253// main.c:
254        box( int ) *b = make_box( 42 ); // illegal, definition of box not visible
255        use_box( b );           // illegal
256\end{lstlisting}
257
258
259\section{Conversions}
260\CFA defines situations where values of one type are automatically converted to another type.
261These conversions are called \define{implicit conversion}s.
262The programmer can request \define{explicit conversion}s using cast expressions.
263
264
265\subsection{Arithmetic operands}
266
267
268\setcounter{subsubsection}{8}
269\subsubsection{Safe arithmetic conversions}
270
271In 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.
272In \CFA, these conversions play a role in overload resolution, and collectively are called the \define{safe arithmetic conversion}s.
273
274Let ©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}} $r$.
275Let ©unsigned$_{mr}$© be the unsigned integer type with maximal rank.
276
277The following conversions are \emph{direct} safe arithmetic conversions.
278\begin{itemize}
279\item
280The \Index{integer promotion}s.
281\item
282For every rank $r$ greater than or equal to the rank of ©int©, conversion from ©int$_r$© to ©unsigned$_r$©.
283\item
284For every rank $r$ greater than or equal to the rank of ©int©, where ©int$_{r+1}$© exists and can represent all values of ©unsigned$_r$©, conversion from ©unsigned$_r$© to ©int$_{r+1}$©.
285\item
286Conversion from ©unsigned$_{mr}$© to ©float©.
287\item
288Conversion from an enumerated type to its compatible integer type.
289\item
290Conversion from ©float© to ©double©, and from ©double© to ©long double©.
291\item
292Conversion from ©float _Complex© to ©double _Complex©, and from ©double _Complex© to ©long double _Complex©.
293\begin{sloppypar}
294\item
295Conversion from ©float _Imaginary© to ©double _Imaginary©, and from ©double _Imaginary© to ©long double _Imaginary©, if the implementation supports imaginary types.
296\end{sloppypar}
297\end{itemize}
298
299If type ©T© can be converted to type ©U© by a safe direct arithmetic conversion and type ©U© can be converted to type ©V© by a safe arithmetic conversion, then the conversion from ©T© to type ©V© is an \emph{indirect} safe arithmetic conversion.
300
301\begin{rationale}
302Note that \Celeven 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.
303\end{rationale}
304
305
306\subsection{Other operands}
307
308
309\setcounter{subsubsection}{3}
310\subsubsection{Anonymous structures and unions}
311\label{anon-conv}
312
313If an expression's type is a pointer to a structure or union type that has a member that is an \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.
314The result of the conversion is a pointer to the member.
315
316\examples
317\begin{lstlisting}
318struct point {
319        int x, y;
320};
321void move_by( struct point * p1, struct point * p2 ) {§\impl{move_by}§
322        p1->x += p2.x;
323        p1->y += p2.y;
324}
325struct color_point {
326        enum { RED, BLUE, GREEN } color;
327        struct point;
328} cp1, cp2;
329move_to( &cp1, &cp2 );
330\end{lstlisting}
331Thanks to implicit conversion, the two arguments that ©move_by()© receives are pointers to ©cp1©'s second member and ©cp2©'s second member.
332
333
334\subsubsection{Specialization}
335A function or value whose type is polymorphic may be implicitly converted to one whose type is \Index{less polymorphic} by binding values to one or more of its \Index{inferred parameter}.
336Any value that is legal for the inferred parameter may be used, including other inferred parameters.
337
338If, 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 type} with or can be specialized to the type of the assertion parameter.
339The assertion parameter is bound to that object or function.
340
341The 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.
342
343\examples
344The type
345\begin{lstlisting}
346forall( otype T, otype U ) void (*)( T, U );
347\end{lstlisting}
348can be specialized to (among other things)
349\begin{lstlisting}
350forall( otype T ) void (*)( T, T );             // U bound to T
351forall( otype T ) void (*)( T, real );  // U bound to real
352forall( otype U ) void (*)( real, U );  // T bound to real
353void f( real, real );                                   // both bound to real
354\end{lstlisting}
355
356The type
357\begin{lstlisting}
358forall( otype T | T ?+?( T, T ) ) T (*)( T );
359\end{lstlisting}
360can be specialized to (among other things)
361\begin{lstlisting}
362int (*)( int );         // T bound to int, and T ?+?(T, T ) bound to int ?+?( int, int )
363\end{lstlisting}
364
365
366\subsubsection{Safe conversions}
367
368A \define{direct safe conversion} is one of the following conversions:
369\begin{itemize}
370\item
371a direct safe arithmetic conversion;
372\item
373from any object type or incomplete type to ©void©;
374\item
375from a pointer to any non-©void© type to a pointer to ©void©;
376\item
377from a pointer to any type to a pointer to a more qualified version of the type\index{qualified type};
378\item
379from 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};
380\item
381within 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.
382\end{itemize}
383
384Conversions that are not safe conversions are \define{unsafe conversion}s.
385\begin{rationale}
386As in C, there is an implicit conversion from ©void *© to any pointer type.
387This is clearly dangerous, and \CC does not have this implicit conversion.
388\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.
389\end{rationale}
390
391
392\subsection{Conversion cost}
393
394The \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.
395It is defined as follows.
396\begin{itemize}
397\item
398The cost of a conversion from any type to itself is 0.
399
400\item
401The cost of a direct safe conversion is 1.
402
403\item
404The cost of an indirect safe arithmetic conversion is the smallest number of direct conversions needed to make up the conversion.
405\end{itemize}
406
407\examples
408In the following, assume an implementation that does not provide any extended integer types.
409
410\begin{itemize}
411\item
412The cost of an implicit conversion from ©int© to ©long© is 1.
413The cost of an implicit conversion from ©long© to ©double© is 3, because it is defined in terms of conversions from ©long© to ©unsigned long©, then to ©float©, and then to ©double©.
414
415\item
416If ©int© can represent all the values of ©unsigned short©, then the cost of an implicit conversion from ©unsigned short© to ©unsigned© is 2: ©unsigned short© to ©int© to ©unsigned©.
417Otherwise, ©unsigned short© is converted directly to ©unsigned©, and the cost is 1.
418
419\item
420If ©long© can represent all the values of ©unsigned©, then the conversion cost of ©unsigned© to ©long© is 1.
421Otherwise, the conversion is an unsafe conversion, and its conversion cost is undefined.
422\end{itemize}
423
424
425\section{Lexical elements}
426
427
428\subsection{Keywords}
429
430\begin{syntax}
431\lhs{keyword} one of
432\rhs \dots
433\rhs \input{keywords}
434\end{syntax}
435
436
437\subsection{Identifiers}
438
439\CFA allows operator \Index{overloading} by associating operators with special function identifiers.
440Furthermore, the constants ``©0©'' and ``©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.
441Programmers can use these identifiers to declare functions and objects that implement operators and constants for their own types.
442
443
444\setcounter{subsubsection}{2}
445\subsubsection{Constant identifiers}
446
447\begin{syntax}
448\oldlhs{identifier}
449\rhs ©0©
450\rhs ©1©
451\end{syntax}
452
453\index{constant identifiers}\index{identifiers!for constants} The tokens ``©0©''\impl{0} and ``©1©''\impl{1} are identifiers.
454No other tokens defined by the rules for integer constants are considered to be identifiers.
455\begin{rationale}
456Why ``©0©'' and ``©1©''? Those integers have special status in C.
457All scalar types can be incremented and decremented, which is defined in terms of adding or subtracting 1.
458The operations ``©&&©'', ``©||©'', and ``©!©'' can be applied to any scalar arguments, and are defined in terms of comparison against 0.
459A \nonterm{constant-expression} that evaluates to 0 is effectively compatible with every pointer type.
460
461In 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 0 as a special case.
462However, 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.
463Defining special constants for a user-defined type is more efficient than defining a conversion to the type from ©_Bool©.
464
465Why \emph{just} ``©0©'' and ``©1©''? Why not other integers? No other integers have special status in C.
466A facility that let programmers declare specific constants---``©const Rational 12©'', for instance---would not be much of an improvement.
467Some facility for defining the creation of values of programmer-defined types from arbitrary integer tokens would be needed.
468The complexity of such a feature doesn't seem worth the gain.
469\end{rationale}
470
471
472\subsubsection{Operator identifiers}
473
474\index{operator identifiers}\index{identifiers!for operators} Table \ref{opids} lists the programmer-definable operator identifiers and the operations they are associated with.
475Functions 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.
476The relationships between operators and function calls are discussed in descriptions of the operators.
477
478\begin{table}[hbt]
479\centering
480\input{operidents}
481\caption{Operator Identifiers}
482\label{opids}
483\end{table}
484
485\begin{rationale}
486Operator identifiers are made up of the characters of the operator token, with question marks added to mark the positions of the arguments of operators.
487The question marks serve as mnemonic devices;
488programmers can not create new operators by arbitrarily mixing question marks and other non-alphabetic characters.
489Note that prefix and postfix versions of the increment and decrement operators are distinguished by the position of the question mark.
490\end{rationale}
491
492\begin{rationale}
493The use of ``©?©'' in identifiers means that some C programs are not \CFA programs.
494For instance, the sequence of characters ``©(i < 0)?--i:i©'' is legal in a C program, but a \CFA compiler detects a syntax error because it treats ``©?--©'' as an identifier, not as the two tokens ``©?©'' and ``©--©''.
495\end{rationale}
496
497\begin{rationale}
498Certain operators \emph{cannot} be defined by the programmer:
499\begin{itemize}
500\item
501The logical operators ``©&&©'' and ``©||©'', and the conditional operator ``©?:©''.
502These 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.
503Note that the definitions of ``©&&©'' and ``©||©'' say that they work by checking that their arguments are unequal to 0, so defining ``©!=©'' and ``©0©'' for user-defined types is enough to allow them to be used in logical expressions.
504
505\item
506The comma operator\index{comma expression}.
507It is a control-flow operator like those above.
508Changing its meaning seems pointless and confusing.
509
510\item
511The ``address of'' operator.
512It would seem useful to define a unary ``©&©'' operator that returns values of some programmer-defined pointer-like type.
513The problem lies with the type of the operator.
514Consider the expression ``©p = &x©'', where ©x© is of type ©T© and ©p© has the programmer-defined type ©T_ptr©.
515The expression might be treated as a call to the unary function ``©&?©''.
516Now what is the type of the function's parameter? It can not be ©T©, because then ©x© would be passed by value, and there is no way to create a useful pointer-like result from a value.
517Hence the parameter must have type ©T *©.
518But then the expression must be rewritten as ``©p = &?( &x )©''
519---which doesn't seem like progress!
520
521The 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''.
522It seems simpler to define a conversion function from ©T *© to ©T_ptr©.
523
524\item
525The ©sizeof© operator.
526It is already defined for every object type, and intimately tied into the language's storage allocation model.
527Redefining it seems pointless.
528
529\item
530The ``member of'' operators ``©.©'' and ``©->©''.
531These are not really infix operators, since their right ``operand'' is not a value or object.
532
533\item
534Cast operators\index{cast expression}.
535Anything that can be done with an explicit cast can be done with a function call.
536The difference in syntax is small.
537\end{itemize}
538\end{rationale}
539
540
541\section{Expressions}
542
543\CFA allows operators and identifiers to be overloaded.
544Hence, each expression can have a number of \define{interpretation}s, each of which has a different type.
545The interpretations that are potentially executable are called \define{valid interpretation}s.
546The set of interpretations depends on the kind of expression and on the interpretations of the subexpressions that it contains.
547The rules for determining the valid interpretations of an expression are discussed below for each kind of expression.
548Eventually the context of the outermost expression chooses one interpretation of that expression.
549
550An \define{ambiguous interpretation} is an interpretation which does not specify the exact object or function denoted by every identifier in the expression.
551An expression can have some interpretations that are ambiguous and others that are unambiguous.
552An expression that is chosen to be executed shall not be ambiguous.
553
554The \define{best valid interpretations} are the valid interpretations that use the fewest unsafe\index{unsafe conversion} conversions.
555Of these, the best are those where the functions and objects involved are the least polymorphic\index{less polymorphic}.
556Of these, the best have the lowest total \Index{conversion cost}, including all implicit conversions in the argument expressions.
557Of these, the best have the highest total conversion cost for the implicit conversions
558(if any) applied to the argument expressions.
559If there is no single best valid interpretation, or if the best valid interpretation is ambiguous, then the resulting interpretation is ambiguous\index{ambiguous interpretation}.
560
561\begin{rationale}
562\CFA's rules for selecting the best interpretation are designed to allow overload resolution to mimic C's operator semantics.
563In 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.
564In \CFA, those conversions are ``safe''.
565The ``fewest unsafe conversions'' rule ensures that the usual conversions are done, if possible.
566The ``lowest total expression cost'' rule chooses the proper common type.
567The 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: ©(double)-i© will be preferred to ©-(double)i©.
568
569The ``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.
570It also gives preference to monomorphic values (such as the ©int© ©0©) over polymorphic values (such as the \Index{null pointer} ©0©\use{0}).
571However, interpretations that call polymorphic functions are preferred to interpretations that perform unsafe conversions, because those conversions potentially lose accuracy or violate strong typing.
572
573There are two notable differences between \CFA's overload resolution rules and the rules for
574\CC defined in \cite{C++}.
575First, the result type of a function plays a role.
576In \CC, a function call must be completely resolved based on the arguments to the call in most circumstances.
577In \CFA, a function call may have several interpretations, each with a different result type, and the interpretations of the containing context choose among them.
578Second, safe conversions are used to choose among interpretations of all sorts of functions;
579in \CC, the ``usual arithmetic conversions'' are a separate set of rules that apply only to the built-in operators.
580\end{rationale}
581
582Expressions involving certain operators\index{operator identifiers} are considered to be equivalent to function calls.
583A transformation from ``operator'' syntax to ``function call'' syntax is defined by \define{rewrite rules}.
584Each operator has a set of predefined functions that overload its identifier.
585Overload resolution determines which member of the set is executed in a given expression.
586The functions have \Index{internal linkage} and are implicitly declared with \Index{file scope}.
587The predefined functions and rewrite rules are discussed below for each of these operators.
588\begin{rationale}
589Predefined functions and constants have internal linkage because that simplifies optimization in traditional compile-and-link environments.
590For instance, ``©an_int + an_int©'' is equivalent to ``©?+?(an_int, an_int)©''.
591If integer addition has not been redefined in the current scope, a compiler can generate code to perform the addition directly.
592If predefined functions had external linkage, this optimization would be difficult.
593\end{rationale}
594
595\begin{rationale}
596Since 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.
597Such an algorithm was first described (for Ada) by Baker~\cite{Baker82}.
598It is extended here to handle polymorphic functions and arithmetic conversions.
599The 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.
600\end{rationale}
601
602\begin{rationale}
603Expression syntax is quoted from the \Celeven standard.
604The syntax itself defines the precedence and associativity of operators.
605The sections are arranged in decreasing order of precedence, with all operators in a section having the same precedence.
606\end{rationale}
607
608
609\subsection{Primary expressions}
610
611\begin{syntax}
612\lhs{primary-expression}
613\rhs \nonterm{identifier}
614\rhs \nonterm{constant}
615\rhs \nonterm{string-literal}
616\rhs ©(© \nonterm{expression} ©)©
617\rhs \nonterm{generic-selection}
618\end{syntax}
619
620\predefined
621\begin{lstlisting}
622const int 1;§\use{1}§
623const int 0;§\use{0}§
624forall( dtype DT ) DT * const 0;
625forall( ftype FT ) FT * const 0;
626\end{lstlisting}
627
628\semantics
629The \Index{valid interpretation} of an \nonterm{identifier} are given by the visible\index{visible} declarations of the identifier.
630
631A \nonterm{constant} or \nonterm{string-literal} has one valid interpretation, which has the type and value defined by \Celeven.
632The predefined integer identifiers ``©1©'' and ``©0©'' have the integer values 1 and 0, respectively.
633The other two predefined ``©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.
634
635A parenthesised expression has the same interpretations as the contained \nonterm{expression}.
636
637\examples
638The expression ©(void *)0©\use{0} specializes the (polymorphic) null pointer to a null pointer to ©void©. ©(const void *)0© does the same, and also uses a safe conversion from ©void *© to ©const void *©.
639In each case, the null pointer conversion is better\index{best valid interpretations} than the unsafe conversion of the integer ©0© to a pointer.
640
641\begin{rationale}
642Note that the predefined identifiers have addresses.
643
644\CFA does not have C's concept of ``null pointer constants'', which are not typed values but special strings of tokens.
645The C token ``©0©'' is an expression of type ©int© with the value ``zero'', and it \emph{also} is a null pointer constant.
646Similarly, ``©(void *)0© is an expression of type ©(void *)© whose value is a null pointer, and it also is a null pointer constant.
647However, in C, ``©(void *)(void *)0©'' is
648\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.
649
650\CFA handles these cases through overload resolution.
651The declaration
652\begin{lstlisting}
653forall( dtype DT ) DT * const 0;
654\end{lstlisting} means that ©0© is a polymorphic object, and contains a value that can have \emph{any} pointer-to-object type or pointer-to-incomplete type.
655The only such value is the null pointer.
656Therefore the type \emph{alone} is enough to identify a null pointer.
657Where C defines an operator with a special case for the null pointer constant, \CFA defines predefined functions with a polymorphic object parameter.
658\end{rationale}
659
660
661\subsubsection{Generic selection}
662
663\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.
664If a generic selection has no ©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.
665
666\semantics
667A generic selection has the same interpretations as its result expression.
668
669
670\subsection{Postfix operators}
671
672\begin{syntax}
673\lhs{postfix-expression}
674\rhs \nonterm{primary-expression}
675\rhs \nonterm{postfix-expression} ©[© \nonterm{expression} ©]©
676\rhs \nonterm{postfix-expression} ©(©
677         \nonterm{argument-expression-list}\opt ©)©
678\rhs \nonterm{postfix-expression} ©.© \nonterm{identifier}
679\rhs \nonterm{postfix-expression} ©->© \nonterm{identifier}
680\rhs \nonterm{postfix-expression} ©++©
681\rhs \nonterm{postfix-expression} ©--©
682\rhs ©(© \nonterm{type-name} ©)© ©{© \nonterm{initializer-list} ©}©
683\rhs ©(© \nonterm{type-name} ©)© ©{© \nonterm{initializer-list} ©,© ©}©
684\lhs{argument-expression-list}
685\rhs \nonterm{assignment-expression}
686\rhs \nonterm{argument-expression-list} ©,©
687         \nonterm{assignment-expression}
688\end{syntax}
689
690\rewriterules
691\begin{lstlisting}
692a[b] => ?[?]( b, a ) // if a has integer type§\use{?[?]}§
693a[b] => ?[?]( a, b ) // otherwise
694a( §\emph{arguments}§ ) => ?()( a, §\emph{arguments}§ )§\use{?()}§
695a++ => ?++(&( a ))§\use{?++}§
696a-- => ?--(&( a ))§\use{?--}§
697\end{lstlisting}
698
699
700\subsubsection{Array subscripting}
701
702\predefined
703\begin{lstlisting}
704forall( otype T ) lvalue T ?[?]( T *, ptrdiff_t );§\use{ptrdiff_t}§
705forall( otype T ) lvalue _Atomic T ?[?]( _Atomic T *, ptrdiff_t );
706forall( otype T ) lvalue const T ?[?]( const T *, ptrdiff_t );
707forall( otype T ) lvalue restrict T ?[?]( restrict T *, ptrdiff_t );
708forall( otype T ) lvalue volatile T ?[?]( volatile T *, ptrdiff_t );
709forall( otype T ) lvalue _Atomic const T ?[?]( _Atomic const T *, ptrdiff_t );
710forall( otype T ) lvalue _Atomic restrict T ?[?]( _Atomic restrict T *, ptrdiff_t );
711forall( otype T ) lvalue _Atomic volatile T ?[?]( _Atomic volatile T *, ptrdiff_t );
712forall( otype T ) lvalue const restrict T ?[?]( const restrict T *, ptrdiff_t );
713forall( otype T ) lvalue const volatile T ?[?]( const volatile T *, ptrdiff_t );
714forall( otype T ) lvalue restrict volatile T ?[?]( restrict volatile T *, ptrdiff_t );
715forall( otype T ) lvalue _Atomic const restrict T ?[?]( _Atomic const restrict T *, ptrdiff_t );
716forall( otype T ) lvalue _Atomic const volatile T ?[?]( _Atomic const volatile T *, ptrdiff_t );
717forall( otype T ) lvalue _Atomic restrict volatile T ?[?]( _Atomic restrict volatile T *, ptrdiff_t );
718forall( otype T ) lvalue const restrict volatile T ?[?]( const restrict volatile T *, ptrdiff_t );
719forall( otype T ) lvalue _Atomic const restrict volatile T ?[?]( _Atomic const restrict volatile T *, ptrdiff_t );
720\end{lstlisting}
721\semantics
722The interpretations of subscript expressions are the interpretations of the corresponding function call expressions.
723\begin{rationale}
724C defines subscripting as pointer arithmetic in a way that makes ©a[i]© and ©i[a]© equivalent. \CFA provides the equivalence through a rewrite rule to reduce the number of overloadings of ©?[?]©.
725
726Subscript expressions are rewritten as function calls that pass the first parameter by value.
727This is somewhat unfortunate, since array-like types tend to be large.
728The alternative is to use the rewrite rule ``©a[b] => ?[?](&(a), b)©''.
729However, C semantics forbid this approach: the ©a© in ``©a[b]©'' can be an arbitrary pointer value, which does not have an address.
730
731The repetitive form of the predefined identifiers shows up a deficiency\index{deficiencies!pointers
732 to qualified types} of \CFA's type system.
733Type 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.
734\end{rationale}
735
736
737\subsubsection{Function calls}
738
739\semantics
740A \define{function designator} is an interpretation of an expression that has function type.
741The
742\nonterm{postfix-expression} in a function call may have some interpretations that are function designators and some that are not.
743
744For those interpretations of the \nonterm{postfix-expression} that are not function designators, the expression is rewritten and becomes a call of a function named ``©?()©''.
745The valid interpretations of the rewritten expression are determined in the manner described below.
746
747Each combination of function designators and argument interpretations is considered.
748For 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:
749\begin{itemize}
750\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
751\item if the function designator's type does not include a prototype or if the argument corresponds to ``©...©'' in a prototype, a \Index{default argument promotion} is applied to it.
752\end{itemize}
753The type of the valid interpretation is the return type of the function designator.
754
755For those combinations where the interpretation of the \nonterm{postfix-expression} is a \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
756\begin{itemize}
757\item
758If the declaration of the implicit parameter uses \Index{type-class} ©type©\use{type}, the implicit argument must be an object type;
759if it uses ©dtype©, the implicit argument must be an object type or an incomplete type;
760and if it uses ©ftype©, the implicit argument must be a function type.
761
762\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.
763
764\item the remaining explicit arguments must match the remaining explicit parameters, as described for monomorphic function designators.
765
766\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.
767\end{itemize}
768There is a valid interpretation for each such set of implicit parameters.
769The type of each valid interpretation is the return type of the function designator with implicit parameter values substituted for the implicit arguments.
770
771A valid interpretation is ambiguous\index{ambiguous interpretation} if the function designator or any of the argument interpretations is ambiguous.
772
773Every valid interpretation whose return type is not compatible with any other valid interpretation's return type is an interpretation of the function call expression.
