source: doc/papers/general/Paper.tex @ 6171841

aaron-thesisarm-ehcleanup-dtorsdeferred_resndemanglerenumforall-pointer-decayjacob/cs343-translationjenkins-sandboxnew-astnew-ast-unique-exprnew-envno_listpersistent-indexerresolv-newwith_gc
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1\documentclass[AMA,STIX1COL]{WileyNJD-v2}
2
3\articletype{RESEARCH ARTICLE}%
4
5\received{26 April 2016}
6\revised{6 June 2016}
7\accepted{6 June 2016}
8
9\raggedbottom
10
11\usepackage{epic,eepic}
12\usepackage{xspace}
13\usepackage{comment}
14\usepackage{upquote}                                            % switch curled `'" to straight
15\usepackage{listings}                                           % format program code
16%\usepackage{enumitem}
17%\setlist[itemize]{topsep=3pt,itemsep=2pt,parsep=0pt}% global
18%\usepackage{rotating}
19\definecolor{ForestGreen}{cmyk}{1, 0, 0.99995, 0}
20\hypersetup{breaklinks=true}
21
22\usepackage[pagewise]{lineno}
23\renewcommand{\linenumberfont}{\scriptsize\sffamily}
24
25\lefthyphenmin=4                                                        % hyphen only after 4 characters
26\righthyphenmin=4
27
28% Names used in the document.
29
30\newcommand{\CFAIcon}{\textsf{C}\raisebox{\depth}{\rotatebox{180}{\textsf{A}}}\xspace} % Cforall symbolic name
31\newcommand{\CFA}{\protect\CFAIcon}             % safe for section/caption
32\newcommand{\CFL}{\textrm{Cforall}\xspace}      % Cforall symbolic name
33\newcommand{\Celeven}{\textrm{C11}\xspace}      % C11 symbolic name
34\newcommand{\CC}{\textrm{C}\kern-.1em\hbox{+\kern-.25em+}\xspace} % C++ symbolic name
35\newcommand{\CCeleven}{\textrm{C}\kern-.1em\hbox{+\kern-.25em+}11\xspace} % C++11 symbolic name
36\newcommand{\CCfourteen}{\textrm{C}\kern-.1em\hbox{+\kern-.25em+}14\xspace} % C++14 symbolic name
37\newcommand{\CCseventeen}{\textrm{C}\kern-.1em\hbox{+\kern-.25em+}17\xspace} % C++17 symbolic name
38\newcommand{\CCtwenty}{\textrm{C}\kern-.1em\hbox{+\kern-.25em+}20\xspace} % C++20 symbolic name
39\newcommand{\CCV}{\rm C\kern-.1em\hbox{+\kern-.25em+}obj\xspace} % C++ virtual symbolic name
40\newcommand{\Csharp}{C\raisebox{-0.7ex}{\Large$^\sharp$}\xspace} % C# symbolic name
41
42%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
43
44\newcommand{\Textbf}[2][red]{{\color{#1}{\textbf{#2}}}}
45%\newcommand{\TODO}[1]{\textbf{TODO}: {\itshape #1}} % TODO included
46\newcommand{\TODO}[1]{} % TODO elided
47
48% Default underscore is too low and wide. Cannot use lstlisting "literate" as replacing underscore
49% removes it as a variable-name character so keywords in variables are highlighted. MUST APPEAR
50% AFTER HYPERREF.
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53
54\makeatletter
55% parindent is relative, i.e., toggled on/off in environments like itemize, so store the value for
56% use rather than use \parident directly.
57\newlength{\parindentlnth}
58\setlength{\parindentlnth}{\parindent}
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60\newcommand{\LstBasicStyle}[1]{{\lst@basicstyle{\lst@basicstyle{#1}}}}
61\newcommand{\LstKeywordStyle}[1]{{\lst@basicstyle{\lst@keywordstyle{#1}}}}
62\newcommand{\LstCommentStyle}[1]{{\lst@basicstyle{\lst@commentstyle{#1}}}}
63
64\newlength{\gcolumnposn}                                        % temporary hack because lstlisting does not handle tabs correctly
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69\newcommand{\CRT}{\global\columnposn=\gcolumnposn}
70
71% Denote newterms in particular font and index them without particular font and in lowercase, e.g., \newterm{abc}.
72% The option parameter provides an index term different from the new term, e.g., \newterm[\texttt{abc}]{abc}
73% The star version does not lowercase the index information, e.g., \newterm*{IBM}.
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78
79% Latin abbreviation
80\newcommand{\abbrevFont}{\textit}                       % set empty for no italics
81\newcommand{\EG}{\abbrevFont{e}.\abbrevFont{g}.}
82\newcommand*{\eg}{%
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84                {\@ifnextchar{:}{\EG}%
85                        {\EG,\xspace}}%
86}%
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89        \@ifnextchar{,}{\IE}%
90                {\@ifnextchar{:}{\IE}%
91                        {\IE,\xspace}}%
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93\newcommand{\ETC}{\abbrevFont{etc}}
94\newcommand*{\etc}{%
95        \@ifnextchar{.}{\ETC}%
96        {\ETC.\xspace}%
97}%
98%\newcommand{\ETAL}{\abbrevFont{et}~\abbrevFont{al}}
99%\newcommand*{\etal}{%
100%       \@ifnextchar{.}{\protect\ETAL}%
101%               {\protect\ETAL.\xspace}%
102%}%
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104\newcommand*{\viz}{%
105        \@ifnextchar{.}{\VIZ}%
106                {\VIZ.\xspace}%
107}%
108\makeatother
109
110\newenvironment{cquote}{%
111        \list{}{\lstset{resetmargins=true,aboveskip=0pt,belowskip=0pt}\topsep=3pt\parsep=0pt\leftmargin=\parindentlnth\rightmargin\leftmargin}%
112        \item\relax
113}{%
114        \endlist
115}% cquote
116
117% CFA programming language, based on ANSI C (with some gcc additions)
118\lstdefinelanguage{CFA}[ANSI]{C}{
119        morekeywords={
120                _Alignas, _Alignof, __alignof, __alignof__, asm, __asm, __asm__, _At, __attribute,
121                __attribute__, auto, _Bool, catch, catchResume, choose, _Complex, __complex, __complex__,
122                __const, __const__, disable, dtype, enable, exception, __extension__, fallthrough, fallthru,
123                finally, forall, ftype, _Generic, _Imaginary, inline, __label__, lvalue, _Noreturn, one_t,
124                otype, restrict, _Static_assert, throw, throwResume, trait, try, ttype, typeof, __typeof,
125                __typeof__, virtual, with, zero_t},
126        morekeywords=[2]{
127                _Atomic, coroutine, is_coroutine, is_monitor, is_thread, monitor, mutex, nomutex, or,
128                resume, suspend, thread, _Thread_local, waitfor, when, yield},
129        moredirectives={defined,include_next}%
130}
131
132\lstset{
133language=CFA,
134columns=fullflexible,
135basicstyle=\linespread{0.9}\sf,                                                 % reduce line spacing and use sanserif font
136stringstyle=\tt,                                                                                % use typewriter font
137tabsize=5,                                                                                              % N space tabbing
138xleftmargin=\parindentlnth,                                                             % indent code to paragraph indentation
139%mathescape=true,                                                                               % LaTeX math escape in CFA code $...$
140escapechar=\$,                                                                                  % LaTeX escape in CFA code
141keepspaces=true,                                                                                %
142showstringspaces=false,                                                                 % do not show spaces with cup
143showlines=true,                                                                                 % show blank lines at end of code
144aboveskip=4pt,                                                                                  % spacing above/below code block
145belowskip=3pt,
146% replace/adjust listing characters that look bad in sanserif
147literate={-}{\makebox[1ex][c]{\raisebox{0.4ex}{\rule{0.8ex}{0.1ex}}}}1 {^}{\raisebox{0.6ex}{$\scriptstyle\land\,$}}1
148        {~}{\raisebox{0.3ex}{$\scriptstyle\sim\,$}}1 % {`}{\ttfamily\upshape\hspace*{-0.1ex}`}1
149        {<-}{$\leftarrow$}2 {=>}{$\Rightarrow$}2 {->}{\makebox[1ex][c]{\raisebox{0.5ex}{\rule{0.8ex}{0.075ex}}}\kern-0.2ex{\textgreater}}2,
150moredelim=**[is][\color{red}]{`}{`},
151}% lstset
152
153\lstnewenvironment{cfa}[1][]
154{\lstset{#1}}
155{}
156\lstnewenvironment{C++}[1][]                            % use C++ style
157{\lstset{language=C++,moredelim=**[is][\protect\color{red}]{`}{`},#1}\lstset{#1}}
158{}
159
160
161\begin{document}
162\linenumbers                                            % comment out to turn off line numbering
163
164\title{\texorpdfstring{\protect\CFA : Adding Modern Programming Language Features to C}{Cforall : Adding Modern Programming Language Features to C}}
165
166\author[1]{Aaron Moss}
167\author[1]{Robert Schluntz}
168\author[1]{Peter A. Buhr*}
169
170\address[1]{\orgdiv{David R. Cheriton School of Computer Science}, \orgname{University of Waterloo}, \orgaddress{\state{Ontario}, \country{Canada}}}
171
172%\corres{*Aaron Moss, \email{a3moss@uwaterloo.ca}}
173\corres{*Peter A. Buhr, \email{pabuhr@uwaterloo.ca}}
174\presentaddress{David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada}
175
176% inline code @...@
177\lstMakeShortInline@%
178
179
180\abstract[Summary]{
181The C programming language is a foundational technology for modern computing with millions of lines of code implementing everything from commercial operating-systems to hobby projects.
182This installation base and the programmers producing it represent a massive software-engineering investment spanning decades and likely to continue for decades more.
183Nevertheless, C, first standardized over thirty years ago, lacks many features that make programming in more modern languages safer and more productive.
184
185The goal of the \CFA project is to create an extension of C that provides modern safety and productivity features while still ensuring strong backwards compatibility with C and its programmers.
186Prior projects have attempted similar goals but failed to honour C programming-style; for instance, adding object-oriented or functional programming with garbage collection is a non-starter for many C developers.
187Specifically, \CFA is designed to have an orthogonal feature-set based closely on the C programming paradigm, so that \CFA features can be added \emph{incrementally} to existing C code-bases, and C programmers can learn \CFA extensions on an as-needed basis, preserving investment in existing code and programmers.
188This paper presents a quick tour of \CFA features showing how their design avoids shortcomings of similar features in C and other C-like languages.
189Finally, experimental results are presented to validate several of the new features.
190}%
191
192\keywords{generic types, tuple types, variadic types, polymorphic functions, C, Cforall}
193
194\maketitle
195
196
197\section{Introduction}
198
199The C programming language is a foundational technology for modern computing with millions of lines of code implementing everything from commercial operating-systems to hobby projects.
200This installation base and the programmers producing it represent a massive software-engineering investment spanning decades and likely to continue for decades more.
201The TIOBE~\cite{TIOBE} ranks the top 5 most \emph{popular} programming languages as: Java 15\%, \Textbf{C 12\%}, \Textbf{\CC 5.5\%}, Python 5\%, \Csharp 4.5\% = 42\%, where the next 50 languages are less than 4\% each with a long tail.
202The top 3 rankings over the past 30 years are:
203\begin{center}
204\setlength{\tabcolsep}{10pt}
205\lstDeleteShortInline@%
206\begin{tabular}{@{}rccccccc@{}}
207                & 2018  & 2013  & 2008  & 2003  & 1998  & 1993  & 1988  \\ \hline
208Java    & 1             & 2             & 1             & 1             & 18    & -             & -             \\
209\Textbf{C}& \Textbf{2} & \Textbf{1} & \Textbf{2} & \Textbf{2} & \Textbf{1} & \Textbf{1} & \Textbf{1} \\
210\CC             & 3             & 4             & 3             & 3             & 2             & 2             & 5             \\
211\end{tabular}
212\lstMakeShortInline@%
213\end{center}
214Love it or hate it, C is extremely popular, highly used, and one of the few systems languages.
215In many cases, \CC is often used solely as a better C.
216Nonetheless, C, first standardized over thirty years ago, lacks many features that make programming in more modern languages safer and more productive.
217
218\CFA (pronounced ``C-for-all'', and written \CFA or Cforall) is an evolutionary extension of the C programming language that aims to add modern language features to C while maintaining both source compatibility with C and a familiar programming model for programmers.
219The four key design goals for \CFA~\cite{Bilson03} are:
220(1) The behaviour of standard C code must remain the same when translated by a \CFA compiler as when translated by a C compiler;
221(2) Standard C code must be as fast and as small when translated by a \CFA compiler as when translated by a C compiler;
222(3) \CFA code must be at least as portable as standard C code;
223(4) Extensions introduced by \CFA must be translated in the most efficient way possible.
224These goals ensure existing C code-bases can be converted to \CFA incrementally with minimal effort, and C programmers can productively generate \CFA code without training beyond the features being used.
225\CC is used similarly, but has the disadvantages of multiple legacy design-choices that cannot be updated and active divergence of the language model from C, requiring significant effort and training to incrementally add \CC to a C-based project.
226
227\CFA is currently implemented as a source-to-source translator from \CFA to the gcc-dialect of C~\cite{GCCExtensions}, allowing it to leverage the portability and code optimizations provided by gcc, meeting goals (1)--(3).
228Ultimately, a compiler is necessary for advanced features and optimal performance.
229All features discussed in this paper are working, unless otherwise stated as under construction.
230
231Finally, it is impossible to describe a programming language without usages before definitions.
232Therefore, syntax and semantics appear before explanations;
233hence, patience is necessary until details are presented.
234
235
236\section{Polymorphic Functions}
237
238\CFA introduces both ad-hoc and parametric polymorphism to C, with a design originally formalized by Ditchfield~\cite{Ditchfield92}, and first implemented by Bilson~\cite{Bilson03}.
239Shortcomings are identified in existing approaches to generic and variadic data types in C-like languages and how these shortcomings are avoided in \CFA.
240Specifically, the solution is both reusable and type-checked, as well as conforming to the design goals of \CFA with ergonomic use of existing C abstractions.
241The new constructs are empirically compared with C and \CC approaches via performance experiments in Section~\ref{sec:eval}.
242
243
244\subsection{Name Overloading}
245\label{s:NameOverloading}
246
247\begin{quote}
248There are only two hard things in Computer Science: cache invalidation and \emph{naming things} -- Phil Karlton
249\end{quote}
250C already has a limited form of ad-hoc polymorphism in the form of its basic arithmetic operators, which apply to a variety of different types using identical syntax.
251\CFA extends the built-in operator overloading by allowing users to define overloads for any function, not just operators, and even any variable;
252Section~\ref{sec:libraries} includes a number of examples of how this overloading simplifies \CFA programming relative to C.
253Code generation for these overloaded functions and variables is implemented by the usual approach of mangling the identifier names to include a representation of their type, while \CFA decides which overload to apply based on the same ``usual arithmetic conversions'' used in C to disambiguate operator overloads.
254As an example:
255
256\begin{cfa}
257int max = 2147483647;                                   $\C[4in]{// (1)}$
258double max = 1.7976931348623157E+308;   $\C{// (2)}$
259int max( int a, int b ) { return a < b ? b : a; }  $\C{// (3)}$
260double max( double a, double b ) { return a < b ? b : a; }  $\C{// (4)}\CRT$
261max( 7, -max );                                         $\C[2.75in]{// uses (3) and (1), by matching int from constant 7}$
262max( max, 3.14 );                                       $\C{// uses (4) and (2), by matching double from constant 3.14}$
263max( max, -max );                                       $\C{// ERROR: ambiguous}$
264int m = max( max, -max );                       $\C{// uses (3) and (1) twice, by matching return type}\CRT$
265\end{cfa}
266
267\CFA maximizes the ability to reuse names to aggressively address the naming problem.
268In some cases, hundreds of names can be reduced to tens, resulting in a significant cognitive reduction.
269In the above, the name @max@ has a consistent meaning, and a programmer only needs to remember the single concept: maximum.
270To prevent significant ambiguities, \CFA uses the return type in selecting overloads, \eg in the assignment to @m@, the compiler use @m@'s type to unambiguously select the most appropriate call to function @max@ (as does Ada).
271As is shown later, there are a number of situations where \CFA takes advantage of available type information to disambiguate, where other programming languages generate ambiguities.
272
273\Celeven added @_Generic@ expressions, which is used in preprocessor macros to provide a form of ad-hoc polymorphism;
274however, this polymorphism is both functionally and ergonomically inferior to \CFA name overloading.
275The macro wrapping the generic expression imposes some limitations;
276\eg, it cannot implement the example above, because the variables @max@ are ambiguous with the functions @max@.
277Ergonomic limitations of @_Generic@ include the necessity to put a fixed list of supported types in a single place and manually dispatch to appropriate overloads, as well as possible namespace pollution from the dispatch functions, which must all have distinct names.
278For backwards compatibility, \CFA supports @_Generic@ expressions, but it is an unnecessary mechanism. \TODO{actually implement that}
279
280% http://fanf.livejournal.com/144696.html
281% http://www.robertgamble.net/2012/01/c11-generic-selections.html
282% https://abissell.com/2014/01/16/c11s-_generic-keyword-macro-applications-and-performance-impacts/
283
284
285\subsection{\texorpdfstring{\protect\lstinline{forall} Functions}{forall Functions}}
286\label{sec:poly-fns}
287
288The signature feature of \CFA is parametric-polymorphic functions~\cite{forceone:impl,Cormack90,Duggan96} with functions generalized using a @forall@ clause (giving the language its name):
289\begin{cfa}
290`forall( otype T )` T identity( T val ) { return val; }
291int forty_two = identity( 42 );         $\C{// T is bound to int, forty\_two == 42}$
292\end{cfa}
293This @identity@ function can be applied to any complete \newterm{object type} (or @otype@).
294The type variable @T@ is transformed into a set of additional implicit parameters encoding sufficient information about @T@ to create and return a variable of that type.
295The \CFA implementation passes the size and alignment of the type represented by an @otype@ parameter, as well as an assignment operator, constructor, copy constructor and destructor.
296If this extra information is not needed, \eg for a pointer, the type parameter can be declared as a \newterm{data type} (or @dtype@).
297
298In \CFA, the polymorphic runtime-cost is spread over each polymorphic call, because more arguments are passed to polymorphic functions;
299the experiments in Section~\ref{sec:eval} show this overhead is similar to \CC virtual-function calls.
300A design advantage is that, unlike \CC template-functions, \CFA polymorphic-functions are compatible with C \emph{separate compilation}, preventing compilation and code bloat.
301
302Since bare polymorphic-types provide a restricted set of available operations, \CFA provides a \newterm{type assertion}~\cite[pp.~37-44]{Alphard} mechanism to provide further type information, where type assertions may be variable or function declarations that depend on a polymorphic type-variable.
303For example, the function @twice@ can be defined using the \CFA syntax for operator overloading:
304\begin{cfa}
305forall( otype T `| { T ?+?(T, T); }` ) T twice( T x ) { return x `+` x; }  $\C{// ? denotes operands}$
306int val = twice( twice( 3.7 ) );
307\end{cfa}
308which works for any type @T@ with a matching addition operator.
309The polymorphism is achieved by creating a wrapper function for calling @+@ with @T@ bound to @double@, then passing this function to the first call of @twice@.
310There is now the option of using the same @twice@ and converting the result to @int@ on assignment, or creating another @twice@ with type parameter @T@ bound to @int@ because \CFA uses the return type~\cite{Cormack81,Baker82,Ada} in its type analysis.
311The first approach has a late conversion from @double@ to @int@ on the final assignment, while the second has an eager conversion to @int@.
312\CFA minimizes the number of conversions and their potential to lose information, so it selects the first approach, which corresponds with C-programmer intuition.
313
314Crucial to the design of a new programming language are the libraries to access thousands of external software features.
315Like \CC, \CFA inherits a massive compatible library-base, where other programming languages must rewrite or provide fragile inter-language communication with C.
