source: doc/papers/general/Paper.tex @ 7f0001c

aaron-thesisarm-ehcleanup-dtorsdeferred_resndemanglerjacob/cs343-translationjenkins-sandboxnew-astnew-ast-unique-exprnew-envno_listpersistent-indexerwith_gc
Last change on this file since 7f0001c was 7f0001c, checked in by Aaron Moss <a3moss@…>, 4 years ago

update timing results in paper

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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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
12
13% Latex packages used in the document.
14
15\usepackage{epic,eepic}
16\usepackage{xspace}
17\usepackage{comment}
18\usepackage{upquote}                                            % switch curled `'" to straight
19\usepackage{listings}                                           % format program code
20\captionsetup{justification=raggedright,singlelinecheck=false}
21%\usepackage{enumitem}
22%\setlist[itemize]{topsep=3pt,itemsep=2pt,parsep=0pt}% global
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24
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27
28\usepackage[pagewise]{lineno}
29\renewcommand{\linenumberfont}{\scriptsize\sffamily}
30
31\lefthyphenmin=3                                                        % hyphen only after 4 characters
32\righthyphenmin=3
33
34%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
35
36% Names used in the document.
37
38\newcommand{\CFAIcon}{\textsf{C}\raisebox{\depth}{\rotatebox{180}{\textsf{A}}}\xspace} % Cforall symbolic name
39\newcommand{\CFA}{\protect\CFAIcon}             % safe for section/caption
40\newcommand{\CFL}{\textrm{Cforall}\xspace}      % Cforall symbolic name
41\newcommand{\Celeven}{\textrm{C11}\xspace}      % C11 symbolic name
42\newcommand{\CC}{\textrm{C}\kern-.1em\hbox{+\kern-.25em+}\xspace} % C++ symbolic name
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47\newcommand{\CCV}{\rm C\kern-.1em\hbox{+\kern-.25em+}obj\xspace} % C++ virtual symbolic name
48\newcommand{\Csharp}{C\raisebox{-0.7ex}{\Large$^\sharp$}\xspace} % C# symbolic name
49
50%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
51
52\newcommand{\Textbf}[2][red]{{\color{#1}{\textbf{#2}}}}
53%\newcommand{\TODO}[1]{\textbf{TODO}: {\itshape #1}} % TODO included
54\newcommand{\TODO}[1]{} % TODO elided
55
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61
62\makeatletter
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71
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78\newcommand{\CRT}{\global\columnposn=\gcolumnposn}
79
80% Denote newterms in particular font and index them without particular font and in lowercase, e.g., \newterm{abc}.
81% The option parameter provides an index term different from the new term, e.g., \newterm[\texttt{abc}]{abc}
82% The star version does not lowercase the index information, e.g., \newterm*{IBM}.
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87
88% Latin abbreviation
89\newcommand{\abbrevFont}{\textit}                       % set empty for no italics
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104\@ifundefined{etc}{
105\newcommand{\ETC}{\abbrevFont{etc}}
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107        \@ifnextchar{.}{\ETC}%
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109}}{}%
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122\makeatother
123
124\newenvironment{cquote}{%
125        \list{}{\lstset{resetmargins=true,aboveskip=0pt,belowskip=0pt}\topsep=3pt\parsep=0pt\leftmargin=\parindentlnth\rightmargin\leftmargin}%
126        \item\relax
127}{%
128        \endlist
129}% cquote
130
131% CFA programming language, based on ANSI C (with some gcc additions)
132\lstdefinelanguage{CFA}[ANSI]{C}{
133        morekeywords={
134                _Alignas, _Alignof, __alignof, __alignof__, asm, __asm, __asm__, __attribute, __attribute__,
135                auto, _Bool, catch, catchResume, choose, _Complex, __complex, __complex__, __const, __const__,
136                coroutine, disable, dtype, enable, exception, __extension__, fallthrough, fallthru, finally,
137                __float80, float80, __float128, float128, forall, ftype, _Generic, _Imaginary, __imag, __imag__,
138                inline, __inline, __inline__, __int128, int128, __label__, monitor, mutex, _Noreturn, one_t, or,
139                otype, restrict, __restrict, __restrict__, __signed, __signed__, _Static_assert, thread,
140                _Thread_local, throw, throwResume, timeout, trait, try, ttype, typeof, __typeof, __typeof__,
141                virtual, __volatile, __volatile__, waitfor, when, with, zero_t},
142        moredirectives={defined,include_next}%
143}
144
145\lstset{
146language=CFA,
147columns=fullflexible,
148basicstyle=\linespread{0.9}\sf,                                                 % reduce line spacing and use sanserif font
149stringstyle=\tt,                                                                                % use typewriter font
150tabsize=5,                                                                                              % N space tabbing
151xleftmargin=\parindentlnth,                                                             % indent code to paragraph indentation
152%mathescape=true,                                                                               % LaTeX math escape in CFA code $...$
153escapechar=\$,                                                                                  % LaTeX escape in CFA code
154keepspaces=true,                                                                                %
155showstringspaces=false,                                                                 % do not show spaces with cup
156showlines=true,                                                                                 % show blank lines at end of code
157aboveskip=4pt,                                                                                  % spacing above/below code block
158belowskip=3pt,
159% replace/adjust listing characters that look bad in sanserif
160literate={-}{\makebox[1ex][c]{\raisebox{0.4ex}{\rule{0.8ex}{0.1ex}}}}1 {^}{\raisebox{0.6ex}{$\scriptstyle\land\,$}}1
161        {~}{\raisebox{0.3ex}{$\scriptstyle\sim\,$}}1 % {`}{\ttfamily\upshape\hspace*{-0.1ex}`}1
162        {<-}{$\leftarrow$}2 {=>}{$\Rightarrow$}2 {->}{\makebox[1ex][c]{\raisebox{0.4ex}{\rule{0.8ex}{0.075ex}}}\kern-0.2ex{\textgreater}}2,
163moredelim=**[is][\color{red}]{`}{`},
164}% lstset
165
166\lstnewenvironment{cfa}[1][]
167{\lstset{#1}}
168{}
169\lstnewenvironment{C++}[1][]                            % use C++ style
170{\lstset{language=C++,moredelim=**[is][\protect\color{red}]{`}{`},#1}\lstset{#1}}
171{}
172
173% inline code @...@
174\lstMakeShortInline@%
175
176
177\title{\texorpdfstring{\protect\CFA : Adding Modern Programming Language Features to C}{Cforall : Adding Modern Programming Language Features to C}}
178
179\author[1]{Aaron Moss}
180\author[1]{Robert Schluntz}
181\author[1]{Peter A. Buhr*}
182\authormark{MOSS \textsc{et al}}
183
184\address[1]{\orgdiv{Cheriton School of Computer Science}, \orgname{University of Waterloo}, \orgaddress{\state{Waterloo, ON}, \country{Canada}}}
185
186\corres{*Peter A. Buhr, Cheriton School of Computer Science, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canada. \email{pabuhr{\char`\@}uwaterloo.ca}}
187
188\fundingInfo{Natural Sciences and Engineering Research Council of Canada}
189
190\abstract[Summary]{
191The 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.
192This installation base and the programmers producing it represent a massive software-engineering investment spanning decades and likely to continue for decades more.
193Nevertheless, C, first standardized over thirty years ago, lacks many features that make programming in more modern languages safer and more productive.
194The 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.
195Prior 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.
196Specifically, \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.
197This paper presents a quick tour of \CFA features showing how their design avoids shortcomings of similar features in C and other C-like languages.
198Finally, experimental results are presented to validate several of the new features.
199}%
200
201\keywords{generic types, tuple types, variadic types, polymorphic functions, C, Cforall}
202
203
204\begin{document}
205\linenumbers                                            % comment out to turn off line numbering
206
207\maketitle
208
209
210\section{Introduction}
211The 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.
212This installation base and the programmers producing it represent a massive software-engineering investment spanning decades and likely to continue for decades more.
213The 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.
214The top 3 rankings over the past 30 years are:
215\begin{center}
216\setlength{\tabcolsep}{10pt}
217\lstDeleteShortInline@%
218\begin{tabular}{@{}rccccccc@{}}
219                & 2018  & 2013  & 2008  & 2003  & 1998  & 1993  & 1988  \\ \hline
220Java    & 1             & 2             & 1             & 1             & 18    & -             & -             \\
221\Textbf{C}& \Textbf{2} & \Textbf{1} & \Textbf{2} & \Textbf{2} & \Textbf{1} & \Textbf{1} & \Textbf{1} \\
222\CC             & 3             & 4             & 3             & 3             & 2             & 2             & 5             \\
223\end{tabular}
224\lstMakeShortInline@%
225\end{center}
226Love it or hate it, C is extremely popular, highly used, and one of the few systems languages.
227In many cases, \CC is often used solely as a better C.
228Nevertheless, C, first standardized over thirty years ago, lacks many features that make programming in more modern languages safer and more productive.
229
230\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 and runtime compatibility with C and a familiar programming model for programmers.
231The four key design goals for \CFA~\cite{Bilson03} are:
232(1) The behaviour of standard C code must remain the same when translated by a \CFA compiler as when translated by a C compiler;
233(2) Standard C code must be as fast and as small when translated by a \CFA compiler as when translated by a C compiler;
234(3) \CFA code must be at least as portable as standard C code;
235(4) Extensions introduced by \CFA must be translated in the most efficient way possible.
236These 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.
237\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.
238
239\CFA is an \emph{open-source} project implemented as an 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).
240Ultimately, a compiler is necessary for advanced features and optimal performance.
241All features discussed in this paper are working, unless otherwise stated as under construction.
242
243Finally, it is impossible to describe a programming language without usages before definitions.
244Therefore, syntax and semantics appear before explanations;
245hence, patience is necessary until details are presented.
246
247
248\section{Polymorphic Functions}
249
250\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}.
251Shortcomings are identified in existing approaches to generic and variadic data types in C-like languages and how these shortcomings are avoided in \CFA.
252Specifically, 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.
253The new constructs are empirically compared with C and \CC approaches via performance experiments in Section~\ref{sec:eval}.
254
255
256\subsection{Name Overloading}
257\label{s:NameOverloading}
258
259\begin{quote}
260There are only two hard things in Computer Science: cache invalidation and \emph{naming things} -- Phil Karlton
261\end{quote}
262C 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.
263\CFA extends the built-in operator overloading by allowing users to define overloads for any function, not just operators, and even any variable;
264Section~\ref{sec:libraries} includes a number of examples of how this overloading simplifies \CFA programming relative to C.
265Code 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.
266As an example:
267\begin{cfa}
268int max = 2147483647;                                           $\C[4in]{// (1)}$
269double max = 1.7976931348623157E+308;           $\C{// (2)}$
270int max( int a, int b ) { return a < b ? b : a; }  $\C{// (3)}$
271double max( double a, double b ) { return a < b ? b : a; }  $\C{// (4)}\CRT$
272max( 7, -max );                                         $\C[2.75in]{// uses (3) and (1), by matching int from constant 7}$
273max( max, 3.14 );                                       $\C{// uses (4) and (2), by matching double from constant 3.14}$
274max( max, -max );                                       $\C{// ERROR: ambiguous}$
275int m = max( max, -max );                       $\C{// uses (3) and (1) twice, by matching return type}\CRT$
276\end{cfa}
277
278\CFA maximizes the ability to reuse names to aggressively address the naming problem.
279In some cases, hundreds of names can be reduced to tens, resulting in a significant cognitive reduction.