774
775Every set of valid interpretations that have mutually compatible\index{compatible type} result types also produces an interpretation of the function call expression.
776The 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}.
777\begin{rationale}
778One 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}.
779For instance, it should be possible to replace a function ``©int f( int );©'' with ``©forall( otype T ) T f( T );©'' without affecting any calls of ©f©.
780
781\CFA\index{deficiencies!generalizability} does not fully possess this property, because \Index{unsafe conversion} are not done when arguments are passed to polymorphic parameters.
782Consider
783\begin{lstlisting}
784float g( float, float );
785int i;
786float f;
787double d;
788f = g( f, f );          // (1)
789f = g( i, f );          // (2) (safe conversion to float)
790f = g( d, f );          // (3) (unsafe conversion to float)
791\end{lstlisting}
792If ©g© was replaced by ``©forall( otype T ) T g( T, T );©'', the first and second calls would be unaffected, but the third would change: ©f© would be converted to ©double©, and the result would be a ©double©.
793
794Another example is the function ``©void h( int *);©''.
795This function can be passed a ©void *© argument, but the generalization ``©forall( otype T ) void h( T *);©'' can not.
796In this case, ©void© is not a valid value for ©T© because it is not an object type.
797If unsafe conversions were allowed, ©T© could be inferred to be \emph{any} object type, which is undesirable.
798\end{rationale}
799
800\examples
801A function called ``©?()©'' might be part of a numerical differentiation package.
802\begin{lstlisting}
803extern otype Derivative;
804extern double ?()( Derivative, double );
805extern Derivative derivative_of( double (*f)( double ) );
806extern double sin( double );
807
808Derivative sin_dx = derivative_of( sin );
809double d;
810d = sin_dx( 12.9 );
811\end{lstlisting}
812Here, the only interpretation of ©sin_dx© is as an object of type ©Derivative©.
813For that interpretation, the function call is treated as ``©?()( sin_dx, 12.9 )©''.
814\begin{lstlisting}
815int f( long );          // (1)
816int f( int, int );      // (2)
817int f( int *);          // (3)
818int i = f( 5 );         // calls (1)
819\end{lstlisting}
820Function (1) provides a valid interpretation of ``©f( 5 )©'', using an implicit ©int© to ©long© conversion.
821The other functions do not, since the second requires two arguments, and since there is no implicit conversion from ©int© to ©int *© that could be used with the third function.
822
823\begin{lstlisting}
824forall( otype T ) T h( T );
825double d = h( 1.5 );
826\end{lstlisting}
827``©1.5©'' is a ©double© constant, so ©T© is inferred to be ©double©, and the result of the function call is a ©double©.
828
829\begin{lstlisting}
830forall( otype T, otype U ) void g( T, U );      // (4)
831forall( otype T ) void g( T, T );                       // (5)
832forall( otype T ) void g( T, long );            // (6)
833void g( long, long );                                           // (7)
834double d;
835int i;
836int *p;
837g( d, d );                                                                      // calls (5)
838g( d, i );                                                                      // calls (6)
839g( i, i );                                                                      // calls (7)
840g( i, p );                                                                      // calls (4)
841\end{lstlisting}
842The first call has valid interpretations for all four versions of ©g©. (6) and (7) are discarded because they involve unsafe ©double©-to-©long© conversions. (5) is chosen because it is less polymorphic than (4).
843
844For the second call, (7) is again discarded.
845Of the remaining interpretations for (4), (5), and (6) (with ©i© converted to ©long©), (6) is chosen because it is the least polymorphic.
846
847The third call has valid interpretations for all of the functions;
848(7) is chosen since it is not polymorphic at all.
849
850The fourth call has no interpretation for (5), because its arguments must have compatible type. (4) is chosen because it does not involve unsafe conversions.
851\begin{lstlisting}
852forall( otype T ) T min( T, T );
853double max( double, double );
854trait min_max( T ) {§\impl{min_max}§
855        T min( T, T );
856        T max( T, T );
857}
858forall( otype U | min_max( U ) ) void shuffle( U, U );
859shuffle( 9, 10 );
860\end{lstlisting}
861The only possibility for ©U© is ©double©, because that is the type used in the only visible ©max© function. 9 and 10 must be converted to ©double©, and ©min© must be specialized with ©T© bound to ©double©.
862\begin{lstlisting}
863extern void q( int );                                           // (8)
864extern void q( void * );                                        // (9)
865extern void r();
866q( 0 );
867r( 0 );
868\end{lstlisting}
869The ©int 0© could be passed to (8), or the ©(void *)© \Index{specialization} of the null pointer\index{null pointer} ©0©\use{0} could be passed to (9).
870The former is chosen because the ©int© ©0© is \Index{less polymorphic}.
871For the same reason, ©int© ©0© is passed to ©r()©, even though it has \emph{no} declared parameter types.
872
873
874\subsubsection{Structure and union members}
875
876\semantics In the member selection expression ``©s©.©m©'', there shall be at least one interpretation of ©s© whose type is a structure type or union type containing a member named ©m©.
877If two or more interpretations of ©s© have members named ©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.
878If an interpretation of ©s© has a member ©m© whose type is not compatible with any other ©s©'s ©m©, then the expression has an interpretation with the member's type.
879The expression has no other interpretations.
880
881The expression ``©p->m©'' has the same interpretations as the expression ``©(*p).m©''.
882
883
884\subsubsection{Postfix increment and decrement operators}
885
886\predefined
887\begin{lstlisting}
888_Bool ?++( volatile _Bool * ), ?++( _Atomic volatile _Bool * );
889char ?++( volatile char * ), ?++( _Atomic volatile char * );
890signed char ?++( volatile signed char * ), ?++( _Atomic volatile signed char * );
891unsigned char ?++( volatile signed char * ), ?++( _Atomic volatile signed char * );
892short int ?++( volatile short int * ), ?++( _Atomic volatile short int * );
893unsigned short int ?++( volatile unsigned short int * ), ?++( _Atomic volatile unsigned short int * );
894int ?++( volatile int * ), ?++( _Atomic volatile int * );
895unsigned int ?++( volatile unsigned int * ), ?++( _Atomic volatile unsigned int * );
896long int ?++( volatile long int * ), ?++( _Atomic volatile long int * );
897long unsigned int ?++( volatile long unsigned int * ), ?++( _Atomic volatile long unsigned int * );
898long long int ?++( volatile long long int * ), ?++( _Atomic volatile long long int * );
899long long unsigned ?++( volatile long long unsigned int * ), ?++( _Atomic volatile long long unsigned int * );
900float ?++( volatile float * ), ?++( _Atomic volatile float * );
901double ?++( volatile double * ), ?++( _Atomic volatile double * );
902long double ?++( volatile long double * ), ?++( _Atomic volatile long double * );
903
904forall( otype T ) T * ?++( T * restrict volatile * ), * ?++( T * _Atomic restrict volatile * );
905forall( otype T ) _Atomic T * ?++( _Atomic T * restrict volatile * ), * ?++( _Atomic T * _Atomic restrict volatile * );
906forall( otype T ) const T * ?++( const T * restrict volatile * ), * ?++( const T * _Atomic restrict volatile * );
907forall( otype T ) volatile T * ?++( volatile T * restrict volatile * ), * ?++( volatile T * _Atomic restrict volatile * );
908forall( otype T ) restrict T * ?++( restrict T * restrict volatile * ), * ?++( restrict T * _Atomic restrict volatile * );
909forall( otype T ) _Atomic const T * ?++( _Atomic const T * restrict volatile * ),
910        * ?++( _Atomic const T * _Atomic restrict volatile * );
911forall( otype T ) _Atomic restrict T * ?++( _Atomic restrict T * restrict volatile * ),
912        * ?++( _Atomic restrict T * _Atomic restrict volatile * );
913forall( otype T ) _Atomic volatile T * ?++( _Atomic volatile T * restrict volatile * ),
914        * ?++( _Atomic volatile T * _Atomic restrict volatile * );
915forall( otype T ) const restrict T * ?++( const restrict T * restrict volatile * ),
916        * ?++( const restrict T * _Atomic restrict volatile * );
917forall( otype T ) const volatile T * ?++( const volatile T * restrict volatile * ),
918        * ?++( const volatile T * _Atomic restrict volatile * );
919forall( otype T ) restrict volatile T * ?++( restrict volatile T * restrict volatile * ),
920        * ?++( restrict volatile T * _Atomic restrict volatile * );
921forall( otype T ) _Atomic const restrict T * ?++( _Atomic const restrict T * restrict volatile * ),
922        * ?++( _Atomic const restrict T * _Atomic restrict volatile * );
923forall( otype T ) _Atomic const volatile T * ?++( _Atomic const volatile T * restrict volatile * ),
924        * ?++( _Atomic const volatile T * _Atomic restrict volatile * );
925forall( otype T ) _Atomic restrict volatile T * ?++( _Atomic restrict volatile T * restrict volatile * ),
926        * ?++( _Atomic restrict volatile T * _Atomic restrict volatile * );
927forall( otype T ) const restrict volatile T * ?++( const restrict volatile T * restrict volatile * ),
928        * ?++( const restrict volatile T * _Atomic restrict volatile * );
929forall( otype T ) _Atomic const restrict volatile T * ?++( _Atomic const restrict volatile T * restrict volatile * ),
930        * ?++( _Atomic const restrict volatile T * _Atomic restrict volatile * );
931
932_Bool ?--( volatile _Bool * ), ?--( _Atomic volatile _Bool * );
933char ?--( volatile char * ), ?--( _Atomic volatile char * );
934signed char ?--( volatile signed char * ), ?--( _Atomic volatile signed char * );
935unsigned char ?--( volatile signed char * ), ?--( _Atomic volatile signed char * );
936short int ?--( volatile short int * ), ?--( _Atomic volatile short int * );
937unsigned short int ?--( volatile unsigned short int * ), ?--( _Atomic volatile unsigned short int * );
938int ?--( volatile int * ), ?--( _Atomic volatile int * );
939unsigned int ?--( volatile unsigned int * ), ?--( _Atomic volatile unsigned int * );
940long int ?--( volatile long int * ), ?--( _Atomic volatile long int * );
941long unsigned int ?--( volatile long unsigned int * ), ?--( _Atomic volatile long unsigned int * );
942long long int ?--( volatile long long int * ), ?--( _Atomic volatile long long int * );
943long long unsigned ?--( volatile long long unsigned int * ), ?--( _Atomic volatile long long unsigned int * );
944float ?--( volatile float * ), ?--( _Atomic volatile float * );
945double ?--( volatile double * ), ?--( _Atomic volatile double * );
946long double ?--( volatile long double * ), ?--( _Atomic volatile long double * );
947
948forall( otype T ) T * ?--( T * restrict volatile * ), * ?--( T * _Atomic restrict volatile * );
949forall( otype T ) _Atomic T * ?--( _Atomic T * restrict volatile * ), * ?--( _Atomic T * _Atomic restrict volatile * );
950forall( otype T ) const T * ?--( const T * restrict volatile * ), * ?--( const T * _Atomic restrict volatile * );
951forall( otype T ) volatile T * ?--( volatile T * restrict volatile * ), * ?--( volatile T * _Atomic restrict volatile * );
952forall( otype T ) restrict T * ?--( restrict T * restrict volatile * ), * ?--( restrict T * _Atomic restrict volatile * );
953forall( otype T ) _Atomic const T * ?--( _Atomic const T * restrict volatile * ),
954        * ?--( _Atomic const T * _Atomic restrict volatile * );
955forall( otype T ) _Atomic restrict T * ?--( _Atomic restrict T * restrict volatile * ),
956        * ?--( _Atomic restrict T * _Atomic restrict volatile * );
957forall( otype T ) _Atomic volatile T * ?--( _Atomic volatile T * restrict volatile * ),
958        * ?--( _Atomic volatile T * _Atomic restrict volatile * );
959forall( otype T ) const restrict T * ?--( const restrict T * restrict volatile * ),
960        * ?--( const restrict T * _Atomic restrict volatile * );
961forall( otype T ) const volatile T * ?--( const volatile T * restrict volatile * ),
962        * ?--( const volatile T * _Atomic restrict volatile * );
963forall( otype T ) restrict volatile T * ?--( restrict volatile T * restrict volatile * ),
964        * ?--( restrict volatile T * _Atomic restrict volatile * );
965forall( otype T ) _Atomic const restrict T * ?--( _Atomic const restrict T * restrict volatile * ),
966        * ?--( _Atomic const restrict T * _Atomic restrict volatile * );
967forall( otype T ) _Atomic const volatile T * ?--( _Atomic const volatile T * restrict volatile * ),
968        * ?--( _Atomic const volatile T * _Atomic restrict volatile * );
969forall( otype T ) _Atomic restrict volatile T * ?--( _Atomic restrict volatile T * restrict volatile * ),
970        * ?--( _Atomic restrict volatile T * _Atomic restrict volatile * );
971forall( otype T ) const restrict volatile T * ?--( const restrict volatile T * restrict volatile * ),
972        * ?--( const restrict volatile T * _Atomic restrict volatile * );
973forall( otype T ) _Atomic const restrict volatile T * ?--( _Atomic const restrict volatile T * restrict volatile * ),
974        * ?--( _Atomic const restrict volatile T * _Atomic restrict volatile * );
975\end{lstlisting}
976For every extended integer type ©X© there exist
977% Don't use predefined: keep this out of prelude.cf.
978\begin{lstlisting}
979X ?++( volatile X * ), ?++( _Atomic volatile X * ),
980  ?--( volatile X * ), ?--( _Atomic volatile X * );
981\end{lstlisting}
982For every complete enumerated type ©E© there exist
983% Don't use predefined: keep this out of prelude.cf.
984\begin{lstlisting}
985E ?++( volatile E * ), ?++( _Atomic volatile E * ),
986  ?--( volatile E * ), ?--( _Atomic volatile E * );
987\end{lstlisting}
988
989\begin{rationale}
990Note that ``©++©'' and ``©--©'' 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.
991This partially enforces the C semantic rule that such operands must be \emph{modifiable} lvalues.
992\end{rationale}
993
994\begin{rationale}
995In C, a semantic rule requires that pointer operands of increment and decrement be pointers to object types.
996Hence, ©void *© objects cannot be incremented.
997In \CFA, the restriction follows from the use of a ©type© parameter in the predefined function definitions, as opposed to ©dtype©, since only object types can be inferred arguments corresponding to the type parameter ©T©.
998\end{rationale}
999
1000\semantics
1001First, each interpretation of the operand of an increment or decrement expression is considered separately.
1002For each interpretation that is a bit-field or is declared with the \Indexc{register}\index{storage-class specifier}, the expression has one valid interpretation, with the type of the operand, and the expression is ambiguous if the operand is.
1003
1004For the remaining interpretations, the expression is rewritten, and the interpretations of the expression are the interpretations of the corresponding function call.
1005Finally, 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.
1006
1007\examples
1008\begin{lstlisting}
1009volatile short int vs;  vs++; // rewritten as ?++( &(vs) )
1010short int s;                    s++;
1011const short int cs;             cs++;
1012_Atomic short int as;   as++;
1013\end{lstlisting}
1014\begin{sloppypar}
1015Since ©&(vs)© has type ©volatile short int *©, the best valid interpretation of ©vs++© calls the ©?++© function with the ©volatile short *© parameter.
1016©s++© does the same, applying the safe conversion from ©short int *© to ©volatile short int *©.
1017Note that there is no conversion that adds an ©_Atomic© qualifier, so the ©_Atomic volatile short int© overloading does not provide a valid interpretation.
1018\end{sloppypar}
1019
1020There is no safe conversion from ©const short int *© to ©volatile short int *©, and no ©?++© function that accepts a ©const *© parameter, so ©cs++© has no valid interpretations.
1021
1022The best valid interpretation of ©as++© calls the ©short ?++© function with the ©_Atomic volatile short int *© parameter, applying a safe conversion to add the ©volatile© qualifier.
1023\begin{lstlisting}
1024char * const restrict volatile * restrict volatile pqpc;
1025pqpc++
1026char * * restrict volatile ppc;
1027ppc++;
1028\end{lstlisting}
1029Since ©&(pqpc)© has type ©char * const restrict volatile * restrict volatile *©, the best valid interpretation of ©pqpc++© calls the polymorphic ©?++© function with the ©const restrict volatile T * restrict volatile *© parameter, inferring ©T© to be ©char *©.
1030
1031©ppc++© calls the same function, again inferring ©T© to be ©char *©, and using the safe conversions from ©T© to ©T const© ©restrict volatile©.
1032
1033\begin{rationale}
1034Increment and decrement expressions show up a deficiency of \CFA's type system.
1035There is no such thing as a pointer to a register object or bit-field\index{deficiencies!pointers to bit-fields}.
1036Therefore, there is no way to define a function that alters them, and hence no way to define increment and decrement functions for them.
1037As a result, the semantics of increment and decrement expressions must treat them specially.
1038This holds true for all of the operators that may modify such objects.
1039\end{rationale}
1040
1041\begin{rationale}
1042The polymorphic overloadings for pointer increment and decrement can be understood by considering increasingly complex types.
1043\begin{enumerate}
1044\item
1045``©char * p; p++;©''.
1046The argument to ©?++© has type ©char * *©, and the result has type ©char *©.
1047The expression would be valid if ©?++© were declared by
1048\begin{lstlisting}
1049forall( otype T ) T * ?++( T * * );
1050\end{lstlisting} with ©T© inferred to be ©char©.
1051
1052\item
1053``©char *restrict volatile qp; qp++©''.
1054The result again has type ©char *©, but the argument now has type ©char *restrict volatile *©, so it cannot be passed to the hypothetical function declared in point 1.
1055Hence the actual predefined function is
1056\begin{lstlisting}
1057forall( otype T ) T * ?++( T * restrict volatile * );
1058\end{lstlisting} which also accepts a ©char * *© argument, because of the safe conversions that add ©volatile© and ©restrict© qualifiers. (The parameter is not const-qualified, so constant pointers cannot be incremented.)
1059
1060\item
1061``©char *_Atomic ap; ap++©''.
1062The result again has type ©char *©, but no safe conversion adds an ©_Atomic© qualifier, so the function in point 2 is not applicable.
1063A separate overloading of ©?++© is required.
1064
1065\item
1066``©char const volatile * pq; pq++©''.
1067Here the result has type ©char const volatile *©, so a new overloading is needed:
1068\begin{lstlisting}
1069forall( otype T ) T const volatile * ?++( T const volatile *restrict volatile * );
1070\end{lstlisting}
1071One overloading is needed for each combination of qualifiers in the pointed-at type\index{deficiencies!pointers to qualified types}.
1072 
1073\item
1074``©float *restrict * prp; prp++©''.
1075The ©restrict© qualifier is handled just like ©const© and ©volatile© in the previous case:
1076\begin{lstlisting}
1077forall( otype T ) T restrict * ?++( T restrict *restrict volatile * );
1078\end{lstlisting} with ©T© inferred to be ©float *©.
1079This looks odd, because \Celeven contains a constraint that requires restrict-qualified types to be pointer-to-object types, and ©T© is not syntactically a pointer type. \CFA loosens the constraint.
1080\end{enumerate}
1081\end{rationale}
1082
1083
1084\subsubsection{Compound literals}
1085
1086\semantics 
1087A compound literal has one interpretation, with the type given by the \nonterm{type-name} of the compound literal.