316A simple example is leveraging the existing type-unsafe (@void *@) C @bsearch@ to binary search a sorted float array:
317\begin{cfa}
318void * bsearch( const void * key, const void * base, size_t nmemb, size_t size,
319                                         int (* compar)( const void *, const void * ));
320int comp( const void * t1, const void * t2 ) {
321         return *(double *)t1 < *(double *)t2 ? -1 : *(double *)t2 < *(double *)t1 ? 1 : 0;
322}
323double key = 5.0, vals[10] = { /* 10 sorted float values */ };
324double * val = (double *)bsearch( &key, vals, 10, sizeof(vals[0]), comp ); $\C{// search sorted array}$
325\end{cfa}
326which can be augmented simply with a generalized, type-safe, \CFA-overloaded wrappers:
327\begin{cfa}
328forall( otype T | { int ?<?( T, T ); } ) T * bsearch( T key, const T * arr, size_t size ) {
329        int comp( const void * t1, const void * t2 ) { /* as above with double changed to T */ }
330        return (T *)bsearch( &key, arr, size, sizeof(T), comp );
331}
332forall( otype T | { int ?<?( T, T ); } ) unsigned int bsearch( T key, const T * arr, size_t size ) {
333        T * result = bsearch( key, arr, size ); $\C{// call first version}$
334        return result ? result - arr : size; $\C{// pointer subtraction includes sizeof(T)}$
335}
336double * val = bsearch( 5.0, vals, 10 ); $\C{// selection based on return type}$
337int posn = bsearch( 5.0, vals, 10 );
338\end{cfa}
339The nested function @comp@ provides the hidden interface from typed \CFA to untyped (@void *@) C, plus the cast of the result.
340Providing a hidden @comp@ function in \CC is awkward as lambdas do not use C calling-conventions and template declarations cannot appear at block scope.
341As well, an alternate kind of return is made available: position versus pointer to found element.
342\CC's type-system cannot disambiguate between the two versions of @bsearch@ because it does not use the return type in overload resolution, nor can \CC separately compile a template @bsearch@.
343
344\CFA has replacement libraries condensing hundreds of existing C functions into tens of \CFA overloaded functions, all without rewriting the actual computations (see Section~\ref{sec:libraries}).
345For example, it is possible to write a type-safe \CFA wrapper @malloc@ based on the C @malloc@:
346\begin{cfa}
347forall( dtype T | sized(T) ) T * malloc( void ) { return (T *)malloc( sizeof(T) ); }
348int * ip = malloc();                                            $\C{// select type and size from left-hand side}$
349double * dp = malloc();
350struct S {...} * sp = malloc();
351\end{cfa}
352where the return type supplies the type/size of the allocation, which is impossible in most type systems.
353
354Call-site inferencing and nested functions provide a localized form of inheritance.
355For example, the \CFA @qsort@ only sorts in ascending order using @<@.
356However, it is trivial to locally change this behaviour:
357\begin{cfa}
358forall( otype T | { int ?<?( T, T ); } ) void qsort( const T * arr, size_t size ) { /* use C qsort */ }
359{
360        int ?<?( double x, double y ) { return x `>` y; } $\C{// locally override behaviour}$
361        qsort( vals, size );                                    $\C{// descending sort}$
362}
363\end{cfa}
364Within the block, the nested version of @?<?@ performs @?>?@ and this local version overrides the built-in @?<?@ so it is passed to @qsort@.
365Hence, programmers can easily form local environments, adding and modifying appropriate functions, to maximize reuse of other existing functions and types.
366
367Under construction is a mechanism to distribute @forall@ over routines/types, where each block declaration is prefixed with the initial @forall@ clause significantly reducing duplication (see @stack@ examples in Section~\ref{sec:eval}):
368\begin{cfa}
369forall( otype `T` ) {                                                   $\C{// forall block}$
370        struct stack { stack_node(`T`) * head; };       $\C{// generic type}$
371        void push( stack(`T`) & s, `T` value ) ...      $\C{// generic operations}$
372        T pop( stack(`T`) & s ) ...
373}
374\end{cfa}
375
376
377\subsection{Traits}
378
379\CFA provides \newterm{traits} to name a group of type assertions, where the trait name allows specifying the same set of assertions in multiple locations, preventing repetition mistakes at each function declaration:
380\begin{cfa}
381trait `summable`( otype T ) {
382        void ?{}( T *, zero_t );                                $\C{// constructor from 0 literal}$
383        T ?+?( T, T );                                                  $\C{// assortment of additions}$
384        T ?+=?( T *, T );
385        T ++?( T * );
386        T ?++( T * );
387};
388forall( otype T `| summable( T )` ) T sum( T a[$\,$], size_t size ) {  // use trait
389        `T` total = { `0` };                                    $\C{// instantiate T from 0 by calling its constructor}$
390        for ( unsigned int i = 0; i < size; i += 1 ) total `+=` a[i]; $\C{// select appropriate +}$
391        return total;
392}
393\end{cfa}
394
395In fact, the set of @summable@ trait operators is incomplete, as it is missing assignment for type @T@, but @otype@ is syntactic sugar for the following implicit trait:
396\begin{cfa}
397trait otype( dtype T | sized(T) ) {  // sized is a pseudo-trait for types with known size and alignment
398        void ?{}( T & );                                                $\C{// default constructor}$
399        void ?{}( T &, T );                                             $\C{// copy constructor}$
400        void ?=?( T &, T );                                             $\C{// assignment operator}$
401        void ^?{}( T & );                                               $\C{// destructor}$
402};
403\end{cfa}
404Given the information provided for an @otype@, variables of polymorphic type can be treated as if they were a complete type: stack-allocatable, default or copy-initialized, assigned, and deleted.
405
406In summation, the \CFA type-system uses \newterm{nominal typing} for concrete types, matching with the C type-system, and \newterm{structural typing} for polymorphic types.
407Hence, trait names play no part in type equivalence;
408the names are simply macros for a list of polymorphic assertions, which are expanded at usage sites.
409Nevertheless, trait names form a logical subtype-hierarchy with @dtype@ at the top, where traits often contain overlapping assertions, \eg operator @+@.
410Traits are used like interfaces in Java or abstract base-classes in \CC, but without the nominal inheritance-relationships.
411Instead, each polymorphic function (or generic type) defines the structural type needed for its execution (polymorphic type-key), and this key is fulfilled at each call site from the lexical environment, which is similar to Go~\cite{Go} interfaces.
412Hence, new lexical scopes and nested functions are used extensively to create local subtypes, as in the @qsort@ example, without having to manage a nominal-inheritance hierarchy.
413(Nominal inheritance can be approximated with traits using marker variables or functions, as is done in Go.)
414
415% Nominal inheritance can be simulated with traits using marker variables or functions:
416% \begin{cfa}
417% trait nominal(otype T) {
418%     T is_nominal;
419% };
420% int is_nominal;                                                               $\C{// int now satisfies the nominal trait}$
421% \end{cfa}
422%
423% Traits, however, are significantly more powerful than nominal-inheritance interfaces; most notably, traits may be used to declare a relationship \emph{among} multiple types, a property that may be difficult or impossible to represent in nominal-inheritance type systems:
424% \begin{cfa}
425% trait pointer_like(otype Ptr, otype El) {
426%     lvalue El *?(Ptr);                                                $\C{// Ptr can be dereferenced into a modifiable value of type El}$
427% }
428% struct list {
429%     int value;
430%     list * next;                                                              $\C{// may omit "struct" on type names as in \CC}$
431% };
432% typedef list * list_iterator;
433%
434% lvalue int *?( list_iterator it ) { return it->value; }
435% \end{cfa}
436% In the example above, @(list_iterator, int)@ satisfies @pointer_like@ by the user-defined dereference function, and @(list_iterator, list)@ also satisfies @pointer_like@ by the built-in dereference operator for pointers. Given a declaration @list_iterator it@, @*it@ can be either an @int@ or a @list@, with the meaning disambiguated by context (\eg @int x = *it;@ interprets @*it@ as an @int@, while @(*it).value = 42;@ interprets @*it@ as a @list@).
437% While a nominal-inheritance system with associated types could model one of those two relationships by making @El@ an associated type of @Ptr@ in the @pointer_like@ implementation, few such systems could model both relationships simultaneously.
438
439
440\section{Generic Types}
441
442A significant shortcoming of standard C is the lack of reusable type-safe abstractions for generic data structures and algorithms.
443Broadly speaking, there are three approaches to implement abstract data-structures in C.
444One approach is to write bespoke data-structures for each context in which they are needed.
445While this approach is flexible and supports integration with the C type-checker and tooling, it is also tedious and error-prone, especially for more complex data structures.
446A second approach is to use @void *@-based polymorphism, \eg the C standard-library functions @bsearch@ and @qsort@, which allow reuse of code with common functionality.
447However, basing all polymorphism on @void *@ eliminates the type-checker's ability to ensure that argument types are properly matched, often requiring a number of extra function parameters, pointer indirection, and dynamic allocation that is not otherwise needed.
448A third approach to generic code is to use preprocessor macros, which does allow the generated code to be both generic and type-checked, but errors may be difficult to interpret.
449Furthermore, writing and using preprocessor macros is unnatural and inflexible.
450
451\CC, Java, and other languages use \newterm{generic types} to produce type-safe abstract data-types.
452\CFA also implements generic types that integrate efficiently and naturally with the existing polymorphic functions, while retaining backwards compatibility with C and providing separate compilation.
453However, for known concrete parameters, the generic-type definition can be inlined, like \CC templates.
454
455A generic type can be declared by placing a @forall@ specifier on a @struct@ or @union@ declaration, and instantiated using a parenthesized list of types after the type name:
456\begin{cfa}
457forall( otype R, otype S ) struct pair {
458        R first;
459        S second;
460};
461forall( otype T ) T value( pair( const char *, T ) p ) { return p.second; } $\C{// dynamic}$
462forall( dtype F, otype T ) T value( pair( F *, T * ) p ) { return *p.second; } $\C{// dtype-static (concrete)}$
463
464pair( const char *, int ) p = { "magic", 42 }; $\C{// concrete}$
465int i = value( p );
466pair( void *, int * ) q = { 0, &p.second }; $\C{// concrete}$
467i = value( q );
468double d = 1.0;
469pair( double *, double * ) r = { &d, &d }; $\C{// concrete}$
470d = value( r );
471\end{cfa}
472
473\CFA classifies generic types as either \newterm{concrete} or \newterm{dynamic}.
474Concrete types have a fixed memory layout regardless of type parameters, while dynamic types vary in memory layout depending on their type parameters.
475A \newterm{dtype-static} type has polymorphic parameters but is still concrete.
476Polymorphic pointers are an example of dtype-static types, \eg @forall(dtype T) T *@ is a polymorphic type, but for any @T@, @T *@  is a fixed-sized pointer, and therefore, can be represented by a @void *@ in code generation.
477
478\CFA generic types also allow checked argument-constraints.
479For example, the following declaration of a sorted set-type ensures the set key supports equality and relational comparison:
480\begin{cfa}
481forall( otype Key | { _Bool ?==?(Key, Key); _Bool ?<?(Key, Key); } ) struct sorted_set;
482\end{cfa}
483
484
485\subsection{Concrete Generic-Types}
486
487The \CFA translator template-expands concrete generic-types into new structure types, affording maximal inlining.
488To enable inter-operation among equivalent instantiations of a generic type, the translator saves the set of instantiations currently in scope and reuses the generated structure declarations where appropriate.
489A function declaration that accepts or returns a concrete generic-type produces a declaration for the instantiated structure in the same scope, which all callers may reuse.
490For example, the concrete instantiation for @pair( const char *, int )@ is:
491\begin{cfa}
492struct _pair_conc0 {
493        const char * first;
494        int second;
495};
496\end{cfa}
497
498A concrete generic-type with dtype-static parameters is also expanded to a structure type, but this type is used for all matching instantiations.
499In the above example, the @pair( F *, T * )@ parameter to @value@ is such a type; its expansion is below and it is used as the type of the variables @q@ and @r@ as well, with casts for member access where appropriate:
500\begin{cfa}
501struct _pair_conc1 {
502        void * first;
503        void * second;
504};
505\end{cfa}
506
507
508\subsection{Dynamic Generic-Types}
509
510Though \CFA implements concrete generic-types efficiently, it also has a fully general system for dynamic generic types.
511As mentioned in Section~\ref{sec:poly-fns}, @otype@ function parameters (in fact all @sized@ polymorphic parameters) come with implicit size and alignment parameters provided by the caller.
512Dynamic generic-types also have an \newterm{offset array} containing structure-member offsets.
513A dynamic generic-@union@ needs no such offset array, as all members are at offset 0, but size and alignment are still necessary.
514Access to members of a dynamic structure is provided at runtime via base-displacement addressing with the structure pointer and the member offset (similar to the @offsetof@ macro), moving a compile-time offset calculation to runtime.
515
516The offset arrays are statically generated where possible.
517If a dynamic generic-type is declared to be passed or returned by value from a polymorphic function, the translator can safely assume the generic type is complete (\ie has a known layout) at any call-site, and the offset array is passed from the caller;
518if the generic type is concrete at the call site, the elements of this offset array can even be statically generated using the C @offsetof@ macro.
519As an example, the body of the second @value@ function is implemented as:
520\begin{cfa}
521_assign_T( _retval, p + _offsetof_pair[1] ); $\C{// return *p.second}$
522\end{cfa}
523@_assign_T@ is passed in as an implicit parameter from @otype T@, and takes two @T *@ (@void *@ in the generated code), a destination and a source; @_retval@ is the pointer to a caller-allocated buffer for the return value, the usual \CFA method to handle dynamically-sized return types.
524@_offsetof_pair@ is the offset array passed into @value@; this array is generated at the call site as:
525\begin{cfa}
526size_t _offsetof_pair[] = { offsetof( _pair_conc0, first ), offsetof( _pair_conc0, second ) }
527\end{cfa}
528
529In some cases the offset arrays cannot be statically generated.
530For instance, modularity is generally provided in C by including an opaque forward-declaration of a structure and associated accessor and mutator functions in a header file, with the actual implementations in a separately-compiled @.c@ file.
531\CFA supports this pattern for generic types, but the caller does not know the actual layout or size of the dynamic generic-type, and only holds it by a pointer.
532The \CFA translator automatically generates \newterm{layout functions} for cases where the size, alignment, and offset array of a generic struct cannot be passed into a function from that function's caller.
533These layout functions take as arguments pointers to size and alignment variables and a caller-allocated array of member offsets, as well as the size and alignment of all @sized@ parameters to the generic structure (un@sized@ parameters are forbidden from being used in a context that affects layout).
534Results of these layout functions are cached so that they are only computed once per type per function. %, as in the example below for @pair@.
535Layout functions also allow generic types to be used in a function definition without reflecting them in the function signature.
536For instance, a function that strips duplicate values from an unsorted @vector(T)@ likely has a pointer to the vector as its only explicit parameter, but uses some sort of @set(T)@ internally to test for duplicate values.
537This function could acquire the layout for @set(T)@ by calling its layout function with the layout of @T@ implicitly passed into the function.
538
539Whether a type is concrete, dtype-static, or dynamic is decided solely on the @forall@'s type parameters.
540This design allows opaque forward declarations of generic types, \eg @forall(otype T)@ @struct Box@ -- like in C, all uses of @Box(T)@ can be separately compiled, and callers from other translation units know the proper calling conventions to use.
541If the definition of a structure type is included in deciding whether a generic type is dynamic or concrete, some further types may be recognized as dtype-static (\eg @forall(otype T)@ @struct unique_ptr { T * p }@ does not depend on @T@ for its layout, but the existence of an @otype@ parameter means that it \emph{could}.), but preserving separate compilation (and the associated C compatibility) in the existing design is judged to be an appropriate trade-off.
542
543
544\subsection{Applications}
545\label{sec:generic-apps}
546
547The reuse of dtype-static structure instantiations enables useful programming patterns at zero runtime cost.
548The most important such pattern is using @forall(dtype T) T *@ as a type-checked replacement for @void *@, \eg creating a lexicographic comparison for pairs of pointers used by @bsearch@ or @qsort@:
549\begin{cfa}
550forall( dtype T ) int lexcmp( pair( T *, T * ) * a, pair( T *, T * ) * b, int (* cmp)( T *, T * ) ) {
551        return cmp( a->first, b->first ) ? : cmp( a->second, b->second );
552}
553\end{cfa}
554Since @pair( T *, T * )@ is a concrete type, there are no implicit parameters passed to @lexcmp@, so the generated code is identical to a function written in standard C using @void *@, yet the \CFA version is type-checked to ensure the fields of both pairs and the arguments to the comparison function match in type.
555
556Another useful pattern enabled by reused dtype-static type instantiations is zero-cost \newterm{tag-structures}.
557Sometimes information is only used for type-checking and can be omitted at runtime, \eg:
558\begin{cfa}
559forall( dtype Unit ) struct scalar { unsigned long value; };
560struct metres {};
561struct litres {};
562
563forall( dtype U ) scalar(U) ?+?( scalar(U) a, scalar(U) b ) {
564        return (scalar(U)){ a.value + b.value };
565}
566scalar(metres) half_marathon = { 21093 };
567scalar(litres) swimming_pool = { 2500000 };
568scalar(metres) marathon = half_marathon + half_marathon;
569scalar(litres) two_pools = swimming_pool + swimming_pool;
570marathon + swimming_pool;                                       $\C{// compilation ERROR}$
571\end{cfa}
572@scalar@ is a dtype-static type, so all uses have a single structure definition, containing @unsigned long@, and can share the same implementations of common functions like @?+?@.
573These implementations may even be separately compiled, unlike \CC template functions.
574However, the \CFA type-checker ensures matching types are used by all calls to @?+?@, preventing nonsensical computations like adding a length to a volume.
575
576
577\section{Tuples}
578\label{sec:tuples}
579
580In many languages, functions can return at most one value;
581however, many operations have multiple outcomes, some exceptional.
582Consider C's @div@ and @remquo@ functions, which return the quotient and remainder for a division of integer and float values, respectively.
583\begin{cfa}
584typedef struct { int quo, rem; } div_t;         $\C{// from include stdlib.h}$
585div_t div( int num, int den );
586double remquo( double num, double den, int * quo );
587div_t qr = div( 13, 5 );                                        $\C{// return quotient/remainder aggregate}$
588int q;
589double r = remquo( 13.5, 5.2, &q );                     $\C{// return remainder, alias quotient}$
590\end{cfa}
591@div@ aggregates the quotient/remainder in a structure, while @remquo@ aliases a parameter to an argument.
592Both approaches are awkward.
593Alternatively, a programming language can directly support returning multiple values, \eg in \CFA:
594\begin{cfa}
595[ int, int ] div( int num, int den );           $\C{// return two integers}$
596[ double, double ] div( double num, double den ); $\C{// return two doubles}$
597int q, r;                                                                       $\C{// overloaded variable names}$
598double q, r;
599[ q, r ] = div( 13, 5 );                                        $\C{// select appropriate div and q, r}$
600[ q, r ] = div( 13.5, 5.2 );                            $\C{// assign into tuple}$
601\end{cfa}
602This approach is straightforward to understand and use;
603therefore, why do few programming languages support this obvious feature or provide it awkwardly?
604To answer, there are complex consequences that cascade through multiple aspects of the language, especially the type-system.
605This section show these consequences and how \CFA handles them.
606
607
608\subsection{Tuple Expressions}
609
610The addition of multiple-return-value functions (MRVF) are \emph{useless} without a syntax for accepting multiple values at the call-site.
611The simplest mechanism for capturing the return values is variable assignment, allowing the values to be retrieved directly.
612As such, \CFA allows assigning multiple values from a function into multiple variables, using a square-bracketed list of lvalue expressions (as above), called a \newterm{tuple}.
613
614However, functions also use \newterm{composition} (nested calls), with the direct consequence that MRVFs must also support composition to be orthogonal with single-returning-value functions (SRVF), \eg:
615\begin{cfa}
616printf( "%d %d\n", div( 13, 5 ) );                      $\C{// return values seperated into arguments}$
617\end{cfa}
618Here, the values returned by @div@ are composed with the call to @printf@ by flattening the tuple into separate arguments.
619However, the \CFA type-system must support significantly more complex composition:
620\begin{cfa}
621[ int, int ] foo$\(_1\)$( int );                        $\C{// overloaded foo functions}$
622[ double ] foo$\(_2\)$( int );
623void bar( int, double, double );
624`bar`( foo( 3 ), foo( 3 ) );
625\end{cfa}
626The type-resolver only has the tuple return-types to resolve the call to @bar@ as the @foo@ parameters are identical, which involves unifying the possible @foo@ functions with @bar@'s parameter list.
627No combination of @foo@s are an exact match with @bar@'s parameters, so the resolver applies C conversions.
628The minimal cost is @bar( foo@$_1$@( 3 ), foo@$_2$@( 3 ) )@, giving (@int@, {\color{ForestGreen}@int@}, @double@) to (@int@, {\color{ForestGreen}@double@}, @double@) with one {\color{ForestGreen}safe} (widening) conversion from @int@ to @double@ versus ({\color{red}@double@}, {\color{ForestGreen}@int@}, {\color{ForestGreen}@int@}) to ({\color{red}@int@}, {\color{ForestGreen}@double@}, {\color{ForestGreen}@double@}) with one {\color{red}unsafe} (narrowing) conversion from @double@ to @int@ and two safe conversions.
629
630
631\subsection{Tuple Variables}
632
633An important observation from function composition is that new variable names are not required to initialize parameters from an MRVF.