280In the above, the name @max@ has a consistent meaning, and a programmer only needs to remember the single concept: maximum.
281To 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).
282As 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.
283
284\Celeven added @_Generic@ expressions, which is used in preprocessor macros to provide a form of ad-hoc polymorphism;
285however, this polymorphism is both functionally and ergonomically inferior to \CFA name overloading.
286The macro wrapping the generic expression imposes some limitations;
287\eg, it cannot implement the example above, because the variables @max@ are ambiguous with the functions @max@.
288Ergonomic 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.
289For backwards compatibility, \CFA supports @_Generic@ expressions, but it is an unnecessary mechanism. \TODO{actually implement that}
290
291% http://fanf.livejournal.com/144696.html
292% http://www.robertgamble.net/2012/01/c11-generic-selections.html
293% https://abissell.com/2014/01/16/c11s-_generic-keyword-macro-applications-and-performance-impacts/
294
295
296\subsection{\texorpdfstring{\protect\lstinline{forall} Functions}{forall Functions}}
297\label{sec:poly-fns}
298
299The 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):
300\begin{cfa}
301`forall( otype T )` T identity( T val ) { return val; }
302int forty_two = identity( 42 );         $\C{// T is bound to int, forty\_two == 42}$
303\end{cfa}
304This @identity@ function can be applied to any complete \newterm{object type} (or @otype@).
305The 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.
306The \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.
307If this extra information is not needed, \eg for a pointer, the type parameter can be declared as a \newterm{data type} (or @dtype@).
308
309In \CFA, the polymorphic runtime-cost is spread over each polymorphic call, because more arguments are passed to polymorphic functions;
310the experiments in Section~\ref{sec:eval} show this overhead is similar to \CC virtual-function calls.
311A design advantage is that, unlike \CC template-functions, \CFA polymorphic-functions are compatible with C \emph{separate compilation}, preventing compilation and code bloat.
312
313Since 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.
314For example, the function @twice@ can be defined using the \CFA syntax for operator overloading:
315\begin{cfa}
316forall( otype T `| { T ?+?(T, T); }` ) T twice( T x ) { return x `+` x; }  $\C{// ? denotes operands}$
317int val = twice( twice( 3.7 ) );
318\end{cfa}
319which works for any type @T@ with a matching addition operator.
320The 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@.
321There 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.
322The first approach has a late conversion from @double@ to @int@ on the final assignment, while the second has an eager conversion to @int@.
323\CFA minimizes the number of conversions and their potential to lose information, so it selects the first approach, which corresponds with C-programmer intuition.
324
325Crucial to the design of a new programming language are the libraries to access thousands of external software features.
326Like \CC, \CFA inherits a massive compatible library-base, where other programming languages must rewrite or provide fragile inter-language communication with C.
327A simple example is leveraging the existing type-unsafe (@void *@) C @bsearch@ to binary search a sorted float array:
328\begin{cfa}
329void * bsearch( const void * key, const void * base, size_t nmemb, size_t size,
330                                int (* compar)( const void *, const void * ));
331int comp( const void * t1, const void * t2 ) {
332         return *(double *)t1 < *(double *)t2 ? -1 : *(double *)t2 < *(double *)t1 ? 1 : 0;
333}
334double key = 5.0, vals[10] = { /* 10 sorted float values */ };
335double * val = (double *)bsearch( &key, vals, 10, sizeof(vals[0]), comp ); $\C{// search sorted array}$
336\end{cfa}
337which can be augmented simply with generalized, type-safe, \CFA-overloaded wrappers:
338\begin{cfa}
339forall( otype T | { int ?<?( T, T ); } ) T * bsearch( T key, const T * arr, size_t size ) {
340        int comp( const void * t1, const void * t2 ) { /* as above with double changed to T */ }
341        return (T *)bsearch( &key, arr, size, sizeof(T), comp );
342}
343forall( otype T | { int ?<?( T, T ); } ) unsigned int bsearch( T key, const T * arr, size_t size ) {
344        T * result = bsearch( key, arr, size ); $\C{// call first version}$
345        return result ? result - arr : size; $\C{// pointer subtraction includes sizeof(T)}$
346}
347double * val = bsearch( 5.0, vals, 10 ); $\C{// selection based on return type}$
348int posn = bsearch( 5.0, vals, 10 );
349\end{cfa}
350The nested function @comp@ provides the hidden interface from typed \CFA to untyped (@void *@) C, plus the cast of the result.
351Providing a hidden @comp@ function in \CC is awkward as lambdas do not use C calling-conventions and template declarations cannot appear at block scope.
352As well, an alternate kind of return is made available: position versus pointer to found element.
353\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@.
354
355\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}).
356For example, it is possible to write a type-safe \CFA wrapper @malloc@ based on the C @malloc@:
357\begin{cfa}
358forall( dtype T | sized(T) ) T * malloc( void ) { return (T *)malloc( sizeof(T) ); }
359int * ip = malloc();                                            $\C{// select type and size from left-hand side}$
360double * dp = malloc();
361struct S {...} * sp = malloc();
362\end{cfa}
363where the return type supplies the type/size of the allocation, which is impossible in most type systems.
364
365Call-site inferencing and nested functions provide a localized form of inheritance.
366For example, the \CFA @qsort@ only sorts in ascending order using @<@.
367However, it is trivial to locally change this behaviour:
368\begin{cfa}
369forall( otype T | { int ?<?( T, T ); } ) void qsort( const T * arr, size_t size ) { /* use C qsort */ }
370{
371        int ?<?( double x, double y ) { return x `>` y; } $\C{// locally override behaviour}$
372        qsort( vals, size );                                    $\C{// descending sort}$
373}
374\end{cfa}
375Within the block, the nested version of @?<?@ performs @?>?@ and this local version overrides the built-in @?<?@ so it is passed to @qsort@.
376Hence, programmers can easily form local environments, adding and modifying appropriate functions, to maximize reuse of other existing functions and types.
377
378To reducing duplication, it is possible to distribute a group of @forall@ (and storage-class qualifiers) over functions/types, so each block declaration is prefixed by the group (see example in Appendix~\ref{s:CforallStack}).
379\begin{cfa}
380forall( otype `T` ) {                                                   $\C{// distribution block, add forall qualifier to declarations}$
381        struct stack { stack_node(`T`) * head; };       $\C{// generic type}$
382        inline {                                                                        $\C{// nested distribution block, add forall/inline to declarations}$
383                void push( stack(`T`) & s, `T` value ) ...      $\C{// generic operations}$
384                T pop( stack(`T`) & s ) ...
385        }
386}
387\end{cfa}
388
389
390\subsection{Traits}
391
392\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:
393\begin{cquote}
394\lstDeleteShortInline@%
395\begin{tabular}{@{}l@{\hspace{\parindentlnth}}|@{\hspace{\parindentlnth}}l@{}}
396\begin{cfa}
397trait `sumable`( otype T ) {
398        void `?{}`( T &, zero_t ); // 0 literal constructor
399        T ?+?( T, T );                   // assortment of additions
400        T `?+=?`( T &, T );
401        T ++?( T & );
402        T ?++( T & );
403};
404\end{cfa}
405&
406\begin{cfa}
407forall( otype T `| sumable( T )` ) // use trait
408T sum( T a[$\,$], size_t size ) {
409        `T` total = { `0` };  // initialize by 0 constructor
410        for ( size_t i = 0; i < size; i += 1 )
411                total `+=` a[i]; // select appropriate +
412        return total;
413}
414\end{cfa}
415\end{tabular}
416\lstMakeShortInline@%
417\end{cquote}
418
419In 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:
420\begin{cfa}
421trait otype( dtype T | sized(T) ) {  // sized is a pseudo-trait for types with known size and alignment
422        void ?{}( T & );                                                $\C{// default constructor}$
423        void ?{}( T &, T );                                             $\C{// copy constructor}$
424        void ?=?( T &, T );                                             $\C{// assignment operator}$
425        void ^?{}( T & );                                               $\C{// destructor}$
426};
427\end{cfa}
428Given 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.
429
430In 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.
431Hence, trait names play no part in type equivalence;
432the names are simply macros for a list of polymorphic assertions, which are expanded at usage sites.
433Nevertheless, trait names form a logical subtype-hierarchy with @dtype@ at the top, where traits often contain overlapping assertions, \eg operator @+@.
434Traits are used like interfaces in Java or abstract base-classes in \CC, but without the nominal inheritance-relationships.
435Instead, 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.
436Hence, 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.
437(Nominal inheritance can be approximated with traits using marker variables or functions, as is done in Go.)
438
439% Nominal inheritance can be simulated with traits using marker variables or functions:
440% \begin{cfa}
441% trait nominal(otype T) {
442%     T is_nominal;
443% };
444% int is_nominal;                                                               $\C{// int now satisfies the nominal trait}$
445% \end{cfa}
446%
447% 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:
448% \begin{cfa}
449% trait pointer_like(otype Ptr, otype El) {
450%     lvalue El *?(Ptr);                                                $\C{// Ptr can be dereferenced into a modifiable value of type El}$
451% }
452% struct list {
453%     int value;
454%     list * next;                                                              $\C{// may omit "struct" on type names as in \CC}$
455% };
456% typedef list * list_iterator;
457%
458% lvalue int *?( list_iterator it ) { return it->value; }
459% \end{cfa}
460% 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@).
461% 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.
462
463
464\section{Generic Types}
465
466A significant shortcoming of standard C is the lack of reusable type-safe abstractions for generic data structures and algorithms.
467Broadly speaking, there are three approaches to implement abstract data-structures in C.
468One approach is to write bespoke data-structures for each context in which they are needed.
469While 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.
470A 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.
471However, 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.
472A 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.
473Furthermore, writing and using preprocessor macros is unnatural and inflexible.
474
475\CC, Java, and other languages use \newterm{generic types} to produce type-safe abstract data-types.
476\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.
477However, for known concrete parameters, the generic-type definition can be inlined, like \CC templates.
478
479A 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:
480\begin{cquote}
481\lstDeleteShortInline@%
482\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
483\begin{cfa}
484forall( otype R, otype S ) struct pair {
485        R first;        S second;
486};
487`forall( otype T )` // dynamic
488T value( pair(const char *, T) p ) { return p.second; }
489`forall( dtype F, otype T )` // dtype-static (concrete)
490T value( pair(F *, T * ) p) { return *p.second; }
491\end{cfa}
492&
493\begin{cfa}
494pair(const char *, int) p = {"magic", 42}; // concrete
495int i = value( p );
496pair(void *, int *) q = { 0, &p.second }; // concrete
497i = value( q );
498double d = 1.0;
499pair(double *, double *) r = { &d, &d }; // concrete
500d = value( r );
501\end{cfa}
502\end{tabular}
503\lstMakeShortInline@%
504\end{cquote}
505
506\CFA classifies generic types as either \newterm{concrete} or \newterm{dynamic}.
507Concrete types have a fixed memory layout regardless of type parameters, while dynamic types vary in memory layout depending on their type parameters.
508A \newterm{dtype-static} type has polymorphic parameters but is still concrete.
509Polymorphic 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.
510
511\CFA generic types also allow checked argument-constraints.
512For example, the following declaration of a sorted set-type ensures the set key supports equality and relational comparison:
513\begin{cfa}
514forall( otype Key | { _Bool ?==?(Key, Key); _Bool ?<?(Key, Key); } ) struct sorted_set;
515\end{cfa}
516
517
518\subsection{Concrete Generic-Types}
519
520The \CFA translator template-expands concrete generic-types into new structure types, affording maximal inlining.