1088
1089
1090\subsection{Unary operators}
1091
1092\begin{syntax}
1093\lhs{unary-expression}
1094        \rhs \nonterm{postfix-expression}
1095        \rhs ©++© \nonterm{unary-expression}
1096        \rhs ©--© \nonterm{unary-expression}
1097        \rhs \nonterm{unary-operator} \nonterm{cast-expression}
1098        \rhs ©sizeof© \nonterm{unary-expression}
1099        \rhs ©sizeof© ©(© \nonterm{type-name} ©)©
1100\lhs{unary-operator} one of
1101        \rhs ©&© ©*© ©+© ©-© ©~© ©!©
1102\end{syntax}
1103
1104\rewriterules
1105\begin{lstlisting}
1106*a      => *?( a )§\use{*?}§
1107+a      => +?( a )§\use{+?}§
1108-a      => -?( a )§\use{-?}§
1109~a      => ~?( a )§\use{~?}§
1110!a      => !?( a )§\use{"!?}§
1111++a     => ++?(&( a ))§\use{++?}§
1112--a     => --?(&( a ))§\use{--?}§
1113\end{lstlisting}
1114
1115
1116\subsubsection{Prefix increment and decrement operators}
1117
1118\predefined
1119\begin{lstlisting}
1120_Bool ++?( volatile _Bool * ), ++?( _Atomic volatile _Bool * );
1121char ++?( volatile char * ), ++?( _Atomic volatile char * );
1122signed char ++?( volatile signed char * ), ++?( _Atomic volatile signed char * );
1123unsigned char ++?( volatile signed char * ), ++?( _Atomic volatile signed char * );
1124short int ++?( volatile short int * ), ++?( _Atomic volatile short int * );
1125unsigned short int ++?( volatile unsigned short int * ), ++?( _Atomic volatile unsigned short int * );
1126int ++?( volatile int * ), ++?( _Atomic volatile int * );
1127unsigned int ++?( volatile unsigned int * ), ++?( _Atomic volatile unsigned int * );
1128long int ++?( volatile long int * ), ++?( _Atomic volatile long int * );
1129long unsigned int ++?( volatile long unsigned int * ), ++?( _Atomic volatile long unsigned int * );
1130long long int ++?( volatile long long int * ), ++?( _Atomic volatile long long int * );
1131long long unsigned ++?( volatile long long unsigned int * ), ++?( _Atomic volatile long long unsigned int * );
1132float ++?( volatile float * ), ++?( _Atomic volatile float * );
1133double ++?( volatile double * ), ++?( _Atomic volatile double * );
1134long double ++?( volatile long double * ), ++?( _Atomic volatile long double * );
1135
1136forall( otype T ) T * ++?( T * restrict volatile * ), * ++?( T * _Atomic restrict volatile * );
1137forall( otype T ) _Atomic T * ++?( _Atomic T * restrict volatile * ), * ++?( _Atomic T * _Atomic restrict volatile * );
1138forall( otype T ) const T * ++?( const T * restrict volatile * ), * ++?( const T * _Atomic restrict volatile * );
1139forall( otype T ) volatile T * ++?( volatile T * restrict volatile * ), * ++?( volatile T * _Atomic restrict volatile * );
1140forall( otype T ) restrict T * ++?( restrict T * restrict volatile * ), * ++?( restrict T * _Atomic restrict volatile * );
1141forall( otype T ) _Atomic const T * ++?( _Atomic const T * restrict volatile * ),
1142        * ++?( _Atomic const T * _Atomic restrict volatile * );
1143forall( otype T ) _Atomic volatile T * ++?( _Atomic volatile T * restrict volatile * ),
1144        * ++?( _Atomic volatile T * _Atomic restrict volatile * );
1145forall( otype T ) _Atomic restrict T * ++?( _Atomic restrict T * restrict volatile * ),
1146        * ++?( _Atomic restrict T * _Atomic restrict volatile * );
1147forall( otype T ) const volatile T * ++?( const volatile T * restrict volatile * ),
1148        * ++?( const volatile T * _Atomic restrict volatile * );
1149forall( otype T ) const restrict T * ++?( const restrict T * restrict volatile * ),
1150        * ++?( const restrict T * _Atomic restrict volatile * );
1151forall( otype T ) restrict volatile T * ++?( restrict volatile T * restrict volatile * ),
1152        * ++?( restrict volatile T * _Atomic restrict volatile * );
1153forall( otype T ) _Atomic const volatile T * ++?( _Atomic const volatile T * restrict volatile * ),
1154        * ++?( _Atomic const volatile T * _Atomic restrict volatile * );
1155forall( otype T ) _Atomic const restrict T * ++?( _Atomic const restrict T * restrict volatile * ),
1156        * ++?( _Atomic const restrict T * _Atomic restrict volatile * );
1157forall( otype T ) _Atomic restrict volatile T * ++?( _Atomic restrict volatile T * restrict volatile * ),
1158        * ++?( _Atomic restrict volatile T * _Atomic restrict volatile * );
1159forall( otype T ) const restrict volatile T * ++?( const restrict volatile T * restrict volatile * ),
1160        * ++?( const restrict volatile T * _Atomic restrict volatile * );
1161forall( otype T ) _Atomic const restrict volatile T * ++?( _Atomic const restrict volatile T * restrict volatile * ),
1162        * ++?( _Atomic const restrict volatile T * _Atomic restrict volatile * );
1163
1164_Bool --?( volatile _Bool * ), --?( _Atomic volatile _Bool * );
1165char --?( volatile char * ), --?( _Atomic volatile char * );
1166signed char --?( volatile signed char * ), --?( _Atomic volatile signed char * );
1167unsigned char --?( volatile signed char * ), --?( _Atomic volatile signed char * );
1168short int --?( volatile short int * ), --?( _Atomic volatile short int * );
1169unsigned short int --?( volatile unsigned short int * ), --?( _Atomic volatile unsigned short int * );
1170int --?( volatile int * ), --?( _Atomic volatile int * );
1171unsigned int --?( volatile unsigned int * ), --?( _Atomic volatile unsigned int * );
1172long int --?( volatile long int * ), --?( _Atomic volatile long int * );
1173long unsigned int --?( volatile long unsigned int * ), --?( _Atomic volatile long unsigned int * );
1174long long int --?( volatile long long int * ), --?( _Atomic volatile long long int * );
1175long long unsigned --?( volatile long long unsigned int * ), --?( _Atomic volatile long long unsigned int * );
1176float --?( volatile float * ), --?( _Atomic volatile float * );
1177double --?( volatile double * ), --?( _Atomic volatile double * );
1178long double --?( volatile long double * ), --?( _Atomic volatile long double * );
1179
1180forall( otype T ) T * --?( T * restrict volatile * ), * --?( T * _Atomic restrict volatile * );
1181forall( otype T ) _Atomic T * --?( _Atomic T * restrict volatile * ), * --?( _Atomic T * _Atomic restrict volatile * );
1182forall( otype T ) const T * --?( const T * restrict volatile * ), * --?( const T * _Atomic restrict volatile * );
1183forall( otype T ) volatile T * --?( volatile T * restrict volatile * ), * --?( volatile T * _Atomic restrict volatile * );
1184forall( otype T ) restrict T * --?( restrict T * restrict volatile * ), * --?( restrict T * _Atomic restrict volatile * );
1185forall( otype T ) _Atomic const T * --?( _Atomic const T * restrict volatile * ),
1186        * --?( _Atomic const T * _Atomic restrict volatile * );
1187forall( otype T ) _Atomic volatile T * --?( _Atomic volatile T * restrict volatile * ),
1188        * --?( _Atomic volatile T * _Atomic restrict volatile * );
1189forall( otype T ) _Atomic restrict T * --?( _Atomic restrict T * restrict volatile * ),
1190        * --?( _Atomic restrict T * _Atomic restrict volatile * );
1191forall( otype T ) const volatile T * --?( const volatile T * restrict volatile * ),
1192        * --?( const volatile T * _Atomic restrict volatile * );
1193forall( otype T ) const restrict T * --?( const restrict T * restrict volatile * ),
1194        * --?( const restrict T * _Atomic restrict volatile * );
1195forall( otype T ) restrict volatile T * --?( restrict volatile T * restrict volatile * ),
1196        * --?( restrict volatile T * _Atomic restrict volatile * );
1197forall( otype T ) _Atomic const volatile T * --?( _Atomic const volatile T * restrict volatile * ),
1198        * --?( _Atomic const volatile T * _Atomic restrict volatile * );
1199forall( otype T ) _Atomic const restrict T * --?( _Atomic const restrict T * restrict volatile * ),
1200        * --?( _Atomic const restrict T * _Atomic restrict volatile * );
1201forall( otype T ) _Atomic restrict volatile T * --?( _Atomic restrict volatile T * restrict volatile * ),
1202        * --?( _Atomic restrict volatile T * _Atomic restrict volatile * );
1203forall( otype T ) const restrict volatile T * --?( const restrict volatile T * restrict volatile * ),
1204        * --?( const restrict volatile T * _Atomic restrict volatile * );
1205forall( otype T ) _Atomic const restrict volatile T * --?( _Atomic const restrict volatile T * restrict volatile * ),
1206        * --?( _Atomic const restrict volatile T * _Atomic restrict volatile * );
1207\end{lstlisting}
1208For every extended integer type ©X© there exist
1209% Don't use predefined: keep this out of prelude.cf.
1210\begin{lstlisting}
1211X       ++?( volatile X * ),
1212        ++?( _Atomic volatile X * ),
1213        --?( volatile X * ),
1214        --?( _Atomic volatile X * );
1215\end{lstlisting}
1216For every complete enumerated type ©E© there exist
1217% Don't use predefined: keep this out of prelude.cf.
1218\begin{lstlisting}
1219E ++?( volatile E * ),
1220        ++?( _Atomic volatile E * ),
1221        ?--( volatile E * ),
1222        ?--( _Atomic volatile E * );
1223\end{lstlisting}
1224
1225\semantics
1226The interpretations of prefix increment and decrement expressions are determined in the same way as the interpretations of postfix increment and decrement expressions.
1227
1228
1229\subsubsection{Address and indirection operators}
1230
1231\predefined
1232\begin{lstlisting}
1233forall( otype T ) lvalue T *?( T * );
1234forall( otype T ) _Atomic lvalue T *?( _Atomic T * );
1235forall( otype T ) const lvalue T *?( const T * );
1236forall( otype T ) volatile lvalue T *?( volatile T * );
1237forall( otype T ) restrict lvalue T *?( restrict T * );
1238forall( otype T ) _Atomic const lvalue T *?( _Atomic const T * );
1239forall( otype T ) _Atomic volatile lvalue T *?( _Atomic volatile T * );
1240forall( otype T ) _Atomic restrict lvalue T *?( _Atomic restrict T * );
1241forall( otype T ) const volatile lvalue T *?( const volatile T * );
1242forall( otype T ) const restrict lvalue T *?( const restrict T * );
1243forall( otype T ) restrict volatile lvalue T *?( restrict volatile T * );
1244forall( otype T ) _Atomic const volatile lvalue T *?( _Atomic const volatile T * );
1245forall( otype T ) _Atomic const restrict lvalue T *?( _Atomic const restrict T * );
1246forall( otype T ) _Atomic restrict volatile lvalue T *?( _Atomic restrict volatile T * );
1247forall( otype T ) const restrict volatile lvalue T *?( const restrict volatile T * );
1248forall( otype T ) _Atomic const restrict volatile lvalue T *?( _Atomic const restrict volatile T * );
1249forall( ftype FT ) FT *?( FT * );
1250\end{lstlisting}
1251
1252\constraints
1253The operand of the unary ``©&©'' operator shall have exactly one \Index{interpretation}\index{ambiguous interpretation}, which shall be unambiguous.
1254
1255\semantics
1256The ``©&©'' expression has one interpretation which is of type ©T *©, where ©T© is the type of the operand.
1257
1258The interpretations of an indirection expression are the interpretations of the corresponding function call.
1259
1260
1261\subsubsection{Unary arithmetic operators}
1262
1263\predefined
1264\begin{lstlisting}
1265int     +?( int ), -?( int ), ~?( int );
1266unsigned int +?( unsigned int ), -?( unsigned int ), ~?( unsigned int );
1267long int +?( long int ), -?( long int ), ~?( long int );
1268long unsigned int +?( long unsigned int ), -?( long unsigned int ), ~?( long unsigned int );
1269long long int +?( long long int ), -?( long long int ), ~?( long long int );
1270long long unsigned int +?( long long unsigned int ), -?( long long unsigned int ), ~?( long long unsigned int );
1271float +?( float ), -?( float );
1272double +?( double ), -?( double );
1273long double +?( long double ), -?( long double );
1274_Complex float +?( _Complex float ), -?( _Complex float );
1275_Complex double +?( _Complex double ), -?( _Complex double );
1276_Complex long double +?( _Complex long double ), -?( _Complex long double );
1277int !?( int ), !?( unsigned int ), !?( long ), !?( long unsigned int ),
1278        !?( long long int ), !?( long long unsigned int ),
1279        !?( float ), !?( double ), !?( long double ),
1280        !?( _Complex float ), !?( _Complex double ), !?( _Complex long double );
1281forall( dtype DT ) int !?( const restrict volatile DT * );
1282forall( dtype DT ) int !?( _Atomic const restrict volatile DT * );
1283forall( ftype FT ) int !?( FT * );
1284\end{lstlisting}
1285For every extended integer type ©X© with \Index{integer conversion rank} greater than the rank of ©int© there exist
1286% Don't use predefined: keep this out of prelude.cf.
1287\begin{lstlisting}
1288X +?( X ), -?( X ), ~?( X );
1289int !?( X );
1290\end{lstlisting}
1291
1292\semantics
1293The interpretations of a unary arithmetic expression are the interpretations of the corresponding function call.
1294
1295\examples
1296\begin{lstlisting}
1297long int li;
1298void eat_double( double );§\use{eat_double}§
1299eat_double(-li ); // => eat_double( -?( li ) );
1300\end{lstlisting}
1301The valid interpretations of ``©-li©'' (assuming no extended integer types exist) are
1302\begin{center}
1303\begin{tabular}{llc} interpretation & result type & expression conversion cost \\
1304\hline
1305©-?( (int)li )©                                         & ©int©                                         & (unsafe) \\
1306©-?( (unsigned)li)©                                     & ©unsigned int©                        & (unsafe) \\
1307©-?( (long)li)©                                         & ©long©                                        & 0 \\
1308©-?( (long unsigned int)li)©            & ©long unsigned int©           & 1 \\
1309©-?( (long long int)li)©                        & ©long long int©                       & 2 \\
1310©-?( (long long unsigned int)li)©       & ©long long unsigned int©      & 3 \\
1311©-?( (float)li)©                                        & ©float©                                       & 4 \\
1312©-?( (double)li)©                                       & ©double©                                      & 5 \\
1313©-?( (long double)li)©                          & ©long double©                         & 6 \\
1314©-?( (_Complex float)li)©                       & ©float©                                       & (unsafe) \\
1315©-?( (_Complex double)li)©                      & ©double©                                      & (unsafe) \\
1316©-?( (_Complex long double)li)©         & ©long double©                         & (unsafe) \\
1317\end{tabular}
1318\end{center}
1319The valid interpretations of the ©eat_double© call, with the cost of the argument conversion and the cost of the entire expression, are
1320\begin{center}
1321\begin{tabular}{lcc} interpretation & argument cost & expression cost \\
1322\hline
1323©eat_double( (double)-?( (int)li) )©                                    & 7                     & (unsafe) \\
1324©eat_double( (double)-?( (unsigned)li) )©                               & 6                     & (unsafe) \\
1325©eat_double( (double)-?(li) )©                                                  & 5                     & \(0+5=5\) \\
1326©eat_double( (double)-?( (long unsigned int)li) )©              & 4                     & \(1+4=5\) \\
1327©eat_double( (double)-?( (long long int)li) )©                  & 3                     & \(2+3=5\) \\
1328©eat_double( (double)-?( (long long unsigned int)li) )© & 2                     & \(3+2=5\) \\
1329©eat_double( (double)-?( (float)li) )©                                  & 1                     & \(4+1=5\) \\
1330©eat_double( (double)-?( (double)li) )©                                 & 0                     & \(5+0=5\) \\
1331©eat_double( (double)-?( (long double)li) )©                    & (unsafe)      & (unsafe) \\
1332©eat_double( (double)-?( (_Complex float)li) )©                 & (unsafe)      & (unsafe) \\
1333©eat_double( (double)-?( (_Complex double)li) )©                & (unsafe)      & (unsafe) \\
1334©eat_double( (double)-?( (_Complex long double)li) )©   & (unsafe)      & (unsafe) \\
1335\end{tabular}
1336\end{center}
1337Each has result type ©void©, so the best must be selected.
1338The interpretations involving unsafe conversions are discarded.
1339The remainder have equal expression conversion costs, so the ``highest argument conversion cost'' rule is invoked, and the chosen interpretation is ©eat_double( (double)-?(li) )©.
1340
1341
1342\subsubsection[The sizeof and \_Alignof operators]{The \lstinline@sizeof@ and \lstinline@_Alignof@ operators}
1343
1344\constraints
1345The operand of ©sizeof© or ©_Alignof© shall not be ©type©, ©dtype©, or ©ftype©.
1346
1347When the ©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 ©sizeof© or ©_Alignof© expression has one interpretation, of type ©size_t©.
1348
1349When ©sizeof© is applied to an identifier declared by a \nonterm{type-declaration} or a
1350\nonterm{type-parameter}, it yields the size in bytes of the type that implements the operand.
1351When the operand is an opaque type or an inferred type parameter\index{inferred parameter}, the expression is not a constant expression.
1352
1353When ©_Alignof© is applied to an identifier declared by a \nonterm{type-declaration} or a
1354\nonterm{type-parameter}, it yields the alignment requirement of the type that implements the operand.
1355When the operand is an opaque type or an inferred type parameter\index{inferred parameter}, the expression is not a constant expression.
1356\begin{rationale}
1357\begin{lstlisting}
1358otype Pair = struct { int first, second; };
1359size_t p_size = sizeof(Pair);           // constant expression
1360extern otype Rational;§\use{Rational}§
1361size_t c_size = sizeof(Rational);       // non-constant expression
1362forall(type T) T f(T p1, T p2) {
1363        size_t t_size = sizeof(T);              // non-constant expression
1364        ...
1365}
1366\end{lstlisting}
1367``©sizeof Rational©'', although not statically known, is fixed.
1368Within ©f()©, ``©sizeof(T)©'' is fixed for each call of ©f()©, but may vary from call to call.
1369\end{rationale}
1370
1371
1372\subsection{Cast operators}
1373
1374\begin{syntax}
1375\lhs{cast-expression}
1376\rhs \nonterm{unary-expression}
1377\rhs ©(© \nonterm{type-name} ©)© \nonterm{cast-expression}
1378\end{syntax}
1379
1380\constraints
1381The \nonterm{type-name} in a \nonterm{cast-expression} shall not be ©type©, ©dtype©, or ©ftype©.
1382
1383\semantics
1384
1385In a \Index{cast expression} ``©(©\nonterm{type-name}©)e©'', if
1386\nonterm{type-name} is the type of an interpretation of ©e©, then that interpretation is the only interpretation of the cast expression;
1387otherwise, ©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.
1388The 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.
1389
1390\begin{rationale}
1391Casts can be used to eliminate ambiguity in expressions by selecting interpretations of subexpressions, and to specialize polymorphic functions and values.
1392\end{rationale}
1393
1394
1395\subsection{Multiplicative operators}
1396
1397\begin{syntax}
1398\lhs{multiplicative-expression}
1399\rhs \nonterm{cast-expression}
1400\rhs \nonterm{multiplicative-expression} ©*© \nonterm{cast-expression}
1401\rhs \nonterm{multiplicative-expression} ©/© \nonterm{cast-expression}
1402\rhs \nonterm{multiplicative-expression} ©%© \nonterm{cast-expression}
1403\end{syntax}
1404
1405\rewriterules
1406\begin{lstlisting}
1407a * b => ?*?( a, b )§\use{?*?}§
1408a / b => ?/?( a, b )§\use{?/?}§
1409a % b => ?%?( a, b )§\use{?%?}§
1410\end{lstlisting}
1411
1412\predefined
1413\begin{lstlisting}
1414int?*?( int, int ), ?/?( int, int ), ?%?( int, int );
1415unsigned int?*?( unsigned int, unsigned int ), ?/?( unsigned int, unsigned int ), ?%?( unsigned int, unsigned int );
1416long int?*?( long int, long int ), ?/?( long, long ), ?%?( long, long );
1417long unsigned int?*?( long unsigned int, long unsigned int ),
1418        ?/?( long unsigned int, long unsigned int ), ?%?( long unsigned int, long unsigned int );
1419long long int?*?( long long int, long long int ), ?/?( long long int, long long int ),
1420        ?%?( long long int, long long int );
1421long long unsigned int ?*?( long long unsigned int, long long unsigned int ),
1422        ?/?( long long unsigned int, long long unsigned int ), ?%?( long long unsigned int, long long unsigned int );
1423float?*?( float, float ), ?/?( float, float );
1424double?*?( double, double ), ?/?( double, double );
1425long double?*?( long double, long double ), ?/?( long double, long double );
1426_Complex float?*?( float, _Complex float ), ?/?( float, _Complex float ),
1427        ?*?( _Complex float, float ), ?/?( _Complex float, float ),
1428        ?*?( _Complex float, _Complex float ), ?/?( _Complex float, _Complex float );
1429_Complex double?*?( double, _Complex double ), ?/?( double, _Complex double ),
1430        ?*?( _Complex double, double ), ?/?( _Complex double, double ),
1431        ?*?( _Complex double, _Complex double ), ?/?( _Complex double, _Complex double );
1432_Complex long double?*?( long double, _Complex long double ), ?/?( long double, _Complex long double ),
1433        ?*?( _Complex long double, long double ), ?/?( _Complex long double, long double ),
1434        ?*?( _Complex long double, _Complex long double ), ?/?( _Complex long double, _Complex long double );
1435\end{lstlisting}
1436For every extended integer type ©X© with \Index{integer conversion rank} greater than the rank of ©int© there exist
1437% Don't use predefined: keep this out of prelude.cf.
1438\begin{lstlisting}
1439X ?*?( X ), ?/?( X ), ?%?( X );
1440\end{lstlisting}
1441
1442\begin{rationale}
1443\Celeven does not include conversions from the \Index{real type}s to \Index{complex type}s in the \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.
1444\end{rationale}
1445
1446\semantics
1447The interpretations of multiplicative expressions are the interpretations of the corresponding function call.
1448
1449\examples
1450\begin{lstlisting}
1451int i;
1452long li;
1453void eat_double( double );§\use{eat_double}§
1454eat_double( li % i );
1455\end{lstlisting}
1456``©li % i©'' is rewritten as ``©?%?(li, i )©''.
1457The valid interpretations of ©?%?(li, i )©, the cost\index{conversion cost} of converting their arguments, and the cost of converting the result to ©double© (assuming no extended integer types are present ) are
1458\begin{center}
1459\begin{tabular}{lcc} interpretation & argument cost & result cost \\
1460\hline
1461© ?%?( (int)li, i )©                                                                            & (unsafe)      & 6     \\
1462© ?%?( (unsigned)li,(unsigned)i )©                                                      & (unsafe)      & 5     \\
1463© ?%?( li, (long)i )©                                                                           & 1                     & 4     \\
1464© ?%?( (long unsigned)li,(long unsigned)i )©                            & 3                     & 3     \\
1465© ?%?( (long long)li,(long long)i )©                                            & 5                     & 2     \\
1466© ?%?( (long long unsigned)li, (long long unsigned)i )©         & 7                     & 1     \\
1467\end{tabular}
1468\end{center}
1469The best interpretation of ©eat_double( li, i )© is ©eat_double( (double)?%?(li, (long)i ))©, which has no unsafe conversions and the lowest total cost.
1470
1471\begin{rationale}
1472\Celeven 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 ©int©.
1473If ©s© is a ©short int©, ``©s *s©'' does not have type ©short int©;
1474it is treated as ``©( (int)s ) * ( (int)s )©'', and has type ©int©. \CFA matches that pattern;
1475it does not predefine ``©short ?*?( short, short )©''.
1476
1477These ``missing'' operators limit polymorphism.
1478Consider
1479\begin{lstlisting}
1480forall( otype T | T ?*?( T, T ) ) T square( T );
1481short s;
1482square( s );
1483\end{lstlisting}
1484Since \CFA does not define a multiplication operator for ©short int©, ©square( s )© is treated as ©square( (int)s )©, and the result has type ©int©.
1485This is mildly surprising, but it follows the \Celeven operator pattern.
1486
1487A more troubling example is
1488\begin{lstlisting}
1489forall( otype T | ?*?( T, T ) ) T product( T[], int n );
1490short sa[5];
1491product( sa, 5);
1492\end{lstlisting}
1493This has no valid interpretations, because \CFA has no conversion from ``array of ©short int©'' to ``array of ©int©''.
1494The alternatives in such situations include
1495\begin{itemize}
1496\item
1497Defining monomorphic overloadings of ©product© for ©short© and the other ``small'' types.
1498\item
1499Defining ``©short ?*?( short, short )©'' within the scope containing the call to ©product©.
1500\item
1501Defining ©product© to take as an argument a conversion function from the ``small'' type to the operator's argument type.