634\CFA also allows declaration of tuple variables that can be initialized from an MRVF, since it can be awkward to declare multiple variables of different types, \eg:
635\begin{cfa}
636[ int, int ] qr = div( 13, 5 );                         $\C{// tuple-variable declaration and initialization}$
637[ double, double ] qr = div( 13.5, 5.2 );
638\end{cfa}
639where the tuple variable-name serves the same purpose as the parameter name(s).
640Tuple variables can be composed of any types, except for array types, since array sizes are generally unknown in C.
641
642One way to access the tuple-variable components is with assignment or composition:
643\begin{cfa}
644[ q, r ] = qr;                                                          $\C{// access tuple-variable components}$
645printf( "%d %d\n", qr );
646\end{cfa}
647\CFA also supports \newterm{tuple indexing} to access single components of a tuple expression:
648\begin{cfa}
649[int, int] * p = &qr;                                           $\C{// tuple pointer}$
650int rem = qr`.1`;                                                       $\C{// access remainder}$
651int quo = div( 13, 5 )`.0`;                                     $\C{// access quotient}$
652p`->0` = 5;                                                                     $\C{// change quotient}$
653bar( qr`.1`, qr );                                                      $\C{// pass remainder and quotient/remainder}$
654rem = [div( 13, 5 ), 42]`.0.1`;                         $\C{// access 2nd component of 1st component}$
655\end{cfa}
656
657
658\subsection{Flattening and Restructuring}
659
660In function call contexts, tuples support implicit flattening and restructuring conversions.
661Tuple flattening recursively expands a tuple into the list of its basic components.
662Tuple structuring packages a list of expressions into a value of tuple type, \eg:
663\begin{cfa}
664int f( int, int );
665int g( [int, int] );
666int h( int, [int, int] );
667[int, int] x;
668int y;
669f( x );                                                                         $\C{// flatten}$
670g( y, 10 );                                                                     $\C{// structure}$
671h( x, y );                                                                      $\C{// flatten and structure}$
672\end{cfa}
673In the call to @f@, @x@ is implicitly flattened so the components of @x@ are passed as the two arguments.
674In the call to @g@, the values @y@ and @10@ are structured into a single argument of type @[int, int]@ to match the parameter type of @g@.
675Finally, in the call to @h@, @x@ is flattened to yield an argument list of length 3, of which the first component of @x@ is passed as the first parameter of @h@, and the second component of @x@ and @y@ are structured into the second argument of type @[int, int]@.
676The flexible structure of tuples permits a simple and expressive function call syntax to work seamlessly with both SRVF and MRVF, and with any number of arguments of arbitrarily complex structure.
677
678
679\subsection{Tuple Assignment}
680
681An assignment where the left side is a tuple type is called \newterm{tuple assignment}.
682There are two kinds of tuple assignment depending on whether the right side of the assignment operator has a tuple type or a non-tuple type, called \newterm{multiple} and \newterm{mass assignment}, respectively.
683\begin{cfa}
684int x = 10;
685double y = 3.5;
686[int, double] z;
687z = [x, y];                                                                     $\C{// multiple assignment}$
688[x, y] = z;                                                                     $\C{// multiple assignment}$
689z = 10;                                                                         $\C{// mass assignment}$
690[y, x] = 3.14;                                                          $\C{// mass assignment}$
691\end{cfa}
692Both kinds of tuple assignment have parallel semantics, so that each value on the left and right side is evaluated before any assignments occur.
693As a result, it is possible to swap the values in two variables without explicitly creating any temporary variables or calling a function, \eg, @[x, y] = [y, x]@.
694This semantics means mass assignment differs from C cascading assignment (\eg @a = b = c@) in that conversions are applied in each individual assignment, which prevents data loss from the chain of conversions that can happen during a cascading assignment.
695For example, @[y, x] = 3.14@ performs the assignments @y = 3.14@ and @x = 3.14@, yielding @y == 3.14@ and @x == 3@;
696whereas, C cascading assignment @y = x = 3.14@ performs the assignments @x = 3.14@ and @y = x@, yielding @3@ in @y@ and @x@.
697Finally, tuple assignment is an expression where the result type is the type of the left-hand side of the assignment, just like all other assignment expressions in C.
698This example shows mass, multiple, and cascading assignment used in one expression:
699\begin{cfa}
700void f( [int, int] );
701f( [x, y] = z = 1.5 );                                          $\C{// assignments in parameter list}$
702\end{cfa}
703
704
705\subsection{Member Access}
706
707It is also possible to access multiple fields from a single expression using a \newterm{member-access}.
708The result is a single tuple-valued expression whose type is the tuple of the types of the members, \eg:
709\begin{cfa}
710struct S { int x; double y; char * z; } s;
711s.[x, y, z] = 0;
712\end{cfa}
713Here, the mass assignment sets all members of @s@ to zero.
714Since tuple-index expressions are a form of member-access expression, it is possible to use tuple-index expressions in conjunction with member tuple expressions to manually restructure a tuple (\eg rearrange, drop, and duplicate components).
715\begin{cfa}
716[int, int, long, double] x;
717void f( double, long );
718x.[0, 1] = x.[1, 0];                                            $\C{// rearrange: [x.0, x.1] = [x.1, x.0]}$
719f( x.[0, 3] );                                                          $\C{// drop: f(x.0, x.3)}$
720[int, int, int] y = x.[2, 0, 2];                        $\C{// duplicate: [y.0, y.1, y.2] = [x.2, x.0.x.2]}$
721\end{cfa}
722It is also possible for a member access to contain other member accesses, \eg:
723\begin{cfa}
724struct A { double i; int j; };
725struct B { int * k; short l; };
726struct C { int x; A y; B z; } v;
727v.[x, y.[i, j], z.k];                                           $\C{// [v.x, [v.y.i, v.y.j], v.z.k]}$
728\end{cfa}
729
730
731\begin{comment}
732\subsection{Casting}
733
734In C, the cast operator is used to explicitly convert between types.
735In \CFA, the cast operator has a secondary use as type ascription.
736That is, a cast can be used to select the type of an expression when it is ambiguous, as in the call to an overloaded function:
737\begin{cfa}
738int f();     // (1)
739double f()// (2)
740
741f();       // ambiguous - (1),(2) both equally viable
742(int)f()// choose (2)
743\end{cfa}
744
745Since casting is a fundamental operation in \CFA, casts should be given a meaningful interpretation in the context of tuples.
746Taking a look at standard C provides some guidance with respect to the way casts should work with tuples:
747\begin{cfa}
748int f();
749void g();
750
751(void)f()// (1)
752(int)g()// (2)
753\end{cfa}
754In C, (1) is a valid cast, which calls @f@ and discards its result.
755On the other hand, (2) is invalid, because @g@ does not produce a result, so requesting an @int@ to materialize from nothing is nonsensical.
756Generalizing these principles, any cast wherein the number of components increases as a result of the cast is invalid, while casts that have the same or fewer number of components may be valid.
757
758Formally, a cast to tuple type is valid when $T_n \leq S_m$, where $T_n$ is the number of components in the target type and $S_m$ is the number of components in the source type, and for each $i$ in $[0, n)$, $S_i$ can be cast to $T_i$.
759Excess elements ($S_j$ for all $j$ in $[n, m)$) are evaluated, but their values are discarded so that they are not included in the result expression.
760This approach follows naturally from the way that a cast to @void@ works in C.
761
762For example, in
763\begin{cfa}
764[int, int, int] f();
765[int, [int, int], int] g();
766
767([int, double])f();           $\C{// (1)}$
768([int, int, int])g();         $\C{// (2)}$
769([void, [int, int]])g();      $\C{// (3)}$
770([int, int, int, int])g();    $\C{// (4)}$
771([int, [int, int, int]])g()$\C{// (5)}$
772\end{cfa}
773
774(1) discards the last element of the return value and converts the second element to @double@.
775Since @int@ is effectively a 1-element tuple, (2) discards the second component of the second element of the return value of @g@.
776If @g@ is free of side effects, this expression is equivalent to @[(int)(g().0), (int)(g().1.0), (int)(g().2)]@.
777Since @void@ is effectively a 0-element tuple, (3) discards the first and third return values, which is effectively equivalent to @[(int)(g().1.0), (int)(g().1.1)]@).
778
779Note that a cast is not a function call in \CFA, so flattening and structuring conversions do not occur for cast expressions\footnote{User-defined conversions have been considered, but for compatibility with C and the existing use of casts as type ascription, any future design for such conversions requires more precise matching of types than allowed for function arguments and parameters.}.
780As such, (4) is invalid because the cast target type contains 4 components, while the source type contains only 3.
781Similarly, (5) is invalid because the cast @([int, int, int])(g().1)@ is invalid.
782That is, it is invalid to cast @[int, int]@ to @[int, int, int]@.
783\end{comment}
784
785
786\subsection{Polymorphism}
787
788Tuples also integrate with \CFA polymorphism as a kind of generic type.
789Due to the implicit flattening and structuring conversions involved in argument passing, @otype@ and @dtype@ parameters are restricted to matching only with non-tuple types, \eg:
790\begin{cfa}
791forall( otype T, dtype U ) void f( T x, U * y );
792f( [5, "hello"] );
793\end{cfa}
794where @[5, "hello"]@ is flattened, giving argument list @5, "hello"@, and @T@ binds to @int@ and @U@ binds to @const char@.
795Tuples, however, may contain polymorphic components.
796For example, a plus operator can be written to sum two triples.
797\begin{cfa}
798forall( otype T | { T ?+?( T, T ); } ) [T, T, T] ?+?( [T, T, T] x, [T, T, T] y ) {
799        return [x.0 + y.0, x.1 + y.1, x.2 + y.2];
800}
801[int, int, int] x;
802int i1, i2, i3;
803[i1, i2, i3] = x + ([10, 20, 30]);
804\end{cfa}
805
806Flattening and restructuring conversions are also applied to tuple types in polymorphic type assertions.
807\begin{cfa}
808int f( [int, double], double );
809forall( otype T, otype U | { T f( T, U, U ); } ) void g( T, U );
810g( 5, 10.21 );
811\end{cfa}
812Hence, function parameter and return lists are flattened for the purposes of type unification allowing the example to pass expression resolution.
813This relaxation is possible by extending the thunk scheme described by Bilson~\cite{Bilson03}.
814% Whenever a candidate's parameter structure does not exactly match the formal parameter's structure, a thunk is generated to specialize calls to the actual function:
815% \begin{cfa}
816% int _thunk( int _p0, double _p1, double _p2 ) { return f( [_p0, _p1], _p2 ); }
817% \end{cfa}
818% so the thunk provides flattening and structuring conversions to inferred functions, improving the compatibility of tuples and polymorphism.
819% These thunks are generated locally using gcc nested-functions, rather hoisting them to the external scope, so they can easily access local state.
820
821
822\subsection{Variadic Tuples}
823\label{sec:variadic-tuples}
824
825To define variadic functions, \CFA adds a new kind of type parameter, @ttype@ (tuple type).
826Matching against a @ttype@ parameter consumes all remaining argument components and packages them into a tuple, binding to the resulting tuple of types.
827In a given parameter list, there must be at most one @ttype@ parameter that occurs last, which matches normal variadic semantics, with a strong feeling of similarity to \CCeleven variadic templates.
828As such, @ttype@ variables are also called \newterm{argument packs}.
829
830Like variadic templates, @ttype@ polymorphic functions are primarily manipulated via recursion.
831Since nothing is known about a parameter pack by default, assertion parameters are key to doing anything meaningful.
832Unlike variadic templates, @ttype@ polymorphic functions can be separately compiled.
833For example, a generalized @sum@ function:
834\begin{cfa}
835int sum$\(_0\)$() { return 0; }
836forall( ttype Params | { int sum( Params ); } ) int sum$\(_1\)$( int x, Params rest ) {
837        return x + sum( rest );
838}
839sum( 10, 20, 30 );
840\end{cfa}
841Since @sum@\(_0\) does not accept any arguments, it is not a valid candidate function for the call @sum(10, 20, 30)@.
842In order to call @sum@\(_1\), @10@ is matched with @x@, and the argument resolution moves on to the argument pack @rest@, which consumes the remainder of the argument list and @Params@ is bound to @[20, 30]@.
843The process continues until @Params@ is bound to @[]@, requiring an assertion @int sum()@, which matches @sum@\(_0\) and terminates the recursion.
844Effectively, this algorithm traces as @sum(10, 20, 30)@ $\rightarrow$ @10 + sum(20, 30)@ $\rightarrow$ @10 + (20 + sum(30))@ $\rightarrow$ @10 + (20 + (30 + sum()))@ $\rightarrow$ @10 + (20 + (30 + 0))@.
845
846It is reasonable to take the @sum@ function a step further to enforce a minimum number of arguments:
847\begin{cfa}
848int sum( int x, int y ) { return x + y; }
849forall( ttype Params | { int sum( int, Params ); } ) int sum( int x, int y, Params rest ) {
850        return sum( x + y, rest );
851}
852\end{cfa}
853One more step permits the summation of any summable type with all arguments of the same type:
854\begin{cfa}
855trait summable( otype T ) {
856        T ?+?( T, T );
857};
858forall( otype R | summable( R ) ) R sum( R x, R y ) {
859        return x + y;
860}
861forall( otype R, ttype Params | summable(R) | { R sum(R, Params); } ) R sum(R x, R y, Params rest) {
862        return sum( x + y, rest );
863}
864\end{cfa}
865Unlike C variadic functions, it is unnecessary to hard code the number and expected types.
866Furthermore, this code is extendable for any user-defined type with a @?+?@ operator.
867Summing arbitrary heterogeneous lists is possible with similar code by adding the appropriate type variables and addition operators.
868
869It is also possible to write a type-safe variadic print function to replace @printf@:
870\begin{cfa}
871struct S { int x, y; };
872forall( otype T, ttype Params | { void print(T); void print(Params); } ) void print(T arg, Params rest) {
873        print(arg);  print(rest);
874}
875void print( const char * x ) { printf( "%s", x ); }
876void print( int x ) { printf( "%d", x ); }
877void print( S s ) { print( "{ ", s.x, ",", s.y, " }" ); }
878print( "s = ", (S){ 1, 2 }, "\n" );
879\end{cfa}
880This example showcases a variadic-template-like decomposition of the provided argument list.
881The individual @print@ functions allow printing a single element of a type.
882The polymorphic @print@ allows printing any list of types, where as each individual type has a @print@ function.
883The individual print functions can be used to build up more complicated @print@ functions, such as @S@, which cannot be done with @printf@ in C.
884This mechanism is used to seamlessly print tuples in the \CFA I/O library (see Section~\ref{s:IOLibrary}).
885
886Finally, it is possible to use @ttype@ polymorphism to provide arbitrary argument forwarding functions.
887For example, it is possible to write @new@ as a library function:
888\begin{cfa}
889forall( otype R, otype S ) void ?{}( pair(R, S) *, R, S );
890forall( dtype T, ttype Params | sized(T) | { void ?{}( T *, Params ); } ) T * new( Params p ) {
891        return ((T *)malloc()){ p };                    $\C{// construct into result of malloc}$
892}
893pair( int, char ) * x = new( 42, '!' );
894\end{cfa}
895The @new@ function provides the combination of type-safe @malloc@ with a \CFA constructor call, making it impossible to forget constructing dynamically allocated objects.
896This function provides the type-safety of @new@ in \CC, without the need to specify the allocated type again, thanks to return-type inference.
897
898
899\subsection{Implementation}
900
901Tuples are implemented in the \CFA translator via a transformation into \newterm{generic types}.
902For each $N$, the first time an $N$-tuple is seen in a scope a generic type with $N$ type parameters is generated, \eg:
903\begin{cfa}
904[int, int] f() {
905        [double, double] x;
906        [int, double, int] y;
907}
908\end{cfa}
909is transformed into:
910\begin{cfa}
911forall( dtype T0, dtype T1 | sized(T0) | sized(T1) ) struct _tuple2 {
912        T0 field_0;                                                             $\C{// generated before the first 2-tuple}$
913        T1 field_1;
914};
915_tuple2(int, int) f() {
916        _tuple2(double, double) x;
917        forall( dtype T0, dtype T1, dtype T2 | sized(T0) | sized(T1) | sized(T2) ) struct _tuple3 {
918                T0 field_0;                                                     $\C{// generated before the first 3-tuple}$
919                T1 field_1;
920                T2 field_2;
921        };
922        _tuple3(int, double, int) y;
923}
924\end{cfa}
925{\sloppy
926Tuple expressions are then simply converted directly into compound literals, \eg @[5, 'x', 1.24]@ becomes @(_tuple3(int, char, double)){ 5, 'x', 1.24 }@.
927\par}%
928
929\begin{comment}
930Since tuples are essentially structures, tuple indexing expressions are just field accesses:
931\begin{cfa}
932void f(int, [double, char]);
933[int, double] x;
934
935x.0+x.1;
936printf("%d %g\n", x);
937f(x, 'z');
938\end{cfa}
939Is transformed into:
940\begin{cfa}
941void f(int, _tuple2(double, char));
942_tuple2(int, double) x;
943
944x.field_0+x.field_1;
945printf("%d %g\n", x.field_0, x.field_1);
946f(x.field_0, (_tuple2){ x.field_1, 'z' });
947\end{cfa}
948Note that due to flattening, @x@ used in the argument position is converted into the list of its fields.
949In the call to @f@, the second and third argument components are structured into a tuple argument.
950Similarly, tuple member expressions are recursively expanded into a list of member access expressions.
951
952Expressions that may contain side effects are made into \newterm{unique expressions} before being expanded by the flattening conversion.
953Each unique expression is assigned an identifier and is guaranteed to be executed exactly once:
954\begin{cfa}
955void g(int, double);
956[int, double] h();
957g(h());
958\end{cfa}
959Internally, this expression is converted to two variables and an expression:
960\begin{cfa}
961void g(int, double);
962[int, double] h();
963
964_Bool _unq0_finished_ = 0;
965[int, double] _unq0;
966g(
967        (_unq0_finished_ ? _unq0 : (_unq0 = f(), _unq0_finished_ = 1, _unq0)).0,
968        (_unq0_finished_ ? _unq0 : (_unq0 = f(), _unq0_finished_ = 1, _unq0)).1,
969);
970\end{cfa}
971Since argument evaluation order is not specified by the C programming language, this scheme is built to work regardless of evaluation order.
972The first time a unique expression is executed, the actual expression is evaluated and the accompanying boolean is set to true.
973Every subsequent evaluation of the unique expression then results in an access to the stored result of the actual expression.
974Tuple member expressions also take advantage of unique expressions in the case of possible impurity.
975
976Currently, the \CFA translator has a very broad, imprecise definition of impurity, where any function call is assumed to be impure.
977This notion could be made more precise for certain intrinsic, auto-generated, and builtin functions, and could analyze function bodies when they are available to recursively detect impurity, to eliminate some unique expressions.
978
979The various kinds of tuple assignment, constructors, and destructors generate GNU C statement expressions.
980A variable is generated to store the value produced by a statement expression, since its fields may need to be constructed with a non-trivial constructor and it may need to be referred to multiple time, \eg in a unique expression.
981The use of statement expressions allows the translator to arbitrarily generate additional temporary variables as needed, but binds the implementation to a non-standard extension of the C language.
982However, there are other places where the \CFA translator makes use of GNU C extensions, such as its use of nested functions, so this restriction is not new.
983\end{comment}
984
985
986\section{Control Structures}
987
988\CFA identifies inconsistent, problematic, and missing control structures in C, and extends, modifies, and adds control structures to increase functionality and safety.
989
990
991\subsection{\texorpdfstring{\protect\lstinline{if} Statement}{if Statement}}
992
993The @if@ expression allows declarations, similar to @for@ declaration expression:
994\begin{cfa}
995if ( int x = f() ) ...                                          $\C{// x != 0}$
996if ( int x = f(), y = g() ) ...                         $\C{// x != 0 \&\& y != 0}$
997if ( int x = f(), y = g(); `x < y` ) ...        $\C{// relational expression}$
998\end{cfa}
999Unless a relational expression is specified, each variable is compared not equal to 0, which is the standard semantics for the @if@ expression, and the results are combined using the logical @&&@ operator.\footnote{\CC only provides a single declaration always compared not equal to 0.}
1000The scope of the declaration(s) is local to the @if@ statement but exist within both the ``then'' and ``else'' clauses.
1001
1002
1003\subsection{\texorpdfstring{\protect\lstinline{switch} Statement}{switch Statement}}
1004
1005There are a number of deficiencies with the C @switch@ statements: enumerating @case@ lists, placement of @case@ clauses, scope of the switch body, and fall through between case clauses.
1006
1007C has no shorthand for specifying a list of case values, whether the list is non-contiguous or contiguous\footnote{C provides this mechanism via fall through.}.