521To 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.
522A 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.
523For example, the concrete instantiation for @pair( const char *, int )@ is:
524\begin{cfa}
525struct _pair_conc0 {
526        const char * first;
527        int second;
528};
529\end{cfa}
530
531A concrete generic-type with dtype-static parameters is also expanded to a structure type, but this type is used for all matching instantiations.
532In 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:
533\begin{cfa}
534struct _pair_conc1 {
535        void * first;
536        void * second;
537};
538\end{cfa}
539
540
541\subsection{Dynamic Generic-Types}
542
543Though \CFA implements concrete generic-types efficiently, it also has a fully general system for dynamic generic types.
544As 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.
545Dynamic generic-types also have an \newterm{offset array} containing structure-member offsets.
546A dynamic generic-@union@ needs no such offset array, as all members are at offset 0, but size and alignment are still necessary.
547Access 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.
548
549The offset arrays are statically generated where possible.
550If 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;
551if 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.
552As an example, the body of the second @value@ function is implemented as:
553\begin{cfa}
554_assign_T( _retval, p + _offsetof_pair[1] ); $\C{// return *p.second}$
555\end{cfa}
556@_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.
557@_offsetof_pair@ is the offset array passed into @value@; this array is generated at the call site as:
558\begin{cfa}
559size_t _offsetof_pair[] = { offsetof( _pair_conc0, first ), offsetof( _pair_conc0, second ) }
560\end{cfa}
561
562In some cases the offset arrays cannot be statically generated.
563For 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.
564\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.
565The \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.
566These 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).
567Results of these layout functions are cached so that they are only computed once per type per function. %, as in the example below for @pair@.
568Layout functions also allow generic types to be used in a function definition without reflecting them in the function signature.
569For 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.
570This function could acquire the layout for @set(T)@ by calling its layout function with the layout of @T@ implicitly passed into the function.
571
572Whether a type is concrete, dtype-static, or dynamic is decided solely on the @forall@'s type parameters.
573This 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.
574If 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.
575
576
577\subsection{Applications}
578\label{sec:generic-apps}
579
580The reuse of dtype-static structure instantiations enables useful programming patterns at zero runtime cost.
581The 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@:
582\begin{cfa}
583forall( dtype T ) int lexcmp( pair( T *, T * ) * a, pair( T *, T * ) * b, int (* cmp)( T *, T * ) ) {
584        return cmp( a->first, b->first ) ? : cmp( a->second, b->second );
585}
586\end{cfa}
587Since @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.
588
589Another useful pattern enabled by reused dtype-static type instantiations is zero-cost \newterm{tag-structures}.
590Sometimes information is only used for type-checking and can be omitted at runtime, \eg:
591\begin{cquote}
592\lstDeleteShortInline@%
593\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
594\begin{cfa}
595forall( dtype Unit ) struct scalar { unsigned long value; };
596struct metres {};
597struct litres {};
598forall( dtype U ) scalar(U) ?+?( scalar(U) a, scalar(U) b ) {
599        return (scalar(U)){ a.value + b.value };
600}
601\end{cfa}
602&
603\begin{cfa}
604scalar(metres) half_marathon = { 21_098 };
605scalar(litres) pool = { 2_500_000 };
606scalar(metres) marathon = half_marathon +
607                                                        half_marathon;
608scalar(litres) two_pools = pool + pool;
609`marathon + pool;`      // compilation ERROR
610\end{cfa}
611\end{tabular}
612\lstMakeShortInline@%
613\end{cquote}
614@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 @?+?@.
615These implementations may even be separately compiled, unlike \CC template functions.
616However, the \CFA type-checker ensures matching types are used by all calls to @?+?@, preventing nonsensical computations like adding a length to a volume.
617
618
619\section{Tuples}
620\label{sec:tuples}
621
622In many languages, functions can return at most one value;
623however, many operations have multiple outcomes, some exceptional.
624Consider C's @div@ and @remquo@ functions, which return the quotient and remainder for a division of integer and float values, respectively.
625\begin{cfa}
626typedef struct { int quo, rem; } div_t;         $\C{// from include stdlib.h}$
627div_t div( int num, int den );
628double remquo( double num, double den, int * quo );
629div_t qr = div( 13, 5 );                                        $\C{// return quotient/remainder aggregate}$
630int q;
631double r = remquo( 13.5, 5.2, &q );                     $\C{// return remainder, alias quotient}$
632\end{cfa}
633@div@ aggregates the quotient/remainder in a structure, while @remquo@ aliases a parameter to an argument.
634Both approaches are awkward.
635Alternatively, a programming language can directly support returning multiple values, \eg in \CFA:
636\begin{cfa}
637[ int, int ] div( int num, int den );           $\C{// return two integers}$
638[ double, double ] div( double num, double den ); $\C{// return two doubles}$
639int q, r;                                                                       $\C{// overloaded variable names}$
640double q, r;
641[ q, r ] = div( 13, 5 );                                        $\C{// select appropriate div and q, r}$
642[ q, r ] = div( 13.5, 5.2 );                            $\C{// assign into tuple}$
643\end{cfa}
644This approach is straightforward to understand and use;
645therefore, why do few programming languages support this obvious feature or provide it awkwardly?
646To answer, there are complex consequences that cascade through multiple aspects of the language, especially the type-system.
647This section show these consequences and how \CFA handles them.
648
649
650\subsection{Tuple Expressions}
651
652The addition of multiple-return-value functions (MRVF) are \emph{useless} without a syntax for accepting multiple values at the call-site.
653The simplest mechanism for capturing the return values is variable assignment, allowing the values to be retrieved directly.
654As 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}.
655
656However, 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:
657\begin{cfa}
658printf( "%d %d\n", div( 13, 5 ) );                      $\C{// return values seperated into arguments}$
659\end{cfa}
660Here, the values returned by @div@ are composed with the call to @printf@ by flattening the tuple into separate arguments.
661However, the \CFA type-system must support significantly more complex composition:
662\begin{cfa}
663[ int, int ] foo$\(_1\)$( int );                        $\C{// overloaded foo functions}$
664[ double ] foo$\(_2\)$( int );
665void bar( int, double, double );
666`bar`( foo( 3 ), foo( 3 ) );
667\end{cfa}
668The type-resolver only has the tuple return-types to resolve the call to @bar@ as the @foo@ parameters are identical, which involves unifying the possible @foo@ functions with @bar@'s parameter list.
669No combination of @foo@s are an exact match with @bar@'s parameters, so the resolver applies C conversions.
670The minimal cost is @bar( foo@$_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.
671
672
673\subsection{Tuple Variables}
674
675An important observation from function composition is that new variable names are not required to initialize parameters from an MRVF.
676\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:
677\begin{cfa}
678[ int, int ] qr = div( 13, 5 );                         $\C{// tuple-variable declaration and initialization}$
679[ double, double ] qr = div( 13.5, 5.2 );
680\end{cfa}
681where the tuple variable-name serves the same purpose as the parameter name(s).
682Tuple variables can be composed of any types, except for array types, since array sizes are generally unknown in C.
683
684One way to access the tuple-variable components is with assignment or composition:
685\begin{cfa}
686[ q, r ] = qr;                                                          $\C{// access tuple-variable components}$
687printf( "%d %d\n", qr );
688\end{cfa}
689\CFA also supports \newterm{tuple indexing} to access single components of a tuple expression:
690\begin{cfa}
691[int, int] * p = &qr;                                           $\C{// tuple pointer}$
692int rem = qr`.1`;                                                       $\C{// access remainder}$
693int quo = div( 13, 5 )`.0`;                                     $\C{// access quotient}$
694p`->0` = 5;                                                                     $\C{// change quotient}$
695bar( qr`.1`, qr );                                                      $\C{// pass remainder and quotient/remainder}$
696rem = [div( 13, 5 ), 42]`.0.1`;                         $\C{// access 2nd component of 1st component}$
697\end{cfa}
698
699
700\subsection{Flattening and Restructuring}
701
702In function call contexts, tuples support implicit flattening and restructuring conversions.
703Tuple flattening recursively expands a tuple into the list of its basic components.
704Tuple structuring packages a list of expressions into a value of tuple type, \eg:
705\begin{cfa}
706int f( int, int );
707[int] g( [int, int] );
708[int] h( int, [int, int] );
709[int, int] x;
710int y;
711f( x );                                                                         $\C{// flatten}$
712g( y, 10 );                                                                     $\C{// structure}$
713h( x, y );                                                                      $\C{// flatten and structure}$
714\end{cfa}
715In the call to @f@, @x@ is implicitly flattened so the components of @x@ are passed as the two arguments.
716In 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@.
717Finally, 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]@.
718The 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.
719
720
721\subsection{Tuple Assignment}
722
723An assignment where the left side is a tuple type is called \newterm{tuple assignment}.
724There 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.
725\begin{cfa}
726int x = 10;
727double y = 3.5;
728[int, double] z;
729z = [x, y];                                                                     $\C{// multiple assignment}$
730[x, y] = z;                                                                     $\C{// multiple assignment}$
731z = 10;                                                                         $\C{// mass assignment}$
732[y, x] = 3.14;                                                          $\C{// mass assignment}$
733\end{cfa}
734Both kinds of tuple assignment have parallel semantics, so that each value on the left and right side is evaluated before any assignments occur.
735As 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]@.
736This 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.
737For example, @[y, x] = 3.14@ performs the assignments @y = 3.14@ and @x = 3.14@, yielding @y == 3.14@ and @x == 3@;
738whereas, C cascading assignment @y = x = 3.14@ performs the assignments @x = 3.14@ and @y = x@, yielding @3@ in @y@ and @x@.
739Finally, 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.
740This example shows mass, multiple, and cascading assignment used in one expression:
741\begin{cfa}
742[void] f( [int, int] );
743f( [x, y] = z = 1.5 );                                          $\C{// assignments in parameter list}$
744\end{cfa}
745
746
747\subsection{Member Access}
748
749It is also possible to access multiple fields from a single expression using a \newterm{member-access}.
750The result is a single tuple-valued expression whose type is the tuple of the types of the members, \eg:
751\begin{cfa}
752struct S { int x; double y; char * z; } s;
753s.[x, y, z] = 0;
754\end{cfa}
755Here, the mass assignment sets all members of @s@ to zero.
756Since 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).
757\begin{cfa}
758[int, int, long, double] x;
759void f( double, long );
760x.[0, 1] = x.[1, 0];                                            $\C{// rearrange: [x.0, x.1] = [x.1, x.0]}$
761f( x.[0, 3] );                                                          $\C{// drop: f(x.0, x.3)}$
762[int, int, int] y = x.[2, 0, 2];                        $\C{// duplicate: [y.0, y.1, y.2] = [x.2, x.0.x.2]}$
763\end{cfa}
764It is also possible for a member access to contain other member accesses, \eg:
765\begin{cfa}
766struct A { double i; int j; };
767struct B { int * k; short l; };
768struct C { int x; A y; B z; } v;
769v.[x, y.[i, j], z.k];                                           $\C{// [v.x, [v.y.i, v.y.j], v.z.k]}$
770\end{cfa}
771
772
773\begin{comment}
774\subsection{Casting}
775
776In C, the cast operator is used to explicitly convert between types.
777In \CFA, the cast operator has a secondary use as type ascription.
778That 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:
779\begin{cfa}
780int f();     // (1)
781double f()// (2)
782
783f();       // ambiguous - (1),(2) both equally viable
784(int)f()// choose (2)
785\end{cfa}
786
787Since casting is a fundamental operation in \CFA, casts should be given a meaningful interpretation in the context of tuples.