1502\end{itemize}
1503\end{rationale}
1504
1505
1506\subsection{Additive operators}
1507
1508\begin{syntax}
1509\lhs{additive-expression}
1510\rhs \nonterm{multiplicative-expression}
1511\rhs \nonterm{additive-expression} ©+© \nonterm{multiplicative-expression}
1512\rhs \nonterm{additive-expression} ©-© \nonterm{multiplicative-expression}
1513\end{syntax}
1514
1515\rewriterules
1516\begin{lstlisting}
1517a + b => ?+?( a, b )§\use{?+?}§
1518a - b => ?-?( a, b )§\use{?-?}§
1519\end{lstlisting}
1520
1521\predefined
1522\begin{lstlisting}
1523int?+?( int, int ), ?-?( int, int );
1524unsigned int?+?( unsigned int, unsigned int ), ?-?( unsigned int, unsigned int );
1525long int?+?( long int, long int ), ?-?( long int, long int );
1526long unsigned int?+?( long unsigned int, long unsigned int ), ?-?( long unsigned int, long unsigned int );
1527long long int?+?( long long int, long long int ), ?-?( long long int, long long int );
1528long long unsigned int ?+?( long long unsigned int, long long unsigned int ),
1529        ?-?( long long unsigned int, long long unsigned int );
1530float?+?( float, float ), ?-?( float, float );
1531double?+?( double, double ), ?-?( double, double );
1532long double?+?( long double, long double ), ?-?( long double, long double );
1533_Complex float?+?( _Complex float, float ), ?-?( _Complex float, float ),
1534        ?+?( float, _Complex float ), ?-?( float, _Complex float ),
1535        ?+?( _Complex float, _Complex float ), ?-?( _Complex float, _Complex float );
1536_Complex double?+?( _Complex double, double ), ?-?( _Complex double, double ),
1537        ?+?( double, _Complex double ), ?-?( double, _Complex double ),
1538        ?+?( _Complex double, _Complex double ), ?-?( _Complex double, _Complex double );
1539_Complex long double?+?( _Complex long double, long double ), ?-?( _Complex long double, long double ),
1540        ?+?( long double, _Complex long double ), ?-?( long double, _Complex long double ),
1541        ?+?( _Complex long double, _Complex long double ), ?-?( _Complex long double, _Complex long double );
1542
1543forall( otype T ) T * ?+?( T *, ptrdiff_t ), * ?+?( ptrdiff_t, T * ), * ?-?( T *, ptrdiff_t );
1544forall( otype T ) _Atomic T * ?+?( _Atomic T *, ptrdiff_t ), * ?+?( ptrdiff_t, _Atomic T * ),
1545        * ?-?( _Atomic T *, ptrdiff_t );
1546forall( otype T ) const T * ?+?( const T *, ptrdiff_t ), * ?+?( ptrdiff_t, const T * ),
1547        * ?-?( const T *, ptrdiff_t );
1548forall( otype T ) restrict T * ?+?( restrict T *, ptrdiff_t ), * ?+?( ptrdiff_t, restrict T * ),
1549        * ?-?( restrict T *, ptrdiff_t );
1550forall( otype T ) volatile T * ?+?( volatile T *, ptrdiff_t ), * ?+?( ptrdiff_t, volatile T * ),
1551        * ?-?( volatile T *, ptrdiff_t );
1552forall( otype T ) _Atomic const T * ?+?( _Atomic const T *, ptrdiff_t ), * ?+?( ptrdiff_t, _Atomic const T * ),
1553        * ?-?( _Atomic const T *, ptrdiff_t );
1554forall( otype T ) _Atomic restrict T * ?+?( _Atomic restrict T *, ptrdiff_t ), * ?+?( ptrdiff_t, _Atomic restrict T * ),
1555        * ?-?( _Atomic restrict T *, ptrdiff_t );
1556forall( otype T ) _Atomic volatile T * ?+?( _Atomic volatile T *, ptrdiff_t ), * ?+?( ptrdiff_t, _Atomic volatile T * ),
1557        * ?-?( _Atomic volatile T *, ptrdiff_t );
1558forall( otype T ) const restrict T * ?+?( const restrict T *, ptrdiff_t ), * ?+?( ptrdiff_t, const restrict T * ),
1559        * ?-?( const restrict T *, ptrdiff_t );
1560forall( otype T ) const volatile T * ?+?( const volatile T *, ptrdiff_t ), * ?+?( ptrdiff_t, const volatile T * ),
1561        * ?-?( const volatile T *, ptrdiff_t );
1562forall( otype T ) restrict volatile T * ?+?( restrict volatile T *, ptrdiff_t ), * ?+?( ptrdiff_t, restrict volatile T * ),
1563        * ?-?( restrict volatile T *, ptrdiff_t );
1564forall( otype T ) _Atomic const restrict T * ?+?( _Atomic const restrict T *, ptrdiff_t ),
1565        * ?+?( ptrdiff_t, _Atomic const restrict T * ),
1566        * ?-?( _Atomic const restrict T *, ptrdiff_t );
1567forall( otype T ) ptrdiff_t
1568        * ?-?( const restrict volatile T *, const restrict volatile T * ),
1569        * ?-?( _Atomic const restrict volatile T *, _Atomic const restrict volatile T * );
1570\end{lstlisting}
1571For every extended integer type ©X© with \Index{integer conversion rank} greater than the rank of ©int© there exist
1572% Don't use predefined: keep this out of prelude.cf.
1573\begin{lstlisting}
1574X ?+?( X ), ?-?( X );
1575\end{lstlisting}
1576
1577\semantics
1578The interpretations of additive expressions are the interpretations of the corresponding function calls.
1579
1580\begin{rationale}
1581©ptrdiff_t© is an implementation-defined identifier defined in ©<stddef.h>© that is synonymous with a signed integral type that is large enough to hold the difference between two pointers.
1582It 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.
1583The \Celeven standard uses ©size_t© in several cases where a library function takes an argument that is used as a subscript, but ©size_t© is unsuitable here because it is an unsigned type.
1584\end{rationale}
1585
1586
1587\subsection{Bitwise shift operators}
1588
1589\begin{syntax}
1590\lhs{shift-expression}
1591\rhs \nonterm{additive-expression}
1592\rhs \nonterm{shift-expression} ©<<© \nonterm{additive-expression}
1593\rhs \nonterm{shift-expression} ©>>© \nonterm{additive-expression}
1594\end{syntax}
1595
1596\rewriterules
1597\begin{lstlisting}
1598a << b => ?<<?( a, b )§\use{?<<?}§
1599a >> b => ?>>?( a, b )§\use{?>>?}§
1600\end{lstlisting}
1601
1602\predefined
1603\begin{lstlisting}
1604int ?<<?( int, int ), ?>>?( int, int );
1605unsigned int ?<<?( unsigned int, int ), ?>>?( unsigned int, int );
1606long int ?<<?( long int, int ), ?>>?( long int, int );
1607long unsigned int ?<<?( long unsigned int, int ), ?>>?( long unsigned int, int );
1608long long int ?<<?( long long int, int ), ?>>?( long long int, int );
1609long long unsigned int ?<<?( long long unsigned int, int ), ?>>?( long long unsigned int, int);
1610\end{lstlisting}
1611For every extended integer type ©X© with \Index{integer conversion rank} greater than the rank of ©int© there exist
1612% Don't use predefined: keep this out of prelude.cf.
1613\begin{lstlisting}
1614X ?<<?( X, int ), ?>>?( X, int );
1615\end{lstlisting}
1616
1617\begin{rationale}
1618The bitwise shift operators break the usual pattern: they do not convert both operands to a common type.
1619The right operand only undergoes \Index{integer promotion}.
1620\end{rationale}
1621
1622\semantics
1623The interpretations of a bitwise shift expression are the interpretations of the corresponding function calls.
1624
1625
1626\subsection{Relational operators}
1627
1628\begin{syntax}
1629\lhs{relational-expression}
1630\rhs \nonterm{shift-expression}
1631\rhs \nonterm{relational-expression} ©< © \nonterm{shift-expression}
1632\rhs \nonterm{relational-expression} ©> © \nonterm{shift-expression}
1633\rhs \nonterm{relational-expression} ©<=© \nonterm{shift-expression}
1634\rhs \nonterm{relational-expression} ©>=© \nonterm{shift-expression}
1635\end{syntax}
1636
1637\rewriterules
1638\begin{lstlisting}
1639a < b => ?<?( a, b )§\use{?<?}§
1640a > b => ?>?( a, b )§\use{?>?}§
1641a <= b => ?<=?( a, b )§\use{?<=?}§
1642a >= b => ?>=?( a, b )§\use{?>=?}§
1643\end{lstlisting}
1644
1645\predefined
1646\begin{lstlisting}
1647int ?<?( int, int ), ?<=?( int, int ),
1648        ?>?( int, int ), ?>=?( int, int );
1649int ?<?( unsigned int, unsigned int ), ?<=?( unsigned int, unsigned int ),
1650        ?>?( unsigned int, unsigned int ), ?>=?( unsigned int, unsigned int );
1651int ?<?( long int, long int ), ?<=?( long int, long int ),
1652        ?>?( long int, long int ), ?>=?( long int, long int );
1653int ?<?( long unsigned int, long unsigned ), ?<=?( long unsigned int, long unsigned ),
1654        ?>?( long unsigned int, long unsigned ), ?>=?( long unsigned int, long unsigned );
1655int ?<?( long long int, long long int ), ?<=?( long long int, long long int ),
1656        ?>?( long long int, long long int ), ?>=?( long long int, long long int );
1657int ?<?( long long unsigned int, long long unsigned ), ?<=?( long long unsigned int, long long unsigned ),
1658        ?>?( long long unsigned int, long long unsigned ), ?>=?( long long unsigned int, long long unsigned );
1659int ?<?( float, float ), ?<=?( float, float ),
1660        ?>?( float, float ), ?>=?( float, float );
1661int ?<?( double, double ), ?<=?( double, double ),
1662        ?>?( double, double ), ?>=?( double, double );
1663int ?<?( long double, long double ), ?<=?( long double, long double ),
1664        ?>?( long double, long double ), ?>=?( long double, long double );
1665forall( dtype DT ) int ?<?( const restrict volatile DT *, const restrict volatile DT * ),
1666        ?<?( _Atomic const restrict volatile DT *, _Atomic const restrict volatile DT * ),
1667        ?<=?( const restrict volatile DT *, const restrict volatile DT * ),
1668        ?<=?( _Atomic const restrict volatile DT *, _Atomic const restrict volatile DT * ),
1669        ?>?( const restrict volatile DT *, const restrict volatile DT * ),
1670        ?>?( _Atomic const restrict volatile DT *, _Atomic const restrict volatile DT * ),
1671        ?>=?( const restrict volatile DT *, const restrict volatile DT * ),
1672        ?>=?( _Atomic const restrict volatile DT *, _Atomic const restrict volatile DT * );
1673\end{lstlisting}
1674For every extended integer type ©X© with \Index{integer conversion rank} greater than the rank of ©int© there exist
1675% Don't use predefined: keep this out of prelude.cf.
1676\begin{lstlisting}
1677int ?<?( X, X ),
1678        ?<=?( X, X ),
1679        ?<?( X, X ),
1680        ?>=?( X, X );
1681\end{lstlisting}
1682
1683\semantics
1684The interpretations of a relational expression are the interpretations of the corresponding function call.
1685
1686
1687\subsection{Equality operators}
1688
1689\begin{syntax}
1690\lhs{equality-expression}
1691\rhs \nonterm{relational-expression}
1692\rhs \nonterm{equality-expression} ©==© \nonterm{relational-expression}
1693\rhs \nonterm{equality-expression} ©!=© \nonterm{relational-expression}
1694\end{syntax}
1695
1696\rewriterules
1697\begin{lstlisting}
1698a == b => ?==?( a, b )§\use{?==?}§
1699a != b => ?!=?( a, b )§\use{?"!=?}§
1700\end{lstlisting}
1701
1702\predefined
1703\begin{lstlisting}
1704int ?==?( int, int ), ?!=?( int, int ),
1705        ?==?( unsigned int, unsigned int ), ?!=?( unsigned int, unsigned int ),
1706        ?==?( long int, long int ), ?!=?( long int, long int ),
1707        ?==?( long unsigned int, long unsigned int ), ?!=?( long unsigned int, long unsigned int ),
1708        ?==?( long long int, long long int ), ?!=?( long long int, long long int ),
1709        ?==?( long long unsigned int, long long unsigned int ), ?!=?( long long unsigned int, long long unsigned int ),
1710        ?==?( float, float ), ?!=?( float, float ),
1711        ?==?( _Complex float, float ), ?!=?( _Complex float, float ),
1712        ?==?( float, _Complex float ), ?!=?( float, _Complex float ),
1713        ?==?( _Complex float, _Complex float ), ?!=?( _Complex float, _Complex float ),
1714        ?==?( double, double ), ?!=?( double, double ),
1715        ?==?( _Complex double, double ), ?!=?( _Complex double, double ),
1716        ?==?( double, _Complex double ), ?!=?( double, _Complex double ),
1717        ?==?( _Complex double, _Complex double ), ?!=?( _Complex double, _Complex double ),
1718        ?==?( long double, long double ), ?!=?( long double, long double ),
1719        ?==?( _Complex long double, long double ), ?!=?( _Complex long double, long double ),
1720        ?==?( long double, _Complex long double ), ?!=?( long double, _Complex long double ),
1721        ?==?( _Complex long double, _Complex long double ), ?!=?( _Complex long double, _Complex long double );
1722forall( dtype DT ) int
1723        ?==?( const restrict volatile DT *, const restrict volatile DT * ),
1724        ?!=?( const restrict volatile DT *, const restrict volatile DT * ),
1725        ?==?( const restrict volatile DT *, const restrict volatile void * ),
1726        ?!=?( const restrict volatile DT *, const restrict volatile void * ),
1727        ?==?( const restrict volatile void *, const restrict volatile DT * ),
1728        ?!=?( const restrict volatile void *, const restrict volatile DT * ),
1729        ?==?( const restrict volatile DT *, forall( dtype DT2) const DT2 * ),
1730        ?!=?( const restrict volatile DT *, forall( dtype DT2) const DT2 * ),
1731        ?==?( forall( dtype DT2) const DT2*, const restrict volatile DT * ),
1732        ?!=?( forall( dtype DT2) const DT2*, const restrict volatile DT * ),
1733        ?==?( forall( dtype DT2) const DT2*, forall( dtype DT3) const DT3 * ),
1734        ?!=?( forall( dtype DT2) const DT2*, forall( dtype DT3) const DT3 * ),
1735
1736        ?==?( _Atomic const restrict volatile DT *, _Atomic const restrict volatile DT * ),
1737        ?!=?( _Atomic const restrict volatile DT *, _Atomic const restrict volatile DT * ),
1738        ?==?( _Atomic const restrict volatile DT *, const restrict volatile void * ),
1739        ?!=?( _Atomic const restrict volatile DT *, const restrict volatile void * ),
1740        ?==?( const restrict volatile void *, _Atomic const restrict volatile DT * ),
1741        ?!=?( const restrict volatile void *, _Atomic const restrict volatile DT * ),
1742        ?==?( _Atomic const restrict volatile DT *, forall( dtype DT2) const DT2 * ),
1743        ?!=?( _Atomic const restrict volatile DT *, forall( dtype DT2) const DT2 * ),
1744        ?==?( forall( dtype DT2) const DT2*, _Atomic const restrict volatile DT * ),
1745        ?!=?( forall( dtype DT2) const DT2*, _Atomic const restrict volatile DT * );
1746forall( ftype FT ) int
1747        ?==?( FT *, FT * ), ?!=?( FT *, FT * ),
1748        ?==?( FT *, forall( ftype FT2) FT2 * ), ?!=?( FT *, forall( ftype FT2) FT2 * ),
1749        ?==?( forall( ftype FT2) FT2*, FT * ), ?!=?( forall( ftype FT2) FT2*, FT * ),
1750        ?==?( forall( ftype FT2) FT2*, forall( ftype FT3) FT3 * ), ?!=?( forall( ftype FT2) FT2*, forall( ftype FT3) FT3 * );
1751\end{lstlisting}
1752For every extended integer type ©X© with \Index{integer conversion rank} greater than the rank of ©int© there exist
1753% Don't use predefined: keep this out of prelude.cf.
1754\begin{lstlisting}
1755int ?==?( X, X ),
1756        ?!=?( X, X );
1757\end{lstlisting}
1758
1759\begin{rationale}
1760The polymorphic equality operations come in three styles: comparisons between pointers of compatible types, between pointers to ©void© and pointers to object types or incomplete types, and between the \Index{null pointer} constant and pointers to any type.
1761In the last case, a special constraint rule for null pointer constant operands has been replaced by a consequence of the \CFA type system.
1762\end{rationale}
1763
1764\semantics
1765The interpretations of an equality expression are the interpretations of the corresponding function call.
1766
1767\begin{sloppypar}
1768The result of an equality comparison between two pointers to predefined functions or predefined values is implementation-defined.
1769\end{sloppypar}
1770\begin{rationale}
1771The implementation-defined status of equality comparisons allows implementations to use one library routine to implement many predefined functions.
1772These optimization are particularly important when the predefined functions are polymorphic, as is the case for most pointer operations
1773\end{rationale}
1774
1775
1776\subsection{Bitwise AND operator}
1777
1778\begin{syntax}
1779\lhs{AND-expression}
1780\rhs \nonterm{equality-expression}
1781\rhs \nonterm{AND-expression} ©&© \nonterm{equality-expression}
1782\end{syntax}
1783
1784\rewriterules
1785\begin{lstlisting}
1786a & b => ?&?( a, b )§\use{?&?}§
1787\end{lstlisting}
1788
1789\predefined
1790\begin{lstlisting}
1791int ?&?( int, int );
1792unsigned int ?&?( unsigned int, unsigned int );
1793long int ?&?( long int, long int );
1794long unsigned int ?&?( long unsigned int, long unsigned int );
1795long long int ?&?( long long int, long long int );
1796long long unsigned int ?&?( long long unsigned int, long long unsigned int );
1797\end{lstlisting}
1798For every extended integer type ©X© with \Index{integer conversion rank} greater than the rank of ©int© there exist
1799% Don't use predefined: keep this out of prelude.cf.
1800\begin{lstlisting}
1801int ?&?( X, X );
1802\end{lstlisting}
1803
1804\semantics
1805The interpretations of a bitwise AND expression are the interpretations of the corresponding function call.
1806
1807
1808\subsection{Bitwise exclusive OR operator}
1809
1810\begin{syntax}
1811\lhs{exclusive-OR-expression}
1812\rhs \nonterm{AND-expression}
1813\rhs \nonterm{exclusive-OR-expression} ©^© \nonterm{AND-expression}
1814\end{syntax}
1815
1816\rewriterules
1817\begin{lstlisting}
1818a ^ b => ?^?( a, b )§\use{?^?}§
1819\end{lstlisting}
1820
1821\predefined
1822\begin{lstlisting}
1823int ?^?( int, int );
1824unsigned int ?^?( unsigned int, unsigned int );
1825long int ?^?( long int, long int );
1826long unsigned int ?^?( long unsigned int, long unsigned int );
1827long long int ?^?( long long int, long long int );
1828long long unsigned int ?^?( long long unsigned int, long long unsigned int );
1829\end{lstlisting}
1830For every extended integer type ©X© with \Index{integer conversion rank} greater than the rank of ©int© there exist
1831% Don't use predefined: keep this out of prelude.cf.
1832\begin{lstlisting}
1833int ?^?( X, X );
1834\end{lstlisting}
1835
1836\semantics
1837The interpretations of a bitwise exclusive OR expression are the interpretations of the corresponding function call.
1838
1839
1840\subsection{Bitwise inclusive OR operator}
1841
1842\begin{syntax}
1843\lhs{inclusive-OR-expression}
1844\rhs \nonterm{exclusive-OR-expression}
1845\rhs \nonterm{inclusive-OR-expression} ©|© \nonterm{exclusive-OR-expression}
1846\end{syntax}
1847
1848\rewriterules
1849\begin{lstlisting}
1850a | b => ?|?( a, b )§\use{?"|?}§
1851\end{lstlisting}
1852
1853\predefined
1854\begin{lstlisting}
1855int ?|?( int, int );
1856unsigned int ?|?( unsigned int, unsigned int );
1857long int ?|?( long int, long int );
1858long unsigned int ?|?( long unsigned int, long unsigned int );
1859long long int ?|?( long long int, long long int );
1860long long unsigned int ?|?( long long unsigned int, long long unsigned int );
1861\end{lstlisting}
1862For every extended integer type ©X© with \Index{integer conversion rank} greater than the rank of ©int© there exist
1863% Don't use predefined: keep this out of prelude.cf.
1864\begin{lstlisting}
1865int ?|?( X, X );
1866\end{lstlisting}
1867
1868\semantics 
1869The interpretations of a bitwise inclusive OR expression are the interpretations of the corresponding function call.
1870
1871
1872\subsection{Logical AND operator}
1873
1874\begin{syntax}
1875\lhs{logical-AND-expression}
1876\rhs \nonterm{inclusive-OR-expression}
1877\rhs \nonterm{logical-AND-expression} ©&&© \nonterm{inclusive-OR-expression}
1878\end{syntax}
1879
1880\semantics The operands of the expression ``©a && b©'' are treated as ``©(int)((a)!=0)©'' and ``©(int)((b)!=0)©'', which shall both be unambiguous.
1881The expression has only one interpretation, which is of type ©int©.
1882\begin{rationale}
1883When the operands of a logical expression are values of built-in types, and ``©!=©'' has not been redefined for those types, the compiler can optimize away the function calls.
1884
1885A common C idiom omits comparisons to ©0© in the controlling expressions of loops and ©if© statements.
1886For instance, the loop below iterates as long as ©rp© points at a ©Rational© value that is non-zero.
1887
1888\begin{lstlisting}
1889extern otype Rational;§\use{Rational}§
1890extern const Rational 0;§\use{0}§
1891extern int ?!=?( Rational, Rational );
1892Rational *rp;
1893while ( rp && *rp ) { ... }
1894\end{lstlisting}
1895The logical expression calls the ©Rational© inequality operator, passing it ©*rp© and the ©Rational 0©, and getting a 1 or 0 as a result.
1896In contrast, \CC would apply a programmer-defined ©Rational©-to-©int© conversion to ©*rp© in the equivalent situation.
1897The conversion to ©int© would produce a general integer value, which is unfortunate, and possibly dangerous if the conversion was not written with this situation in mind.
1898\end{rationale}
1899
1900
1901\subsection{Logical OR operator}
1902
1903\begin{syntax}
1904\lhs{logical-OR-expression}
1905\rhs \nonterm{logical-AND-expression}
1906\rhs \nonterm{logical-OR-expression} ©||© \nonterm{logical-AND-expression}
1907\end{syntax}
1908
1909\semantics
1910
1911The operands of the expression ``©a || b©'' are treated as ``©(int)((a)!=0)©'' and ``©(int)((b))!=0)©'', which shall both be unambiguous.
1912The expression has only one interpretation, which is of type ©int©.
1913
1914
1915\subsection{Conditional operator}
1916
1917\begin{syntax}
1918\lhs{conditional-expression}
1919\rhs \nonterm{logical-OR-expression}
1920\rhs \nonterm{logical-OR-expression} ©?© \nonterm{expression}
1921         ©:© \nonterm{conditional-expression}
1922\end{syntax}
1923
1924\semantics
1925In the conditional expression\use{?:} ``©a?b:c©'', if the second and third operands both have an interpretation with ©void© type, then the expression has an interpretation with type ©void©, equivalent to
1926\begin{lstlisting}
1927( int)(( a)!=0) ? ( void)( b) : ( void)( c)
1928\end{lstlisting}
1929
1930If the second and third operands both have interpretations with non-©void© types, the expression is treated as if it were the call ``©cond((a)!=0, b, c)©'', with ©cond© declared as
1931\begin{lstlisting}
1932forall( otype T ) T cond( int, T, T );
1933forall( dtype D ) void * cond( int, D *, void * ), * cond( int, void *, D * );
1934forall( dtype D ) _atomic void * cond(
1935        int, _Atomic D *, _Atomic void * ), * cond( int, _Atomic void *, _Atomic D * );
1936forall( dtype D ) const void * cond(
1937        int, const D *, const void * ), * cond( int, const void *, const D * );
1938forall( dtype D ) restrict void * cond(
1939        int, restrict D *, restrict void * ), * cond( int, restrict void *, restrict D * );
1940forall( dtype D ) volatile void * cond(
1941        int, volatile D *, volatile void * ), * cond( int, volatile void *, volatile D * );
1942forall( dtype D ) _Atomic const void * cond(
1943        int, _Atomic const D *, _Atomic const void * ), * cond( int, _Atomic const void *, _Atomic const D * );
1944forall( dtype D ) _Atomic restrict void * cond(
1945        int, _Atomic restrict D *, _Atomic restrict void * ), * cond( int, _Atomic restrict void *, _Atomic restrict D * );
1946forall( dtype D ) _Atomic volatile void * cond(
1947        int, _Atomic volatile D *, _Atomic volatile void * ), * cond( int, _Atomic volatile void *, _Atomic volatile D * );
1948forall( dtype D ) const restrict void * cond(
1949        int, const restrict D *, const restrict void * ), * cond( int, const restrict void *, const restrict D * );
1950forall( dtype D ) const volatile void * cond(
1951        int, const volatile D *, const volatile void * ), * cond( int, const volatile void *, const volatile D * );
1952forall( dtype D ) restrict volatile void * cond(
1953        int, restrict volatile D *, restrict volatile void * ), * cond( int, restrict volatile void *, restrict volatile D * );
1954forall( dtype D ) _Atomic const restrict void * cond(
1955        int, _Atomic const restrict D *, _Atomic const restrict void * ),
1956        * cond( int, _Atomic const restrict void *, _Atomic const restrict D * );
1957forall( dtype D ) _Atomic const volatile void * cond(
1958        int, _Atomic const volatile D *, _Atomic const volatile void * ),
1959        * cond( int, _Atomic const volatile void *, _Atomic const volatile D * );
1960forall( dtype D ) _Atomic restrict volatile void * cond(
1961        int, _Atomic restrict volatile D *, _Atomic restrict volatile void * ),
1962        * cond( int, _Atomic restrict volatile void *, _Atomic restrict volatile D * );
1963forall( dtype D ) const restrict volatile void * cond(
1964        int, const restrict volatile D *, const restrict volatile void * ),
1965        * cond( int, const restrict volatile void *, const restrict volatile D * );
1966forall( dtype D ) _Atomic const restrict volatile void * cond(
1967        int, _Atomic const restrict volatile D *, _Atomic const restrict volatile void * ),
1968        * cond( int, _Atomic const restrict volatile void *, _Atomic const restrict volatile D * );
1969\end{lstlisting}
1970
1971\begin{rationale}
1972The 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.