1008\CFA provides a shorthand for a non-contiguous list:
1009\begin{cquote}
1010\lstDeleteShortInline@%
1011\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
1012\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
1013\begin{cfa}
1014case 2, 10, 34, 42:
1015\end{cfa}
1016&
1017\begin{cfa}
1018case 2: case 10: case 34: case 42:
1019\end{cfa}
1020\end{tabular}
1021\lstMakeShortInline@%
1022\end{cquote}
1023for a contiguous list:\footnote{gcc has the same mechanism but awkward syntax, \lstinline@2 ...42@, because a space is required after a number, otherwise the period is a decimal point.}
1024\begin{cquote}
1025\lstDeleteShortInline@%
1026\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
1027\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
1028\begin{cfa}
1029case 2~42:
1030\end{cfa}
1031&
1032\begin{cfa}
1033case 2: case 3: ... case 41: case 42:
1034\end{cfa}
1035\end{tabular}
1036\lstMakeShortInline@%
1037\end{cquote}
1038and a combination:
1039\begin{cfa}
1040case -12~-4, -1~5, 14~21, 34~42:
1041\end{cfa}
1042
1043C allows placement of @case@ clauses \emph{within} statements nested in the @switch@ body (called Duff's device~\cite{Duff83});
1044\begin{cfa}
1045switch ( i ) {
1046  case 0:
1047        for ( int i = 0; i < 10; i += 1 ) {
1048                ...
1049  `case 1:`             // no initialization of loop index
1050                ...
1051        }
1052}
1053\end{cfa}
1054\CFA precludes this form of transfer \emph{into} a control structure because it causes undefined behaviour, especially with respect to missed initialization, and provides very limited functionality.
1055
1056C allows placement of declaration within the @switch@ body and unreachable code at the start, resulting in undefined behaviour:
1057\begin{cfa}
1058switch ( x ) {
1059        `int y = 1;`                                                    $\C{// unreachable initialization}$
1060        `x = 7;`                                                                $\C{// unreachable code without label/branch}$
1061  case 0:
1062        ...
1063        `int z = 0;`                                                    $\C{// unreachable initialization, cannot appear after case}$
1064        z = 2;
1065  case 1:
1066        `x = z;`                                                                $\C{// without fall through, z is undefined}$
1067}
1068\end{cfa}
1069\CFA allows the declaration of local variables, \eg @y@, at the start of the @switch@ with scope across the entire @switch@ body, \ie all @case@ clauses.
1070\CFA disallows the declaration of local variable, \eg @z@, directly within the @switch@ body, because a declaration cannot occur immediately after a @case@ since a label can only be attached to a statement, and the use of @z@ is undefined in @case 1@ as neither storage allocation nor initialization may have occurred.
1071
1072C @switch@ provides multiple entry points into the statement body, but once an entry point is selected, control continues across \emph{all} @case@ clauses until the end of the @switch@ body, called \newterm{fall through};
1073@case@ clauses are made disjoint by the @break@ statement.
1074While fall through \emph{is} a useful form of control flow, it does not match well with programmer intuition, resulting in errors from missing @break@ statements.
1075For backwards compatibility, \CFA provides a \emph{new} control structure, @choose@, which mimics @switch@, but reverses the meaning of fall through (see Figure~\ref{f:ChooseSwitchStatements}), similar to Go.
1076
1077\begin{figure}
1078\centering
1079\lstDeleteShortInline@%
1080\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
1081\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
1082\begin{cfa}
1083`choose` ( day ) {
1084  case Mon~Thu:  // program
1085
1086  case Fri:  // program
1087        wallet += pay;
1088        `fallthrough;`
1089  case Sat:  // party
1090        wallet -= party;
1091
1092  case Sun:  // rest
1093
1094  default:  // error
1095}
1096\end{cfa}
1097&
1098\begin{cfa}
1099switch ( day ) {
1100  case Mon: case Tue: case Wed: case Thu:  // program
1101        `break;`
1102  case Fri:  // program
1103        wallet += pay;
1104
1105  case Sat:  // party
1106        wallet -= party;
1107        `break;`
1108  case Sun:  // rest
1109        `break;`
1110  default:  // error
1111}
1112\end{cfa}
1113\end{tabular}
1114\lstMakeShortInline@%
1115\caption{\lstinline|choose| versus \lstinline|switch| Statements}
1116\label{f:ChooseSwitchStatements}
1117\end{figure}
1118
1119Finally, Figure~\ref{f:FallthroughStatement} shows @fallthrough@ may appear in contexts other than terminating a @case@ clause, and have an explicit transfer label allowing separate cases but common final-code for a set of cases.
1120The target label must be below the @fallthrough@, \ie @fallthrough@ cannot form a loop, and the label may not be nested in a control structure, \ie it must be at the same level as the @case@ clauses;
1121the target label may be case @default@.
1122
1123\begin{figure}
1124\centering
1125\lstDeleteShortInline@%
1126\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
1127\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{non-terminator}}  & \multicolumn{1}{c}{\textbf{target label}}     \\
1128\begin{cfa}
1129choose ( ... ) {
1130  case 3:
1131        if ( ... ) {
1132                ... `fallthrough;`  // goto case 4
1133        } else {
1134                ...
1135        }
1136        // implicit break
1137  case 4:
1138\end{cfa}
1139&
1140\begin{cfa}
1141choose ( ... ) {
1142  case 3:
1143        ... `fallthrough common;`
1144  case 4:
1145        ... `fallthrough common;`
1146  common: // below fallthrough at same level as case clauses
1147        ...      // common code for cases 3 and 4
1148        // implicit break
1149  case 4:
1150\end{cfa}
1151\end{tabular}
1152\lstMakeShortInline@%
1153\caption{\lstinline|fallthrough| Statement}
1154\label{f:FallthroughStatement}
1155\end{figure}
1156
1157Collectively, these control-structure enhancements reduce programmer burden and increase readability and safety.
1158
1159
1160\subsection{\texorpdfstring{Labelled \protect\lstinline{continue} / \protect\lstinline{break}}{Labelled continue / break}}
1161
1162While C provides @continue@ and @break@ statements for altering control flow, both are restricted to one level of nesting for a particular control structure.
1163Unfortunately, this restriction forces programmers to use @goto@ to achieve the equivalent control-flow for more than one level of nesting.
1164To prevent having to switch to the @goto@, \CFA extends the @continue@ and @break@ with a target label to support static multi-level exit~\cite{Buhr85}, as in Java.
1165For both @continue@ and @break@, the target label must be directly associated with a @for@, @while@ or @do@ statement;
1166for @break@, the target label can also be associated with a @switch@, @if@ or compound (@{}@) statement.
1167Figure~\ref{f:MultiLevelExit} shows @continue@ and @break@ indicating the specific control structure, and the corresponding C program using only @goto@ and labels.
1168The innermost loop has 7 exit points, which cause continuation or termination of one or more of the 7 nested control-structures.
1169
1170\begin{figure}
1171\lstDeleteShortInline@%
1172\begin{tabular}{@{\hspace{\parindentlnth}}l@{\hspace{\parindentlnth}}l@{\hspace{\parindentlnth}}l@{}}
1173\multicolumn{1}{@{\hspace{\parindentlnth}}c@{\hspace{\parindentlnth}}}{\textbf{\CFA}}   & \multicolumn{1}{@{\hspace{\parindentlnth}}c}{\textbf{C}}      \\
1174\begin{cfa}
1175`LC:` {
1176        ... $declarations$ ...
1177        `LS:` switch ( ... ) {
1178          case 3:
1179                `LIF:` if ( ... ) {
1180                        `LF:` for ( ... ) {
1181                                `LW:` while ( ... ) {
1182                                        ... break `LC`; ...
1183                                        ... break `LS`; ...
1184                                        ... break `LIF`; ...
1185                                        ... continue `LF;` ...
1186                                        ... break `LF`; ...
1187                                        ... continue `LW`; ...
1188                                        ... break `LW`; ...
1189                                } // while
1190                        } // for
1191                } else {
1192                        ... break `LIF`; ...
1193                } // if
1194        } // switch
1195} // compound
1196\end{cfa}
1197&
1198\begin{cfa}
1199{
1200        ... $declarations$ ...
1201        switch ( ... ) {
1202          case 3:
1203                if ( ... ) {
1204                        for ( ... ) {
1205                                while ( ... ) {
1206                                        ... goto `LC`; ...
1207                                        ... goto `LS`; ...
1208                                        ... goto `LIF`; ...
1209                                        ... goto `LFC`; ...
1210                                        ... goto `LFB`; ...
1211                                        ... goto `LWC`; ...
1212                                        ... goto `LWB`; ...
1213                                  `LWC`: ; } `LWB:` ;
1214                          `LFC:` ; } `LFB:` ;
1215                } else {
1216                        ... goto `LIF`; ...
1217                } `LIF:` ;
1218        } `LS:` ;
1219} `LC:` ;
1220\end{cfa}
1221&
1222\begin{cfa}
1223
1224
1225
1226
1227
1228
1229
1230// terminate compound
1231// terminate switch
1232// terminate if
1233// continue loop
1234// terminate loop
1235// continue loop
1236// terminate loop
1237
1238
1239
1240// terminate if
1241
1242
1243
1244\end{cfa}
1245\end{tabular}
1246\lstMakeShortInline@%
1247\caption{Multi-level Exit}
1248\label{f:MultiLevelExit}
1249\end{figure}
1250
1251With respect to safety, both labelled @continue@ and @break@ are a @goto@ restricted in the following ways:
1252\begin{itemize}
1253\item
1254They cannot create a loop, which means only the looping constructs cause looping.
1255This restriction means all situations resulting in repeated execution are clearly delineated.
1256\item
1257They cannot branch into a control structure.
1258This restriction prevents missing declarations and/or initializations at the start of a control structure resulting in undefined behaviour.
1259\end{itemize}
1260The advantage of the labelled @continue@/@break@ is allowing static multi-level exits without having to use the @goto@ statement, and tying control flow to the target control structure rather than an arbitrary point in a program.
1261Furthermore, the location of the label at the \emph{beginning} of the target control structure informs the reader (eye candy) that complex control-flow is occurring in the body of the control structure.
1262With @goto@, the label is at the end of the control structure, which fails to convey this important clue early enough to the reader.
1263Finally, using an explicit target for the transfer instead of an implicit target allows new constructs to be added or removed without affecting existing constructs.
1264Otherwise, the implicit targets of the current @continue@ and @break@, \ie the closest enclosing loop or @switch@, change as certain constructs are added or removed.
1265
1266
1267\subsection{Exception Handling}
1268
1269The following framework for \CFA exception handling is in place, excluding some runtime type-information and virtual functions.
1270\CFA provides two forms of exception handling: \newterm{fix-up} and \newterm{recovery} (see Figure~\ref{f:CFAExceptionHandling})~\cite{Buhr92b,Buhr00a}.
1271Both mechanisms provide dynamic call to a handler using dynamic name-lookup, where fix-up has dynamic return and recovery has static return from the handler.
1272\CFA restricts exception types to those defined by aggregate type @exception@.
1273The form of the raise dictates the set of handlers examined during propagation: \newterm{resumption propagation} (@resume@) only examines resumption handlers (@catchResume@); \newterm{terminating propagation} (@throw@) only examines termination handlers (@catch@).
1274If @resume@ or @throw@ have no exception type, it is a reresume/rethrow, meaning the currently exception continues propagation.
1275If there is no current exception, the reresume/rethrow results in a runtime error.
1276
1277\begin{figure}
1278\begin{cquote}
1279\lstDeleteShortInline@%
1280\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
1281\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{Resumption}}      & \multicolumn{1}{c}{\textbf{Termination}}      \\
1282\begin{cfa}
1283`exception R { int fix; };`
1284void f() {
1285        R r;
1286        ... `resume( r );` ...
1287        ... r.fix // control returns here after handler
1288}
1289`try` {
1290        ... f(); ...
1291} `catchResume( R r )` {
1292        ... r.fix = ...; // return correction to raise
1293} // dynamic return to _Resume
1294\end{cfa}
1295&
1296\begin{cfa}
1297`exception T {};`
1298void f() {
1299
1300        ... `throw( T{} );` ...
1301        // control does NOT return here after handler
1302}
1303`try` {
1304        ... f(); ...
1305} `catch( T t )` {
1306        ... // recover and continue
1307} // static return to next statement
1308\end{cfa}
1309\end{tabular}
1310\lstMakeShortInline@%
1311\end{cquote}
1312\caption{\CFA Exception Handling}
1313\label{f:CFAExceptionHandling}
1314\end{figure}
1315
1316The set of exception types in a list of catch clause may include both a resumption and termination handler:
1317\begin{cfa}
1318try {
1319        ... resume( `R{}` ); ...
1320} catchResume( `R` r ) { ... throw( R{} ); ... } $\C{\color{red}// H1}$
1321   catch( `R` r ) { ... }                                       $\C{\color{red}// H2}$
1322
1323\end{cfa}
1324The resumption propagation raises @R@ and the stack is not unwound;
1325the exception is caught by the @catchResume@ clause and handler H1 is invoked.
1326The termination propagation in handler H1 raises @R@ and the stack is unwound;
1327the exception is caught by the @catch@ clause and handler H2 is invoked.
1328The termination handler is available because the resumption propagation did not unwind the stack.
1329
1330An additional feature is conditional matching in a catch clause:
1331\begin{cfa}
1332try {
1333        ... write( `datafile`, ... ); ...               $\C{// may throw IOError}$
1334        ... write( `logfile`, ... ); ...
1335} catch ( IOError err; `err.file == datafile` ) { ... } $\C{// handle datafile error}$
1336   catch ( IOError err; `err.file == logfile` ) { ... } $\C{// handle logfile error}$
1337   catch ( IOError err ) { ... }                        $\C{// handler error from other files}$
1338\end{cfa}
1339where the throw inserts the failing file-handle into the I/O exception.
1340Conditional catch cannot be trivially mimicked by other mechanisms because once an exception is caught, handler clauses in that @try@ statement are no longer eligible..
1341
1342The resumption raise can specify an alternate stack on which to raise an exception, called a \newterm{nonlocal raise}:
1343\begin{cfa}
1344resume( $\emph{exception-type}$, $\emph{alternate-stack}$ )
1345resume( $\emph{alternate-stack}$ )
1346\end{cfa}
1347These overloads of @resume@ raise the specified exception or the currently propagating exception (reresume) at another \CFA coroutine or task\footnote{\CFA coroutine and concurrency features are discussed in a separately submitted paper.}~\cite{Delisle18}.
1348Nonlocal raise is restricted to resumption to provide the exception handler the greatest flexibility because processing the exception does not unwind its stack, allowing it to continue after the handler returns.
1349
1350To facilitate nonlocal raise, \CFA provides dynamic enabling and disabling of nonlocal exception-propagation.
1351The constructs for controlling propagation of nonlocal exceptions are the @enable@ and the @disable@ blocks:
1352\begin{cquote}
1353\lstDeleteShortInline@%
1354\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
1355\begin{cfa}
1356enable $\emph{exception-type-list}$ {
1357        // allow non-local raise
1358}
1359\end{cfa}
1360&
1361\begin{cfa}
1362disable $\emph{exception-type-list}$ {
1363        // disallow non-local raise
1364}
1365\end{cfa}
1366\end{tabular}
1367\lstMakeShortInline@%
1368\end{cquote}
1369The arguments for @enable@/@disable@ specify the exception types allowed to be propagated or postponed, respectively.
1370Specifying no exception type is shorthand for specifying all exception types.
1371Both @enable@ and @disable@ blocks can be nested, turning propagation on/off on entry, and on exit, the specified exception types are restored to their prior state.
1372Coroutines and tasks start with non-local exceptions disabled, allowing handlers to be put in place, before non-local exceptions are explicitly enabled.
1373\begin{cfa}
1374void main( mytask & t ) {                                       $\C{// thread starts here}$
1375        // non-local exceptions disabled
1376        try {                                                                   $\C{// establish handles for non-local exceptions}$
1377                enable {                                                        $\C{// allow non-local exception delivery}$
1378                        // task body
1379                }
1380        // appropriate catchResume/catch handlers
1381        }
1382}
1383\end{cfa}
1384
1385Finally, \CFA provides a Java like  @finally@ clause after the catch clauses:
1386\begin{cfa}
1387try {
1388        ... f(); ...
1389// catchResume or catch clauses
1390} `finally` {
1391        // house keeping
1392}
1393\end{cfa}
1394The finally clause is always executed, i.e., if the try block ends normally or if an exception is raised.
1395If an exception is raised and caught, the handler is run before the finally clause.
1396Like a destructor (see Section~\ref{s:ConstructorsDestructors}), a finally clause can raise an exception but not if there is an exception being propagated.
1397Mimicking the @finally@ clause with mechanisms like RAII is non-trivially when there are multiple types and local accesses.
1398
1399
1400\subsection{\texorpdfstring{\protect\lstinline{with} Statement}{with Statement}}
1401\label{s:WithStatement}
1402
1403Grouping heterogeneous data into \newterm{aggregate}s (structure/union) is a common programming practice, and an aggregate can be further organized into more complex structures, such as arrays and containers:
1404\begin{cfa}
1405struct S {                                                                      $\C{// aggregate}$
1406        char c;                                                                 $\C{// fields}$
1407        int i;
1408        double d;
1409};
1410S s, as[10];
1411\end{cfa}
1412However, functions manipulating aggregates must repeat the aggregate name to access its containing fields:
1413\begin{cfa}
1414void f( S s ) {
1415        `s.`c; `s.`i; `s.`d;                                    $\C{// access containing fields}$
1416}
1417\end{cfa}
1418which extends to multiple levels of qualification for nested aggregates.
1419A similar situation occurs in object-oriented programming, \eg \CC:
1420\begin{C++}
1421struct S {
1422        char c;                                                                 $\C{// fields}$
1423        int i;
1424        double d;
1425        void f() {                                                              $\C{// implicit ``this'' aggregate}$
1426                `this->`c; `this->`i; `this->`d;        $\C{// access containing fields}$
1427        }
1428}
1429\end{C++}
1430Object-oriented nesting of member functions in a \lstinline[language=C++]@class/struct@ allows eliding \lstinline[language=C++]@this->@ because of lexical scoping.
1431However, for other aggregate parameters, qualification is necessary:
1432\begin{cfa}
1433struct T { double m, n; };
1434int S::f( T & t ) {                                                     $\C{// multiple aggregate parameters}$
1435        c; i; d;                                                                $\C{\color{red}// this--{\textgreater}.c, this--{\textgreater}.i, this--{\textgreater}.d}$
1436        `t.`m; `t.`n;                                                   $\C{// must qualify}$
1437}
1438\end{cfa}
1439
1440To simplify the programmer experience, \CFA provides a @with@ statement (see Pascal~\cite[\S~4.F]{Pascal}) to elide aggregate qualification to fields by opening a scope containing the field identifiers.
1441Hence, the qualified fields become variables with the side-effect that it is easier to optimizing field references in a block.
1442\begin{cfa}
1443void f( S & this ) `with ( this )` {            $\C{// with statement}$
1444        c; i; d;                                                                $\C{\color{red}// this.c, this.i, this.d}$
1445}
1446\end{cfa}
1447with the generality of opening multiple aggregate-parameters:
1448\begin{cfa}
1449void f( S & s, T & t ) `with ( s, t )` {                $\C{// multiple aggregate parameters}$
1450        c; i; d;                                                                $\C{\color{red}// s.c, s.i, s.d}$
1451        m; n;                                                                   $\C{\color{red}// t.m, t.n}$
1452}
1453\end{cfa}
1454
1455In detail, the @with@ statement has the form:
1456\begin{cfa}
1457$\emph{with-statement}$:
1458        'with' '(' $\emph{expression-list}$ ')' $\emph{compound-statement}$
1459\end{cfa}
1460and may appear as the body of a function or nested within a function body.
1461Each expression in the expression-list provides a type and object.
1462The type must be an aggregate type.
1463(Enumerations are already opened.)
1464The object is the implicit qualifier for the open structure-fields.
1465
1466All expressions in the expression list are open in parallel within the compound statement.
1467This semantic is different from Pascal, which nests the openings from left to right.
1468The difference between parallel and nesting occurs for fields with the same name and type:
1469\begin{cfa}
1470struct S { int `i`; int j; double m; } s, w;
1471struct T { int `i`; int k; int m; } t, w;
1472with ( s, t ) {
1473        j + k;                                                                  $\C{// unambiguous, s.j + t.k}$
1474        m = 5.0;                                                                $\C{// unambiguous, t.m = 5.0}$
1475        m = 1;                                                                  $\C{// unambiguous, s.m = 1}$
1476        int a = m;                                                              $\C{// unambiguous, a = s.i }$
1477        double b = m;                                                   $\C{// unambiguous, b = t.m}$
1478        int c = s.i + t.i;                                              $\C{// unambiguous, qualification}$
1479        (double)m;                                                              $\C{// unambiguous, cast}$
1480}
1481\end{cfa}
1482For parallel semantics, both @s.i@ and @t.i@ are visible, so @i@ is ambiguous without qualification;
1483for nested semantics, @t.i@ hides @s.i@, so @i@ implies @t.i@.