788Taking a look at standard C provides some guidance with respect to the way casts should work with tuples:
789\begin{cfa}
790int f();
791void g();
792
793(void)f()// (1)
794(int)g()// (2)
795\end{cfa}
796In C, (1) is a valid cast, which calls @f@ and discards its result.
797On the other hand, (2) is invalid, because @g@ does not produce a result, so requesting an @int@ to materialize from nothing is nonsensical.
798Generalizing 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.
799
800Formally, 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 $T_i$.
801Excess 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.
802This approach follows naturally from the way that a cast to @void@ works in C.
803
804For example, in
805\begin{cfa}
806[int, int, int] f();
807[int, [int, int], int] g();
808
809([int, double])f();           $\C{// (1)}$
810([int, int, int])g();         $\C{// (2)}$
811([void, [int, int]])g();      $\C{// (3)}$
812([int, int, int, int])g();    $\C{// (4)}$
813([int, [int, int, int]])g()$\C{// (5)}$
814\end{cfa}
815
816(1) discards the last element of the return value and converts the second element to @double@.
817Since @int@ is effectively a 1-element tuple, (2) discards the second component of the second element of the return value of @g@.
818If @g@ is free of side effects, this expression is equivalent to @[(int)(g().0), (int)(g().1.0), (int)(g().2)]@.
819Since @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)]@).
820
821Note 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.}.
822As such, (4) is invalid because the cast target type contains 4 components, while the source type contains only 3.
823Similarly, (5) is invalid because the cast @([int, int, int])(g().1)@ is invalid.
824That is, it is invalid to cast @[int, int]@ to @[int, int, int]@.
825\end{comment}
826
827
828\subsection{Polymorphism}
829
830Tuples also integrate with \CFA polymorphism as a kind of generic type.
831Due 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:
832\begin{cfa}
833forall( otype T, dtype U ) void f( T x, U * y );
834f( [5, "hello"] );
835\end{cfa}
836where @[5, "hello"]@ is flattened, giving argument list @5, "hello"@, and @T@ binds to @int@ and @U@ binds to @const char@.
837Tuples, however, may contain polymorphic components.
838For example, a plus operator can be written to sum two triples.
839\begin{cfa}
840forall( otype T | { T ?+?( T, T ); } ) [T, T, T] ?+?( [T, T, T] x, [T, T, T] y ) {
841        return [x.0 + y.0, x.1 + y.1, x.2 + y.2];
842}
843[int, int, int] x;
844int i1, i2, i3;
845[i1, i2, i3] = x + ([10, 20, 30]);
846\end{cfa}
847
848Flattening and restructuring conversions are also applied to tuple types in polymorphic type assertions.
849\begin{cfa}
850[int] f( [int, double], double );
851forall( otype T, otype U | { T f( T, U, U ); } ) void g( T, U );
852g( 5, 10.21 );
853\end{cfa}
854Hence, function parameter and return lists are flattened for the purposes of type unification allowing the example to pass expression resolution.
855This relaxation is possible by extending the thunk scheme described by Bilson~\cite{Bilson03}.
856% 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:
857% \begin{cfa}
858% int _thunk( int _p0, double _p1, double _p2 ) { return f( [_p0, _p1], _p2 ); }
859% \end{cfa}
860% so the thunk provides flattening and structuring conversions to inferred functions, improving the compatibility of tuples and polymorphism.
861% These thunks are generated locally using gcc nested-functions, rather hoisting them to the external scope, so they can easily access local state.
862
863
864\subsection{Variadic Tuples}
865\label{sec:variadic-tuples}
866
867To define variadic functions, \CFA adds a new kind of type parameter, @ttype@ (tuple type).
868Matching against a @ttype@ parameter consumes all remaining argument components and packages them into a tuple, binding to the resulting tuple of types.
869In 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.
870As such, @ttype@ variables are also called \newterm{argument packs}.
871
872Like variadic templates, @ttype@ polymorphic functions are primarily manipulated via recursion.
873Since nothing is known about a parameter pack by default, assertion parameters are key to doing anything meaningful.
874Unlike variadic templates, @ttype@ polymorphic functions can be separately compiled.
875For example, a generalized @sum@ function:
876\begin{cfa}
877int sum$\(_0\)$() { return 0; }
878forall( ttype Params | { int sum( Params ); } ) int sum$\(_1\)$( int x, Params rest ) {
879        return x + sum( rest );
880}
881sum( 10, 20, 30 );
882\end{cfa}
883Since @sum@\(_0\) does not accept any arguments, it is not a valid candidate function for the call @sum(10, 20, 30)@.
884In 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]@.
885The process continues until @Params@ is bound to @[]@, requiring an assertion @int sum()@, which matches @sum@\(_0\) and terminates the recursion.
886Effectively, 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))@.
887
888It is reasonable to take the @sum@ function a step further to enforce a minimum number of arguments:
889\begin{cfa}
890int sum( int x, int y ) { return x + y; }
891forall( ttype Params | { int sum( int, Params ); } ) int sum( int x, int y, Params rest ) {
892        return sum( x + y, rest );
893}
894\end{cfa}
895One more step permits the summation of any summable type with all arguments of the same type:
896\begin{cfa}
897trait summable( otype T ) {
898        T ?+?( T, T );
899};
900forall( otype R | summable( R ) ) R sum( R x, R y ) {
901        return x + y;
902}
903forall( otype R, ttype Params | summable(R) | { R sum(R, Params); } ) R sum(R x, R y, Params rest) {
904        return sum( x + y, rest );
905}
906\end{cfa}
907Unlike C variadic functions, it is unnecessary to hard code the number and expected types.
908Furthermore, this code is extendable for any user-defined type with a @?+?@ operator.
909Summing arbitrary heterogeneous lists is possible with similar code by adding the appropriate type variables and addition operators.
910
911It is also possible to write a type-safe variadic print function to replace @printf@:
912\begin{cfa}
913struct S { int x, y; };
914forall( otype T, ttype Params | { void print(T); void print(Params); } ) void print(T arg, Params rest) {
915        print(arg);  print(rest);
916}
917void print( const char * x ) { printf( "%s", x ); }
918void print( int x ) { printf( "%d", x ); }
919void print( S s ) { print( "{ ", s.x, ",", s.y, " }" ); }
920print( "s = ", (S){ 1, 2 }, "\n" );
921\end{cfa}
922This example showcases a variadic-template-like decomposition of the provided argument list.
923The individual @print@ functions allow printing a single element of a type.
924The polymorphic @print@ allows printing any list of types, where as each individual type has a @print@ function.
925The individual print functions can be used to build up more complicated @print@ functions, such as @S@, which cannot be done with @printf@ in C.
926This mechanism is used to seamlessly print tuples in the \CFA I/O library (see Section~\ref{s:IOLibrary}).
927
928Finally, it is possible to use @ttype@ polymorphism to provide arbitrary argument forwarding functions.
929For example, it is possible to write @new@ as a library function:
930\begin{cfa}
931forall( otype R, otype S ) void ?{}( pair(R, S) *, R, S );
932forall( dtype T, ttype Params | sized(T) | { void ?{}( T *, Params ); } ) T * new( Params p ) {
933        return ((T *)malloc()){ p };                    $\C{// construct into result of malloc}$
934}
935pair( int, char ) * x = new( 42, '!' );
936\end{cfa}
937The @new@ function provides the combination of type-safe @malloc@ with a \CFA constructor call, making it impossible to forget constructing dynamically allocated objects.
938This function provides the type-safety of @new@ in \CC, without the need to specify the allocated type again, thanks to return-type inference.
939
940
941\subsection{Implementation}
942
943Tuples are implemented in the \CFA translator via a transformation into \newterm{generic types}.
944For each $N$, the first time an $N$-tuple is seen in a scope a generic type with $N$ type parameters is generated, \eg:
945\begin{cfa}
946[int, int] f() {
947        [double, double] x;
948        [int, double, int] y;
949}
950\end{cfa}
951is transformed into:
952\begin{cfa}
953forall( dtype T0, dtype T1 | sized(T0) | sized(T1) ) struct _tuple2 {
954        T0 field_0;                                                             $\C{// generated before the first 2-tuple}$
955        T1 field_1;
956};
957_tuple2(int, int) f() {
958        _tuple2(double, double) x;
959        forall( dtype T0, dtype T1, dtype T2 | sized(T0) | sized(T1) | sized(T2) ) struct _tuple3 {
960                T0 field_0;                                                     $\C{// generated before the first 3-tuple}$
961                T1 field_1;
962                T2 field_2;
963        };
964        _tuple3(int, double, int) y;
965}
966\end{cfa}
967{\sloppy
968Tuple expressions are then simply converted directly into compound literals, \eg @[5, 'x', 1.24]@ becomes @(_tuple3(int, char, double)){ 5, 'x', 1.24 }@.
969\par}%
970
971\begin{comment}
972Since tuples are essentially structures, tuple indexing expressions are just field accesses:
973\begin{cfa}
974void f(int, [double, char]);
975[int, double] x;
976
977x.0+x.1;
978printf("%d %g\n", x);
979f(x, 'z');
980\end{cfa}
981Is transformed into:
982\begin{cfa}
983void f(int, _tuple2(double, char));
984_tuple2(int, double) x;
985
986x.field_0+x.field_1;
987printf("%d %g\n", x.field_0, x.field_1);
988f(x.field_0, (_tuple2){ x.field_1, 'z' });
989\end{cfa}
990Note that due to flattening, @x@ used in the argument position is converted into the list of its fields.
991In the call to @f@, the second and third argument components are structured into a tuple argument.
992Similarly, tuple member expressions are recursively expanded into a list of member access expressions.
993
994Expressions that may contain side effects are made into \newterm{unique expressions} before being expanded by the flattening conversion.
995Each unique expression is assigned an identifier and is guaranteed to be executed exactly once:
996\begin{cfa}
997void g(int, double);
998[int, double] h();
999g(h());
1000\end{cfa}
1001Internally, this expression is converted to two variables and an expression:
1002\begin{cfa}
1003void g(int, double);
1004[int, double] h();
1005
1006_Bool _unq0_finished_ = 0;
1007[int, double] _unq0;
1008g(
1009        (_unq0_finished_ ? _unq0 : (_unq0 = f(), _unq0_finished_ = 1, _unq0)).0,
1010        (_unq0_finished_ ? _unq0 : (_unq0 = f(), _unq0_finished_ = 1, _unq0)).1,
1011);
1012\end{cfa}
1013Since argument evaluation order is not specified by the C programming language, this scheme is built to work regardless of evaluation order.
1014The first time a unique expression is executed, the actual expression is evaluated and the accompanying boolean is set to true.
1015Every subsequent evaluation of the unique expression then results in an access to the stored result of the actual expression.
1016Tuple member expressions also take advantage of unique expressions in the case of possible impurity.
1017
1018Currently, the \CFA translator has a very broad, imprecise definition of impurity, where any function call is assumed to be impure.
1019This 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.
1020
1021The various kinds of tuple assignment, constructors, and destructors generate GNU C statement expressions.
1022A 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.
1023The 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.
1024However, 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.
1025\end{comment}
1026
1027
1028\section{Control Structures}
1029
1030\CFA identifies inconsistent, problematic, and missing control structures in C, and extends, modifies, and adds control structures to increase functionality and safety.