1973\end{rationale}
1974
1975\examples
1976\begin{lstlisting}
1977#include <stdlib.h>
1978int i;
1979long l;
1980rand() ? i : l;
1981\end{lstlisting}
1982The best interpretation infers the expression's type to be ©long© and applies the safe ©int©-to-©long© conversion to ©i©.
1983
1984\begin{lstlisting}
1985const int *cip;
1986volatile int *vip;
1987rand() ? cip : vip;
1988\end{lstlisting}
1989The expression has type ©const volatile int *©, with safe conversions applied to the second and third operands to add ©volatile© and ©const© qualifiers, respectively.
1990
1991\begin{lstlisting}
1992rand() ? cip : 0;
1993\end{lstlisting}
1994The expression has type ©const int *©, with a specialization conversion applied to ©0©.
1995
1996
1997\subsection{Assignment operators}
1998
1999\begin{syntax}
2000\lhs{assignment-expression}
2001\rhs \nonterm{conditional-expression}
2002\rhs \nonterm{unary-expression} \nonterm{assignment-operator}
2003         \nonterm{assignment-expression}
2004\lhs{assignment-operator} one of
2005\rhs ©=©\ \ ©*=©\ \ ©/=©\ \ ©%=©\ \ ©+=©\ \ ©-=©\ \ ©<<=©\ \ ©>>=©\ \ ©&=©\ \ ©^=©\ \ ©|=©
2006\end{syntax}
2007
2008\rewriterules
2009Let ``©<-©'' be any of the assignment operators.
2010Then
2011\use{?=?}\use{?*=?}\use{?/=?}\use{?%=?}\use{?+=?}\use{?-=?}\use{?>>=?}\use{?&=?}\use{?^=?}\use{?"|=?}%use{?<<=?}
2012\begin{lstlisting}
2013a <- b => ?<-?( &( a ), b )
2014\end{lstlisting}
2015
2016\semantics
2017Each interpretation of the left operand of an assignment expression is considered separately.
2018For each interpretation that is a bit-field or is declared with the ©register© storage class specifier, the expression has one valid interpretation, with the type of the left operand.
2019The right operand is cast to that type, and the assignment expression is ambiguous if either operand is.
2020For the remaining interpretations, the expression is rewritten, and the interpretations of the assignment expression are the interpretations of the corresponding function call.
2021Finally, 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;
2022where interpretations have compatible result types, the best interpretations are selected in the manner described for function call expressions.
2023
2024
2025\subsubsection{Simple assignment}
2026
2027\predefined
2028\begin{lstlisting}
2029_Bool
2030        ?=?( volatile _Bool *, _Bool ),
2031        ?=?( volatile _Bool *, forall( dtype D ) D * ),
2032        ?=?( volatile _Bool *, forall( ftype F ) F * ),
2033        ?=?( _Atomic volatile _Bool *, _Bool ),
2034        ?=?( _Atomic volatile _Bool *, forall( dtype D ) D * ),
2035        ?=?( _Atomic volatile _Bool *, forall( ftype F ) F * );
2036char
2037        ?=?( volatile char *, char ),
2038        ?=?( _Atomic volatile char *, char );
2039unsigned char
2040        ?=?( volatile unsigned char *, unsigned char ),
2041        ?=?( _Atomic volatile unsigned char *, unsigned char );
2042signed char
2043        ?=?( volatile signed char *, signed char ),
2044        ?=?( _Atomic volatile signed char *, signed char );
2045short int
2046        ?=?( volatile short int *, short int ),
2047        ?=?( _Atomic volatile short int *, short int );
2048unsigned short
2049        ?=?( volatile unsigned int *, unsigned int ),
2050        ?=?( _Atomic volatile unsigned int *, unsigned int );
2051int
2052        ?=?( volatile int *, int ),
2053        ?=?( _Atomic volatile int *, int );
2054unsigned int
2055        ?=?( volatile unsigned int *, unsigned int ),
2056        ?=?( _Atomic volatile unsigned int *, unsigned int );
2057long int
2058        ?=?( volatile long int *, long int ),
2059        ?=?( _Atomic volatile long int *, long int );
2060unsigned long int
2061        ?=?( volatile unsigned long int *, unsigned long int ),
2062        ?=?( _Atomic volatile unsigned long int *, unsigned long int );
2063long long int
2064        ?=?( volatile long long int *, long long int ),
2065        ?=?( _Atomic volatile long long int *, long long int );
2066unsigned long long int
2067        ?=?( volatile unsigned long long int *, unsigned long long int ),
2068        ?=?( _Atomic volatile unsigned long long int *, unsigned long long int );
2069float
2070        ?=?( volatile float *, float ),
2071        ?=?( _Atomic volatile float *, float );
2072double
2073        ?=?( volatile double *, double ),
2074        ?=?( _Atomic volatile double *, double );
2075long double
2076        ?=?( volatile long double *, long double ),
2077        ?=?( _Atomic volatile long double *, long double );
2078_Complex float
2079        ?=?( volatile float *, float ),
2080        ?=?( _Atomic volatile float *, float );
2081_Complex double
2082        ?=?( volatile double *, double ),
2083        ?=?( _Atomic volatile double *, double );
2084_Complex long double
2085        ?=?( volatile _Complex long double *, _Complex long double ),
2086        ?=?( _Atomic volatile _Complex long double *, _Atomic _Complex long double );
2087forall( ftype FT ) FT
2088        * ?=?( FT * volatile *, FT * ),
2089        * ?=?( FT * volatile *, forall( ftype F ) F * );
2090forall( ftype FT ) FT const
2091        * ?=?( FT const * volatile *, FT const * ),
2092        * ?=?( FT const * volatile *, forall( ftype F ) F * );
2093forall( ftype FT ) FT volatile
2094        * ?=?( FT volatile * volatile *, FT * ),
2095        * ?=?( FT volatile * volatile *, forall( ftype F ) F * );
2096forall( ftype FT ) FT const
2097        * ?=?( FT const volatile * volatile *, FT const * ),
2098        * ?=?( FT const volatile * volatile *, forall( ftype F ) F * );
2099forall( dtype DT ) DT
2100        * ?=?( DT * restrict volatile *, DT * ),
2101        * ?=?( DT * restrict volatile *, void * ),
2102        * ?=?( DT * restrict volatile *, forall( dtype D ) D * ),
2103        * ?=?( DT * _Atomic restrict volatile *, DT * ),
2104        * ?=?( DT * _Atomic restrict volatile *, void * ),
2105        * ?=?( DT * _Atomic restrict volatile *, forall( dtype D ) D * );
2106forall( dtype DT ) DT _Atomic
2107        * ?=?( _Atomic DT * restrict volatile *, DT _Atomic * ),
2108        * ?=?( _Atomic DT * restrict volatile *, void * ),
2109        * ?=?( _Atomic DT * restrict volatile *, forall( dtype D ) D * ),
2110        * ?=?( _Atomic DT * _Atomic restrict volatile *, DT _Atomic * ),
2111        * ?=?( _Atomic DT * _Atomic restrict volatile *, void * ),
2112        * ?=?( _Atomic DT * _Atomic restrict volatile *, forall( dtype D ) D * );
2113forall( dtype DT ) DT const
2114        * ?=?( DT const * restrict volatile *, DT const * ),
2115        * ?=?( DT const * restrict volatile *, void const * ),
2116        * ?=?( DT const * restrict volatile *, forall( dtype D ) D * ),
2117        * ?=?( DT const * _Atomic restrict volatile *, DT const * ),
2118        * ?=?( DT const * _Atomic restrict volatile *, void const * ),
2119        * ?=?( DT const * _Atomic restrict volatile *, forall( dtype D ) D * );
2120forall( dtype DT ) DT restrict
2121        * ?=?( restrict DT * restrict volatile *, DT restrict * ),
2122        * ?=?( restrict DT * restrict volatile *, void * ),
2123        * ?=?( restrict DT * restrict volatile *, forall( dtype D ) D * ),
2124        * ?=?( restrict DT * _Atomic restrict volatile *, DT restrict * ),
2125        * ?=?( restrict DT * _Atomic restrict volatile *, void * ),
2126        * ?=?( restrict DT * _Atomic restrict volatile *, forall( dtype D ) D * );
2127forall( dtype DT ) DT volatile
2128        * ?=?( DT volatile * restrict volatile *, DT volatile * ),
2129        * ?=?( DT volatile * restrict volatile *, void volatile * ),
2130        * ?=?( DT volatile * restrict volatile *, forall( dtype D ) D * ),
2131        * ?=?( DT volatile * _Atomic restrict volatile *, DT volatile * ),
2132        * ?=?( DT volatile * _Atomic restrict volatile *, void volatile * ),
2133        * ?=?( DT volatile * _Atomic restrict volatile *, forall( dtype D ) D * );
2134forall( dtype DT ) DT _Atomic const
2135        * ?=?( DT _Atomic const * restrict volatile *, DT _Atomic const * ),
2136        * ?=?( DT _Atomic const * restrict volatile *, void const * ),
2137        * ?=?( DT _Atomic const * restrict volatile *, forall( dtype D ) D * ),
2138        * ?=?( DT _Atomic const * _Atomic restrict volatile *, DT _Atomic const * ),
2139        * ?=?( DT _Atomic const * _Atomic restrict volatile *, void const * ),
2140        * ?=?( DT _Atomic const * _Atomic restrict volatile *, forall( dtype D ) D * );
2141forall( dtype DT ) DT _Atomic restrict
2142        * ?=?( _Atomic restrict DT * restrict volatile *, DT _Atomic restrict * ),
2143        * ?=?( _Atomic restrict DT * restrict volatile *, void * ),
2144        * ?=?( _Atomic restrict DT * restrict volatile *, forall( dtype D ) D * ),
2145        * ?=?( _Atomic restrict DT * _Atomic restrict volatile *, DT _Atomic restrict * ),
2146        * ?=?( _Atomic restrict DT * _Atomic restrict volatile *, void * ),
2147        * ?=?( _Atomic restrict DT * _Atomic restrict volatile *, forall( dtype D ) D * );
2148forall( dtype DT ) DT _Atomic volatile
2149        * ?=?( DT _Atomic volatile * restrict volatile *, DT _Atomic volatile * ),
2150        * ?=?( DT _Atomic volatile * restrict volatile *, void volatile * ),
2151        * ?=?( DT _Atomic volatile * restrict volatile *, forall( dtype D ) D * ),
2152        * ?=?( DT _Atomic volatile * _Atomic restrict volatile *, DT _Atomic volatile * ),
2153        * ?=?( DT _Atomic volatile * _Atomic restrict volatile *, void volatile * ),
2154        * ?=?( DT _Atomic volatile * _Atomic restrict volatile *, forall( dtype D ) D * );
2155forall( dtype DT ) DT const restrict
2156        * ?=?( DT const restrict * restrict volatile *, DT const restrict * ),
2157        * ?=?( DT const restrict * restrict volatile *, void const * ),
2158        * ?=?( DT const restrict * restrict volatile *, forall( dtype D ) D * ),
2159        * ?=?( DT const restrict * _Atomic restrict volatile *, DT const restrict * ),
2160        * ?=?( DT const restrict * _Atomic restrict volatile *, void const * ),
2161        * ?=?( DT const restrict * _Atomic restrict volatile *, forall( dtype D ) D * );
2162forall( dtype DT ) DT const volatile
2163        * ?=?( DT const volatile * restrict volatile *, DT const volatile * ),
2164        * ?=?( DT const volatile * restrict volatile *, void const volatile * ),
2165        * ?=?( DT const volatile * restrict volatile *, forall( dtype D ) D * ),
2166        * ?=?( DT const volatile * _Atomic restrict volatile *, DT const volatile * ),
2167        * ?=?( DT const volatile * _Atomic restrict volatile *, void const volatile * ),
2168        * ?=?( DT const volatile * _Atomic restrict volatile *, forall( dtype D ) D * );
2169forall( dtype DT ) DT restrict volatile
2170        * ?=?( DT restrict volatile * restrict volatile *, DT restrict volatile * ),
2171        * ?=?( DT restrict volatile * restrict volatile *, void volatile * ),
2172        * ?=?( DT restrict volatile * restrict volatile *, forall( dtype D ) D * ),
2173        * ?=?( DT restrict volatile * _Atomic restrict volatile *, DT restrict volatile * ),
2174        * ?=?( DT restrict volatile * _Atomic restrict volatile *, void volatile * ),
2175        * ?=?( DT restrict volatile * _Atomic restrict volatile *, forall( dtype D ) D * );
2176forall( dtype DT ) DT _Atomic const restrict
2177        * ?=?( DT _Atomic const restrict * restrict volatile *,
2178         DT _Atomic const restrict * ),
2179        * ?=?( DT _Atomic const restrict * restrict volatile *,
2180         void const * ),
2181        * ?=?( DT _Atomic const restrict * restrict volatile *,
2182         forall( dtype D ) D * ),
2183        * ?=?( DT _Atomic const restrict * _Atomic restrict volatile *,
2184         DT _Atomic const restrict * ),
2185        * ?=?( DT _Atomic const restrict * _Atomic restrict volatile *,
2186         void const * ),
2187        * ?=?( DT _Atomic const restrict * _Atomic restrict volatile *,
2188         forall( dtype D ) D * );
2189forall( dtype DT ) DT _Atomic const volatile
2190        * ?=?( DT _Atomic const volatile * restrict volatile *,
2191         DT _Atomic const volatile * ),
2192        * ?=?( DT _Atomic const volatile * restrict volatile *,
2193         void const volatile * ),
2194        * ?=?( DT _Atomic const volatile * restrict volatile *,
2195         forall( dtype D ) D * ),
2196        * ?=?( DT _Atomic const volatile * _Atomic restrict volatile *,
2197         DT _Atomic const volatile * ),
2198        * ?=?( DT _Atomic const volatile * _Atomic restrict volatile *,
2199         void const volatile * ),
2200        * ?=?( DT _Atomic const volatile * _Atomic restrict volatile *,
2201         forall( dtype D ) D * );
2202forall( dtype DT ) DT _Atomic restrict volatile
2203        * ?=?( DT _Atomic restrict volatile * restrict volatile *,
2204         DT _Atomic restrict volatile * ),
2205        * ?=?( DT _Atomic restrict volatile * restrict volatile *,
2206         void volatile * ),
2207        * ?=?( DT _Atomic restrict volatile * restrict volatile *,
2208         forall( dtype D ) D * ),
2209        * ?=?( DT _Atomic restrict volatile * _Atomic restrict volatile *,
2210         DT _Atomic restrict volatile * ),
2211        * ?=?( DT _Atomic restrict volatile * _Atomic restrict volatile *,
2212         void volatile * ),
2213        * ?=?( DT _Atomic restrict volatile * _Atomic restrict volatile *,
2214         forall( dtype D ) D * );
2215forall( dtype DT ) DT const restrict volatile
2216        * ?=?( DT const restrict volatile * restrict volatile *,
2217         DT const restrict volatile * ),
2218        * ?=?( DT const restrict volatile * restrict volatile *,
2219         void const volatile * ),
2220        * ?=?( DT const restrict volatile * restrict volatile *,
2221         forall( dtype D ) D * ),
2222        * ?=?( DT const restrict volatile * _Atomic restrict volatile *,
2223         DT const restrict volatile * ),
2224        * ?=?( DT const restrict volatile * _Atomic restrict volatile *,
2225         void const volatile * ),
2226        * ?=?( DT const restrict volatile * _Atomic restrict volatile *,
2227         forall( dtype D ) D * );
2228forall( dtype DT ) DT _Atomic const restrict volatile
2229        * ?=?( DT _Atomic const restrict volatile * restrict volatile *,
2230         DT _Atomic const restrict volatile * ),
2231        * ?=?( DT _Atomic const restrict volatile * restrict volatile *,
2232         void const volatile * ),
2233        * ?=?( DT _Atomic const restrict volatile * restrict volatile *,
2234         forall( dtype D ) D * ),
2235        * ?=?( DT _Atomic const restrict volatile * _Atomic restrict volatile *,
2236         DT _Atomic const restrict volatile * ),
2237        * ?=?( DT _Atomic const restrict volatile * _Atomic restrict volatile *,
2238         void const volatile * ),
2239        * ?=?( DT _Atomic const restrict volatile * _Atomic restrict volatile *,
2240         forall( dtype D ) D * );
2241forall( dtype DT ) void
2242        * ?=?( void * restrict volatile *, DT * );
2243forall( dtype DT ) void const
2244        * ?=?( void const * restrict volatile *, DT const * );
2245forall( dtype DT ) void volatile
2246        * ?=?( void volatile * restrict volatile *, DT volatile * );
2247forall( dtype DT ) void const volatile
2248        * ?=?( void const volatile * restrict volatile *, DT const volatile * );
2249\end{lstlisting}
2250\begin{rationale}
2251The pattern of overloadings for simple assignment resembles that of pointer increment and decrement, except that the polymorphic pointer assignment functions declare a ©dtype© parameter, instead of a ©type© parameter, because the left operand may be a pointer to an incomplete type.
2252\end{rationale}
2253
2254For every complete structure or union type ©S© there exist
2255% Don't use predefined: keep this out of prelude.cf.
2256\begin{lstlisting}
2257S ?=?( S volatile *, S ), ?=?( S _Atomic volatile *, S );
2258\end{lstlisting}
2259
2260For every extended integer type ©X© there exist
2261% Don't use predefined: keep this out of prelude.cf.
2262\begin{lstlisting}
2263X ?=?( X volatile *, X ), ?=?( X _Atomic volatile *, X );
2264\end{lstlisting}
2265
2266For every complete enumerated type ©E© there exist
2267% Don't use predefined: keep this out of prelude.cf.
2268\begin{lstlisting}
2269E ?=?( E volatile *, int ), ?=?( E _Atomic volatile *, int );
2270\end{lstlisting}
2271\begin{rationale}
2272The right-hand argument is ©int© because enumeration constants have type ©int©.
2273\end{rationale}
2274
2275\semantics
2276The structure assignment functions provide member-wise assignment;
2277each 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.
2278All other assignment functions have the same effect as the corresponding C assignment expression.
2279\begin{rationale}
2280Note 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.