1484\CFA's ability to overload variables means fields with the same name but different types are automatically disambiguated, eliminating most qualification when opening multiple aggregates.
1485Qualification or a cast is used to disambiguate.
1486
1487There is an interesting problem between parameters and the function-body @with@, \eg:
1488\begin{cfa}
1489void ?{}( S & s, int i ) with ( s ) {           $\C{// constructor}$
1490        `s.i = i;`  j = 3;  m = 5.5;                    $\C{// initialize fields}$
1491}
1492\end{cfa}
1493Here, the assignment @s.i = i@ means @s.i = s.i@, which is meaningless, and there is no mechanism to qualify the parameter @i@, making the assignment impossible using the function-body @with@.
1494To solve this problem, parameters are treated like an initialized aggregate:
1495\begin{cfa}
1496struct Params {
1497        S & s;
1498        int i;
1499} params;
1500\end{cfa}
1501and implicitly opened \emph{after} a function-body open, to give them higher priority:
1502\begin{cfa}
1503void ?{}( S & s, int `i` ) with ( s ) `with( $\emph{\color{red}params}$ )` {
1504        s.i = `i`; j = 3; m = 5.5;
1505}
1506\end{cfa}
1507Finally, a cast may be used to disambiguate among overload variables in a @with@ expression:
1508\begin{cfa}
1509with ( w ) { ... }                                                      $\C{// ambiguous, same name and no context}$
1510with ( (S)w ) { ... }                                           $\C{// unambiguous, cast}$
1511\end{cfa}
1512and @with@ expressions may be complex expressions with type reference (see Section~\ref{s:References}) to aggregate:
1513\begin{cfa}
1514struct S { int i, j; } sv;
1515with ( sv ) {                                                           $\C{// implicit reference}$
1516        S & sr = sv;
1517        with ( sr ) {                                                   $\C{// explicit reference}$
1518                S * sp = &sv;
1519                with ( *sp ) {                                          $\C{// computed reference}$
1520                        i = 3; j = 4;                                   $\C{\color{red}// sp--{\textgreater}i, sp--{\textgreater}j}$
1521                }
1522                i = 2; j = 3;                                           $\C{\color{red}// sr.i, sr.j}$
1523        }
1524        i = 1; j = 2;                                                   $\C{\color{red}// sv.i, sv.j}$
1525}
1526\end{cfa}
1527
1528
1529\section{Declarations}
1530
1531Declarations in C have weaknesses and omissions.
1532\CFA attempts to correct and add to C declarations, while ensuring \CFA subjectively ``feels like'' C.
1533An important part of this subjective feel is maintaining C's syntax and procedural paradigm, as opposed to functional and object-oriented approaches in other systems languages such as \CC and Rust.
1534Maintaining the C approach means that C coding-patterns remain not only useable but idiomatic in \CFA, reducing the mental burden of retraining C programmers and switching between C and \CFA development.
1535Nevertheless, some features from other approaches are undeniably convenient;
1536\CFA attempts to adapt these features to the C paradigm.
1537
1538
1539\subsection{Alternative Declaration Syntax}
1540
1541C declaration syntax is notoriously confusing and error prone.
1542For example, many C programmers are confused by a declaration as simple as:
1543\begin{cquote}
1544\lstDeleteShortInline@%
1545\begin{tabular}{@{}ll@{}}
1546\begin{cfa}
1547int * x[5]
1548\end{cfa}
1549&
1550\raisebox{-0.75\totalheight}{\input{Cdecl}}
1551\end{tabular}
1552\lstMakeShortInline@%
1553\end{cquote}
1554Is this an array of 5 pointers to integers or a pointer to an array of 5 integers?
1555If there is any doubt, it implies productivity and safety issues even for basic programs.
1556Another example of confusion results from the fact that a function name and its parameters are embedded within the return type, mimicking the way the return value is used at the function's call site.
1557For example, a function returning a pointer to an array of integers is defined and used in the following way:
1558\begin{cfa}
1559int `(*`f`())[`5`]` {...};                                      $\C{// definition}$
1560 ... `(*`f`())[`3`]` += 1;                                      $\C{// usage}$
1561\end{cfa}
1562Essentially, the return type is wrapped around the function name in successive layers (like an onion).
1563While attempting to make the two contexts consistent is a laudable goal, it has not worked out in practice.
1564
1565\CFA provides its own type, variable and function declarations, using a different syntax~\cite[pp.~856--859]{Buhr94a}.
1566The new declarations place qualifiers to the left of the base type, while C declarations place qualifiers to the right.
1567The qualifiers have the same meaning but are ordered left to right to specify a variable's type.
1568\begin{cquote}
1569\lstDeleteShortInline@%
1570\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{\hspace{2\parindentlnth}}l@{}}
1571\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
1572\begin{cfa}
1573`[5] *` int x1;
1574`* [5]` int x2;
1575`[* [5] int]` f( int p );
1576\end{cfa}
1577&
1578\begin{cfa}
1579int `*` x1 `[5]`;
1580int `(*`x2`)[5]`;
1581`int (*`f( int p )`)[5]`;
1582\end{cfa}
1583&
1584\begin{cfa}
1585// array of 5 pointers to int
1586// pointer to array of 5 int
1587// function returning pointer to array of 5 int and taking int
1588\end{cfa}
1589\end{tabular}
1590\lstMakeShortInline@%
1591\end{cquote}
1592The only exception is bit field specification, which always appear to the right of the base type.
1593% Specifically, the character @*@ is used to indicate a pointer, square brackets @[@\,@]@ are used to represent an array or function return value, and parentheses @()@ are used to indicate a function parameter.
1594However, unlike C, \CFA type declaration tokens are distributed across all variables in the declaration list.
1595For instance, variables @x@ and @y@ of type pointer to integer are defined in \CFA as follows:
1596\begin{cquote}
1597\lstDeleteShortInline@%
1598\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
1599\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
1600\begin{cfa}
1601`*` int x, y;
1602int y;
1603\end{cfa}
1604&
1605\begin{cfa}
1606int `*`x, `*`y;
1607
1608\end{cfa}
1609\end{tabular}
1610\lstMakeShortInline@%
1611\end{cquote}
1612The downside of the \CFA semantics is the need to separate regular and pointer declarations.
1613
1614\begin{comment}
1615Other examples are:
1616\begin{cquote}
1617\lstDeleteShortInline@%
1618\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{\hspace{2\parindentlnth}}l@{}}
1619\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{C}}     \\
1620\begin{cfa}
1621[ 5 ] int z;
1622[ 5 ] * char w;
1623* [ 5 ] double v;
1624struct s {
1625        int f0:3;
1626        * int f1;
1627        [ 5 ] * int f2;
1628};
1629\end{cfa}
1630&
1631\begin{cfa}
1632int z[ 5 ];
1633char * w[ 5 ];
1634double (* v)[ 5 ];
1635struct s {
1636        int f0:3;
1637        int * f1;
1638        int * f2[ 5 ]
1639};
1640\end{cfa}
1641&
1642\begin{cfa}
1643// array of 5 integers
1644// array of 5 pointers to char
1645// pointer to array of 5 doubles
1646
1647// common bit field syntax
1648
1649
1650
1651\end{cfa}
1652\end{tabular}
1653\lstMakeShortInline@%
1654\end{cquote}
1655\end{comment}
1656
1657All specifiers (@extern@, @static@, \etc) and qualifiers (@const@, @volatile@, \etc) are used in the normal way with the new declarations and also appear left to right, \eg:
1658\begin{cquote}
1659\lstDeleteShortInline@%
1660\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{\hspace{2\parindentlnth}}l@{}}
1661\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{C}}     \\
1662\begin{cfa}
1663extern const * const int x;
1664static const * [5] const int y;
1665\end{cfa}
1666&
1667\begin{cfa}
1668int extern const * const x;
1669static const int (* const y)[5]
1670\end{cfa}
1671&
1672\begin{cfa}
1673// external const pointer to const int
1674// internal const pointer to array of 5 const int
1675\end{cfa}
1676\end{tabular}
1677\lstMakeShortInline@%
1678\end{cquote}
1679Specifiers must appear at the start of a \CFA function declaration\footnote{\label{StorageClassSpecifier}
1680The placement of a storage-class specifier other than at the beginning of the declaration specifiers in a declaration is an obsolescent feature.~\cite[\S~6.11.5(1)]{C11}}.
1681
1682The new declaration syntax can be used in other contexts where types are required, \eg casts and the pseudo-function @sizeof@:
1683\begin{cquote}
1684\lstDeleteShortInline@%
1685\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
1686\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
1687\begin{cfa}
1688y = (* int)x;
1689i = sizeof([ 5 ] * int);
1690\end{cfa}
1691&
1692\begin{cfa}
1693y = (int *)x;
1694i = sizeof(int * [ 5 ]);
1695\end{cfa}
1696\end{tabular}
1697\lstMakeShortInline@%
1698\end{cquote}
1699
1700The syntax of the new function-prototype declaration follows directly from the new function-definition syntax;
1701as well, parameter names are optional, \eg:
1702\begin{cfa}
1703[ int x ] f ( /* void */ );             $\C[2.5in]{// returning int with no parameters}$
1704[ int x ] f (...);                              $\C{// returning int with unknown parameters}$
1705[ * int ] g ( int y );                  $\C{// returning pointer to int with int parameter}$
1706[ void ] h ( int, char );               $\C{// returning no result with int and char parameters}$
1707[ * int, int ] j ( int );               $\C{// returning pointer to int and int with int parameter}$
1708\end{cfa}
1709This syntax allows a prototype declaration to be created by cutting and pasting source text from the function-definition header (or vice versa).
1710Like C, it is possible to declare multiple function-prototypes in a single declaration, where the return type is distributed across \emph{all} function names in the declaration list, \eg:
1711\begin{cquote}
1712\lstDeleteShortInline@%
1713\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
1714\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
1715\begin{cfa}
1716[double] foo(), foo( int ), foo( double ) {...}
1717\end{cfa}
1718&
1719\begin{cfa}
1720double foo1( void ), foo2( int ), foo3( double );
1721\end{cfa}
1722\end{tabular}
1723\lstMakeShortInline@%
1724\end{cquote}
1725where \CFA allows the last function in the list to define its body.
1726
1727The syntax for pointers to \CFA functions specifies the pointer name on the right, \eg:
1728\begin{cfa}
1729* [ int x ] () fp;                              $\C{// pointer to function returning int with no parameters}$
1730* [ * int ] ( int y ) gp;               $\C{// pointer to function returning pointer to int with int parameter}$
1731* [ ] ( int, char ) hp;                 $\C{// pointer to function returning no result with int and char parameters}$
1732* [ * int, int ] ( int ) jp;    $\C{// pointer to function returning pointer to int and int with int parameter}$
1733\end{cfa}
1734Note, a function name cannot be specified:
1735\begin{cfa}
1736* [ int x ] f () fp;                    $\C{// function name "f" is disallowed}\CRT$
1737\end{cfa}
1738
1739Finally, new \CFA declarations may appear together with C declarations in the same program block, but cannot be mixed within a specific declaration.
1740Therefore, a programmer has the option of either continuing to use traditional C declarations or take advantage of the new style.
1741Clearly, both styles need to be supported for some time due to existing C-style header-files, particularly for UNIX-like systems.
1742
1743
1744\subsection{References}
1745\label{s:References}
1746
1747All variables in C have an \newterm{address}, a \newterm{value}, and a \newterm{type};
1748at the position in the program's memory denoted by the address, there exists a sequence of bits (the value), with the length and semantic meaning of this bit sequence defined by the type.
1749The C type-system does not always track the relationship between a value and its address;
1750a value that does not have a corresponding address is called a \newterm{rvalue} (for ``right-hand value''), while a value that does have an address is called a \newterm{lvalue} (for ``left-hand value'').
1751For example, in @int x; x = 42;@ the variable expression @x@ on the left-hand-side of the assignment is a lvalue, while the constant expression @42@ on the right-hand-side of the assignment is a rvalue.
1752Despite the nomenclature of ``left-hand'' and ``right-hand'', an expression's classification as lvalue or rvalue is entirely dependent on whether it has an address or not; in imperative programming, the address of a value is used for both reading and writing (mutating) a value, and as such, lvalues can be converted to rvalues and read from, but rvalues cannot be mutated because they lack a location to store the updated value.
1753
1754Within a lexical scope, lvalue expressions have an \newterm{address interpretation} for writing a value or a \newterm{value interpretation} to read a value.
1755For example, in @x = y@, @x@ has an address interpretation, while @y@ has a value interpretation.
1756While this duality of interpretation is useful, C lacks a direct mechanism to pass lvalues between contexts, instead relying on \newterm{pointer types} to serve a similar purpose.
1757In C, for any type @T@ there is a pointer type @T *@, the value of which is the address of a value of type @T@.
1758A pointer rvalue can be explicitly \newterm{dereferenced} to the pointed-to lvalue with the dereference operator @*?@, while the rvalue representing the address of a lvalue can be obtained with the address-of operator @&?@.
1759
1760\begin{cfa}
1761int x = 1, y = 2, * p1, * p2, ** p3;
1762p1 = &x;                                                                        $\C{// p1 points to x}$
1763p2 = &y;                                                                        $\C{// p2 points to y}$
1764p3 = &p1;                                                                       $\C{// p3 points to p1}$
1765*p2 = ((*p1 + *p2) * (**p3 - *p1)) / (**p3 - 15);
1766\end{cfa}
1767
1768Unfortunately, the dereference and address-of operators introduce a great deal of syntactic noise when dealing with pointed-to values rather than pointers, as well as the potential for subtle bugs because of pointer arithmetic.
1769For both brevity and clarity, it is desirable for the compiler to figure out how to elide the dereference operators in a complex expression such as the assignment to @*p2@ above.
1770However, since C defines a number of forms of \newterm{pointer arithmetic}, two similar expressions involving pointers to arithmetic types (\eg @*p1 + x@ and @p1 + x@) may each have well-defined but distinct semantics, introducing the possibility that a programmer may write one when they mean the other, and precluding any simple algorithm for elision of dereference operators.
1771To solve these problems, \CFA introduces reference types @T &@;
1772a @T &@ has exactly the same value as a @T *@, but where the @T *@ takes the address interpretation by default, a @T &@ takes the value interpretation by default, as below:
1773
1774\begin{cfa}
1775int x = 1, y = 2, & r1, & r2, && r3;
1776&r1 = &x;                                                                       $\C{// r1 points to x}$
1777&r2 = &y;                                                                       $\C{// r2 points to y}$
1778&&r3 = &&r1;                                                            $\C{// r3 points to r2}$
1779r2 = ((r1 + r2) * (r3 - r1)) / (r3 - 15);       $\C{// implicit dereferencing}$
1780\end{cfa}
1781
1782Except for auto-dereferencing by the compiler, this reference example is exactly the same as the previous pointer example.
1783Hence, a reference behaves like a variable name -- an lvalue expression which is interpreted as a value -- but also has the type system track the address of that value.
1784One way to conceptualize a reference is via a rewrite rule, where the compiler inserts a dereference operator before the reference variable for each reference qualifier in the reference variable declaration, so the previous example implicitly acts like:
1785
1786\begin{cfa}
1787`*`r2 = ((`*`r1 + `*`r2) * (`**`r3 - `*`r1)) / (`**`r3 - 15);
1788\end{cfa}
1789
1790References in \CFA are similar to those in \CC, with important improvements, which can be seen in the example above.
1791Firstly, \CFA does not forbid references to references.
1792This provides a much more orthogonal design for library implementors, obviating the need for workarounds such as @std::reference_wrapper@.
1793Secondly, \CFA references are rebindable, whereas \CC references have a fixed address.
1794\newsavebox{\LstBox}
1795\begin{lrbox}{\LstBox}
1796\lstset{basicstyle=\footnotesize\linespread{0.9}\sf}
1797\begin{cfa}
1798int & r = *new( int );
1799...                                                                                     $\C{// non-null reference}$
1800delete &r;                                                                      $\C{// unmanaged (programmer) memory-management}$
1801r += 1;                                                                         $\C{// undefined reference}$
1802\end{cfa}
1803\end{lrbox}
1804Rebinding allows \CFA references to be default-initialized (\eg to a null pointer\footnote{
1805While effort has been made into non-null reference checking in \CC and Java, the exercise seems moot for any non-managed languages (C/\CC), given that it only handles one of many different error situations:
1806\begin{cquote}
1807\usebox{\LstBox}
1808\end{cquote}
1809}%
1810) and point to different addresses throughout their lifetime, like pointers.
1811Rebinding is accomplished by extending the existing syntax and semantics of the address-of operator in C.
1812
1813In C, the address of a lvalue is always a rvalue, as in general that address is not stored anywhere in memory, and does not itself have an address.
1814In \CFA, the address of a @T &@ is a lvalue @T *@, as the address of the underlying @T@ is stored in the reference, and can thus be mutated there.
1815The result of this rule is that any reference can be rebound using the existing pointer assignment semantics by assigning a compatible pointer into the address of the reference, \eg @&r1 = &x;@ above.
1816This rebinding occurs to an arbitrary depth of reference nesting;
1817loosely speaking, nested address-of operators produce a nested lvalue pointer up to the depth of the reference.
1818These explicit address-of operators can be thought of as ``cancelling out'' the implicit dereference operators, \eg @(&`*`)r1 = &x@ or @(&(&`*`)`*`)r3 = &(&`*`)r1@ or even @(&`*`)r2 = (&`*`)`*`r3@ for @&r2 = &r3@.
1819More precisely:
1820\begin{itemize}
1821\item
1822if @R@ is an rvalue of type {@T &@$_1 \cdots$@ &@$_r$} where $r \ge 1$ references (@&@ symbols) than @&R@ has type {@T `*`&@$_{\color{red}2} \cdots$@ &@$_{\color{red}r}$}, \\ \ie @T@ pointer with $r-1$ references (@&@ symbols).
1823       
1824\item
1825if @L@ is an lvalue of type {@T &@$_1 \cdots$@ &@$_l$} where $l \ge 0$ references (@&@ symbols) then @&L@ has type {@T `*`&@$_{\color{red}1} \cdots$@ &@$_{\color{red}l}$}, \\ \ie @T@ pointer with $l$ references (@&@ symbols).
1826\end{itemize}
1827Since pointers and references share the same internal representation, code using either is equally performant; in fact the \CFA compiler converts references to pointers internally, and the choice between them is made solely on convenience, \eg many pointer or value accesses.
1828
1829By analogy to pointers, \CFA references also allow cv-qualifiers such as @const@:
1830\begin{cfa}
1831const int cx = 5;                                                       $\C{// cannot change cx}$
1832const int & cr = cx;                                            $\C{// cannot change cr's referred value}$
1833&cr = &cx;                                                                      $\C{// rebinding cr allowed}$
1834cr = 7;                                                                         $\C{// ERROR, cannot change cr}$
1835int & const rc = x;                                                     $\C{// must be initialized, like in \CC}$
1836&rc = &x;                                                                       $\C{// ERROR, cannot rebind rc}$
1837rc = 7;                                                                         $\C{// x now equal to 7}$
1838\end{cfa}
1839Given that a reference is meant to represent a lvalue, \CFA provides some syntactic shortcuts when initializing references.
1840There are three initialization contexts in \CFA: declaration initialization, argument/parameter binding, and return/temporary binding.
1841In each of these contexts, the address-of operator on the target lvalue is elided.
1842The syntactic motivation is clearest when considering overloaded operator-assignment, \eg @int ?+=?(int &, int)@; given @int x, y@, the expected call syntax is @x += y@, not @&x += y@.
1843
1844More generally, this initialization of references from lvalues rather than pointers is an instance of a ``lvalue-to-reference'' conversion rather than an elision of the address-of operator;
1845this conversion is used in any context in \CFA where an implicit conversion is allowed.
1846Similarly, use of a the value pointed to by a reference in an rvalue context can be thought of as a ``reference-to-rvalue'' conversion, and \CFA also includes a qualifier-adding ``reference-to-reference'' conversion, analogous to the @T *@ to @const T *@ conversion in standard C.
1847The final reference conversion included in \CFA is ``rvalue-to-reference'' conversion, implemented by means of an implicit temporary.
1848When an rvalue is used to initialize a reference, it is instead used to initialize a hidden temporary value with the same lexical scope as the reference, and the reference is initialized to the address of this temporary.