1031
1032
1033\subsection{\texorpdfstring{\protect\lstinline{if} Statement}{if Statement}}
1034
1035The @if@ expression allows declarations, similar to @for@ declaration expression:
1036\begin{cfa}
1037if ( int x = f() ) ...                                          $\C{// x != 0}$
1038if ( int x = f(), y = g() ) ...                         $\C{// x != 0 \&\& y != 0}$
1039if ( int x = f(), y = g(); `x < y` ) ...        $\C{// relational expression}$
1040\end{cfa}
1041Unless 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.}
1042The scope of the declaration(s) is local to the @if@ statement but exist within both the ``then'' and ``else'' clauses.
1043
1044
1045\subsection{\texorpdfstring{\protect\lstinline{switch} Statement}{switch Statement}}
1046
1047There 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.
1048
1049C 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.}.
1050\CFA provides a shorthand for a non-contiguous list:
1051\begin{cquote}
1052\lstDeleteShortInline@%
1053\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
1054\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
1055\begin{cfa}
1056case 2, 10, 34, 42:
1057\end{cfa}
1058&
1059\begin{cfa}
1060case 2: case 10: case 34: case 42:
1061\end{cfa}
1062\end{tabular}
1063\lstMakeShortInline@%
1064\end{cquote}
1065for a contiguous list:\footnote{gcc has the same mechanism but awkward syntax, \lstinline@2 ...42@, as a space is required after a number, otherwise the first period is a decimal point.}
1066\begin{cquote}
1067\lstDeleteShortInline@%
1068\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
1069\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
1070\begin{cfa}
1071case 2~42:
1072\end{cfa}
1073&
1074\begin{cfa}
1075case 2: case 3: ... case 41: case 42:
1076\end{cfa}
1077\end{tabular}
1078\lstMakeShortInline@%
1079\end{cquote}
1080and a combination:
1081\begin{cfa}
1082case -12~-4, -1~5, 14~21, 34~42:
1083\end{cfa}
1084
1085C allows placement of @case@ clauses \emph{within} statements nested in the @switch@ body (called Duff's device~\cite{Duff83});
1086\begin{cfa}
1087switch ( i ) {
1088  case 0:
1089        for ( int i = 0; i < 10; i += 1 ) {
1090                ...
1091  `case 1:`             // no initialization of loop index
1092                ...
1093        }
1094}
1095\end{cfa}
1096\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.
1097
1098C allows placement of declaration within the @switch@ body and unreachable code at the start, resulting in undefined behaviour:
1099\begin{cfa}
1100switch ( x ) {
1101        `int y = 1;`                                                    $\C{// unreachable initialization}$
1102        `x = 7;`                                                                $\C{// unreachable code without label/branch}$
1103  case 0:
1104        ...
1105        `int z = 0;`                                                    $\C{// unreachable initialization, cannot appear after case}$
1106        z = 2;
1107  case 1:
1108        `x = z;`                                                                $\C{// without fall through, z is undefined}$
1109}
1110\end{cfa}
1111\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.
1112\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.
1113
1114C @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};
1115@case@ clauses are made disjoint by the @break@ statement.
1116While 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.
1117For 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.
1118
1119\begin{figure}
1120\centering
1121\lstDeleteShortInline@%
1122\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
1123\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
1124\begin{cfa}
1125`choose` ( day ) {
1126  case Mon~Thu:  // program
1127
1128  case Fri:  // program
1129        wallet += pay;
1130        `fallthrough;`
1131  case Sat:  // party
1132        wallet -= party;
1133
1134  case Sun:  // rest
1135
1136  default:  // error
1137}
1138\end{cfa}
1139&
1140\begin{cfa}
1141switch ( day ) {
1142  case Mon: case Tue: case Wed: case Thu:  // program
1143        `break;`
1144  case Fri:  // program
1145        wallet += pay;
1146
1147  case Sat:  // party
1148        wallet -= party;
1149        `break;`
1150  case Sun:  // rest
1151        `break;`
1152  default:  // error
1153}
1154\end{cfa}
1155\end{tabular}
1156\lstMakeShortInline@%
1157\caption{\lstinline|choose| versus \lstinline|switch| Statements}
1158\label{f:ChooseSwitchStatements}
1159\end{figure}
1160
1161Finally, 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.
1162The target label must be below the @fallthrough@ and may not be nested in a control structure, \ie @fallthrough@ cannot form a loop, and the target label must be at the same or higher level as the containing @case@ clause and located at the same level as a @case@ clause;
1163the target label may be case @default@, but only associated with the current @switch@/@choose@ statement.
1164
1165\begin{figure}
1166\centering
1167\lstDeleteShortInline@%
1168\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
1169\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{non-terminator}}  & \multicolumn{1}{c}{\textbf{target label}}     \\
1170\begin{cfa}
1171choose ( ... ) {
1172  case 3:
1173        if ( ... ) {
1174                ... `fallthrough;`  // goto case 4
1175        } else {
1176                ...
1177        }
1178        // implicit break
1179  case 4:
1180\end{cfa}
1181&
1182\begin{cfa}
1183choose ( ... ) {
1184  case 3:
1185        ... `fallthrough common;`
1186  case 4:
1187        ... `fallthrough common;`
1188  `common`: // below fallthrough at same level as case clauses
1189        ...      // common code for cases 3 and 4
1190        // implicit break
1191  case 4:
1192\end{cfa}
1193\end{tabular}
1194\lstMakeShortInline@%
1195\caption{\lstinline|fallthrough| Statement}
1196\label{f:FallthroughStatement}
1197\end{figure}
1198
1199
1200\subsection{\texorpdfstring{Labelled \protect\lstinline{continue} / \protect\lstinline{break}}{Labelled continue / break}}
1201
1202While C provides @continue@ and @break@ statements for altering control flow, both are restricted to one level of nesting for a particular control structure.
1203Unfortunately, this restriction forces programmers to use @goto@ to achieve the equivalent control-flow for more than one level of nesting.
1204To 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.
1205For both @continue@ and @break@, the target label must be directly associated with a @for@, @while@ or @do@ statement;
1206for @break@, the target label can also be associated with a @switch@, @if@ or compound (@{}@) statement.
1207Figure~\ref{f:MultiLevelExit} shows @continue@ and @break@ indicating the specific control structure, and the corresponding C program using only @goto@ and labels.
1208The innermost loop has 7 exit points, which cause continuation or termination of one or more of the 7 nested control-structures.
1209
1210\begin{figure}
1211\lstDeleteShortInline@%
1212\begin{tabular}{@{\hspace{\parindentlnth}}l@{\hspace{\parindentlnth}}l@{\hspace{\parindentlnth}}l@{}}
1213\multicolumn{1}{@{\hspace{\parindentlnth}}c@{\hspace{\parindentlnth}}}{\textbf{\CFA}}   & \multicolumn{1}{@{\hspace{\parindentlnth}}c}{\textbf{C}}      \\
1214\begin{cfa}
1215`LC:` {
1216        ... $declarations$ ...
1217        `LS:` switch ( ... ) {
1218          case 3:
1219                `LIF:` if ( ... ) {
1220                        `LF:` for ( ... ) {
1221                                ... break `LC`; ...
1222                                ... break `LS`; ...
1223                                ... break `LIF`; ...
1224                                ... continue `LF;` ...
1225                                ... break `LF`; ...
1226                        } // for
1227                } else {
1228                        ... break `LIF`; ...
1229                } // if
1230        } // switch
1231} // compound
1232\end{cfa}
1233&
1234\begin{cfa}
1235{
1236        ... $declarations$ ...
1237        switch ( ... ) {
1238          case 3:
1239                if ( ... ) {
1240                        for ( ... ) {
1241                                ... goto `LC`; ...
1242                                ... goto `LS`; ...
1243                                ... goto `LIF`; ...
1244                                ... goto `LFC`; ...
1245                                ... goto `LFB`; ...
1246                          `LFC:` ; } `LFB:` ;
1247                } else {
1248                        ... goto `LIF`; ...
1249                } `LIF:` ;
1250        } `LS:` ;
1251} `LC:` ;
1252\end{cfa}
1253&
1254\begin{cfa}
1255
1256
1257
1258
1259
1260
1261
1262// terminate compound
1263// terminate switch
1264// terminate if
1265// continue loop
1266// terminate loop
1267
1268
1269
1270// terminate if
1271
1272\end{cfa}
1273\end{tabular}
1274\lstMakeShortInline@%
1275\caption{Multi-level Exit}
1276\label{f:MultiLevelExit}
1277\end{figure}
1278
1279With respect to safety, both labelled @continue@ and @break@ are a @goto@ restricted in the following ways:
1280\begin{itemize}
1281\item
1282They cannot create a loop, which means only the looping constructs cause looping.
1283This restriction means all situations resulting in repeated execution are clearly delineated.
1284\item
1285They cannot branch into a control structure.
1286This restriction prevents missing declarations and/or initializations at the start of a control structure resulting in undefined behaviour.
1287\end{itemize}
1288The 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.
1289Furthermore, 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.
1290With @goto@, the label is at the end of the control structure, which fails to convey this important clue early enough to the reader.
1291Finally, using an explicit target for the transfer instead of an implicit target allows new constructs to be added or removed without affecting existing constructs.
1292Otherwise, the implicit targets of the current @continue@ and @break@, \ie the closest enclosing loop or @switch@, change as certain constructs are added or removed.
1293
1294
1295\subsection{Exception Handling}
1296
1297The following framework for \CFA exception handling is in place, excluding some runtime type-information and virtual functions.
1298\CFA provides two forms of exception handling: \newterm{fix-up} and \newterm{recovery} (see Figure~\ref{f:CFAExceptionHandling})~\cite{Buhr92b,Buhr00a}.
1299Both 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.
1300\CFA restricts exception types to those defined by aggregate type @exception@.
1301The 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@).
1302If @resume@ or @throw@ have no exception type, it is a reresume/rethrow, meaning the currently exception continues propagation.
1303If there is no current exception, the reresume/rethrow results in a runtime error.
1304
1305\begin{figure}
1306\begin{cquote}
1307\lstDeleteShortInline@%
1308\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
1309\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{Resumption}}      & \multicolumn{1}{c}{\textbf{Termination}}      \\
1310\begin{cfa}
1311`exception R { int fix; };`
1312void f() {
1313        R r;
1314        ... `resume( r );` ...
1315        ... r.fix // control returns here after handler
1316}
1317`try` {
1318        ... f(); ...
1319} `catchResume( R r )` {
1320        ... r.fix = ...; // return correction to raise
1321} // dynamic return to _Resume
1322\end{cfa}
1323&
1324\begin{cfa}
1325`exception T {};`
1326void f() {
1327
1328        ... `throw( T{} );` ...
1329        // control does NOT return here after handler
1330}
1331`try` {
1332        ... f(); ...
1333} `catch( T t )` {
1334        ... // recover and continue
1335} // static return to next statement
1336\end{cfa}
1337\end{tabular}
1338\lstMakeShortInline@%
1339\end{cquote}
1340\caption{\CFA Exception Handling}
1341\label{f:CFAExceptionHandling}
1342\end{figure}
1343
1344The set of exception types in a list of catch clause may include both a resumption and termination handler:
1345\begin{cfa}
1346try {
1347        ... resume( `R{}` ); ...
1348} catchResume( `R` r ) { ... throw( R{} ); ... } $\C{\color{red}// H1}$
1349   catch( `R` r ) { ... }                                       $\C{\color{red}// H2}$
1350
1351\end{cfa}
1352The resumption propagation raises @R@ and the stack is not unwound;
1353the exception is caught by the @catchResume@ clause and handler H1 is invoked.