2281\end{rationale}
2282
2283
2284\subsubsection{Compound assignment}
2285
2286\predefined
2287\begin{lstlisting}
2288forall( otype T ) T
2289        * ?+=?( T * restrict volatile *, ptrdiff_t ),
2290        * ?-=?( T * restrict volatile *, ptrdiff_t ),
2291        * ?+=?( T * _Atomic restrict volatile *, ptrdiff_t ),
2292        * ?-=?( T * _Atomic restrict volatile *, ptrdiff_t );
2293forall( otype T ) T _Atomic
2294        * ?+=?( T _Atomic * restrict volatile *, ptrdiff_t ),
2295        * ?-=?( T _Atomic * restrict volatile *, ptrdiff_t ),
2296        * ?+=?( T _Atomic * _Atomic restrict volatile *, ptrdiff_t ),
2297        * ?-=?( T _Atomic * _Atomic restrict volatile *, ptrdiff_t );
2298forall( otype T ) T const
2299        * ?+=?( T const * restrict volatile *, ptrdiff_t ),
2300        * ?-=?( T const * restrict volatile *, ptrdiff_t ),
2301        * ?+=?( T const * _Atomic restrict volatile *, ptrdiff_t ),
2302        * ?-=?( T const * _Atomic restrict volatile *, ptrdiff_t );
2303forall( otype T ) T restrict
2304        * ?+=?( T restrict * restrict volatile *, ptrdiff_t ),
2305        * ?-=?( T restrict * restrict volatile *, ptrdiff_t ),
2306        * ?+=?( T restrict * _Atomic restrict volatile *, ptrdiff_t ),
2307        * ?-=?( T restrict * _Atomic restrict volatile *, ptrdiff_t );
2308forall( otype T ) T volatile
2309        * ?+=?( T volatile * restrict volatile *, ptrdiff_t ),
2310        * ?-=?( T volatile * restrict volatile *, ptrdiff_t ),
2311        * ?+=?( T volatile * _Atomic restrict volatile *, ptrdiff_t ),
2312        * ?-=?( T volatile * _Atomic restrict volatile *, ptrdiff_t );
2313forall( otype T ) T _Atomic const
2314        * ?+=?( T _Atomic const restrict volatile *, ptrdiff_t ),
2315        * ?-=?( T _Atomic const restrict volatile *, ptrdiff_t ),
2316        * ?+=?( T _Atomic const _Atomic restrict volatile *, ptrdiff_t ),
2317        * ?-=?( T _Atomic const _Atomic restrict volatile *, ptrdiff_t );
2318forall( otype T ) T _Atomic restrict
2319        * ?+=?( T _Atomic restrict * restrict volatile *, ptrdiff_t ),
2320        * ?-=?( T _Atomic restrict * restrict volatile *, ptrdiff_t ),
2321        * ?+=?( T _Atomic restrict * _Atomic restrict volatile *, ptrdiff_t ),
2322        * ?-=?( T _Atomic restrict * _Atomic restrict volatile *, ptrdiff_t );
2323forall( otype T ) T _Atomic volatile
2324        * ?+=?( T _Atomic volatile * restrict volatile *, ptrdiff_t ),
2325        * ?-=?( T _Atomic volatile * restrict volatile *, ptrdiff_t ),
2326        * ?+=?( T _Atomic volatile * _Atomic restrict volatile *, ptrdiff_t ),
2327        * ?-=?( T _Atomic volatile * _Atomic restrict volatile *, ptrdiff_t );
2328forall( otype T ) T const restrict
2329        * ?+=?( T const restrict * restrict volatile *, ptrdiff_t ),
2330        * ?-=?( T const restrict * restrict volatile *, ptrdiff_t ),
2331        * ?+=?( T const restrict * _Atomic restrict volatile *, ptrdiff_t ),
2332        * ?-=?( T const restrict * _Atomic restrict volatile *, ptrdiff_t );
2333forall( otype T ) T const volatile
2334        * ?+=?( T const volatile * restrict volatile *, ptrdiff_t ),
2335        * ?-=?( T const volatile * restrict volatile *, ptrdiff_t ),
2336        * ?+=?( T const volatile * _Atomic restrict volatile *, ptrdiff_t ),
2337        * ?-=?( T const volatile * _Atomic restrict volatile *, ptrdiff_t );
2338forall( otype T ) T restrict volatile
2339        * ?+=?( T restrict volatile * restrict volatile *, ptrdiff_t ),
2340        * ?-=?( T restrict volatile * restrict volatile *, ptrdiff_t ),
2341        * ?+=?( T restrict volatile * _Atomic restrict volatile *, ptrdiff_t ),
2342        * ?-=?( T restrict volatile * _Atomic restrict volatile *, ptrdiff_t );
2343forall( otype T ) T _Atomic const restrict
2344        * ?+=?( T _Atomic const restrict * restrict volatile *, ptrdiff_t ),
2345        * ?-=?( T _Atomic const restrict * restrict volatile *, ptrdiff_t ),
2346        * ?+=?( T _Atomic const restrict * _Atomic restrict volatile *, ptrdiff_t ),
2347        * ?-=?( T _Atomic const restrict * _Atomic restrict volatile *, ptrdiff_t );
2348forall( otype T ) T _Atomic const volatile
2349        * ?+=?( T _Atomic const volatile * restrict volatile *, ptrdiff_t ),
2350        * ?-=?( T _Atomic const volatile * restrict volatile *, ptrdiff_t ),
2351        * ?+=?( T _Atomic const volatile * _Atomic restrict volatile *, ptrdiff_t ),
2352        * ?-=?( T _Atomic const volatile * _Atomic restrict volatile *, ptrdiff_t );
2353forall( otype T ) T _Atomic restrict volatile
2354        * ?+=?( T _Atomic restrict volatile * restrict volatile *, ptrdiff_t ),
2355        * ?-=?( T _Atomic restrict volatile * restrict volatile *, ptrdiff_t ),
2356        * ?+=?( T _Atomic restrict volatile * _Atomic restrict volatile *, ptrdiff_t ),
2357        * ?-=?( T _Atomic restrict volatile * _Atomic restrict volatile *, ptrdiff_t );
2358forall( otype T ) T const restrict volatile
2359        * ?+=?( T const restrict volatile * restrict volatile *, ptrdiff_t ),
2360        * ?-=?( T const restrict volatile * restrict volatile *, ptrdiff_t ),
2361        * ?+=?( T const restrict volatile * _Atomic restrict volatile *, ptrdiff_t ),
2362        * ?-=?( T const restrict volatile * _Atomic restrict volatile *, ptrdiff_t );
2363forall( otype T ) T _Atomic const restrict volatile
2364        * ?+=?( T _Atomic const restrict volatile * restrict volatile *, ptrdiff_t ),
2365        * ?-=?( T _Atomic const restrict volatile * restrict volatile *, ptrdiff_t ),
2366        * ?+=?( T _Atomic const restrict volatile * _Atomic restrict volatile *, ptrdiff_t ),
2367        * ?-=?( T _Atomic const restrict volatile * _Atomic restrict volatile *, ptrdiff_t );
2368
2369_Bool
2370        ?*=?( _Bool volatile *, _Bool ),
2371        ?/=?( _Bool volatile *, _Bool ),
2372        ?+=?( _Bool volatile *, _Bool ),
2373        ?-=?( _Bool volatile *, _Bool ),
2374        ?%=?( _Bool volatile *, _Bool ),
2375        ?<<=?( _Bool volatile *, int ),
2376        ?>>=?( _Bool volatile *, int ),
2377        ?&=?( _Bool volatile *, _Bool ),
2378        ?^=?( _Bool volatile *, _Bool ),
2379        ?|=?( _Bool volatile *, _Bool );
2380char
2381        ?*=?( char volatile *, char ),
2382        ?/=?( char volatile *, char ),
2383        ?+=?( char volatile *, char ),
2384        ?-=?( char volatile *, char ),
2385        ?%=?( char volatile *, char ),
2386        ?<<=?( char volatile *, int ),
2387        ?>>=?( char volatile *, int ),
2388        ?&=?( char volatile *, char ),
2389        ?^=?( char volatile *, char ),
2390        ?|=?( char volatile *, char );
2391unsigned char
2392        ?*=?( unsigned char volatile *, unsigned char ),
2393        ?/=?( unsigned char volatile *, unsigned char ),
2394        ?+=?( unsigned char volatile *, unsigned char ),
2395        ?-=?( unsigned char volatile *, unsigned char ),
2396        ?%=?( unsigned char volatile *, unsigned char ),
2397        ?<<=?( unsigned char volatile *, int ),
2398        ?>>=?( unsigned char volatile *, int ),
2399        ?&=?( unsigned char volatile *, unsigned char ),
2400        ?^=?( unsigned char volatile *, unsigned char ),
2401        ?|=?( unsigned char volatile *, unsigned char );
2402signed char
2403        ?*=?( signed char volatile *, signed char ),
2404        ?/=?( signed char volatile *, signed char ),
2405        ?+=?( signed char volatile *, signed char ),
2406        ?-=?( signed char volatile *, signed char ),
2407        ?%=?( signed char volatile *, signed char ),
2408        ?<<=?( signed char volatile *, int ),
2409        ?>>=?( signed char volatile *, int ),
2410        ?&=?( signed char volatile *, signed char ),
2411        ?^=?( signed char volatile *, signed char ),
2412        ?|=?( signed char volatile *, signed char );
2413short int
2414        ?*=?( short int volatile *, short int ),
2415        ?/=?( short int volatile *, short int ),
2416        ?+=?( short int volatile *, short int ),
2417        ?-=?( short int volatile *, short int ),
2418        ?%=?( short int volatile *, short int ),
2419        ?<<=?( short int volatile *, int ),
2420        ?>>=?( short int volatile *, int ),
2421        ?&=?( short int volatile *, short int ),
2422        ?^=?( short int volatile *, short int ),
2423        ?|=?( short int volatile *, short int );
2424unsigned short int
2425        ?*=?( unsigned short int volatile *, unsigned short int ),
2426        ?/=?( unsigned short int volatile *, unsigned short int ),
2427        ?+=?( unsigned short int volatile *, unsigned short int ),
2428        ?-=?( unsigned short int volatile *, unsigned short int ),
2429        ?%=?( unsigned short int volatile *, unsigned short int ),
2430        ?<<=?( unsigned short int volatile *, int ),
2431        ?>>=?( unsigned short int volatile *, int ),
2432        ?&=?( unsigned short int volatile *, unsigned short int ),
2433        ?^=?( unsigned short int volatile *, unsigned short int ),
2434        ?|=?( unsigned short int volatile *, unsigned short int );
2435int
2436        ?*=?( int volatile *, int ),
2437        ?/=?( int volatile *, int ),
2438        ?+=?( int volatile *, int ),
2439        ?-=?( int volatile *, int ),
2440        ?%=?( int volatile *, int ),
2441        ?<<=?( int volatile *, int ),
2442        ?>>=?( int volatile *, int ),
2443        ?&=?( int volatile *, int ),
2444        ?^=?( int volatile *, int ),
2445        ?|=?( int volatile *, int );
2446unsigned int
2447        ?*=?( unsigned int volatile *, unsigned int ),
2448        ?/=?( unsigned int volatile *, unsigned int ),
2449        ?+=?( unsigned int volatile *, unsigned int ),
2450        ?-=?( unsigned int volatile *, unsigned int ),
2451        ?%=?( unsigned int volatile *, unsigned int ),
2452        ?<<=?( unsigned int volatile *, int ),
2453        ?>>=?( unsigned int volatile *, int ),
2454        ?&=?( unsigned int volatile *, unsigned int ),
2455        ?^=?( unsigned int volatile *, unsigned int ),
2456        ?|=?( unsigned int volatile *, unsigned int );
2457long int
2458        ?*=?( long int volatile *, long int ),
2459        ?/=?( long int volatile *, long int ),
2460        ?+=?( long int volatile *, long int ),
2461        ?-=?( long int volatile *, long int ),
2462        ?%=?( long int volatile *, long int ),
2463        ?<<=?( long int volatile *, int ),
2464        ?>>=?( long int volatile *, int ),
2465        ?&=?( long int volatile *, long int ),
2466        ?^=?( long int volatile *, long int ),
2467        ?|=?( long int volatile *, long int );
2468unsigned long int
2469        ?*=?( unsigned long int volatile *, unsigned long int ),
2470        ?/=?( unsigned long int volatile *, unsigned long int ),
2471        ?+=?( unsigned long int volatile *, unsigned long int ),
2472        ?-=?( unsigned long int volatile *, unsigned long int ),
2473        ?%=?( unsigned long int volatile *, unsigned long int ),
2474        ?<<=?( unsigned long int volatile *, int ),
2475        ?>>=?( unsigned long int volatile *, int ),
2476        ?&=?( unsigned long int volatile *, unsigned long int ),
2477        ?^=?( unsigned long int volatile *, unsigned long int ),
2478        ?|=?( unsigned long int volatile *, unsigned long int );
2479long long int
2480        ?*=?( long long int volatile *, long long int ),
2481        ?/=?( long long int volatile *, long long int ),
2482        ?+=?( long long int volatile *, long long int ),
2483        ?-=?( long long int volatile *, long long int ),
2484        ?%=?( long long int volatile *, long long int ),
2485        ?<<=?( long long int volatile *, int ),
2486        ?>>=?( long long int volatile *, int ),
2487        ?&=?( long long int volatile *, long long int ),
2488        ?^=?( long long int volatile *, long long int ),
2489        ?|=?( long long int volatile *, long long int );
2490unsigned long long int
2491        ?*=?( unsigned long long int volatile *, unsigned long long int ),
2492        ?/=?( unsigned long long int volatile *, unsigned long long int ),
2493        ?+=?( unsigned long long int volatile *, unsigned long long int ),
2494        ?-=?( unsigned long long int volatile *, unsigned long long int ),
2495        ?%=?( unsigned long long int volatile *, unsigned long long int ),
2496        ?<<=?( unsigned long long int volatile *, int ),
2497        ?>>=?( unsigned long long int volatile *, int ),
2498        ?&=?( unsigned long long int volatile *, unsigned long long int ),
2499        ?^=?( unsigned long long int volatile *, unsigned long long int ),
2500        ?|=?( unsigned long long int volatile *, unsigned long long int );
2501float
2502        ?*=?( float volatile *, float ),
2503        ?/=?( float volatile *, float ),
2504        ?+=?( float volatile *, float ),
2505        ?-=?( float volatile *, float );
2506double
2507        ?*=?( double volatile *, double ),
2508        ?/=?( double volatile *, double ),
2509        ?+=?( double volatile *, double ),
2510        ?-=?( double volatile *, double );
2511long double
2512        ?*=?( long double volatile *, long double ),
2513        ?/=?( long double volatile *, long double ),
2514        ?+=?( long double volatile *, long double ),
2515        ?-=?( long double volatile *, long double );
2516_Complex float
2517        ?*=?( _Complex float volatile *, _Complex float ),
2518        ?/=?( _Complex float volatile *, _Complex float ),
2519        ?+=?( _Complex float volatile *, _Complex float ),
2520        ?-=?( _Complex float volatile *, _Complex float );
2521_Complex double
2522        ?*=?( _Complex double volatile *, _Complex double ),
2523        ?/=?( _Complex double volatile *, _Complex double ),
2524        ?+=?( _Complex double volatile *, _Complex double ),
2525        ?-=?( _Complex double volatile *, _Complex double );
2526_Complex long double
2527        ?*=?( _Complex long double volatile *, _Complex long double ),
2528        ?/=?( _Complex long double volatile *, _Complex long double ),
2529        ?+=?( _Complex long double volatile *, _Complex long double ),
2530        ?-=?( _Complex long double volatile *, _Complex long double );
2531\end{lstlisting}
2532
2533For every extended integer type ©X© there exist
2534% Don't use predefined: keep this out of prelude.cf.
2535\begin{lstlisting}
2536?*=?( X volatile *, X ),
2537?/=?( X volatile *, X ),
2538?+=?( X volatile *, X ),
2539?-=?( X volatile *, X ),
2540?%=?( X volatile *, X ),
2541?<<=?( X volatile *, int ),
2542?>>=?( X volatile *, int ),
2543?&=?( X volatile *, X ),
2544?^=?( X volatile *, X ),
2545?|=?( X volatile *, X );
2546\end{lstlisting}
2547
2548For every complete enumerated type ©E© there exist
2549% Don't use predefined: keep this out of prelude.cf.
2550\begin{lstlisting}
2551?*=?( E volatile *, E ),
2552?/=?( E volatile *, E ),
2553?+=?( E volatile *, E ),
2554?-=?( E volatile *, E ),
2555?%=?( E volatile *, E ),
2556?<<=?( E volatile *, int ),
2557?>>=?( E volatile *, int ),
2558?&=?( E volatile *, E ),
2559?^=?( E volatile *, E ),
2560?|=?( E volatile *, E );
2561\end{lstlisting}
2562
2563
2564\subsection{Comma operator}
2565
2566\begin{syntax}
2567\lhs{expression}
2568\rhs \nonterm{assignment-expression}
2569\rhs \nonterm{expression} ©,© \nonterm{assignment-expression}
2570\end{syntax}
2571
2572\semantics
2573In the comma expression ``©a, b©'', the first operand is interpreted as ``©( void )(a)©'', which shall be unambiguous\index{ambiguous interpretation}.
2574The interpretations of the expression are the interpretations of the second operand.
2575
2576
2577\section{Constant expressions}
2578
2579
2580\section{Declarations}
2581
2582\begin{syntax}
2583\oldlhs{declaration}
2584\rhs \nonterm{type-declaration}
2585\rhs \nonterm{spec-definition}
2586\end{syntax}
2587
2588\constraints
2589If 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:
2590\begin{itemize}
2591\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;
2592\item tags may be redeclared as specified in section 6.7.2.3 of the \Celeven standard.
2593\end{itemize}
2594\begin{rationale}
2595This constraint adds the phrase ``with compatible types'' to the \Celeven constraint, to allow overloading.
2596\end{rationale}
2597
2598An identifier declared by a type declaration shall not be redeclared as a parameter in a function definition whose declarator includes an identifier list.
2599\begin{rationale}
2600This restriction echos \Celeven's ban on the redeclaration of typedef names as parameters.
2601This avoids an ambiguity between old-style function declarations and new-style function prototypes:
2602\begin{lstlisting}
2603void f( Complex,        // ... 3000 characters ...
2604void g( Complex,        // ... 3000 characters ...
2605int Complex;
2606{ ... }
2607\end{lstlisting}
2608Without the rule, ©Complex© would be a type in the first case, and a parameter name in the second.
2609\end{rationale}
2610
2611
2612\setcounter{subsection}{1}
2613\subsection{Type specifiers}
2614
2615\begin{syntax}
2616\oldlhs{type-specifier}
2617\rhs \nonterm{forall-specifier}
2618\end{syntax}
2619
2620\semantics
2621Forall specifiers are discussed in \VRef{forall}.
2622
2623
2624\subsubsection{Structure and union specifiers}
2625
2626\semantics 
2627\CFA extends the \Celeven definition of \define{anonymous structure} to include structure specifiers with tags, and extends the \Celeven definition of \define{anonymous union} to include union specifiers with tags.
2628\begin{rationale}
2629This extension imitates an extension in the Plan 9 C compiler \cite{Thompson90new}.
2630\end{rationale}
2631
2632\examples
2633\begin{lstlisting}
2634struct point {§\impl{point}§
2635        int x, y;
2636};
2637struct color_point {§\impl{color_point}§
2638        enum { RED, BLUE, GREEN } color;
2639        struct point;
2640};
2641struct color_point cp;
2642cp.x = 0;
2643cp.color = RED;
2644struct literal {§\impl{literal}§
2645        enum { NUMBER, STRING } tag;
2646        union {
2647                double n;
2648                char *s;
2649        };
2650};
2651struct literal *next;
2652int length;
2653extern int strlen( const char * );
2654...
2655if ( next->tag == STRING ) length = strlen( next->s );
2656\end{lstlisting}
2657
2658
2659\setcounter{subsubsection}{4}
2660\subsubsection{Forall specifiers}
2661\label{forall}
2662
2663\begin{syntax}
2664\lhs{forall-specifier}
2665\rhs ©forall© ©(© \nonterm{type-parameter-list} ©)©
2666\end{syntax}
2667
2668\begin{comment}
2669\constraints
2670If 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}.
2671\begin{rationale}
2672This 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.
2673\begin{lstlisting}
2674forall( otype T ) struct Pair { T a, b;
2675} mkPair( T, T ); // illegal
2676\end{lstlisting}
2677If an instance of ©struct Pair© was declared later in the current scope, what would the members' type be?
2678\end{rationale}
2679\end{comment}
2680
2681\semantics
2682The \nonterm{type-parameter-list}s and assertions of the \nonterm{forall-specifier}s declare type identifiers, function and object identifiers with \Index{no linkage}.
2683
2684If, in the declaration ``©T D©'', ©T© contains \nonterm{forall-specifier}s and ©D© has the form
2685\begin{lstlisting}
2686D( §\normalsize\nonterm{parameter-type-list}§ )
2687\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 ©D©, and it is used in the type of a parameter in the following
2688\nonterm{type-parameter-list} or it and an inferred parameter are used as arguments of a \Index{specification} in one of the \nonterm{forall-specifier}s.
2689The identifiers declared by assertions that use an inferred parameter of a function declarator are \Index{assertion parameter}s of that function declarator.
2690
2691\begin{comment}
2692\begin{rationale}
2693Since 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.
2694
2695If this restriction were lifted, it would be possible to write
2696\begin{lstlisting}
2697forall( otype T ) T * alloc( void );§\use{alloc}§ int *p = alloc();
2698\end{lstlisting}
2699Here ©alloc()© would receive ©int© as an inferred argument, and return an ©int *©.
2700In general, if a call to ©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 ©T© to be bound.
2701
2702With the current restriction, ©alloc()© must be given an argument that determines ©T©:
2703\begin{lstlisting}
2704forall( otype T ) T * alloc( T initial_value );§\use{alloc}§
2705\end{lstlisting}
2706\end{rationale}
2707\end{comment}
2708
2709If a function declarator is part of a function definition, its inferred parameters and assertion parameters have \Index{block scope};
2710otherwise, identifiers declared by assertions have a \define{declaration scope}, which terminates at the end of the \nonterm{declaration}.
2711
2712A function type that has at least one inferred parameter is a \define{polymorphic function} type.
2713Function types with no inferred parameters are \define{monomorphic function} types.
2714One 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.
2715
2716The names of inferred parameters and the order of identifiers in forall specifiers are not relevant to polymorphic function type compatibility.
2717Let $f$ 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.
2718Let $f'$ be $f$ with every occurrence of $f_i$ replaced by $g_i$, for all $i$.
2719Then $f$ and $g$ are \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.
2720
2721\examples
2722Consider these analogous monomorphic and polymorphic declarations.
2723\begin{lstlisting}
2724int fi( int );
2725forall( otype T ) T fT( T );
2726\end{lstlisting}
2727©fi()© takes an ©int© and returns an ©int©. ©fT()© takes a ©T© and returns a ©T©, for any type ©T©.
2728\begin{lstlisting}
2729int (*pfi )( int ) = fi;
2730forall( otype T ) T (*pfT )( T ) = fT;
2731\end{lstlisting}
2732©pfi© and ©pfT© are pointers to functions. ©pfT© is not polymorphic, but the function it points at is.
2733\begin{lstlisting}
2734int (*fvpfi( void ))( int ) {
2735        return pfi;
2736}
2737forall( otype T ) T (*fvpfT( void ))( T ) {
2738        return pfT;
2739}
2740\end{lstlisting}
2741©fvpfi()© and ©fvpfT()© are functions taking no arguments and returning pointers to functions. ©fvpfT()© is monomorphic, but the function that its return value points at is polymorphic.
2742\begin{lstlisting}
2743forall( otype T ) int ( *fTpfi( T ) )( int );
2744forall( otype T ) T ( *fTpfT( T ) )( T );
2745forall( otype T, otype U ) U ( *fTpfU( T ) )( U );
2746\end{lstlisting}
2747©fTpfi()© is a polymorphic function that returns a pointer to a monomorphic function taking an integer and returning an integer.
2748It could return ©pfi©. ©fTpfT()© is subtle: it is a polymorphic function returning a \emph{monomorphic} function taking and returning
2749©T©, where ©T© is an inferred parameter of ©fTpfT()©.
2750For instance, in the expression ``©fTpfT(17)©'', ©T© is inferred to be ©int©, and the returned value would have type ©int ( * )( int )©. ``©fTpfT(17)(13)©'' and ``©fTpfT("yes")("no")©'' are legal, but ``©fTpfT(17)("no")©'' is illegal.
2751©fTpfU()© is polymorphic ( in type ©T©), and returns a pointer to a function that is polymorphic ( in type ©U©). ``©f5(17)("no")©'' is a legal expression of type ©char *©.
2752\begin{lstlisting}
2753forall( otype T, otype U, otype V ) U * f( T *, U, V * const );
2754forall( otype U, otype V, otype W ) U * g( V *, U, W * const );
2755\end{lstlisting}
2756The functions ©f()© and ©g()© have compatible types.
2757Let \(f\) and \(g\) be their types;
2758then \(f_1\) = ©T©, \(f_2\) = ©U©, \(f_3\) = ©V©, \(g_1\)
2759= ©V©, \(g_2\) = ©U©, and \(g_3\) = ©W©.
2760Replacing every \(f_i\) by \(g_i\) in \(f\) gives
2761\begin{lstlisting}
2762forall( otype V, otype U, otype W ) U * f( V *, U, W * const );
2763\end{lstlisting} which has a return type and parameter list that is compatible with \(g\).
2764\begin{rationale}
2765The word ``©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.
2766
2767Even without parameterized types, I might try to allow
2768\begin{lstlisting}
2769forall( int n ) int sum( int vector[n] );
2770\end{lstlisting} but C currently rewrites array parameters as pointer parameters, so the effects of such a change require more thought.
2771\end{rationale}
2772
2773\begin{rationale}
2774A polymorphic declaration must do two things: it must introduce type parameters, and it must apply assertions to those types.
2775Adding this to existing C declaration syntax and semantics was delicate, and not entirely successful.
2776
2777C depends on declaration-before-use, so a forall specifier must introduce type names before they can be used in the declaration specifiers.
2778This could be done by making the forall specifier part of the declaration specifiers, or by making it a new introductory clause of declarations.
2779
2780Assertions are also part of polymorphic function types, because it must be clear which functions have access to the assertion parameters declared by the assertions.
2781All attempts to put assertions inside an introductory clause produced complex semantics and confusing code.
2782Building 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.
2783Assertions are also used with type parameters of specifications, and by type declarations.
2784For 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.
2785\end{rationale}
2786%HERE
2787
2788
2789\subsection{Type qualifiers}
2790
2791\CFA defines a new type qualifier ©lvalue©\impl{lvalue}\index{lvalue}.