1849\begin{cfa}
1850struct S { double x, y; };
1851int i, j;
1852void f( int & i, int & j, S & s, int v[] );
1853f( 3, i + j, (S){ 1.0, 7.0 }, (int [3]){ 1, 2, 3 } );   $\C{// pass rvalue to lvalue \(\Rightarrow\) implicit temporary}$
1854\end{cfa}
1855This allows complex values to be succinctly and efficiently passed to functions, without the syntactic overhead of explicit definition of a temporary variable or the runtime cost of pass-by-value.
1856\CC allows a similar binding, but only for @const@ references; the more general semantics of \CFA are an attempt to avoid the \newterm{const hell} problem, in which addition of a @const@ qualifier to one reference requires a cascading chain of added qualifiers.
1857
1858
1859\subsection{Type Nesting}
1860
1861Nested types provide a mechanism to organize associated types and refactor a subset of fields into a named aggregate (\eg sub-aggregates @name@, @address@, @department@, within aggregate @employe@).
1862Java nested types are dynamic (apply to objects), \CC are static (apply to the \lstinline[language=C++]@class@), and C hoists (refactors) nested types into the enclosing scope, meaning there is no need for type qualification.
1863Since \CFA in not object-oriented, adopting dynamic scoping does not make sense;
1864instead \CFA adopts \CC static nesting, using the field-selection operator ``@.@'' for type qualification, as does Java, rather than the \CC type-selection operator ``@::@'' (see Figure~\ref{f:TypeNestingQualification}).
1865\begin{figure}
1866\centering
1867\lstDeleteShortInline@%
1868\begin{tabular}{@{}l@{\hspace{3em}}l|l@{}}
1869\multicolumn{1}{c@{\hspace{3em}}}{\textbf{C Type Nesting}}      & \multicolumn{1}{c}{\textbf{C Implicit Hoisting}}      & \multicolumn{1}{|c}{\textbf{\CFA}}    \\
1870\hline
1871\begin{cfa}
1872struct S {
1873        enum C { R, G, B };
1874        struct T {
1875                union U { int i, j; };
1876                enum C c;
1877                short int i, j;
1878        };
1879        struct T t;
1880} s;
1881
1882int rtn() {
1883        s.t.c = R;
1884        struct T t = { R, 1, 2 };
1885        enum C c;
1886        union U u;
1887}
1888\end{cfa}
1889&
1890\begin{cfa}
1891enum C { R, G, B };
1892union U { int i, j; };
1893struct T {
1894        enum C c;
1895        short int i, j;
1896};
1897struct S {
1898        struct T t;
1899} s;
1900       
1901
1902
1903
1904
1905
1906
1907\end{cfa}
1908&
1909\begin{cfa}
1910struct S {
1911        enum C { R, G, B };
1912        struct T {
1913                union U { int i, j; };
1914                enum C c;
1915                short int i, j;
1916        };
1917        struct T t;
1918} s;
1919
1920int rtn() {
1921        s.t.c = `S.`R;  // type qualification
1922        struct `S.`T t = { `S.`R, 1, 2 };
1923        enum `S.`C c;
1924        union `S.T.`U u;
1925}
1926\end{cfa}
1927\end{tabular}
1928\lstMakeShortInline@%
1929\caption{Type Nesting / Qualification}
1930\label{f:TypeNestingQualification}
1931\end{figure}
1932In the C left example, types @C@, @U@ and @T@ are implicitly hoisted outside of type @S@ into the containing block scope.
1933In the \CFA right example, the types are not hoisted and accessible.
1934
1935
1936\subsection{Constructors and Destructors}
1937\label{s:ConstructorsDestructors}
1938
1939One of the strengths (and weaknesses) of C is memory-management control, allowing resource release to be precisely specified versus unknown release with garbage-collected memory-management.
1940However, this manual approach is often verbose, and it is useful to manage resources other than memory (\eg file handles) using the same mechanism as memory.
1941\CC addresses these issues using Resource Aquisition Is Initialization (RAII), implemented by means of \newterm{constructor} and \newterm{destructor} functions;
1942\CFA adopts constructors and destructors (and @finally@) to facilitate RAII.
1943While constructors and destructors are a common feature of object-oriented programming-languages, they are an independent capability allowing \CFA to adopt them while retaining a procedural paradigm.
1944Specifically, \CFA constructors and destructors are denoted by name and first parameter-type versus name and nesting in an aggregate type.
1945Constructor calls seamlessly integrate with existing C initialization syntax, providing a simple and familiar syntax to C programmers and allowing constructor calls to be inserted into legacy C code with minimal code changes.
1946
1947In \CFA, a constructor is named @?{}@ and a destructor is named @^?{}@\footnote{%
1948The symbol \lstinline+^+ is used for the destructor name because it was the last binary operator that could be used in a unary context.}.
1949The name @{}@ comes from the syntax for the initializer: @struct S { int i, j; } s = `{` 2, 3 `}`@.
1950Like other \CFA operators, these names represent the syntax used to call the constructor or destructor, \eg @?{}(x, ...)@ or @^{}(x, ...)@.
1951The constructor and destructor have return type @void@, and the first parameter is a reference to the object type to be constructed or destructed.
1952While the first parameter is informally called the @this@ parameter, as in object-oriented languages, any variable name may be used.
1953Both constructors and destructors allow additional parametes after the @this@ parameter for specifying values for initialization/de-initialization\footnote{
1954Destruction parameters are useful for specifying storage-management actions, such as de-initialize but not deallocate.}.
1955\begin{cfa}
1956struct VLA { int len, * data; };
1957void ?{}( VLA & vla ) with ( vla ) { len = 10;  data = alloc( len ); }  $\C{// default constructor}$
1958void ^?{}( VLA & vla ) with ( vla ) { free( data ); } $\C{// destructor}$
1959{
1960        VLA x;                                                                  $\C{// implicit:  ?\{\}( x );}$
1961}                                                                                       $\C{// implicit:  ?\^{}\{\}( x );}$
1962\end{cfa}
1963@VLA@ is a \newterm{managed type}\footnote{
1964A managed type affects the runtime environment versus a self-contained type.}: a type requiring a non-trivial constructor or destructor, or with a field of a managed type.
1965A managed type is implicitly constructed at allocation and destructed at deallocation to ensure proper interaction with runtime resources, in this case, the @data@ array in the heap.
1966For details of the code-generation placement of implicit constructor and destructor calls among complex executable statements see~\cite[\S~2.2]{Schluntz17}.
1967
1968\CFA also provides syntax for \newterm{initialization} and \newterm{copy}:
1969\begin{cfa}
1970void ?{}( VLA & vla, int size, char fill ) with ( vla ) {  $\C{// initialization}$
1971        len = size;  data = alloc( len, fill );
1972}
1973void ?{}( VLA & vla, VLA other ) {                      $\C{// copy, shallow}$
1974        vla.len = other.len;  vla.data = other.data;
1975}
1976\end{cfa}
1977(Note, the example is purposely simplified using shallow-copy semantics.)
1978An initialization constructor-call has the same syntax as a C initializer, except the initialization values are passed as arguments to a matching constructor (number and type of paremeters).
1979\begin{cfa}
1980VLA va = `{` 20, 0 `}`,  * arr = alloc()`{` 5, 0 `}`;
1981\end{cfa}
1982Note, the use of a \newterm{constructor expression} to initialize the storage from the dynamic storage-allocation.
1983Like \CC, the copy constructor has two parameters, the second of which is a value parameter with the same type as the first parameter;
1984appropriate care is taken to not recursively call the copy constructor when initializing the second parameter.
1985
1986\CFA constructors may be explicitly call, like Java, and destructors may be explicitly called, like \CC.
1987Explicit calls to constructors double as a \CC-style \emph{placement syntax}, useful for construction of member fields in user-defined constructors and reuse of existing storage allocations.
1988While existing call syntax works for explicit calls to constructors and destructors, \CFA also provides a more concise \newterm{operator syntax} for both:
1989\begin{cfa}
1990{
1991        VLA  x,            y = { 20, 0x01 },     z = y; $\C{// z points to y}$
1992        //      ?{}( x );  ?{}( y, 20, 0x01 );  ?{}( z, y );
1993        ^x{};                                                                   $\C{// deallocate x}$
1994        x{};                                                                    $\C{// reallocate x}$
1995        z{ 5, 0xff };                                                   $\C{// reallocate z, not pointing to y}$
1996        ^y{};                                                                   $\C{// deallocate y}$
1997        y{ x };                                                                 $\C{// reallocate y, points to x}$
1998        x{};                                                                    $\C{// reallocate x, not pointing to y}$
1999        // ^?{}(z);  ^?{}(y);  ^?{}(x);
2000}
2001\end{cfa}
2002
2003To provide a uniform type interface for @otype@ polymorphism, the \CFA compiler automatically generates a default constructor, copy constructor, assignment operator, and destructor for all types.
2004These default functions can be overridden by user-generated versions.
2005For compatibility with the standard behaviour of C, the default constructor and destructor for all basic, pointer, and reference types do nothing, while the copy constructor and assignment operator are bitwise copies;
2006if default zero-initialization is desired, the default constructors can be overridden.
2007For user-generated types, the four functions are also automatically generated.
2008@enum@ types are handled the same as their underlying integral type, and unions are also bitwise copied and no-op initialized and destructed.
2009For compatibility with C, a copy constructor from the first union member type is also defined.
2010For @struct@ types, each of the four functions are implicitly defined to call their corresponding functions on each member of the struct.
2011To better simulate the behaviour of C initializers, a set of \newterm{field constructors} is also generated for structures.
2012A constructor is generated for each non-empty prefix of a structure's member-list to copy-construct the members passed as parameters and default-construct the remaining members.
2013To allow users to limit the set of constructors available for a type, when a user declares any constructor or destructor, the corresponding generated function and all field constructors for that type are hidden from expression resolution;
2014similarly, the generated default constructor is hidden upon declaration of any constructor.
2015These semantics closely mirror the rule for implicit declaration of constructors in \CC\cite[p.~186]{ANSI98:C++}.
2016
2017In some circumstance programmers may not wish to have constructor and destructor calls.
2018In these cases, \CFA provides the initialization syntax \lstinline|S x @= {}|, and the object becomes unmanaged, so implicit constructor and destructor calls are not generated.
2019Any C initializer can be the right-hand side of an \lstinline|@=| initializer, \eg \lstinline|VLA a @= { 0, 0x0 }|, with the usual C initialization semantics.
2020The point of \lstinline|@=| is to provide a migration path from legacy C code to \CFA, by providing a mechanism to incrementally convert to implicit initialization.
2021
2022
2023% \subsection{Default Parameters}
2024
2025
2026\section{Literals}
2027
2028C already includes limited polymorphism for literals -- @0@ can be either an integer or a pointer literal, depending on context, while the syntactic forms of literals of the various integer and float types are very similar, differing from each other only in suffix.
2029In keeping with the general \CFA approach of adding features while respecting the ``C-style'' of doing things, C's polymorphic constants and typed literal syntax are extended to interoperate with user-defined types, while maintaining a backwards-compatible semantics.
2030
2031A simple example is allowing the underscore, as in Ada, to separate prefixes, digits, and suffixes in all \CFA constants, \eg @0x`_`1.ffff`_`ffff`_`p`_`128`_`l@, where the underscore is also the standard separator in C identifiers.
2032\CC uses a single quote as a separator but it is restricted among digits, precluding its use in the literal prefix or suffix, \eg @0x1.ffff@@`'@@ffffp128l@, and causes problems with most IDEs, which must be extended to deal with this alternate use of the single quote.
2033
2034
2035\subsection{Integral Suffixes}
2036
2037Additional integral suffixes are added to cover all the integral types and lengths.
2038\begin{cquote}
2039\lstDeleteShortInline@%
2040\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{\hspace{2\parindentlnth}}l@{}}
2041\begin{cfa}
204220_`hh`     // signed char
204321_`hhu`   // unsigned char
204422_`h`       // signed short int
204523_`uh`     // unsigned short int
204624_`z`       // size_t
2047\end{cfa}
2048&
2049\begin{cfa}
205020_`L8`      // int8_t
205121_`ul8`     // uint8_t
205222_`l16`     // int16_t
205323_`ul16`   // uint16_t
205424_`l32`     // int32_t
2055\end{cfa}
2056&
2057\begin{cfa}
205825_`ul32`      // uint32_t
205926_`l64`        // int64_t
206027_`l64u`      // uint64_t
206126_`L128`     // int128
206227_`L128u`   // unsigned int128
2063\end{cfa}
2064\end{tabular}
2065\lstMakeShortInline@%
2066\end{cquote}
2067
2068
2069\subsection{0/1}
2070
2071In C, @0@ has the special property that it is the only ``false'' value;
2072from the standard, any value that compares equal to @0@ is false, while any value that compares unequal to @0@ is true.
2073As such, an expression @x@ in any boolean context (such as the condition of an @if@ or @while@ statement, or the arguments to @&&@, @||@, or @?:@\,) can be rewritten as @x != 0@ without changing its semantics.
2074Operator overloading in \CFA provides a natural means to implement this truth-value comparison for arbitrary types, but the C type system is not precise enough to distinguish an equality comparison with @0@ from an equality comparison with an arbitrary integer or pointer.
2075To provide this precision, \CFA introduces a new type @zero_t@ as the type of literal @0@ (somewhat analagous to @nullptr_t@ and @nullptr@ in \CCeleven);
2076@zero_t@ can only take the value @0@, but has implicit conversions to the integer and pointer types so that C code involving @0@ continues to work.
2077With this addition, \CFA rewrites @if (x)@ and similar expressions to @if ((x) != 0)@ or the appropriate analogue, and any type @T@ is ``truthy'' by defining an operator overload @int ?!=?(T, zero_t)@.
2078\CC makes types truthy by adding a conversion to @bool@;
2079prior to the addition of explicit cast operators in \CCeleven, this approach had the pitfall of making truthy types transitively convertable to any numeric type;
2080\CFA avoids this issue.
2081
2082Similarly, \CFA also has a special type for @1@, @one_t@;
2083like @zero_t@, @one_t@ has built-in implicit conversions to the various integral types so that @1@ maintains its expected semantics in legacy code for operations @++@ and @--@.
2084The addition of @one_t@ allows generic algorithms to handle the unit value uniformly for types where it is meaningful.
2085\TODO{Make this sentence true}
2086In particular, polymorphic functions in the \CFA prelude define @++x@ and @x++@ in terms of @x += 1@, allowing users to idiomatically define all forms of increment for a type @T@ by defining the single function @T & ?+=(T &, one_t)@;
2087analogous overloads for the decrement operators are present as well.
2088
2089
2090\subsection{User Literals}
2091
2092For readability, it is useful to associate units to scale literals, \eg weight (stone, pound, kilogram) or time (seconds, minutes, hours).
2093The left of Figure~\ref{f:UserLiteral} shows the \CFA alternative call-syntax (literal argument before function name), using the backquote, to convert basic literals into user literals.
2094The backquote is a small character, making the unit (function name) predominate.
2095For examples, the multi-precision integer-type in Section~\ref{s:MultiPrecisionIntegers} has user literals:
2096{\lstset{language=CFA,moredelim=**[is][\color{red}]{|}{|},deletedelim=**[is][]{`}{`}}
2097\begin{cfa}
2098y = 9223372036854775807L|`mp| * 18446744073709551615UL|`mp|;
2099y = "12345678901234567890123456789"|`mp| + "12345678901234567890123456789"|`mp|;
2100\end{cfa}
2101Because \CFA uses a standard function, all types and literals are applicable, as well as overloading and conversions.
2102}%
2103
2104The right of Figure~\ref{f:UserLiteral} shows the equivalent \CC version using the underscore for the call-syntax.
2105However, \CC restricts the types, \eg @unsigned long long int@ and @long double@ to represent integral and floating literals.
2106After which, user literals must match (no conversions);
2107hence, it is necessary to overload the unit with all appropriate types.
2108
2109\begin{figure}
2110\centering
2111\lstset{language=CFA,moredelim=**[is][\color{red}]{|}{|},deletedelim=**[is][]{`}{`}}
2112\lstDeleteShortInline@%
2113\begin{tabular}{@{}l@{\hspace{\parindentlnth}}l@{}}
2114\multicolumn{1}{c@{\hspace{\parindentlnth}}}{\textbf{\CFA}}     & \multicolumn{1}{c}{\textbf{\CC}}      \\
2115\begin{cfa}
2116struct W {
2117        double stones;
2118};
2119void ?{}( W & w ) { w.stones = 0; }
2120void ?{}( W & w, double w ) { w.stones = w; }
2121W ?+?( W l, W r ) {
2122        return (W){ l.stones + r.stones };
2123}
2124W |?`st|(double w) { return (W){ w }; }
2125W |?`lb|(double w) { return (W){ w/14.0 }; }
2126W |?`kg|(double w) { return (W){ w*0.16 }; }
2127
2128
2129
2130int main() {
2131        W w, heavy = { 20 };
2132        w = 155|`lb|;
2133        w = 0b_1111|`st|;
2134        w = 0_233|`lb|;
2135        w = 0x_9b_u|`kg|;
2136        w = 5.5|`st| + 8|`kg| + 25.01|`lb| + heavy;
2137}
2138\end{cfa}
2139&
2140\begin{cfa}
2141struct W {
2142        double stones;
2143        W() { stones = 0.0; }
2144        W( double w ) { stones = w; }
2145};
2146W operator+( W l, W r ) {
2147        return W( l.stones + r.stones );
2148}
2149W |operator""_st|(unsigned long long int w) {return W(w); }
2150W |operator""_lb|(unsigned long long int w) {return W(w/14.0); }
2151W |operator""_kg|(unsigned long long int w) {return W(w*0.16); }
2152W |operator""_st|(long double w ) { return W( w ); }
2153W |operator""_lb|(long double w ) { return W( w / 14.0 ); }
2154W |operator""_kg|(long double w ) { return W( w * 0.16 ); }
2155int main() {
2156        W w, heavy = { 20 };
2157        w = 155|_lb|;
2158        w = 0b1111|_lb|;       // error, binary unsupported
2159        w = 0${\color{red}\LstBasicStyle{'}}$233|_lb|;          // quote separator
2160        w = 0x9b|_kg|;
2161        w = 5.5d|_st| + 8|_kg| + 25.01|_lb| + heavy;
2162}
2163\end{cfa}
2164\end{tabular}
2165\lstMakeShortInline@%
2166\caption{User Literal}
2167\label{f:UserLiteral}
2168\end{figure}
2169
2170
2171\section{Libraries}
2172\label{sec:libraries}
2173
2174As stated in Section~\ref{sec:poly-fns}, \CFA inherits a large corpus of library code, where other programming languages must rewrite or provide fragile inter-language communication with C.
2175\CFA has replacement libraries condensing hundreds of existing C names into tens of \CFA overloaded names, all without rewriting the actual computations.
2176In many cases, the interface is an inline wrapper providing overloading during compilation but zero cost at runtime.
2177The following sections give a glimpse of the interface reduction to many C libraries.
2178In many cases, @signed@/@unsigned@ @char@, @short@, and @_Complex@ functions are available (but not shown) to ensure expression computations remain in a single type, as conversions can distort results.
2179
2180
2181\subsection{Limits}
2182
2183C library @limits.h@ provides lower and upper bound constants for the basic types.
2184\CFA name overloading is used to condense these typed constants, \eg:
2185\begin{cquote}
2186\lstDeleteShortInline@%
2187\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
2188\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{Definition}}      & \multicolumn{1}{c}{\textbf{Usage}}    \\
2189\begin{cfa}
2190const short int `MIN` = -32768;
2191const int `MIN` = -2147483648;
2192const long int `MIN` = -9223372036854775808L;
2193\end{cfa}
2194&
2195\begin{cfa}
2196short int si = `MIN`;
2197int i = `MIN`;
2198long int li = `MIN`;
2199\end{cfa}
2200\end{tabular}
2201\lstMakeShortInline@%
2202\end{cquote}
2203The result is a significant reduction in names to access typed constants, \eg:
2204\begin{cquote}
2205\lstDeleteShortInline@%
2206\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
2207\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
2208\begin{cfa}
2209MIN
2210
2211MAX
2212
2213PI
2214E
2215\end{cfa}
2216&
2217\begin{cfa}
2218SCHAR_MIN, CHAR_MIN, SHRT_MIN, INT_MIN, LONG_MIN, LLONG_MIN,
2219                FLT_MIN, DBL_MIN, LDBL_MIN
2220SCHAR_MAX, UCHAR_MAX, SHRT_MAX, INT_MAX, LONG_MAX, LLONG_MAX,
2221                FLT_MAX, DBL_MAX, LDBL_MAX
2222M_PI, M_PIl
2223M_E, M_El
2224\end{cfa}
2225\end{tabular}
2226\lstMakeShortInline@%
2227\end{cquote}
2228
2229
2230\subsection{Math}
2231
2232C library @math.h@ provides many mathematical functions.