1354The termination propagation in handler H1 raises @R@ and the stack is unwound;
1355the exception is caught by the @catch@ clause and handler H2 is invoked.
1356The termination handler is available because the resumption propagation did not unwind the stack.
1357
1358An additional feature is conditional matching in a catch clause:
1359\begin{cfa}
1360try {
1361        ... write( `datafile`, ... ); ...               $\C{// may throw IOError}$
1362        ... write( `logfile`, ... ); ...
1363} catch ( IOError err; `err.file == datafile` ) { ... } $\C{// handle datafile error}$
1364   catch ( IOError err; `err.file == logfile` ) { ... } $\C{// handle logfile error}$
1365   catch ( IOError err ) { ... }                        $\C{// handler error from other files}$
1366\end{cfa}
1367where the throw inserts the failing file-handle into the I/O exception.
1368Conditional catch cannot be trivially mimicked by other mechanisms because once an exception is caught, handler clauses in that @try@ statement are no longer eligible..
1369
1370The resumption raise can specify an alternate stack on which to raise an exception, called a \newterm{nonlocal raise}:
1371\begin{cfa}
1372resume( $\emph{exception-type}$, $\emph{alternate-stack}$ )
1373resume( $\emph{alternate-stack}$ )
1374\end{cfa}
1375These 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}.
1376Nonlocal 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.
1377
1378To facilitate nonlocal raise, \CFA provides dynamic enabling and disabling of nonlocal exception-propagation.
1379The constructs for controlling propagation of nonlocal exceptions are the @enable@ and the @disable@ blocks:
1380\begin{cquote}
1381\lstDeleteShortInline@%
1382\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
1383\begin{cfa}
1384enable $\emph{exception-type-list}$ {
1385        // allow non-local raise
1386}
1387\end{cfa}
1388&
1389\begin{cfa}
1390disable $\emph{exception-type-list}$ {
1391        // disallow non-local raise
1392}
1393\end{cfa}
1394\end{tabular}
1395\lstMakeShortInline@%
1396\end{cquote}
1397The arguments for @enable@/@disable@ specify the exception types allowed to be propagated or postponed, respectively.
1398Specifying no exception type is shorthand for specifying all exception types.
1399Both @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.
1400Coroutines and tasks start with non-local exceptions disabled, allowing handlers to be put in place, before non-local exceptions are explicitly enabled.
1401\begin{cfa}
1402void main( mytask & t ) {                                       $\C{// thread starts here}$
1403        // non-local exceptions disabled
1404        try {                                                                   $\C{// establish handles for non-local exceptions}$
1405                enable {                                                        $\C{// allow non-local exception delivery}$
1406                        // task body
1407                }
1408        // appropriate catchResume/catch handlers
1409        }
1410}
1411\end{cfa}
1412
1413Finally, \CFA provides a Java like  @finally@ clause after the catch clauses:
1414\begin{cfa}
1415try {
1416        ... f(); ...
1417// catchResume or catch clauses
1418} `finally` {
1419        // house keeping
1420}
1421\end{cfa}
1422The finally clause is always executed, i.e., if the try block ends normally or if an exception is raised.
1423If an exception is raised and caught, the handler is run before the finally clause.
1424Like a destructor (see Section~\ref{s:ConstructorsDestructors}), a finally clause can raise an exception but not if there is an exception being propagated.
1425Mimicking the @finally@ clause with mechanisms like RAII is non-trivially when there are multiple types and local accesses.
1426
1427
1428\subsection{\texorpdfstring{\protect\lstinline{with} Statement}{with Statement}}
1429\label{s:WithStatement}
1430
1431Heterogeneous data is often aggregated into a structure/union.
1432To reduce syntactic noise, \CFA provides a @with@ statement (see Pascal~\cite[\S~4.F]{Pascal}) to elide aggregate field-qualification by opening a scope containing the field identifiers.
1433\begin{cquote}
1434\vspace*{-\baselineskip}%???
1435\lstDeleteShortInline@%
1436\begin{cfa}
1437struct S { char c; int i; double d; };
1438struct T { double m, n; };
1439// multiple aggregate parameters
1440\end{cfa}
1441\begin{tabular}{@{}l@{\hspace{\parindentlnth}}|@{\hspace{\parindentlnth}}l@{}}
1442\begin{cfa}
1443void f( S & s, T & t ) {
1444        `s.`c; `s.`i; `s.`d;
1445        `t.`m; `t.`n;
1446}
1447\end{cfa}
1448&
1449\begin{cfa}
1450void f( S & s, T & t ) `with ( s, t )` {
1451        c; i; d;                // no qualification
1452        m; n;
1453}
1454\end{cfa}
1455\end{tabular}
1456\lstMakeShortInline@%
1457\end{cquote}
1458Object-oriented programming languages only provide implicit qualification for the receiver.
1459
1460In detail, the @with@ statement has the form:
1461\begin{cfa}
1462$\emph{with-statement}$:
1463        'with' '(' $\emph{expression-list}$ ')' $\emph{compound-statement}$
1464\end{cfa}
1465and may appear as the body of a function or nested within a function body.
1466Each expression in the expression-list provides a type and object.
1467The type must be an aggregate type.
1468(Enumerations are already opened.)
1469The object is the implicit qualifier for the open structure-fields.
1470
1471All expressions in the expression list are open in parallel within the compound statement, which is different from Pascal, which nests the openings from left to right.
1472The difference between parallel and nesting occurs for fields with the same name and type:
1473\begin{cfa}
1474struct S { int `i`; int j; double m; } s, w;
1475struct T { int `i`; int k; int m; } t, w;
1476with ( s, t ) {
1477        j + k;                                                                  $\C{// unambiguous, s.j + t.k}$
1478        m = 5.0;                                                                $\C{// unambiguous, t.m = 5.0}$
1479        m = 1;                                                                  $\C{// unambiguous, s.m = 1}$
1480        int a = m;                                                              $\C{// unambiguous, a = s.i }$
1481        double b = m;                                                   $\C{// unambiguous, b = t.m}$
1482        int c = s.i + t.i;                                              $\C{// unambiguous, qualification}$
1483        (double)m;                                                              $\C{// unambiguous, cast}$
1484}
1485\end{cfa}
1486For parallel semantics, both @s.i@ and @t.i@ are visible, so @i@ is ambiguous without qualification;
1487for nested semantics, @t.i@ hides @s.i@, so @i@ implies @t.i@.
1488\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.
1489Qualification or a cast is used to disambiguate.
1490
1491There is an interesting problem between parameters and the function-body @with@, \eg:
1492\begin{cfa}
1493void ?{}( S & s, int i ) with ( s ) {           $\C{// constructor}$
1494        `s.i = i;`  j = 3;  m = 5.5;                    $\C{// initialize fields}$
1495}
1496\end{cfa}
1497Here, 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@.
1498To solve this problem, parameters are treated like an initialized aggregate:
1499\begin{cfa}
1500struct Params {
1501        S & s;
1502        int i;
1503} params;
1504\end{cfa}
1505and implicitly opened \emph{after} a function-body open, to give them higher priority:
1506\begin{cfa}
1507void ?{}( S & s, int `i` ) with ( s ) `with( $\emph{\color{red}params}$ )` {
1508        s.i = `i`; j = 3; m = 5.5;
1509}
1510\end{cfa}
1511Finally, a cast may be used to disambiguate among overload variables in a @with@ expression:
1512\begin{cfa}
1513with ( w ) { ... }                                                      $\C{// ambiguous, same name and no context}$
1514with ( (S)w ) { ... }                                           $\C{// unambiguous, cast}$
1515\end{cfa}
1516and @with@ expressions may be complex expressions with type reference (see Section~\ref{s:References}) to aggregate:
1517\begin{cfa}
1518struct S { int i, j; } sv;
1519with ( sv ) {                                                           $\C{// implicit reference}$
1520        S & sr = sv;
1521        with ( sr ) {                                                   $\C{// explicit reference}$
1522                S * sp = &sv;
1523                with ( *sp ) {                                          $\C{// computed reference}$
1524                        i = 3; j = 4;                                   $\C{\color{red}// sp--{\textgreater}i, sp--{\textgreater}j}$
1525                }
1526                i = 2; j = 3;                                           $\C{\color{red}// sr.i, sr.j}$
1527        }
1528        i = 1; j = 2;                                                   $\C{\color{red}// sv.i, sv.j}$
1529}
1530\end{cfa}
1531
1532Collectively, these control-structure enhancements reduce programmer burden and increase readability and safety.
1533
1534
1535\section{Declarations}
1536
1537Declarations in C have weaknesses and omissions.
1538\CFA attempts to correct and add to C declarations, while ensuring \CFA subjectively ``feels like'' C.
1539An 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.
1540Maintaining 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.
1541Nevertheless, some features from other approaches are undeniably convenient;
1542\CFA attempts to adapt these features to the C paradigm.
1543
1544
1545\subsection{Alternative Declaration Syntax}
1546
1547C declaration syntax is notoriously confusing and error prone.
1548For example, many C programmers are confused by a declaration as simple as:
1549\begin{cquote}
1550\lstDeleteShortInline@%
1551\begin{tabular}{@{}ll@{}}
1552\begin{cfa}
1553int * x[5]
1554\end{cfa}
1555&
1556\raisebox{-0.75\totalheight}{\input{Cdecl}}
1557\end{tabular}
1558\lstMakeShortInline@%
1559\end{cquote}
1560Is this an array of 5 pointers to integers or a pointer to an array of 5 integers?
1561If there is any doubt, it implies productivity and safety issues even for basic programs.
1562Another 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.
1563For example, a function returning a pointer to an array of integers is defined and used in the following way:
1564\begin{cfa}
1565int `(*`f`())[`5`]` {...};                                      $\C{// definition}$
1566 ... `(*`f`())[`3`]` += 1;                                      $\C{// usage}$
1567\end{cfa}
1568Essentially, the return type is wrapped around the function name in successive layers (like an onion).
1569While attempting to make the two contexts consistent is a laudable goal, it has not worked out in practice.
1570
1571\CFA provides its own type, variable and function declarations, using a different syntax~\cite[pp.~856--859]{Buhr94a}.
1572The new declarations place qualifiers to the left of the base type, while C declarations place qualifiers to the right.
1573The qualifiers have the same meaning but are ordered left to right to specify a variable's type.
1574\begin{cquote}
1575\lstDeleteShortInline@%
1576\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{\hspace{2\parindentlnth}}l@{}}
1577\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
1578\begin{cfa}
1579`[5] *` int x1;
1580`* [5]` int x2;
1581`[* [5] int]` f( int p );
1582\end{cfa}
1583&
1584\begin{cfa}
1585int `*` x1 `[5]`;
1586int `(*`x2`)[5]`;
1587`int (*`f( int p )`)[5]`;
1588\end{cfa}
1589&
1590\begin{cfa}
1591// array of 5 pointers to int
1592// pointer to array of 5 int
1593// function returning pointer to array of 5 int and taking int
1594\end{cfa}
1595\end{tabular}
1596\lstMakeShortInline@%
1597\end{cquote}
1598The only exception is bit field specification, which always appear to the right of the base type.
1599% 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.
1600However, unlike C, \CFA type declaration tokens are distributed across all variables in the declaration list.
1601For instance, variables @x@ and @y@ of type pointer to integer are defined in \CFA as follows:
1602\begin{cquote}
1603\lstDeleteShortInline@%
1604\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
1605\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
1606\begin{cfa}
1607`*` int x, y;
1608int y;
1609\end{cfa}
1610&
1611\begin{cfa}
1612int `*`x, `*`y;
1613
1614\end{cfa}
1615\end{tabular}
1616\lstMakeShortInline@%
1617\end{cquote}
1618The downside of the \CFA semantics is the need to separate regular and pointer declarations.