2792\begin{syntax}
2793\oldlhs{type-qualifier}
2794\rhs ©lvalue©
2795\end{syntax}
2796
2797\constraints
2798\Indexc{restrict} Types other than type parameters and pointer types whose referenced type is an object type shall not be restrict-qualified.
2799
2800\semantics
2801An object's type may be a restrict-qualified type parameter.
2802©restrict© does not establish any special semantics in that case.
2803
2804\begin{rationale}
2805\CFA loosens the constraint on the restrict qualifier so that restrict-qualified pointers may be passed to polymorphic functions.
2806\end{rationale}
2807
2808©lvalue© may be used to qualify the return type of a function type.
2809Let ©T© be an unqualified version of a type;
2810then the result of calling a function with return type ©lvalue T© is a \Index{modifiable lvalue} of type ©T©.
2811©const©\use{const} and ©volatile©\use{volatile} qualifiers may also be added to indicate that the function result is a constant or volatile lvalue.
2812\begin{rationale}
2813The ©const© and ©volatile© qualifiers can only be sensibly used to qualify the return type of a function if the ©lvalue© qualifier is also used.
2814\end{rationale}
2815
2816An {lvalue}-qualified type may be used in a \Index{cast expression} if the operand is an lvalue;
2817the result of the expression is an lvalue.
2818
2819\begin{rationale}
2820©lvalue© provides some of the functionality of \CC's ``©T&©'' ( reference to object of type ©T©) type.
2821Reference types have four uses in \CC.
2822\begin{itemize}
2823\item
2824They are necessary for user-defined operators that return lvalues, such as ``subscript'' and ``dereference''.
2825
2826\item
2827A 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 ©with© statement.
2828The following \CC code gives an example.
2829\begin{lstlisting}
2830{
2831        char &code = long_name.some_field[i].data->code;
2832        code = toupper( code );
2833}
2834\end{lstlisting}
2835This is not very useful.
2836
2837\item
2838A reference parameter can be used to allow a function to modify an argument without forcing the caller to pass the address of the argument.
2839This is most useful for user-defined assignment operators.
2840In \CC, plain assignment is done by a function called ``©operator=©'', and the two expressions
2841\begin{lstlisting}
2842a = b;
2843operator=( a, b );
2844\end{lstlisting} are equivalent.
2845If ©a© and ©b© are of type ©T©, then the first parameter of ©operator=© must have type ``©T&©''.
2846It cannot have type ©T©, because then assignment couldn't alter the variable, and it can't have type ``©T *©'', because the assignment would have to be written ``©&a = b;©''.
2847
2848In 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 ``©a = b;©'' is equivalent to ``©operator=(&( a), b )©''.
2849Reference 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 ``©&©''.
2850
2851\item
2852References to \Index{const-qualified} types can be used instead of value parameters.  Given the
2853\CC function call ``©fiddle( a_thing )©'', where the type of ©a_thing© is
2854©Thing©, the type of ©fiddle© could be either of
2855\begin{lstlisting}
2856void fiddle( Thing );
2857void fiddle( const Thing & );
2858\end{lstlisting}
2859If 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 ©fiddle© the parameter is subject to the usual problems caused by aliases.
2860The reference form might be chosen for efficiency's sake if ©Thing©s are too large or their constructors or destructors are too expensive.
2861An implementation may switch between them without causing trouble for well-behaved clients.
2862This leaves the implementor to define ``too large'' and ``too expensive''.
2863
2864I propose to push this job onto the compiler by allowing it to implement
2865\begin{lstlisting}
2866void fiddle( const volatile Thing );
2867\end{lstlisting} with call-by-reference.
2868Since it knows all about the size of ©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''.
2869\end{itemize}
2870
2871In summary, since references are only really necessary for returning lvalues, I'll only provide lvalue functions.
2872\end{rationale}
2873
2874
2875\setcounter{subsection}{8}
2876\subsection{Initialization}
2877
2878An expression that is used as an \nonterm{initializer} is treated as being cast to the type of the object being initialized.
2879An expression used in an \nonterm{initializer-list} is treated as being cast to the type of the aggregate member that it initializes.
2880In either case the cast must have a single unambiguous \Index{interpretation}.
2881
2882
2883\setcounter{subsection}{10}
2884\subsection{Specification definitions}
2885
2886\begin{syntax}
2887\lhs{spec-definition}
2888\rhs ©spec© \nonterm{identifier} 
2889        ©(© \nonterm{type-parameter-list} ©)©
2890        ©{© \nonterm{spec-declaration-list}\opt ©}©
2891\lhs{spec-declaration-list}
2892\rhs \nonterm{spec-declaration} ©;©
2893\rhs \nonterm{spec-declaration-list} \nonterm{spec-declaration} ©;©
2894\lhs{spec-declaration}
2895\rhs \nonterm{specifier-qualifier-list} \nonterm{declarator-list}
2896\lhs{declarator-list}
2897\rhs \nonterm{declarator}
2898\rhs \nonterm{declarator-list} ©,© \nonterm{declarator}
2899\end{syntax}
2900\begin{rationale}
2901The 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.
2902\end{rationale}
2903
2904\semantics
2905A \define{specification definition} defines a name for a \define{specification}: a parameterized collection of object and function declarations.
2906
2907The declarations in a specification consist of the declarations in the
2908\nonterm{spec-declaration-list} and declarations produced by any assertions in the
2909\nonterm{spec-parameter-list}.
2910If 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.
2911
2912
2913\subsubsection{Assertions}
2914
2915\begin{syntax}
2916\lhs{assertion-list}
2917\rhs \nonterm{assertion}
2918\rhs \nonterm{assertion-list} \nonterm{assertion}
2919\lhs{assertion}
2920\rhs ©|© \nonterm{identifier} ©(© \nonterm{type-name-list} ©)©
2921\rhs ©|© \nonterm{spec-declaration}
2922\lhs{type-name-list}
2923\rhs \nonterm{type-name}
2924\rhs \nonterm{type-name-list} ©,© \nonterm{type-name}
2925\end{syntax}
2926
2927\constraints
2928The \nonterm{identifier} in an assertion that is not a \nonterm{spec-declaration} shall be the name of a specification.
2929The \nonterm{type-name-list} shall contain one \nonterm{type-name} argument for each \nonterm{type-parameter} in that specification's \nonterm{spec-parameter-list}.
2930If the
2931\nonterm{type-parameter} uses type-class ©type©\use{type}, the argument shall be the type name of an \Index{object type};
2932if it uses ©dtype©, the argument shall be the type name of an object type or an \Index{incomplete type};
2933and if it uses ©ftype©, the argument shall be the type name of a \Index{function type}.
2934
2935\semantics
2936An \define{assertion} is a declaration of a collection of objects and functions, called \define{assertion parameters}.
2937
2938The 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.
2939
2940The collection of assertion parameters produced by the \nonterm{assertion-list} are found by combining the declarations produced by each assertion.
2941If 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.
2942
2943\examples
2944\begin{lstlisting}
2945forall( otype T | T ?*?( T, T ))§\use{?*?}§
2946T square( T val ) {§\impl{square}§
2947        return val + val;
2948}
2949trait summable( otype T ) {§\impl{summable}§
2950        T ?+=?( T *, T );§\use{?+=?}§
2951        const T 0;§\use{0}§
2952};
2953trait list_of( otype List, otype Element ) {§\impl{list_of}§
2954        Element car( List );
2955        List cdr( List );
2956        List cons( Element, List );
2957        List nil;
2958        int is_nil( List );
2959};
2960trait sum_list( otype List, otype Element | summable( Element ) | list_of( List, Element ) ) {};
2961\end{lstlisting}
2962©sum_list© contains seven declarations, which describe a list whose elements can be added up.
2963The assertion ``©|sum_list( i_list, int )©''\use{sum_list} produces the assertion parameters
2964\begin{lstlisting}
2965int ?+=?( int *, int );
2966const int 0;
2967int car( i_list );
2968i_list cdr( i_list );
2969i_list cons( int, i_list );
2970i_list nil;
2971int is_nil;
2972\end{lstlisting}
2973
2974
2975\subsection{Type declarations}
2976
2977\begin{syntax}
2978\lhs{type-parameter-list}
2979\rhs \nonterm{type-parameter}
2980\rhs \nonterm{type-parameter-list} ©,© \nonterm{type-parameter}
2981\lhs{type-parameter}
2982\rhs \nonterm{type-class} \nonterm{identifier} \nonterm{assertion-list}\opt
2983\lhs{type-class}
2984\rhs ©type©
2985\rhs ©dtype©
2986\rhs ©ftype©
2987\lhs{type-declaration}
2988\rhs \nonterm{storage-class-specifier}\opt ©type© \nonterm{type-declarator-list} \verb|;|
2989\lhs{type-declarator-list}
2990\rhs \nonterm{type-declarator}
2991\rhs \nonterm{type-declarator-list} ©,© \nonterm{type-declarator}
2992\lhs{type-declarator}
2993\rhs \nonterm{identifier} \nonterm{assertion-list}\opt ©=© \nonterm{type-name}
2994\rhs \nonterm{identifier} \nonterm{assertion-list}\opt
2995\end{syntax}
2996
2997\constraints
2998If a type declaration has block scope, and the declared identifier has external or internal linkage, the declaration shall have no initializer for the identifier.
2999
3000\semantics
3001A \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.
3002
3003An identifier declared by a \nonterm{type-parameter} has \Index{no linkage}.
3004Identifiers declared with type-class ©type©\use{type} are \Index{object type}s;
3005those declared with type-class ©dtype©\use{dtype} are \Index{incomplete type}s;
3006and those declared with type-class ©ftype©\use{ftype} are \Index{function type}s.
3007The 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}.
3008
3009A \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.
3010The type in the initializer is called the \define{implementation
3011  type}.
3012Within 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.
3013
3014A type declaration without an \Index{initializer} and without a \Index{storage-class specifier} or with storage-class specifier ©static©\use{static} defines an \Index{incomplete type}.
3015If a \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).
3016\begin{rationale}
3017Incomplete type declarations allow compact mutually-recursive types.
3018\begin{lstlisting}
3019otype t1; // incomplete type declaration
3020otype t2 = struct { t1 * p; ... };
3021otype t1 = struct { t2 * p; ... };
3022\end{lstlisting}
3023Without them, mutual recursion could be handled by declaring mutually recursive structures, then initializing the types to those structures.
3024\begin{lstlisting}
3025struct s1;
3026otype t2 = struct s2 { struct s1 * p; ... };
3027otype t1 = struct s1 { struct s2 * p; ... };
3028\end{lstlisting}
3029This introduces extra names, and may force the programmer to cast between the types and their implementations.
3030\end{rationale}
3031
3032A type declaration without an initializer and with \Index{storage-class specifier} ©extern©\use{extern} is an \define{opaque type declaration}.
3033Opaque types are \Index{object type}s.
3034An opaque type is not a \nonterm{constant-expression};
3035neither is a structure or union that has a member whose type is not a \nonterm{constant-expression}.
3036Every other \Index{object type} is a \nonterm{constant-expression}.
3037Objects with static storage duration shall be declared with a type that is a \nonterm{constant-expression}.
3038\begin{rationale}
3039Type declarations can declare identifiers with external linkage, whereas typedef declarations declare identifiers that only exist within a translation unit.
3040These opaque types can be used in declarations, but the implementation of the type is not visible.
3041
3042Static objects can not have opaque types because space for them would have to be allocated at program start-up.
3043This is a deficiency\index{deficiencies!static opaque objects}, but I don't want to deal with ``module initialization'' code just now.
3044\end{rationale}
3045
3046An \Index{incomplete type} which is not a qualified version\index{qualified type} of a type is a value of \Index{type-class} ©dtype©.
3047An object type\index{object types} which is not a qualified version of a type is a value of type-classes ©type© and ©dtype©.
3048A \Index{function type} is a value of type-class ©ftype©.
3049\begin{rationale}
3050Syntactically, a type value is a \nonterm{type-name}, which is a declaration for an object which omits the identifier being declared.
3051
3052Object types are precisely the types that can be instantiated.
3053Type 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.
3054For 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.
3055
3056Type qualifiers are a weak point of C's type system.
3057Consider the standard library function ©strchr()© which, given a string and a character, returns a pointer to the first occurrence of the character in the string.
3058\begin{lstlisting}
3059char *strchr( const char *s, int c ) {§\impl{strchr}§
3060        char real_c = c; // done because c was declared as int.
3061        for ( ; *s != real_c; s++ )
3062                if ( *s == '\0' ) return NULL;
3063        return ( char * )s;
3064}
3065\end{lstlisting}
3066The parameter ©s© must be ©const char *©, because ©strchr()© might be used to search a constant string, but the return type must be ©char *©, because the result might be used to modify a non-constant string.
3067Hence the body must perform a cast, and ( even worse) ©strchr()© provides a type-safe way to attempt to modify constant strings.
3068What is needed is some way to say that ©s©'s type might contain qualifiers, and the result type has exactly the same qualifiers.
3069Polymorphic functions do not provide a fix for this deficiency\index{deficiencies!pointers to qualified types}, because type qualifiers are not part of type values.
3070Instead, overloading can be used to define ©strchr()© for each combination of qualifiers.
3071\end{rationale}
3072
3073\begin{rationale}
3074Since \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.
3075This prevents the declaration of types that contain each other.
3076\begin{lstlisting}
3077otype t1;
3078otype t2 = t1; // illegal: incomplete type t1
3079otype t1 = t2;
3080\end{lstlisting}
3081
3082The initializer in a file-scope declaration must be a constant expression.
3083This means type declarations can not build on opaque types, which is a deficiency\index{deficiencies!nesting opaque
3084 types}.
3085\begin{lstlisting}
3086extern otype Huge; // extended-precision integer type
3087otype Rational = struct {
3088        Huge numerator, denominator;    // illegal
3089};
3090struct Pair {
3091        Huge first, second;                             // legal
3092};
3093\end{lstlisting}
3094Without this restriction, \CFA might require ``module initialization'' code ( since ©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 ©Huge© and the translation that declares ©Rational©.
3095
3096A 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.
3097\begin{lstlisting}
3098//  File a.c:
3099        extern type t1;
3100        type t2 = struct { t1 f1; ... } // illegal
3101//  File b.c:
3102        extern type t2;
3103        type t1 = struct { t2 f2; ... } // illegal
3104\end{lstlisting}
3105\end{rationale}
3106
3107\begin{rationale}
3108Since a \nonterm{type-declaration} is a \nonterm{declaration} and not a
3109\nonterm{struct-declaration}, type declarations can not be structure members.
3110The form of
3111\nonterm{type-declaration} forbids arrays of, pointers to, and functions returning ©type©.
3112Hence the syntax of \nonterm{type-specifier} does not have to be extended to allow type-valued expressions.
3113It also side-steps the problem of type-valued expressions producing different values in different declarations.
3114
3115Since a type declaration is not a \nonterm{parameter-declaration}, functions can not have explicit type parameters.
3116This may be too restrictive, but it attempts to make compilation simpler.
3117Recall 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.
3118A type parameter would add a type name to the current scope.
3119The 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.
3120
3121Explicit type parameters don't seem to be very useful, anyway, because their scope would not include the return type of the function.
3122Consider the following attempt to define a type-safe memory allocation function.
3123\begin{lstlisting}
3124#include <stdlib.h>
3125T * new( otype T ) { return ( T * )malloc( sizeof( T) ); };
3126... int * ip = new( int );
3127\end{lstlisting}
3128This looks sensible, but \CFA's declaration-before-use rules mean that ``©T©'' in the function body refers to the parameter, but the ``©T©'' in the return type refers to the meaning of ©T© in the scope that contains ©new©;
3129it could be undefined, or a type name, or a function or variable name.
3130Nothing good can result from such a situation.
3131\end{rationale}
3132
3133\examples
3134Since type declarations create new types, instances of types are always passed by value.
3135\begin{lstlisting}
3136otype A1 = int[2];
3137void f1( A1 a ) { a[0] = 0; };
3138otypedef int A2[2];
3139void f2( A2 a ) { a[0] = 0; };
3140A1 v1;
3141A2 v2;
3142f1( v1 );
3143f2( v2 );
3144\end{lstlisting}
3145©V1© is passed by value, so ©f1()©'s assignment to ©a[0]© does not modify v1.  ©V2© is converted to a pointer, so ©f2()© modifies ©v2[0]©.
3146
3147A translation unit containing the declarations
3148\begin{lstlisting}
3149extern type Complex;§\use{Complex}§ // opaque type declaration
3150extern float abs( Complex );§\use{abs}§
3151\end{lstlisting} can contain declarations of complex numbers, which can be passed to ©abs©.
3152Some other translation unit must implement ©Complex© and ©abs©.
3153That unit might contain the declarations
3154\begin{lstlisting}
3155otype Complex = struct { float re, im; }\impl{Complex}§
3156Complex cplx_i = { 0.0, 1.0 }\impl{cplx_i}§
3157float abs( Complex c ) {§\impl{abs( Complex )}§
3158        return sqrt( c.re * c.re + c.im * c.im );
3159}
3160\end{lstlisting}
3161Note that ©c© is implicitly converted to a ©struct© so that its components can be retrieved.
3162
3163\begin{lstlisting}
3164otype Time_of_day = int;§\impl{Time_of_day}§ // seconds since midnight.
3165Time_of_day ?+?( Time_of_day t1, int seconds ) {§\impl{?+?}§
3166        return (( int)t1 + seconds ) % 86400;
3167}
3168\end{lstlisting}
3169©t1© must be cast to its implementation type to prevent infinite recursion.
3170
3171\begin{rationale}
3172Within the scope of a type definition, an instance of the type can be viewed as having that type or as having the implementation type.
3173In the ©Time_of_day© example, the difference is important.
3174Different languages have treated the distinction between the abstraction and the implementation in different ways.
3175\begin{itemize}
3176\item
3177Inside a Clu cluster \cite{CLU}, the declaration of an instance states which view applies.
3178Two primitives called ©up© and ©down© can be used to convert between the views.
3179\item
3180The Simula class \cite{SIMULA87} is essentially a record type.
3181Since 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.
3182In \CC
3183\cite{C++}, operations on class instances include assignment and ``©&©'', which can be overloaded.
3184A ``scope resolution'' operator can be used inside the class to specify whether the abstract or implementation version of the operation should be used.
3185\item
3186An 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.
3187The derived subprograms are clones of the existing subprograms with the old type replaced by the derived type.
3188Literals and aggregates of the old type are also cloned.
3189In other words, the abstract view provides exactly the same operations as the implementation view.
3190This allows the abstract view to be used in all cases.
3191
3192The derived subprograms can be replaced by programmer-specified subprograms.
3193This is an exception to the normal scope rules, which forbid duplicate definitions of a subprogram in a scope.
3194In this case, explicit conversions between the derived type and the old type can be used.
3195\end{itemize}
3196\CFA's rules are like Clu's, except that implicit conversions and conversion costs allow it to do away with most uses of ©up© and ©down©.
3197\end{rationale}
3198
3199
3200\subsubsection{Default functions and objects}
3201
3202A declaration\index{type declaration} of a type identifier ©T© with type-class ©type© implicitly declares a \define{default assignment} function ©T ?=?( T *, T )©\use{?=?}, with the same \Index{scope} and \Index{linkage} as the identifier ©T©.
3203\begin{rationale}
3204Assignment 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).
3205Without this rule, nearly every inferred type parameter would need an accompanying assignment assertion parameter.
3206If a type parameter should not have an assignment operation, ©dtype© should be used.
3207If 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.
3208\end{rationale}
3209
3210A definition\index{type definition} of a type identifier ©T© with \Index{implementation type} ©I© and type-class ©type© implicitly defines a default assignment function.
3211A definition\index{type definition} of a type identifier ©T© with implementation type ©I© and an assertion list implicitly defines \define{default function}s and \define{default object}s as declared by the assertion declarations.
3212The default objects and functions have the same \Index{scope} and \Index{linkage} as the identifier ©T©.
3213Their values are determined as follows:
3214\begin{itemize}
3215\item
3216If at the definition of ©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 ©I© replaced by ©T© is compatible with the type of the default object, then the default object is initialized with that object.
3217Otherwise the scope of the declaration of ©T© must contain a definition of the default object.
3218
3219\item 
3220If at the definition of ©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 ©I© replaced by ©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.
3221
3222Otherwise, if ©I© contains exactly one anonymous member\index{anonymous member} such that at the definition of ©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 ©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.
3223
3224Otherwise the scope of the declaration of ©T© must contain a definition of the default function.
3225\end{itemize}
3226\begin{rationale}
3227Note that a pointer to a default function will not compare as equal to a pointer to the inherited function.
3228\end{rationale}
3229
3230A 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 ©T© replaces the default function or object.
3231
3232\examples
3233\begin{lstlisting}
3234trait s( otype T ) {
3235        T a, b;
3236} struct impl { int left, right; } a = { 0, 0 };
3237otype Pair | s( Pair ) = struct impl;
3238Pair b = { 1, 1 };
3239\end{lstlisting}
3240The definition of ©Pair© implicitly defines two objects ©a© and ©b©.
3241©Pair a© inherits its value from the ©struct impl a©.
3242The definition of ©Pair b© is compulsory because there is no ©struct impl b© to construct a value from.
3243\begin{lstlisting}
3244trait ss( otype T ) {
3245        T clone( T );
3246        void munge( T * );
3247}
3248otype Whatsit | ss( Whatsit );§\use{Whatsit}§
3249otype Doodad | ss( Doodad ) = struct doodad {§\use{Doodad}§
3250        Whatsit; // anonymous member
3251        int extra;
3252};
3253Doodad clone( Doodad ) { ... }
3254\end{lstlisting}
3255The definition of ©Doodad© implicitly defines three functions:
3256\begin{lstlisting}
3257Doodad ?=?( Doodad *, Doodad );
3258Doodad clone( Doodad );
3259void munge( Doodad * );
3260\end{lstlisting}
3261The assignment function inherits ©struct doodad©'s assignment function because the types match when ©struct doodad©  is replaced by ©Doodad© throughout.
3262©munge()© inherits ©Whatsit©'s ©munge()© because the types match when ©Whatsit© is replaced by ©Doodad© in the parameter list. ©clone()© does \emph{not} inherit ©Whatsit©'s ©clone()©: replacement in the parameter list yields ``©Whatsit clone( Doodad )©'', which is not compatible with ©Doodad©'s ©clone()©'s type.
3263Hence the definition of ``©Doodad clone( Doodad )©'' is necessary.
3264
3265Default functions and objects are subject to the normal scope rules.
3266\begin{lstlisting}
3267otype T = ...;
3268T a_T = ...;            // Default assignment used.
3269T ?=?( T *, T );
3270T a_T = ...;            // Programmer-defined assignment called.
3271\end{lstlisting}
3272\begin{rationale}
3273A compiler warning would be helpful in this situation.
3274\end{rationale}
3275
3276\begin{rationale}
3277The \emph{class} construct of object-oriented programming languages performs three independent functions.
3278It \emph{encapsulates} a data structure;
3279it defines a \emph{subtype} relationship, whereby instances of one class may be used in contexts that require instances of another;
3280and it allows one class to \emph{inherit} the implementation of another.
3281
3282In \CFA, encapsulation is provided by opaque types and the scope rules, and subtyping is provided by specifications and assertions.
3283Inheritance is provided by default functions and objects.