2233\CFA function overloading is used to condense these mathematical functions, \eg:
2234\begin{cquote}
2235\lstDeleteShortInline@%
2236\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
2237\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{Definition}}      & \multicolumn{1}{c}{\textbf{Usage}}    \\
2238\begin{cfa}
2239float `log`( float x );
2240double `log`( double );
2241double _Complex `log`( double _Complex x );
2242\end{cfa}
2243&
2244\begin{cfa}
2245float f = `log`( 3.5 );
2246double d = `log`( 3.5 );
2247double _Complex dc = `log`( 3.5+0.5I );
2248\end{cfa}
2249\end{tabular}
2250\lstMakeShortInline@%
2251\end{cquote}
2252The result is a significant reduction in names to access math functions, \eg:
2253\begin{cquote}
2254\lstDeleteShortInline@%
2255\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
2256\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
2257\begin{cfa}
2258log
2259sqrt
2260sin
2261\end{cfa}
2262&
2263\begin{cfa}
2264logf, log, logl, clogf, clog, clogl
2265sqrtf, sqrt, sqrtl, csqrtf, csqrt, csqrtl
2266sinf, sin, sinl, csinf, csin, csinl
2267\end{cfa}
2268\end{tabular}
2269\lstMakeShortInline@%
2270\end{cquote}
2271While \Celeven has type-generic math~\cite[\S~7.25]{C11} in @tgmath.h@ to provide a similar mechanism, these macros are limited, matching a function name with a single set of floating type(s).
2272For example, it is impossible to overload @atan@ for both one and two arguments;
2273instead the names @atan@ and @atan2@ are required (see Section~\ref{s:NameOverloading}).
2274The key observation is that only a restricted set of type-generic macros are provided for a limited set of function names, which do not generalize across the type system, as in \CFA.
2275
2276
2277\subsection{Standard}
2278
2279C library @stdlib.h@ provides many general functions.
2280\CFA function overloading is used to condense these utility functions, \eg:
2281\begin{cquote}
2282\lstDeleteShortInline@%
2283\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
2284\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{Definition}}      & \multicolumn{1}{c}{\textbf{Usage}}    \\
2285\begin{cfa}
2286unsigned int `abs`( int );
2287double `abs`( double );
2288double abs( double _Complex );
2289\end{cfa}
2290&
2291\begin{cfa}
2292unsigned int i = `abs`( -1 );
2293double d = `abs`( -1.5 );
2294double d = `abs`( -1.5+0.5I );
2295\end{cfa}
2296\end{tabular}
2297\lstMakeShortInline@%
2298\end{cquote}
2299The result is a significant reduction in names to access utility functions, \eg:
2300\begin{cquote}
2301\lstDeleteShortInline@%
2302\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
2303\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
2304\begin{cfa}
2305abs
2306strto
2307random
2308\end{cfa}
2309&
2310\begin{cfa}
2311abs, labs, llabs, fabsf, fabs, fabsl, cabsf, cabs, cabsl
2312strtol, strtoul, strtoll, strtoull, strtof, strtod, strtold
2313srand48, mrand48, lrand48, drand48
2314\end{cfa}
2315\end{tabular}
2316\lstMakeShortInline@%
2317\end{cquote}
2318In additon, there are polymorphic functions, like @min@ and @max@, that work on any type with operators @?<?@ or @?>?@.
2319
2320The following shows one example where \CFA \emph{extends} an existing standard C interface to reduce complexity and provide safety.
2321C/\Celeven provide a number of complex and overlapping storage-management operation to support the following capabilities:
2322\begin{description}%[topsep=3pt,itemsep=2pt,parsep=0pt]
2323\item[fill]
2324an allocation with a specified character.
2325\item[resize]
2326an existing allocation to decreased or increased its size.
2327In either case, new storage may or may not be allocated and, if there is a new allocation, as much data from the existing allocation is copied.
2328For an increase in storage size, new storage after the copied data may be filled.
2329\item[align]
2330an allocation on a specified memory boundary, \eg, an address multiple of 64 or 128 for cache-line purposes.
2331\item[array]
2332allocation with a specified number of elements.
2333An array may be filled, resized, or aligned.
2334\end{description}
2335Table~\ref{t:StorageManagementOperations} shows the capabilities provided by C/\Celeven allocation-functions and how all the capabilities can be combined into two \CFA functions.
2336\CFA storage-management functions extend the C equivalents by overloading, providing shallow type-safety, and removing the need to specify the base allocation-size.
2337Figure~\ref{f:StorageAllocation} contrasts \CFA and C storage-allocation performing the same operations with the same type safety.
2338
2339\begin{table}
2340\centering
2341\lstDeleteShortInline@%
2342\lstMakeShortInline~%
2343\begin{tabular}{@{}r|r|l|l|l|l@{}}
2344\multicolumn{1}{c}{}&           & \multicolumn{1}{c|}{fill}     & resize        & align & array \\
2345\hline
2346C               & ~malloc~                      & no                    & no            & no            & no    \\
2347                & ~calloc~                      & yes (0 only)  & no            & no            & yes   \\
2348                & ~realloc~                     & no/copy               & yes           & no            & no    \\
2349                & ~memalign~            & no                    & no            & yes           & no    \\
2350                & ~posix_memalign~      & no                    & no            & yes           & no    \\
2351\hline
2352C11             & ~aligned_alloc~       & no                    & no            & yes           & no    \\
2353\hline
2354\CFA    & ~alloc~                       & yes/copy              & no/yes        & no            & yes   \\
2355                & ~align_alloc~         & yes                   & no            & yes           & yes   \\
2356\end{tabular}
2357\lstDeleteShortInline~%
2358\lstMakeShortInline@%
2359\caption{Storage-Management Operations}
2360\label{t:StorageManagementOperations}
2361\end{table}
2362
2363\begin{figure}
2364\centering
2365\begin{cquote}
2366\begin{cfa}[aboveskip=0pt]
2367size_t  dim = 10;                                                       $\C{// array dimension}$
2368char fill = '\xff';                                                     $\C{// initialization fill value}$
2369int * ip;
2370\end{cfa}
2371\lstDeleteShortInline@%
2372\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
2373\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
2374\begin{cfa}
2375ip = alloc();
2376ip = alloc( fill );
2377ip = alloc( dim );
2378ip = alloc( dim, fill );
2379ip = alloc( ip, 2 * dim );
2380ip = alloc( ip, 4 * dim, fill );
2381
2382ip = align_alloc( 16 );
2383ip = align_alloc( 16, fill );
2384ip = align_alloc( 16, dim );
2385ip = align_alloc( 16, dim, fill );
2386\end{cfa}
2387&
2388\begin{cfa}
2389ip = (int *)malloc( sizeof( int ) );
2390ip = (int *)malloc( sizeof( int ) ); memset( ip, fill, sizeof( int ) );
2391ip = (int *)malloc( dim * sizeof( int ) );
2392ip = (int *)malloc( sizeof( int ) ); memset( ip, fill, dim * sizeof( int ) );
2393ip = (int *)realloc( ip, 2 * dim * sizeof( int ) );
2394ip = (int *)realloc( ip, 4 * dim * sizeof( int ) );
2395                        memset( ip, fill, 4 * dim * sizeof( int ) );
2396ip = memalign( 16, sizeof( int ) );
2397ip = memalign( 16, sizeof( int ) ); memset( ip, fill, sizeof( int ) );
2398ip = memalign( 16, dim * sizeof( int ) );
2399ip = memalign( 16, dim * sizeof( int ) ); memset( ip, fill, dim * sizeof( int ) );
2400\end{cfa}
2401\end{tabular}
2402\lstMakeShortInline@%
2403\end{cquote}
2404\caption{\CFA versus C Storage-Allocation}
2405\label{f:StorageAllocation}
2406\end{figure}
2407
2408Variadic @new@ (see Section~\ref{sec:variadic-tuples}) cannot support the same overloading because extra parameters are for initialization.
2409Hence, there are @new@ and @anew@ functions for single and array variables, and the fill value is the arguments to the constructor, \eg:
2410\begin{cfa}
2411struct S { int i, j; };
2412void ?{}( S & s, int i, int j ) { s.i = i; s.j = j; }
2413S * s = new( 2, 3 );                                            $\C{// allocate storage and run constructor}$
2414S * as = anew( dim, 2, 3 );                                     $\C{// each array element initialized to 2, 3}$
2415\end{cfa}
2416Note, \CC can only initialization array elements via the default constructor.
2417
2418Finally, the \CFA memory-allocator has \newterm{sticky properties} for dynamic storage: fill and alignment are remembered with an object's storage in the heap.
2419When a @realloc@ is performed, the sticky properties are respected, so that new storage is correctly aligned and initialized with the fill character.
2420
2421
2422\subsection{I/O}
2423\label{s:IOLibrary}
2424
2425The goal of \CFA I/O is to simplify the common cases, while fully supporting polymorphism and user defined types in a consistent way.
2426The approach combines ideas from \CC and Python.
2427The \CFA header file for the I/O library is @fstream@.
2428
2429The common case is printing out a sequence of variables separated by whitespace.
2430\begin{cquote}
2431\lstDeleteShortInline@%
2432\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
2433\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{\CC}}      \\
2434\begin{cfa}
2435int x = 1, y = 2, z = 3;
2436sout | x `|` y `|` z | endl;
2437\end{cfa}
2438&
2439\begin{cfa}
2440
2441cout << x `<< " "` << y `<< " "` << z << endl;
2442\end{cfa}
2443\\
2444\begin{cfa}[showspaces=true,aboveskip=0pt,belowskip=0pt]
24451` `2` `3
2446\end{cfa}
2447&
2448\begin{cfa}[showspaces=true,aboveskip=0pt,belowskip=0pt]
24491 2 3
2450\end{cfa}
2451\end{tabular}
2452\lstMakeShortInline@%
2453\end{cquote}
2454The \CFA form has half the characters of the \CC form, and is similar to Python I/O with respect to implicit separators.
2455Similar simplification occurs for tuple I/O, which prints all tuple values separated by ``\lstinline[showspaces=true]@, @''.
2456\begin{cfa}
2457[int, [ int, int ] ] t1 = [ 1, [ 2, 3 ] ], t2 = [ 4, [ 5, 6 ] ];
2458sout | t1 | t2 | endl;                                  $\C{// print tuples}$
2459\end{cfa}
2460\begin{cfa}[showspaces=true,aboveskip=0pt]
24611`, `2`, `3 4`, `5`, `6
2462\end{cfa}
2463Finally, \CFA uses the logical-or operator for I/O as it is the lowest-priority overloadable operator, other than assignment.
2464Therefore, fewer output expressions require parenthesis.
2465\begin{cquote}
2466\lstDeleteShortInline@%
2467\begin{tabular}{@{}ll@{}}
2468\textbf{\CFA:}
2469&
2470\begin{cfa}
2471sout | x * 3 | y + 1 | z << 2 | x == y | (x | y) | (x || y) | (x > z ? 1 : 2) | endl;
2472\end{cfa}
2473\\
2474\textbf{\CC:}
2475&
2476\begin{cfa}
2477cout << x * 3 << y + 1 << `(`z << 2`)` << `(`x == y`)` << (x | y) << (x || y) << (x > z ? 1 : 2) << endl;
2478\end{cfa}
2479\\
2480&
2481\begin{cfa}[showspaces=true,aboveskip=0pt]
24823 3 12 0 3 1 2
2483\end{cfa}
2484\end{tabular}
2485\lstMakeShortInline@%
2486\end{cquote}
2487There is a weak similarity between the \CFA logical-or operator and the Shell pipe-operator for moving data, where data flows in the correct direction for input but the opposite direction for output.
2488
2489The implicit separator character (space/blank) is a separator not a terminator.
2490The rules for implicitly adding the separator are:
2491\begin{itemize}
2492\item
2493A separator does not appear at the start or end of a line.
2494\item
2495A separator does not appear before or after a character literal or variable.
2496\item
2497A separator does not appear before or after a null (empty) C string, which is a local mechanism to disable insertion of the separator character.
2498\item
2499A separator does not appear before a C string starting with the characters: \lstinline[mathescape=off,basicstyle=\tt]@([{=$@
2500\item
2501A separator does not appear after a C string ending with the characters: \lstinline[basicstyle=\tt]@,.;!?)]}%@
2502\item
2503{\lstset{language=CFA,deletedelim=**[is][]{`}{`}}
2504A separator does not appear before or after a C string beginning/ending with the quote or whitespace characters: \lstinline[basicstyle=\tt,showspaces=true]@`'": \t\v\f\r\n@
2505}%
2506\end{itemize}
2507There are functions to set and get the separator string, and manipulators to toggle separation on and off in the middle of output.
2508
2509
2510\subsection{Multi-precision Integers}
2511\label{s:MultiPrecisionIntegers}
2512
2513\CFA has an interface to the GMP multi-precision signed-integers~\cite{GMP}, similar to the \CC interface provided by GMP.
2514The \CFA interface wraps GMP functions into operator functions to make programming with multi-precision integers identical to using fixed-sized integers.
2515The \CFA type name for multi-precision signed-integers is @Int@ and the header file is @gmp@.
2516Figure~\ref{f:GMPInterface} shows a multi-precision factorial-program contrasting the GMP interface in \CFA and C.
2517
2518\begin{figure}
2519\centering
2520\lstDeleteShortInline@%
2521\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}@{\hspace{2\parindentlnth}}l@{}}
2522\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{@{\hspace{2\parindentlnth}}c}{\textbf{C}}     \\
2523\begin{cfa}
2524#include <gmp>
2525int main( void ) {
2526        sout | "Factorial Numbers" | endl;
2527        Int fact = 1;
2528        sout | 0 | fact | endl;
2529        for ( unsigned int i = 1; i <= 40; i += 1 ) {
2530                fact *= i;
2531                sout | i | fact | endl;
2532        }
2533}
2534\end{cfa}
2535&
2536\begin{cfa}
2537#include <gmp.h>
2538int main( void ) {
2539        `gmp_printf`( "Factorial Numbers\n" );
2540        `mpz_t` fact;  `mpz_init_set_ui`( fact, 1 );
2541        `gmp_printf`( "%d %Zd\n", 0, fact );
2542        for ( unsigned int i = 1; i <= 40; i += 1 ) {
2543                `mpz_mul_ui`( fact, fact, i );
2544                `gmp_printf`( "%d %Zd\n", i, fact );
2545        }
2546}
2547\end{cfa}
2548\end{tabular}
2549\lstMakeShortInline@%
2550\caption{GMP Interface \CFA versus C}
2551\label{f:GMPInterface}
2552\end{figure}
2553
2554
2555\section{Evaluation}
2556\label{sec:eval}
2557
2558Though \CFA provides significant added functionality over C, these features have a low runtime penalty.
2559In fact, \CFA's features for generic programming can enable faster runtime execution than idiomatic @void *@-based C code.
2560This claim is demonstrated through a set of generic-code-based micro-benchmarks in C, \CFA, and \CC (see stack implementations in Appendix~\ref{sec:BenchmarkStackImplementation}).
2561Since all these languages share a subset essentially comprising standard C, maximal-performance benchmarks should show little runtime variance, differing only in length and clarity of source code.
2562A more illustrative comparison measures the costs of idiomatic usage of each language's features.
2563Figure~\ref{fig:BenchmarkTest} shows the \CFA benchmark tests for a generic stack based on a singly linked-list.
2564The benchmark test is similar for the other languages.
2565The experiment uses element types @int@ and @pair(short, char)@, and pushes $N=40M$ elements on a generic stack, copies the stack, clears one of the stacks, and finds the maximum value in the other stack.
2566
2567\begin{figure}
2568\begin{cfa}[xleftmargin=3\parindentlnth,aboveskip=0pt,belowskip=0pt]
2569int main() {
2570        int max = 0, val = 42;
2571        stack( int ) si, ti;
2572
2573        REPEAT_TIMED( "push_int", N, push( si, val ); )
2574        TIMED( "copy_int", ti{ si }; )
2575        TIMED( "clear_int", clear( si ); )
2576        REPEAT_TIMED( "pop_int", N, int x = pop( ti ); if ( x > max ) max = x; )
2577
2578        pair( short, char ) max = { 0h, '\0' }, val = { 42h, 'a' };
2579        stack( pair( short, char ) ) sp, tp;
2580
2581        REPEAT_TIMED( "push_pair", N, push( sp, val ); )
2582        TIMED( "copy_pair", tp{ sp }; )
2583        TIMED( "clear_pair", clear( sp ); )
2584        REPEAT_TIMED( "pop_pair", N, pair(short, char) x = pop( tp ); if ( x > max ) max = x; )
2585}
2586\end{cfa}
2587\caption{\protect\CFA Benchmark Test}
2588\label{fig:BenchmarkTest}
2589\end{figure}
2590
2591The structure of each benchmark implemented is: C with @void *@-based polymorphism, \CFA with the presented features, \CC with templates, and \CC using only class inheritance for polymorphism, called \CCV.
2592The \CCV variant illustrates an alternative object-oriented idiom where all objects inherit from a base @object@ class, mimicking a Java-like interface;
2593hence runtime checks are necessary to safely down-cast objects.
2594The most notable difference among the implementations is in memory layout of generic types: \CFA and \CC inline the stack and pair elements into corresponding list and pair nodes, while C and \CCV lack such a capability and instead must store generic objects via pointers to separately-allocated objects.
2595Note that the C benchmark uses unchecked casts as there is no runtime mechanism to perform such checks, while \CFA and \CC provide type-safety statically.
2596
2597Figure~\ref{fig:eval} and Table~\ref{tab:eval} show the results of running the benchmark in Figure~\ref{fig:BenchmarkTest} and its C, \CC, and \CCV equivalents.
2598The graph plots the median of 5 consecutive runs of each program, with an initial warm-up run omitted.
2599All code is compiled at \texttt{-O2} by gcc or g++ 6.3.0, with all \CC code compiled as \CCfourteen.
2600The benchmarks are run on an Ubuntu 16.04 workstation with 16 GB of RAM and a 6-core AMD FX-6300 CPU with 3.5 GHz maximum clock frequency.
2601
2602\begin{figure}
2603\centering
2604\input{timing}
2605\caption{Benchmark Timing Results (smaller is better)}
2606\label{fig:eval}
2607\end{figure}
2608
2609\begin{table}
2610\centering
2611\caption{Properties of benchmark code}
2612\label{tab:eval}
2613\newcommand{\CT}[1]{\multicolumn{1}{c}{#1}}
2614\begin{tabular}{rrrrr}
2615                                                                        & \CT{C}        & \CT{\CFA}     & \CT{\CC}      & \CT{\CCV}             \\ \hline
2616maximum memory usage (MB)                       & 10,001        & 2,502         & 2,503         & 11,253                \\
2617source code size (lines)                        & 196           & 186           & 125           & 290                   \\
2618redundant type annotations (lines)      & 27            & 0                     & 2                     & 16                    \\
2619binary size (KB)                                        & 14            & 257           & 14            & 37                    \\
2620\end{tabular}
2621\end{table}
2622
2623The C and \CCV variants are generally the slowest with the largest memory footprint, because of their less-efficient memory layout and the pointer-indirection necessary to implement generic types;
2624this inefficiency is exacerbated by the second level of generic types in the pair benchmarks.
2625By contrast, the \CFA and \CC variants run in roughly equivalent time for both the integer and pair of @short@ and @char@ because the storage layout is equivalent, with the inlined libraries (\ie no separate compilation) and greater maturity of the \CC compiler contributing to its lead.
2626\CCV is slower than C largely due to the cost of runtime type-checking of down-casts (implemented with @dynamic_cast@);
2627The outlier in the graph for \CFA, pop @pair@, results from the complexity of the generated-C polymorphic code.
2628The gcc compiler is unable to optimize some dead code and condense nested calls; a compiler designed for \CFA could easily perform these optimizations.
2629Finally, the binary size for \CFA is larger because of static linking with the \CFA libraries.
2630
2631\CFA is also competitive in terms of source code size, measured as a proxy for programmer effort. The line counts in Table~\ref{tab:eval} include implementations of @pair@ and @stack@ types for all four languages for purposes of direct comparison, though it should be noted that \CFA and \CC have pre-written data structures in their standard libraries that programmers would generally use instead. Use of these standard library types has minimal impact on the performance benchmarks, but shrinks the \CFA and \CC benchmarks to 39 and 42 lines, respectively.
2632The difference between the \CFA and \CC line counts is primarily declaration duplication to implement separate compilation; a header-only \CFA library would be similar in length to the \CC version.
2633On the other hand, C does not have a generic collections-library in its standard distribution, resulting in frequent reimplementation of such collection types by C programmers.
2634\CCV does not use the \CC standard template library by construction, and in fact includes the definition of @object@ and wrapper classes for @char@, @short@, and @int@ in its line count, which inflates this count somewhat, as an actual object-oriented language would include these in the standard library;
2635with their omission, the \CCV line count is similar to C.