1619
1620\begin{comment}
1621Other examples are:
1622\begin{cquote}
1623\lstDeleteShortInline@%
1624\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{\hspace{2\parindentlnth}}l@{}}
1625\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{C}}     \\
1626\begin{cfa}
1627[ 5 ] int z;
1628[ 5 ] * char w;
1629* [ 5 ] double v;
1630struct s {
1631        int f0:3;
1632        * int f1;
1633        [ 5 ] * int f2;
1634};
1635\end{cfa}
1636&
1637\begin{cfa}
1638int z[ 5 ];
1639char * w[ 5 ];
1640double (* v)[ 5 ];
1641struct s {
1642        int f0:3;
1643        int * f1;
1644        int * f2[ 5 ]
1645};
1646\end{cfa}
1647&
1648\begin{cfa}
1649// array of 5 integers
1650// array of 5 pointers to char
1651// pointer to array of 5 doubles
1652
1653// common bit field syntax
1654
1655
1656
1657\end{cfa}
1658\end{tabular}
1659\lstMakeShortInline@%
1660\end{cquote}
1661\end{comment}
1662
1663All 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:
1664\begin{cquote}
1665\lstDeleteShortInline@%
1666\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{\hspace{2\parindentlnth}}l@{}}
1667\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{C}}     \\
1668\begin{cfa}
1669extern const * const int x;
1670static const * [5] const int y;
1671\end{cfa}
1672&
1673\begin{cfa}
1674int extern const * const x;
1675static const int (* const y)[5]
1676\end{cfa}
1677&
1678\begin{cfa}
1679// external const pointer to const int
1680// internal const pointer to array of 5 const int
1681\end{cfa}
1682\end{tabular}
1683\lstMakeShortInline@%
1684\end{cquote}
1685Specifiers must appear at the start of a \CFA function declaration\footnote{\label{StorageClassSpecifier}
1686The 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}}.
1687
1688The new declaration syntax can be used in other contexts where types are required, \eg casts and the pseudo-function @sizeof@:
1689\begin{cquote}
1690\lstDeleteShortInline@%
1691\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
1692\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
1693\begin{cfa}
1694y = (* int)x;
1695i = sizeof([ 5 ] * int);
1696\end{cfa}
1697&
1698\begin{cfa}
1699y = (int *)x;
1700i = sizeof(int * [ 5 ]);
1701\end{cfa}
1702\end{tabular}
1703\lstMakeShortInline@%
1704\end{cquote}
1705
1706The syntax of the new function-prototype declaration follows directly from the new function-definition syntax;
1707as well, parameter names are optional, \eg:
1708\begin{cfa}
1709[ int x ] f ( /* void */ );             $\C[2.5in]{// returning int with no parameters}$
1710[ int x ] f (...);                              $\C{// returning int with unknown parameters}$
1711[ * int ] g ( int y );                  $\C{// returning pointer to int with int parameter}$
1712[ void ] h ( int, char );               $\C{// returning no result with int and char parameters}$
1713[ * int, int ] j ( int );               $\C{// returning pointer to int and int with int parameter}$
1714\end{cfa}
1715This syntax allows a prototype declaration to be created by cutting and pasting source text from the function-definition header (or vice versa).
1716Like 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:
1717\begin{cquote}
1718\lstDeleteShortInline@%
1719\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
1720\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
1721\begin{cfa}
1722[double] foo(), foo( int ), foo( double ) {...}
1723\end{cfa}
1724&
1725\begin{cfa}
1726double foo1( void ), foo2( int ), foo3( double );
1727\end{cfa}
1728\end{tabular}
1729\lstMakeShortInline@%
1730\end{cquote}
1731where \CFA allows the last function in the list to define its body.
1732
1733The syntax for pointers to \CFA functions specifies the pointer name on the right, \eg:
1734\begin{cfa}
1735* [ int x ] () fp;                              $\C{// pointer to function returning int with no parameters}$
1736* [ * int ] ( int y ) gp;               $\C{// pointer to function returning pointer to int with int parameter}$
1737* [ ] ( int, char ) hp;                 $\C{// pointer to function returning no result with int and char parameters}$
1738* [ * int, int ] ( int ) jp;    $\C{// pointer to function returning pointer to int and int with int parameter}$
1739\end{cfa}
1740Note, a function name cannot be specified:
1741\begin{cfa}
1742* [ int x ] f () fp;                    $\C{// function name "f" is disallowed}\CRT$
1743\end{cfa}
1744
1745Finally, new \CFA declarations may appear together with C declarations in the same program block, but cannot be mixed within a specific declaration.
1746Therefore, a programmer has the option of either continuing to use traditional C declarations or take advantage of the new style.
1747Clearly, both styles need to be supported for some time due to existing C-style header-files, particularly for UNIX-like systems.
1748
1749
1750\subsection{References}
1751\label{s:References}
1752
1753All variables in C have an \newterm{address}, a \newterm{value}, and a \newterm{type};
1754at 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.
1755The C type-system does not always track the relationship between a value and its address;
1756a 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'').
1757For 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.
1758Despite 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.
1759
1760Within a lexical scope, lvalue expressions have an \newterm{address interpretation} for writing a value or a \newterm{value interpretation} to read a value.
1761For example, in @x = y@, @x@ has an address interpretation, while @y@ has a value interpretation.
1762While 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.
1763In C, for any type @T@ there is a pointer type @T *@, the value of which is the address of a value of type @T@.
1764A 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 @&?@.
1765
1766\begin{cfa}
1767int x = 1, y = 2, * p1, * p2, ** p3;
1768p1 = &x;                                                                        $\C{// p1 points to x}$
1769p2 = &y;                                                                        $\C{// p2 points to y}$
1770p3 = &p1;                                                                       $\C{// p3 points to p1}$
1771*p2 = ((*p1 + *p2) * (**p3 - *p1)) / (**p3 - 15);
1772\end{cfa}
1773
1774Unfortunately, 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.
1775For 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.
1776However, 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.
1777To solve these problems, \CFA introduces reference types @T &@;
1778a @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:
1779
1780\begin{cfa}
1781int x = 1, y = 2, & r1, & r2, && r3;
1782&r1 = &x;                                                                       $\C{// r1 points to x}$
1783&r2 = &y;                                                                       $\C{// r2 points to y}$
1784&&r3 = &&r1;                                                            $\C{// r3 points to r2}$
1785r2 = ((r1 + r2) * (r3 - r1)) / (r3 - 15);       $\C{// implicit dereferencing}$
1786\end{cfa}
1787
1788Except for auto-dereferencing by the compiler, this reference example is exactly the same as the previous pointer example.
1789Hence, 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.
1790One 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:
1791
1792\begin{cfa}
1793`*`r2 = ((`*`r1 + `*`r2) * (`**`r3 - `*`r1)) / (`**`r3 - 15);
1794\end{cfa}
1795
1796References in \CFA are similar to those in \CC, with important improvements, which can be seen in the example above.
1797Firstly, \CFA does not forbid references to references.
1798This provides a much more orthogonal design for library implementors, obviating the need for workarounds such as @std::reference_wrapper@.
1799Secondly, \CFA references are rebindable, whereas \CC references have a fixed address.
1800\newsavebox{\LstBox}
1801\begin{lrbox}{\LstBox}
1802\lstset{basicstyle=\footnotesize\linespread{0.9}\sf}
1803\begin{cfa}
1804int & r = *new( int );
1805...                                                                                     $\C{// non-null reference}$
1806delete &r;                                                                      $\C{// unmanaged (programmer) memory-management}$
1807r += 1;                                                                         $\C{// undefined reference}$
1808\end{cfa}
1809\end{lrbox}
1810Rebinding allows \CFA references to be default-initialized (\eg to a null pointer\footnote{
1811While 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:
1812\begin{cquote}
1813\usebox{\LstBox}
1814\end{cquote}
1815}%
1816) and point to different addresses throughout their lifetime, like pointers.
1817Rebinding is accomplished by extending the existing syntax and semantics of the address-of operator in C.
1818
1819In 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.
1820In \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.
1821The 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.
1822This rebinding occurs to an arbitrary depth of reference nesting;
1823loosely speaking, nested address-of operators produce a nested lvalue pointer up to the depth of the reference.
1824These 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@.
1825More precisely:
1826\begin{itemize}
1827\item
1828if @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).
1829       
1830\item
1831if @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).
1832\end{itemize}
1833Since 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.
1834
1835By analogy to pointers, \CFA references also allow cv-qualifiers such as @const@:
1836\begin{cfa}
1837const int cx = 5;                                                       $\C{// cannot change cx}$
1838const int & cr = cx;                                            $\C{// cannot change cr's referred value}$
1839&cr = &cx;                                                                      $\C{// rebinding cr allowed}$
1840cr = 7;                                                                         $\C{// ERROR, cannot change cr}$
1841int & const rc = x;                                                     $\C{// must be initialized, like in \CC}$
1842&rc = &x;                                                                       $\C{// ERROR, cannot rebind rc}$
1843rc = 7;                                                                         $\C{// x now equal to 7}$
1844\end{cfa}
1845Given that a reference is meant to represent a lvalue, \CFA provides some syntactic shortcuts when initializing references.
1846There are three initialization contexts in \CFA: declaration initialization, argument/parameter binding, and return/temporary binding.
1847In each of these contexts, the address-of operator on the target lvalue is elided.
1848The 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@.
1849
1850More 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;
1851this conversion is used in any context in \CFA where an implicit conversion is allowed.
1852Similarly, 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.
1853The final reference conversion included in \CFA is ``rvalue-to-reference'' conversion, implemented by means of an implicit temporary.
1854When 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.
1855\begin{cfa}
1856struct S { double x, y; };
1857int x, y;
1858void f( int & i, int & j, S & s, int v[] );
1859f( 3, x + y, (S){ 1.0, 7.0 }, (int [3]){ 1, 2, 3 } ); $\C{// pass rvalue to lvalue \(\Rightarrow\) implicit temporary}$
1860\end{cfa}
1861This 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.
1862\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.
1863
1864
1865\subsection{Type Nesting}
1866
1867Nested 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@).
1868Java 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.
1869Since \CFA in not object-oriented, adopting dynamic scoping does not make sense;
1870instead \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}).
1871\begin{figure}
1872\centering
1873\lstDeleteShortInline@%
1874\begin{tabular}{@{}l@{\hspace{3em}}l|l@{}}
1875\multicolumn{1}{c@{\hspace{3em}}}{\textbf{C Type Nesting}}      & \multicolumn{1}{c|}{\textbf{C Implicit Hoisting}}     & \multicolumn{1}{c}{\textbf{\CFA}}     \\
1876\hline
1877\begin{cfa}
1878struct S {
1879        enum C { R, G, B };
1880        struct T {
1881                union U { int i, j; };
1882                enum C c;
1883                short int i, j;
1884        };
1885        struct T t;
1886} s;
1887
1888int rtn() {
1889        s.t.c = R;
1890        struct T t = { R, 1, 2 };
1891        enum C c;
1892        union U u;
1893}
1894\end{cfa}
1895&
1896\begin{cfa}
1897enum C { R, G, B };
1898union U { int i, j; };
1899struct T {
1900        enum C c;
1901        short int i, j;
1902};
1903struct S {
1904        struct T t;
1905} s;
1906       
1907
1908
1909
1910
1911
1912
1913\end{cfa}
1914&
1915\begin{cfa}
1916struct S {
1917        enum C { R, G, B };
1918        struct T {
1919                union U { int i, j; };
1920                enum C c;
1921                short int i, j;
1922        };
1923        struct T t;
1924} s;
1925
1926int rtn() {
1927        s.t.c = `S.`R;  // type qualification
1928        struct `S.`T t = { `S.`R, 1, 2 };
1929        enum `S.`C c;
1930        union `S.T.`U u;
1931}
1932\end{cfa}
1933\end{tabular}
1934\lstMakeShortInline@%
1935\caption{Type Nesting / Qualification}
1936\label{f:TypeNestingQualification}
1937\end{figure}
1938In the C left example, types @C@, @U@ and @T@ are implicitly hoisted outside of type @S@ into the containing block scope.