3284\end{rationale}
3285
3286
3287\section{Statements and blocks}
3288
3289\begin{syntax}
3290\oldlhs{statement}
3291\rhs \nonterm{exception-statement}
3292\end{syntax}
3293
3294Many statements contain expressions, which may have more than one interpretation.
3295The following sections describe how the \CFA translator selects an interpretation.
3296In all cases the result of the selection shall be a single unambiguous \Index{interpretation}.
3297
3298
3299\subsection{Labeled statements}
3300
3301\begin{syntax}
3302\oldlhs{labeled-statement}
3303\rhs ©case© \nonterm{case-value-list} : \nonterm{statement}
3304\lhs{case-value-list}
3305\rhs \nonterm{case-value}
3306\rhs \nonterm{case-value-list} ©,© \nonterm{case-value}
3307\lhs{case-value}
3308\rhs \nonterm{constant-expression}
3309\rhs \nonterm{subrange}
3310\lhs{subrange}
3311\rhs \nonterm{constant-expression} ©~© \nonterm{constant-expression}
3312\end{syntax}
3313
3314The following have identical meaning:
3315\begin{lstlisting}
3316case 1:  case 2:  case 3:  case 4:  case 5:
3317case 1, 2, 3, 4, 5:
3318case 1~5:
3319\end{lstlisting}
3320Multiple subranges are allowed:
3321\begin{lstlisting}
3322case 1~4, 9~14, 27~32:
3323\end{lstlisting}
3324The ©case© and ©default© clauses are restricted within the ©switch© and ©choose© statements, precluding Duff's device.
3325
3326
3327\subsection{Expression and null statements}
3328
3329The expression in an expression statement is treated as being cast to ©void©.
3330
3331
3332\subsection{Selection statements}
3333
3334\begin{syntax}
3335\oldlhs{selection-statement}
3336\rhs ©choose© ©(© \nonterm{expression} ©)© \nonterm{statement}
3337\end{syntax}
3338
3339The controlling expression ©E© in the ©switch© and ©choose© statement:
3340\begin{lstlisting}
3341switch ( E ) ...
3342choose ( E ) ...
3343\end{lstlisting} may have more than one interpretation, but it shall have only one interpretation with an integral type.
3344An \Index{integer promotion} is performed on the expression if necessary.
3345The constant expressions in ©case© statements with the switch are converted to the promoted type.
3346
3347
3348\setcounter{subsubsection}{3}
3349\subsubsection[The choose statement]{The \lstinline@choose@ statement}
3350
3351The ©choose© statement is the same as the ©switch© statement except control transfers to the end of the ©choose© statement at a ©case© or ©default© labeled statement.
3352The ©fallthru© statement is used to fall through to the next ©case© or ©default© labeled statement.
3353The following have identical meaning:
3354\begin{flushleft}
3355\begin{tabular}{@{\hspace{2em}}l@{\hspace{2em}}l@{}}
3356\begin{lstlisting}
3357switch (...) {
3358  case 1: ... ; break;
3359  case 2: ... ; break;
3360  case 3: ... ; // fall through
3361  case 4: ... ; // fall through
3362  default: ... break;
3363}
3364\end{lstlisting}
3365&
3366\begin{lstlisting}
3367choose (...) {
3368  case 1: ... ; // exit
3369  case 2: ... ; // exit
3370  case 3: ... ; fallthru;
3371  case 4: ... ; fallthru;
3372  default: ... ; // exit
3373}
3374\end{lstlisting}
3375\end{tabular}
3376\end{flushleft}
3377The ©choose© statement addresses the problem of accidental fall-through associated with the ©switch© statement.
3378
3379
3380\subsection{Iteration statements}
3381
3382The controlling expression ©E© in the loops
3383\begin{lstlisting}
3384if ( E ) ...
3385while ( E ) ...
3386do ... while ( E );
3387\end{lstlisting}
3388is treated as ``©( int )((E)!=0)©''.
3389
3390The statement
3391\begin{lstlisting}
3392for ( a; b; c ) ...
3393\end{lstlisting} is treated as
3394\begin{lstlisting}
3395for ( ( void )( a ); ( int )(( b )!=0); ( void )( c ) ) ...
3396\end{lstlisting}
3397
3398
3399\subsection{Jump statements}
3400
3401\begin{syntax}
3402\oldlhs{jump-statement}
3403\rhs ©continue© \nonterm{identifier}\opt
3404\rhs ©break© \nonterm{identifier}\opt
3405\rhs \ldots
3406\rhs ©throw© \nonterm{assignment-expression}\opt
3407\rhs ©throwResume© \nonterm{assignment-expression}\opt \nonterm{at-expression}\opt
3408\lhs{at-expression} ©_At© \nonterm{assignment-expression}
3409\end{syntax}
3410
3411Labeled ©continue© and ©break© allow useful but restricted control-flow that reduces the need for the ©goto© statement for exiting multiple nested control-structures.
3412\begin{lstlisting}
3413L1: {                                                   // compound
3414  L2: switch ( ... ) {                  // switch
3415          case ...:
3416          L3: for ( ;; ) {                      // outer for
3417                L4: for ( ;; ) {                // inner for
3418                                continue L1;    // error: not enclosing iteration
3419                                continue L2;    // error: not enclosing iteration
3420                                continue L3;    // next iteration of outer for
3421                                continue L4;    // next iteration of inner for
3422                                break L1;               // exit compound
3423                                break L2;               // exit switch
3424                                break L3;               // exit outer for
3425                                break L4;               // exit inner for
3426                        } // for
3427                } // for
3428                break;                                  // exit switch
3429          default:
3430                break L1;                               // exit compound
3431        } // switch
3432        ...
3433} // compound
3434\end{lstlisting}
3435
3436
3437\setcounter{subsubsection}{1}
3438\subsubsection[The continue statement]{The \lstinline@continue@ statement}
3439
3440The identifier in a ©continue© statement shall name a label located on an enclosing iteration statement.
3441
3442
3443\subsubsection[The break statement]{The \lstinline@break@ statement}
3444
3445The identifier in a ©break© statement shall name a label located on an enclosing compound, selection or iteration statement.
3446
3447
3448\subsubsection[The return statement]{The \lstinline@return@ statement}
3449
3450An expression in a ©return© statement is treated as being cast to the result type of the function.
3451
3452
3453\subsubsection[The throw statement]{The \lstinline@throw@ statement}
3454
3455When an exception is raised, \Index{propagation} directs control from a raise in the source execution to a handler in the faulting execution.
3456
3457
3458\subsubsection[The throwResume statement]{The \lstinline@throwResume@ statement}
3459
3460
3461\subsection{Exception statements}
3462
3463\begin{syntax}
3464\lhs{exception-statement}
3465\rhs ©try© \nonterm{compound-statement} \nonterm{handler-list}
3466\rhs ©try© \nonterm{compound-statement} \nonterm{finally-clause}
3467\rhs ©try© \nonterm{compound-statement} \nonterm{handler-list} \nonterm{finally-clause}
3468\lhs{handler-list}
3469\rhs \nonterm{handler-clause}
3470\rhs ©catch© ©(© \ldots ©)© \nonterm{compound-statement}
3471\rhs \nonterm{handler-clause} ©catch© ©(© \ldots ©)© \nonterm{compound-statement}
3472\rhs ©catchResume© ©(© \ldots ©)© \nonterm{compound-statement}
3473\rhs \nonterm{handler-clause} ©catchResume© ©(© \ldots ©)© \nonterm{compound-statement}
3474\lhs{handler-clause}
3475\rhs ©catch© ©(© \nonterm{exception-declaration} ©)© \nonterm{compound-statement}
3476\rhs \nonterm{handler-clause} ©catch© ©(© \nonterm{exception-declaration} ©)© \nonterm{compound-statement}
3477\rhs ©catchResume© ©(© \nonterm{exception-declaration} ©)© \nonterm{compound-statement}
3478\rhs \nonterm{handler-clause} ©catchResume© ©(© \nonterm{exception-declaration} ©)© \nonterm{compound-statement}
3479\lhs{finally-clause}
3480\rhs ©finally© \nonterm{compound-statement}
3481\lhs{exception-declaration}
3482\rhs \nonterm{type-specifier}
3483\rhs \nonterm{type-specifier} \nonterm{declarator}
3484\rhs \nonterm{type-specifier} \nonterm{abstract-declarator}
3485\rhs \nonterm{new-abstract-declarator-tuple} \nonterm{identifier}
3486\rhs \nonterm{new-abstract-declarator-tuple}
3487\lhs{asynchronous-statement}
3488\rhs ©enable© \nonterm{identifier-list} \nonterm{compound-statement}
3489\rhs ©disable© \nonterm{identifier-list} \nonterm{compound-statement}
3490\end{syntax}
3491
3492\Index{Exception statement}s allow a dynamic call to a handler for \Index{recovery} (\Index{termination}) or \Index{correction} (\Index{resumption}) of an \Index{abnormal event}.
3493
3494
3495\subsubsection[The try statement]{The \lstinline@try@ statement}
3496
3497The ©try© statement is a block with associated handlers, called a \Index{guarded block};
3498all other blocks are \Index{unguarded block}s.
3499A ©goto©, ©break©, ©return©, or ©continue© statement can be used to transfer control out of a try block or handler, but not into one.
3500
3501
3502\subsubsection[The enable/disable statements]{The \lstinline@enable@/\lstinline@disable@ statements}
3503
3504The ©enable©/©disable© statements toggle delivery of \Index{asynchronous exception}s.
3505
3506
3507\setcounter{section}{9}
3508\section{Preprocessing directives}
3509
3510
3511\setcounter{subsection}{7}
3512\subsection{Predefined macro names}
3513
3514The implementation shall define the macro names ©__LINE__©, ©__FILE__©, ©__DATE__©, and ©__TIME__©, as in the \Celeven standard.
3515It shall not define the macro name ©__STDC__©.
3516
3517In addition, the implementation shall define the macro name ©__CFORALL__© to be the decimal constant 1.
3518
3519
3520\appendix
3521
3522
3523\chapter{Examples}
3524
3525
3526\section{C types}
3527This 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.
3528
3529
3530\subsection{Scalar, arithmetic, and integral types}
3531
3532The pointer, integral, and floating-point types are all \define{scalar types}.
3533All of these types can be logically negated and compared.
3534The assertion ``©scalar( Complex )©'' should be read as ``type ©Complex© is scalar''.
3535\begin{lstlisting}
3536trait scalar( otype T ) {§\impl{scalar}§
3537        int !?( T );
3538        int ?<?( T, T ), ?<=?( T, T ), ?==?( T, T ), ?>=?( T, T ), ?>?( T, T ), ?!=?( T, T );
3539};
3540\end{lstlisting}
3541
3542The integral and floating-point types are \define{arithmetic types}, which support the basic arithmetic operators.
3543The 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 ).
3544This is equivalent to inheritance of specifications.
3545\begin{lstlisting}
3546trait arithmetic( otype T | scalar( T ) ) {§\impl{arithmetic}§§\use{scalar}§
3547        T +?( T ), -?( T );
3548        T ?*?( T, T ), ?/?( T, T ), ?+?( T, T ), ?-?( T, T );
3549};
3550\end{lstlisting}
3551
3552The various flavors of ©char© and ©int© and the enumerated types make up the \define{integral types}.
3553\begin{lstlisting}
3554trait integral( otype T | arithmetic( T ) ) {§\impl{integral}§§\use{arithmetic}§
3555        T ~?( T );
3556        T ?&?( T, T ), ?|?( T, T ), ?^?( T, T );
3557        T ?%?( T, T );
3558        T ?<<?( T, T ), ?>>?( T, T );
3559};
3560\end{lstlisting}
3561
3562
3563\subsection{Modifiable types}
3564\index{modifiable lvalue}
3565
3566The only operation that can be applied to all modifiable lvalues is simple assignment.
3567\begin{lstlisting}
3568trait m_lvalue( otype T ) {§\impl{m_lvalue}§
3569        T ?=?( T *, T );
3570};
3571\end{lstlisting}
3572
3573Modifiable scalar lvalues are scalars and are modifiable lvalues, and assertions in the
3574\nonterm{spec-parameter-list} reflect those relationships.
3575This is equivalent to multiple inheritance of specifications.
3576Scalars can also be incremented and decremented.
3577\begin{lstlisting}
3578trait m_l_scalar( otype T | scalar( T ) | m_lvalue( T ) ) {§\impl{m_l_scalar}§
3579        T ?++( T * ), ?--( T * );§\use{scalar}§§\use{m_lvalue}§
3580        T ++?( T * ), --?( T * );
3581};
3582\end{lstlisting}
3583
3584Modifiable arithmetic lvalues are both modifiable scalar lvalues and arithmetic.
3585Note that this results in the ``inheritance'' of ©scalar© along both paths.
3586\begin{lstlisting}
3587trait m_l_arithmetic( otype T | m_l_scalar( T ) | arithmetic( T ) ) {§\impl{m_l_arithmetic}§
3588        T ?/=?( T *, T ), ?*=?( T *, T );§\use{m_l_scalar}§§\use{arithmetic}§
3589        T ?+=?( T *, T ), ?-=?( T *, T );
3590};
3591trait m_l_integral( otype T | m_l_arithmetic( T ) | integral( T ) ) {§\impl{m_l_integral}§
3592        T ?&=?( T *, T ), ?|=?( T *, T ), ?^=?( T *, T );§\use{m_l_arithmetic}§
3593        T ?%=?( T *, T ), ?<<=?( T *, T ), ?>>=?( T *, T );§\use{integral}§
3594};
3595\end{lstlisting}
3596
3597
3598\subsection{Pointer and array types}
3599
3600Array types can barely be said to exist in \Celeven, since in most cases an array name is treated as a constant pointer to the first element of the array, and the subscript expression ``©a[i]©'' is equivalent to the dereferencing expression ``©(*( a+( i )))©''.
3601Technically, pointer arithmetic and pointer comparisons other than ``©==©'' and ``©!=©'' are only defined for pointers to array elements, but the type system does not enforce those restrictions.
3602Consequently, there is no need for a separate ``array type'' specification.
3603
3604Pointer types are scalar types.
3605Like other scalar types, they have ``©+©'' and ``©-©'' operators, but the types do not match the types of the operations in ©arithmetic©, so these operators cannot be consolidated in ©scalar©.
3606\begin{lstlisting}
3607trait pointer( type P | scalar( P ) ) {§\impl{pointer}§§\use{scalar}§
3608        P ?+?( P, long int ), ?+?( long int, P ), ?-?( P, long int );
3609        ptrdiff_t ?-?( P, P );
3610};
3611trait m_l_pointer( type P | pointer( P ) | m_l_scalar( P ) ) {§\impl{m_l_pointer}§
3612        P ?+=?( P *, long int ), ?-=?( P *, long int );
3613        P ?=?( P *, void * );
3614        void * ?=?( void **, P );
3615};
3616\end{lstlisting}
3617
3618Specifications 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.
3619Different specifications are needed for each set of \Index{type qualifier}s, because qualifiers are not included in types.
3620The assertion ``©|ptr_to( Safe_pointer, int )©'' should be read as ``©Safe_pointer© acts like a pointer to ©int©''.
3621\begin{lstlisting}
3622trait ptr_to( otype P | pointer( P ), otype T ) {§\impl{ptr_to}§§\use{pointer}§
3623        lvalue T *?( P );
3624        lvalue T ?[?]( P, long int );
3625};
3626trait ptr_to_const( otype P | pointer( P ), otype T ) {§\impl{ptr_to_const}§
3627        const lvalue T *?( P );
3628        const lvalue T ?[?]( P, long int );§\use{pointer}§
3629};
3630trait ptr_to_volatile( otype P | pointer( P ), otype T ) }§\impl{ptr_to_volatile}§
3631        volatile lvalue T *?( P );
3632        volatile lvalue T ?[?]( P, long int );§\use{pointer}§
3633};
3634trait ptr_to_const_volatile( otype P | pointer( P ), otype T ) }§\impl{ptr_to_const_volatile}§
3635        const volatile lvalue T *?( P );§\use{pointer}§
3636        const volatile lvalue T ?[?]( P, long int );
3637};
3638\end{lstlisting}
3639
3640Assignment 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 ``©T *©'' can be assigned to a ``©const T *©'', a ``©volatile T *©'', and a ``©const volatile T *©''.
3641Again, the pointed-at type is passed in, so that assertions can connect these specifications to the ``©ptr_to©'' specifications.
3642\begin{lstlisting}
3643trait m_l_ptr_to( otype P | m_l_pointer( P ),§\use{m_l_pointer}§§\impl{m_l_ptr_to}§ otype T | ptr_to( P, T )§\use{ptr_to}§ {
3644        P ?=?( P *, T * );
3645        T * ?=?( T **, P );
3646};
3647trait m_l_ptr_to_const( otype P | m_l_pointer( P ),§\use{m_l_pointer}§§\impl{m_l_ptr_to_const}§ otype T | ptr_to_const( P, T )§\use{ptr_to_const}§) {
3648        P ?=?( P *, const T * );
3649        const T * ?=?( const T **, P );
3650};
3651trait m_l_ptr_to_volatile( otype P | m_l_pointer( P ),§\use{m_l_pointer}§§\impl{m_l_ptr_to_volatile}§ otype T | ptr_to_volatile( P, T )) {§\use{ptr_to_volatile}§
3652        P ?=?( P *, volatile T * );
3653        volatile T * ?=?( volatile T **, P );
3654};
3655trait m_l_ptr_to_const_volatile( otype P | ptr_to_const_volatile( P ),§\use{ptr_to_const_volatile}§§\impl{m_l_ptr_to_const_volatile}§
3656                otype 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}§
3657        P ?=?( P *, const volatile T * );
3658        const volatile T * ?=?( const volatile T **, P );
3659};
3660\end{lstlisting}
3661
3662Note the regular manner in which type qualifiers appear in those specifications.
3663An 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.
3664\begin{lstlisting}
3665trait 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 ) ) {
3666        MyP ?=?( MyP *, CP );
3667        CP ?=?( CP *, MyP );
3668};
3669\end{lstlisting}
3670The assertion ``©| m_l_ptr_like( Safe_ptr, const int * )©'' should be read as ``©Safe_ptr© is a pointer type like ©const int *©''.
3671This specification has two defects, compared to the original four: there is no automatic assertion that dereferencing a ©MyP© produces an lvalue of the type that ©CP© points at, and the ``©|m_l_pointer( CP )©'' assertion provides only a weak assurance that the argument passed to ©CP© really is a pointer type.
3672
3673
3674\section{Relationships between operations}
3675
3676Different operators often have related meanings;
3677for instance, in C, ``©+©'', ``©+=©'', and the two versions of ``©++©'' perform variations of addition.
3678Languages 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.
3679Completeness and consistency is left to the good taste and discretion of the programmer.
3680It 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.
3681
3682In \CFA, polymorphic functions provide the equivalent of these generic operators, and specifications explicitly define the minimal implementation that a programmer should provide.
3683This section shows a few examples.
3684
3685
3686\subsection{Relational and equality operators}
3687
3688The different comparison operators have obvious relationships, but there is no obvious subset of the operations to use in the implementation of the others.
3689However, 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;
3690the library function ©strcmp© is an example.
3691
3692C and \CFA have an extra, non-obvious comparison operator: ``©!©'', logical negation, returns 1 if its operand compares equal to 0, and 0 otherwise.
3693\begin{lstlisting}
3694trait comparable( otype T ) {
3695        const T 0;
3696        int compare( T, T );
3697}
3698forall( otype T | comparable( T ) ) int ?<?( T l, T r ) {
3699        return compare( l, r ) < 0;
3700}
3701// ... similarly for <=, ==, >=, >, and !=.
3702forall( otype T | comparable( T ) ) int !?( T operand ) {
3703        return !compare( operand, 0 );
3704}
3705\end{lstlisting}
3706
3707
3708\subsection{Arithmetic and integer operations}
3709
3710A complete arithmetic type would provide the arithmetic operators and the corresponding assignment operators.
3711Of 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.
3712Similarly, a complete integral type would provide integral operations based on integral assignment operations.
3713\begin{lstlisting}
3714trait arith_base( otype T ) {
3715        const T 1;
3716        T ?+=?( T *, T ), ?-=?( T *, T ), ?*=?( T *, T ), ?/=?( T *, T );
3717}
3718forall( otype T | arith_base( T ) ) T ?+?( T l, T r ) {
3719        return l += r;
3720}
3721forall( otype T | arith_base( T ) ) T ?++( T * operand ) {
3722        T temporary = *operand;
3723        *operand += 1;
3724        return temporary;
3725}
3726forall( otype T | arith_base( T ) ) T ++?( T * operand ) {
3727        return *operand += 1;
3728}
3729// ... similarly for -, --, *, and /.
3730trait int_base( otype T ) {
3731        T ?&=?( T *, T ), ?|=?( T *, T ), ?^=?( T *, T );
3732        T ?%=?( T *, T ), ?<<=?( T *, T ), ?>>=?( T *, T );
3733}
3734forall( otype T | int_base( T ) ) T ?&?( T l, T r ) {
3735        return l &= r;
3736}
3737// ... similarly for |, ^, %, <<, and >>.
3738\end{lstlisting}
3739
3740Note 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 ©int_base©, ©arith_base© and ©comparable©.
3741Note also that these declarations provide guidance and assistance, but they do not define an absolutely minimal set of requirements.
3742A truly minimal implementation of an arithmetic type might only provide ©0©, ©1©, and ©?-=?©, which would be used by polymorphic ©?+=?©, ©?*=?©, and ©?/=?© functions.
3743
3744Note also that ©short© is an integer type in C11 terms, but has no operations!
3745
3746
3747\chapter{TODO}
3748Review index entries.
3749
3750Restrict allowed to qualify anything, or type/dtype parameters, but only affects pointers.
3751This gets into ©noalias© territory.
3752Qualifying anything (``©short restrict rs©'') means pointer parameters of ©?++©, etc, would need restrict qualifiers.
3753
3754Enumerated types.
3755Constants are not ints.
3756Overloading.
3757Definition should be ``representable as an integer type'', not ``as an int''.
3758C11 usual conversions freely convert to and from ordinary integer types via assignment, which works between any integer types.
3759Does enum Color ?*?( enum
3760Color, enum Color ) really make sense? ?++ does, but it adds (int)1.
3761
3762Operators on {,signed,unsigned} char and other small types. ©?<?© harmless;
3763?*? questionable for chars.
3764Generic selections make these choices visible.
3765Safe conversion operators? Predefined ``promotion'' function?
3766
3767©register© assignment might be handled as assignment to a temporary with copying back and forth, but copying must not be done by assignment.
3768
3769Don't use ©ptrdiff_t© by name in the predefineds.
3770
3771Polymorphic objects.
3772Polymorphic typedefs and type declarations.
3773
3774
3775\bibliographystyle{plain}
3776\bibliography{pl}
3777
3778
3779\addcontentsline{toc}{chapter}{\indexname} % add index name to table of contents
3780\begin{theindex}
3781Italic page numbers give the location of the main entry for the referenced term.
3782Plain page numbers denote uses of the indexed term.
3783Entries for grammar non-terminals are italicized.
3784A typewriter font is used for grammar terminals and program identifiers.
3785\indexspace
3786\input{refrat.ind}
3787\end{theindex}
3788
3789
3790\end{document}
3791
3792% Local Variables: %
3793% tab-width: 4 %
3794% fill-column: 100 %
3795% compile-command: "make" %
3796% End: %
Note: See TracBrowser for help on using the repository browser.