2636We justify the given line count by noting that many object-oriented languages do not allow implementing new interfaces on library types without subclassing or wrapper types, which may be similarly verbose.
2637
2638Line-count is a fairly rough measure of code complexity;
2639another important factor is how much type information the programmer must specify manually, especially where that information is not compiler-checked.
2640Such unchecked type information produces a heavier documentation burden and increased potential for runtime bugs, and is much less common in \CFA than C, with its manually specified function pointer arguments and format codes, or \CCV, with its extensive use of untype-checked downcasts, \eg @object@ to @integer@ when popping a stack.
2641To quantify this manual typing, the ``redundant type annotations'' line in Table~\ref{tab:eval} counts the number of lines on which the type of a known variable is respecified, either as a format specifier, explicit downcast, type-specific function, or by name in a @sizeof@, struct literal, or @new@ expression.
2642The \CC benchmark uses two redundant type annotations to create a new stack nodes, while the C and \CCV benchmarks have several such annotations spread throughout their code.
2643The \CFA benchmark is able to eliminate all redundant type annotations through use of the polymorphic @alloc@ function discussed in Section~\ref{sec:libraries}.
2644
2645
2646\section{Related Work}
2647
2648
2649\subsection{Polymorphism}
2650
2651\CC provides three disjoint polymorphic extensions to C: overloading, inheritance, and templates.
2652The overloading is restricted because resolution does not use the return type, inheritance requires learning object-oriented programming and coping with a restricted nominal-inheritance hierarchy, templates cannot be separately compiled resulting in compilation/code bloat and poor error messages, and determining how these mechanisms interact and which to use is confusing.
2653In contrast, \CFA has a single facility for polymorphic code supporting type-safe separate-compilation of polymorphic functions and generic (opaque) types, which uniformly leverage the C procedural paradigm.
2654The key mechanism to support separate compilation is \CFA's \emph{explicit} use of assumed type properties.
2655Until \CC concepts~\cite{C++Concepts} are standardized (anticipated for \CCtwenty), \CC provides no way to specify the requirements of a generic function beyond compilation errors during template expansion;
2656furthermore, \CC concepts are restricted to template polymorphism.
2657
2658Cyclone~\cite{Grossman06} also provides capabilities for polymorphic functions and existential types, similar to \CFA's @forall@ functions and generic types.
2659Cyclone existential types can include function pointers in a construct similar to a virtual function-table, but these pointers must be explicitly initialized at some point in the code, a tedious and potentially error-prone process.
2660Furthermore, Cyclone's polymorphic functions and types are restricted to abstraction over types with the same layout and calling convention as @void *@, \ie only pointer types and @int@.
2661In \CFA terms, all Cyclone polymorphism must be dtype-static.
2662While the Cyclone design provides the efficiency benefits discussed in Section~\ref{sec:generic-apps} for dtype-static polymorphism, it is more restrictive than \CFA's general model.
2663Smith and Volpano~\cite{Smith98} present Polymorphic C, an ML dialect with polymorphic functions, C-like syntax, and pointer types; it lacks many of C's features, however, most notably structure types, and so is not a practical C replacement.
2664
2665Objective-C~\cite{obj-c-book} is an industrially successful extension to C.
2666However, Objective-C is a radical departure from C, using an object-oriented model with message-passing.
2667Objective-C did not support type-checked generics until recently \cite{xcode7}, historically using less-efficient runtime checking of object types.
2668The GObject~\cite{GObject} framework also adds object-oriented programming with runtime type-checking and reference-counting garbage-collection to C;
2669these features are more intrusive additions than those provided by \CFA, in addition to the runtime overhead of reference-counting.
2670Vala~\cite{Vala} compiles to GObject-based C, adding the burden of learning a separate language syntax to the aforementioned demerits of GObject as a modernization path for existing C code-bases.
2671Java~\cite{Java8} included generic types in Java~5, which are type-checked at compilation and type-erased at runtime, similar to \CFA's.
2672However, in Java, each object carries its own table of method pointers, while \CFA passes the method pointers separately to maintain a C-compatible layout.
2673Java is also a garbage-collected, object-oriented language, with the associated resource usage and C-interoperability burdens.
2674
2675D~\cite{D}, Go, and Rust~\cite{Rust} are modern, compiled languages with abstraction features similar to \CFA traits, \emph{interfaces} in D and Go and \emph{traits} in Rust.
2676However, each language represents a significant departure from C in terms of language model, and none has the same level of compatibility with C as \CFA.
2677D and Go are garbage-collected languages, imposing the associated runtime overhead.
2678The necessity of accounting for data transfer between managed runtimes and the unmanaged C runtime complicates foreign-function interfaces to C.
2679Furthermore, while generic types and functions are available in Go, they are limited to a small fixed set provided by the compiler, with no language facility to define more.
2680D restricts garbage collection to its own heap by default, while Rust is not garbage-collected, and thus has a lighter-weight runtime more interoperable with C.
2681Rust also possesses much more powerful abstraction capabilities for writing generic code than Go.
2682On the other hand, Rust's borrow-checker provides strong safety guarantees but is complex and difficult to learn and imposes a distinctly idiomatic programming style.
2683\CFA, with its more modest safety features, allows direct ports of C code while maintaining the idiomatic style of the original source.
2684
2685
2686\subsection{Tuples/Variadics}
2687
2688Many programming languages have some form of tuple construct and/or variadic functions, \eg SETL, C, KW-C, \CC, D, Go, Java, ML, and Scala.
2689SETL~\cite{SETL} is a high-level mathematical programming language, with tuples being one of the primary data types.
2690Tuples in SETL allow subscripting, dynamic expansion, and multiple assignment.
2691C provides variadic functions through @va_list@ objects, but the programmer is responsible for managing the number of arguments and their types, so the mechanism is type unsafe.
2692KW-C~\cite{Buhr94a}, a predecessor of \CFA, introduced tuples to C as an extension of the C syntax, taking much of its inspiration from SETL.
2693The main contributions of that work were adding MRVF, tuple mass and multiple assignment, and record-field access.
2694\CCeleven introduced @std::tuple@ as a library variadic template structure.
2695Tuples are a generalization of @std::pair@, in that they allow for arbitrary length, fixed-size aggregation of heterogeneous values.
2696Operations include @std::get<N>@ to extract values, @std::tie@ to create a tuple of references used for assignment, and lexicographic comparisons.
2697\CCseventeen proposes \emph{structured bindings}~\cite{Sutter15} to eliminate pre-declaring variables and use of @std::tie@ for binding the results.
2698This extension requires the use of @auto@ to infer the types of the new variables, so complicated expressions with a non-obvious type must be documented with some other mechanism.
2699Furthermore, structured bindings are not a full replacement for @std::tie@, as it always declares new variables.
2700Like \CC, D provides tuples through a library variadic-template structure.
2701Go does not have tuples but supports MRVF.
2702Java's variadic functions appear similar to C's but are type-safe using homogeneous arrays, which are less useful than \CFA's heterogeneously-typed variadic functions.
2703Tuples are a fundamental abstraction in most functional programming languages, such as Standard ML~\cite{sml} and~\cite{Scala}, which decompose tuples using pattern matching.
2704
2705
2706\subsection{C Extensions}
2707
2708\CC is the best known C-based language, and is similar to \CFA in that both are extensions to C with source and runtime backwards compatibility.
2709Specific difference between \CFA and \CC have been identified in prior sections, with a final observation that \CFA has equal or fewer tokens to express the same notion in many cases.
2710The key difference in design philosophies is that \CFA is easier for C programmers to understand by maintaining a procedural paradigm and avoiding complex interactions among extensions.
2711\CC, on the other hand, has multiple overlapping features (such as the three forms of polymorphism), many of which have complex interactions with its object-oriented design.
2712As a result, \CC has a steep learning curve for even experienced C programmers, especially when attempting to maintain performance equivalent to C legacy-code.
2713
2714There are several other C extension-languages with less usage and even more dramatic changes than \CC.
2715Objective-C and Cyclone are two other extensions to C with different design goals than \CFA, as discussed above.
2716Other languages extend C with more focused features.
2717$\mu$\CC~\cite{uC++book}, CUDA~\cite{Nickolls08}, ispc~\cite{Pharr12}, and Sierra~\cite{Leissa14} add concurrent or data-parallel primitives to C or \CC;
2718data-parallel features have not yet been added to \CFA, but are easily incorporated within its design, while concurrency primitives similar to those in $\mu$\CC have already been added~\cite{Delisle18}.
2719Finally, CCured~\cite{Necula02} and Ironclad \CC~\cite{DeLozier13} attempt to provide a more memory-safe C by annotating pointer types with garbage collection information; type-checked polymorphism in \CFA covers several of C's memory-safety issues, but more aggressive approaches such as annotating all pointer types with their nullability or requiring runtime garbage collection are contradictory to \CFA's backwards compatibility goals.
2720
2721
2722\begin{comment}
2723\subsection{Control Structures / Declarations / Literals}
2724
2725Java has default fall through like C/\CC.
2726Pascal/Ada/Go/Rust do not have default fall through.
2727\Csharp does not have fall through but still requires a break.
2728Python uses dictionary mapping. \\
2729\CFA choose is like Rust match.
2730
2731Java has labelled break/continue. \\
2732Languages with and without exception handling.
2733
2734Alternative C declarations. \\
2735Different references \\
2736Constructors/destructors
2737
27380/1 Literals \\
2739user defined: D, Objective-C
2740\end{comment}
2741
2742
2743\section{Conclusion and Future Work}
2744
2745The goal of \CFA is to provide an evolutionary pathway for large C development-environments to be more productive and safer, while respecting the talent and skill of C programmers.
2746While other programming languages purport to be a better C, they are in fact new and interesting languages in their own right, but not C extensions.
2747The purpose of this paper is to introduce \CFA, and showcase language features that illustrate the \CFA type-system and approaches taken to achieve the goal of evolutionary C extension.
2748The contributions are a powerful type-system using parametric polymorphism and overloading, generic types, tuples, advanced control structures, and extended declarations, which all have complex interactions.
2749The work is a challenging design, engineering, and implementation exercise.
2750On the surface, the project may appear as a rehash of similar mechanisms in \CC.
2751However, every \CFA feature is different than its \CC counterpart, often with extended functionality, better integration with C and its programmers, and always supporting separate compilation.
2752All of these new features are being used by the \CFA development-team to build the \CFA runtime-system.
2753Finally, we demonstrate that \CFA performance for some idiomatic cases is better than C and close to \CC, showing the design is practically applicable.
2754
2755There is ongoing work on a wide range of \CFA features, including arrays with size, runtime type-information, virtual functions, user-defined conversions, concurrent primitives, and modules.
2756While all examples in the paper compile and run, a public beta-release of \CFA will take another 8--12 months to finalize these extensions.
2757There are also interesting future directions for the polymorphism design.
2758Notably, \CC template functions trade compile time and code bloat for optimal runtime of individual instantiations of polymorphic functions.
2759\CFA polymorphic functions use dynamic virtual-dispatch;
2760the runtime overhead of this approach is low, but not as low as inlining, and it may be beneficial to provide a mechanism for performance-sensitive code.
2761Two promising approaches are an @inline@ annotation at polymorphic function call sites to create a template-specialization of the function (provided the code is visible) or placing an @inline@ annotation on polymorphic function-definitions to instantiate a specialized version for some set of types (\CC template specialization).
2762These approaches are not mutually exclusive and allow performance optimizations to be applied only when necessary, without suffering global code-bloat.
2763In general, we believe separate compilation, producing smaller code, works well with loaded hardware-caches, which may offset the benefit of larger inlined-code.
2764
2765
2766\section{Acknowledgments}
2767
2768The authors would like to recognize the design assistance of Glen Ditchfield, Richard Bilson, Thierry Delisle, Andrew Beach and Brice Dobry on the features described in this paper, and thank Magnus Madsen for feedback on the writing.
2769This work is supported by a corporate partnership with Huawei Ltd.\ (\url{http://www.huawei.com}), and Aaron Moss and Peter Buhr are partially funded by the Natural Sciences and Engineering Research Council of Canada.
2770
2771
2772\bibliography{pl}
2773
2774
2775\appendix
2776
2777\section{Benchmark Stack Implementation}
2778\label{sec:BenchmarkStackImplementation}
2779
2780Throughout, @/***/@ designates a counted redundant type annotation; code reformatted for brevity.
2781
2782\smallskip\noindent
2783C
2784\begin{cfa}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
2785struct stack_node {
2786        void * value;
2787        struct stack_node * next;
2788};
2789struct stack { struct stack_node* head; };
2790void clear_stack( struct stack * s, void (*free_el)( void * ) ) {
2791        for ( struct stack_node * next = s->head; next; ) {
2792                struct stack_node * crnt = next;
2793                next = crnt->next;
2794                free_el( crnt->value );
2795                free( crnt );
2796        }
2797        s->head = NULL;
2798}
2799struct stack new_stack() { return (struct stack){ NULL }; /***/ }
2800void copy_stack( struct stack * s, const struct stack * t, void * (*copy)( const void * ) ) {
2801        struct stack_node ** crnt = &s->head;
2802        for ( struct stack_node * next = t->head; next; next = next->next ) {
2803                *crnt = malloc( sizeof(struct stack_node) ); /***/
2804                (*crnt)->value = copy( next->value );
2805                crnt = &(*crnt)->next;
2806        }
2807        *crnt = NULL;
2808}
2809struct stack * assign_stack( struct stack * s, const struct stack * t,
2810                void * (*copy_el)( const void * ), void (*free_el)( void * ) ) {
2811        if ( s->head == t->head ) return s;
2812        clear_stack( s, free_el ); /***/
2813        copy_stack( s, t, copy_el ); /***/
2814        return s;
2815}
2816_Bool stack_empty( const struct stack * s ) { return s->head == NULL; }
2817void push_stack( struct stack * s, void * v ) {
2818        struct stack_node * n = malloc( sizeof(struct stack_node) ); /***/
2819        *n = (struct stack_node){ v, s->head }; /***/
2820        s->head = n;
2821}
2822void * pop_stack( struct stack * s ) {
2823        struct stack_node * n = s->head;
2824        s->head = n->next;
2825        void * v = n->value;
2826        free( n );
2827        return v;
2828}
2829\end{cfa}
2830
2831\medskip\noindent
2832\CFA
2833\begin{cfa}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
2834forall( otype T ) struct stack_node {
2835        T value;
2836        stack_node(T) * next;
2837};
2838forall( otype T ) struct stack { stack_node(T) * head; };
2839forall( otype T ) void clear( stack(T) & s ) with( s ) {
2840        for ( stack_node(T) * next = head; next; ) {
2841                stack_node(T) * crnt = next;
2842                next = crnt->next;
2843                ^(*crnt){};
2844                free(crnt);
2845        }
2846        head = 0;
2847}
2848forall( otype T ) void ?{}( stack(T) & s ) { (s.head){ 0 }; }
2849forall( otype T ) void ?{}( stack(T) & s, stack(T) t ) {
2850        stack_node(T) ** crnt = &s.head;
2851        for ( stack_node(T) * next = t.head; next; next = next->next ) {
2852                *crnt = alloc();
2853                ((*crnt)->value){ next->value };
2854                crnt = &(*crnt)->next;
2855        }
2856        *crnt = 0;
2857}
2858forall( otype T ) stack(T) ?=?( stack(T) & s, stack(T) t ) {
2859        if ( s.head == t.head ) return s;
2860        clear( s );
2861        s{ t };
2862        return s;
2863}
2864forall( otype T ) void ^?{}( stack(T) & s) { clear( s ); }
2865forall( otype T ) _Bool empty( const stack(T) & s ) { return s.head == 0; }
2866forall( otype T ) void push( stack(T) & s, T value ) with( s ) {
2867        stack_node(T) * n = alloc();
2868        (*n){ value, head };
2869        head = n;
2870}
2871forall( otype T ) T pop( stack(T) & s ) with( s ) {
2872        stack_node(T) * n = head;
2873        head = n->next;
2874        T v = n->value;
2875        ^(*n){};
2876        free( n );
2877        return v;
2878}
2879\end{cfa}
2880
2881\begin{comment}
2882forall( otype T ) {
2883        struct stack_node {
2884                T value;
2885                stack_node(T) * next;
2886        };
2887        struct stack { stack_node(T) * head; };
2888        void clear( stack(T) & s ) with( s ) {
2889                for ( stack_node(T) * next = head; next; ) {
2890                        stack_node(T) * crnt = next;
2891                        next = crnt->next;
2892                        ^(*crnt){};
2893                        free(crnt);
2894                }
2895                head = 0;
2896        }
2897        void ?{}( stack(T) & s ) { (s.head){ 0 }; }
2898        void ?{}( stack(T) & s, stack(T) t ) {
2899                stack_node(T) ** crnt = &s.head;
2900                for ( stack_node(T) * next = t.head; next; next = next->next ) {
2901                        *crnt = alloc();
2902                        ((*crnt)->value){ next->value };
2903                        crnt = &(*crnt)->next;
2904                }
2905                *crnt = 0;
2906        }
2907        stack(T) ?=?( stack(T) & s, stack(T) t ) {
2908                if ( s.head == t.head ) return s;
2909                clear( s );
2910                s{ t };
2911                return s;
2912        }
2913        void ^?{}( stack(T) & s) { clear( s ); }
2914        _Bool empty( const stack(T) & s ) { return s.head == 0; }
2915        void push( stack(T) & s, T value ) with( s ) {
2916                stack_node(T) * n = alloc();
2917                (*n){ value, head };
2918                head = n;
2919        }
2920        T pop( stack(T) & s ) with( s ) {
2921                stack_node(T) * n = head;
2922                head = n->next;
2923                T v = n->value;
2924                ^(*n){};
2925                free( n );
2926                return v;
2927        }
2928}
2929\end{comment}
2930
2931\medskip\noindent
2932\CC
2933\begin{cfa}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
2934template<typename T> struct stack {
2935        struct node {
2936                T value;
2937                node * next;
2938                node( const T & v, node * n = nullptr ) : value( v ), next( n ) {}
2939        };
2940        node * head;
2941        stack() : head( nullptr ) {}
2942        stack( const stack<T> & o ) { copy( o ); }
2943        void clear() {
2944                for ( node * next = head; next; ) {
2945                        node * crnt = next;
2946                        next = crnt->next;
2947                        delete crnt;
2948                }
2949                head = nullptr;
2950        }
2951        void copy( const stack<T> & o ) {
2952                node ** crnt = &head;
2953                for ( node * next = o.head; next; next = next->next ) {
2954                        *crnt = new node{ next->value }; /***/
2955                        crnt = &(*crnt)->next;
2956                }
2957                *crnt = nullptr;
2958        }
2959        ~stack() { clear(); }
2960        stack & operator= ( const stack<T> & o ) {
2961                if ( this == &o ) return *this;
2962                clear();
2963                copy( o );
2964                return *this;
2965        }
2966        bool empty() const { return head == nullptr; }
2967        void push( const T & value ) { head = new node{ value, head };  /***/ }
2968        T pop() {
2969                node * n = head;
2970                head = n->next;
2971                T v = std::move( n->value );
2972                delete n;
2973                return v;
2974        }
2975};
2976\end{cfa}
2977
2978\medskip\noindent
2979\CCV
2980\begin{cfa}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
2981struct stack {
2982        struct node {
2983                ptr<object> value;
2984                node * next;
2985                node( const object & v, node * n = nullptr ) : value( v.new_copy() ), next( n ) {}
2986        };
2987        node * head;
2988        void clear() {
2989                for ( node * next = head; next; ) {
2990                        node * crnt = next;
2991                        next = crnt->next;
2992                        delete crnt;
2993                }
2994                head = nullptr;
2995        }
2996        void copy( const stack & o ) {
2997                node ** crnt = &head;
2998                for ( node * next = o.head; next; next = next->next ) {
2999                        *crnt = new node{ *next->value }; /***/
3000                        crnt = &(*crnt)->next;
3001                }
3002                *crnt = nullptr;
3003        }
3004        stack() : head( nullptr ) {}
3005        stack( const stack & o ) { copy( o ); }
3006        ~stack() { clear(); }
3007        stack & operator= ( const stack & o ) {
3008                if ( this == &o ) return *this;
3009                clear();
3010                copy( o );
3011                return *this;
3012        }
3013        bool empty() const { return head == nullptr; }
3014        void push( const object & value ) { head = new node{ value, head }; /***/ }
3015        ptr<object> pop() {
3016                node * n = head;
3017                head = n->next;
3018                ptr<object> v = std::move( n->value );
3019                delete n;
3020                return v;
3021        }
3022};
3023\end{cfa}
3024
3025
3026\end{document}
3027
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