1939In the \CFA right example, the types are not hoisted and accessible.
1940
1941
1942\subsection{Constructors and Destructors}
1943\label{s:ConstructorsDestructors}
1944
1945One 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.
1946However, this manual approach is verbose, and it is useful to manage resources other than memory (\eg file handles) using the same mechanism as memory.
1947\CC addresses these issues using Resource Aquisition Is Initialization (RAII), implemented by means of \newterm{constructor} and \newterm{destructor} functions;
1948\CFA adopts constructors and destructors (and @finally@) to facilitate RAII.
1949While 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.
1950Specifically, \CFA constructors and destructors are denoted by name and first parameter-type versus name and nesting in an aggregate type.
1951Constructor 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.
1952
1953In \CFA, a constructor is named @?{}@ and a destructor is named @^?{}@\footnote{%
1954The symbol \lstinline+^+ is used for the destructor name because it was the last binary operator that could be used in a unary context.}.
1955The name @{}@ comes from the syntax for the initializer: @struct S { int i, j; } s = `{` 2, 3 `}`@.
1956Like other \CFA operators, these names represent the syntax used to call the constructor or destructor, \eg @?{}(x, ...)@ or @^{}(x, ...)@.
1957The constructor and destructor have return type @void@, and the first parameter is a reference to the object type to be constructed or destructed.
1958While the first parameter is informally called the @this@ parameter, as in object-oriented languages, any variable name may be used.
1959Both constructors and destructors allow additional parametes after the @this@ parameter for specifying values for initialization/de-initialization\footnote{
1960Destruction parameters are useful for specifying storage-management actions, such as de-initialize but not deallocate.}.
1961\begin{cfa}
1962struct VLA { int len, * data; };
1963void ?{}( VLA & vla ) with ( vla ) { len = 10;  data = alloc( len ); }  $\C{// default constructor}$
1964void ^?{}( VLA & vla ) with ( vla ) { free( data ); } $\C{// destructor}$
1965{
1966        VLA x;                                                                  $\C{// implicit:  ?\{\}( x );}$
1967}                                                                                       $\C{// implicit:  ?\^{}\{\}( x );}$
1968\end{cfa}
1969@VLA@ is a \newterm{managed type}\footnote{
1970A 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.
1971A 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.
1972For details of the code-generation placement of implicit constructor and destructor calls among complex executable statements see~\cite[\S~2.2]{Schluntz17}.
1973
1974\CFA also provides syntax for \newterm{initialization} and \newterm{copy}:
1975\begin{cfa}
1976void ?{}( VLA & vla, int size, char fill ) with ( vla ) {  $\C{// initialization}$
1977        len = size;  data = alloc( len, fill );
1978}
1979void ?{}( VLA & vla, VLA other ) {                      $\C{// copy, shallow}$
1980        vla.len = other.len;  vla.data = other.data;
1981}
1982\end{cfa}
1983(Note, the example is purposely simplified using shallow-copy semantics.)
1984An 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).
1985\begin{cfa}
1986VLA va = `{` 20, 0 `}`,  * arr = alloc()`{` 5, 0 `}`;
1987\end{cfa}
1988Note, the use of a \newterm{constructor expression} to initialize the storage from the dynamic storage-allocation.
1989Like \CC, the copy constructor has two parameters, the second of which is a value parameter with the same type as the first parameter;
1990appropriate care is taken to not recursively call the copy constructor when initializing the second parameter.
1991
1992\CFA constructors may be explicitly call, like Java, and destructors may be explicitly called, like \CC.
1993Explicit 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.
1994While existing call syntax works for explicit calls to constructors and destructors, \CFA also provides a more concise \newterm{operator syntax} for both:
1995\begin{cfa}
1996{
1997        VLA  x,            y = { 20, 0x01 },     z = y; $\C{// z points to y}$
1998        //      ?{}( x );   ?{}( y, 20, 0x01 );   ?{}( z, y );
1999        ^x{};                                                                   $\C{// deallocate x}$
2000        x{};                                                                    $\C{// reallocate x}$
2001        z{ 5, 0xff };                                                   $\C{// reallocate z, not pointing to y}$
2002        ^y{};                                                                   $\C{// deallocate y}$
2003        y{ x };                                                                 $\C{// reallocate y, points to x}$
2004        x{};                                                                    $\C{// reallocate x, not pointing to y}$
2005        // ^?{}(z);  ^?{}(y);  ^?{}(x);
2006}
2007\end{cfa}
2008
2009To 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.
2010These default functions can be overridden by user-generated versions.
2011For 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;
2012if default zero-initialization is desired, the default constructors can be overridden.
2013For user-generated types, the four functions are also automatically generated.
2014@enum@ types are handled the same as their underlying integral type, and unions are also bitwise copied and no-op initialized and destructed.
2015For compatibility with C, a copy constructor from the first union member type is also defined.
2016For @struct@ types, each of the four functions are implicitly defined to call their corresponding functions on each member of the struct.
2017To better simulate the behaviour of C initializers, a set of \newterm{field constructors} is also generated for structures.
2018A 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.
2019To 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;
2020similarly, the generated default constructor is hidden upon declaration of any constructor.
2021These semantics closely mirror the rule for implicit declaration of constructors in \CC\cite[p.~186]{ANSI98:C++}.
2022
2023In some circumstance programmers may not wish to have implicit constructor and destructor generation and calls.
2024In these cases, \CFA provides the initialization syntax \lstinline|S x `@=` {}|, and the object becomes unmanaged, so implicit constructor and destructor calls are not generated.
2025Any C initializer can be the right-hand side of an \lstinline|@=| initializer, \eg \lstinline|VLA a @= { 0, 0x0 }|, with the usual C initialization semantics.
2026The same syntax can be used in a compound literal, \eg \lstinline|a = VLA`@`{ 0, 0x0 }|, to create a C-style literal.
2027The 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.
2028
2029
2030% \subsection{Default Parameters}
2031
2032
2033\section{Literals}
2034
2035C 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.
2036In 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.
2037
2038A 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.
2039\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.
2040
2041
2042\subsection{Integral Suffixes}
2043
2044New integral suffixes @hh@ (half of half of @int@) for @char@, @h@ (half of @int@) for @short@, and @z@ for @size_t@, and length suffixes for 8, 16, 32, 64, and 128 bit integers.
2045%Additional integral suffixes are added to cover all the integral types and lengths.
2046\begin{cquote}
2047\lstDeleteShortInline@%
2048\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{\hspace{2\parindentlnth}}l@{}}
2049\begin{cfa}
205020_`hh`     // signed char
205121_`hh`u   // unsigned char
205222_`h`       // signed short int
205323_u`h`     // unsigned short int
205424`z`         // size_t
2055\end{cfa}
2056&
2057\begin{cfa}
205820_`L8`      // int8_t
205921_u`l8`     // uint8_t
206022_`l16`     // int16_t
206123_u`l16`   // uint16_t
206224_`l32`     // int32_t
2063\end{cfa}
2064&
2065\begin{cfa}
206625_u`l32`      // uint32_t
206726_`l64`        // int64_t
206827_`l64`u      // uint64_t
206926_`L128`     // int128
207027_`L128`u   // unsigned int128
2071\end{cfa}
2072\end{tabular}
2073\lstMakeShortInline@%
2074\end{cquote}
2075
2076
2077\subsection{0/1}
2078
2079In C, @0@ has the special property that it is the only ``false'' value;
2080from the standard, any value that compares equal to @0@ is false, while any value that compares unequal to @0@ is true.
2081As 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.
2082Operator 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.
2083To 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);
2084@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.
2085With 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 )@.
2086\CC makes types truthy by adding a conversion to @bool@;
2087prior to the addition of explicit cast operators in \CCeleven, this approach had the pitfall of making truthy types transitively convertable to any numeric type;
2088\CFA avoids this issue.
2089
2090Similarly, \CFA also has a special type for @1@, @one_t@;
2091like @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 @--@.
2092The addition of @one_t@ allows generic algorithms to handle the unit value uniformly for types where it is meaningful.
2093\TODO{Make this sentence true}
2094In 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)@;
2095analogous overloads for the decrement operators are present as well.
2096
2097
2098\subsection{User Literals}
2099
2100For readability, it is useful to associate units to scale literals, \eg weight (stone, pound, kilogram) or time (seconds, minutes, hours).
2101The left of Figure~\ref{f:UserLiteral} shows the \CFA alternative call-syntax (postfix: literal argument before function name), using the backquote, to convert basic literals into user literals.
2102The backquote is a small character, making the unit (function name) predominate.
2103For examples, the multi-precision integer-type in Section~\ref{s:MultiPrecisionIntegers} has user literals:
2104{\lstset{language=CFA,moredelim=**[is][\color{red}]{|}{|},deletedelim=**[is][]{`}{`}}
2105\begin{cfa}
2106y = 9223372036854775807L|`mp| * 18446744073709551615UL|`mp|;
2107y = "12345678901234567890123456789"|`mp| + "12345678901234567890123456789"|`mp|;
2108\end{cfa}
2109Because \CFA uses a standard function, all types and literals are applicable, as well as overloading and conversions, where @?`@ denotes a postfix-function name and @`@ denotes a postfix-function call.
2110}%
2111\begin{cquote}
2112\lstset{language=CFA,moredelim=**[is][\color{red}]{|}{|},deletedelim=**[is][]{`}{`}}
2113\lstDeleteShortInline@%
2114\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{\hspace{2\parindentlnth}}l@{\hspace{2\parindentlnth}}l@{}}
2115\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{postfix function}}        & \multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{constant}}      & \multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{variable/expression}}   & \multicolumn{1}{c}{\textbf{postfix pointer}}  \\
2116\begin{cfa}
2117int |?`h|( int s );
2118int |?`h|( double s );
2119int |?`m|( char c );
2120int |?`m|( const char * s );
2121int |?`t|( int a, int b, int c );
2122\end{cfa}
2123&
2124\begin{cfa}
21250 |`h|;
21263.5|`h|;
2127'1'|`m|;
2128"123" "456"|`m|;
2129[1,2,3]|`t|;
2130\end{cfa}
2131&
2132\begin{cfa}
2133int i = 7;
2134i|`h|;
2135(i + 3)|`h|;
2136(i + 3.5)|`h|;
2137
2138\end{cfa}
2139&
2140\begin{cfa}
2141int (* |?`p|)( int i );
2142|?`p| = |?`h|;
21433|`p|;
2144i|`p|;
2145(i + 3)|`p|;
2146\end{cfa}
2147\end{tabular}
2148\lstMakeShortInline@%
2149\end{cquote}
2150
2151The right of Figure~\ref{f:UserLiteral} shows the equivalent \CC version using the underscore for the call-syntax.
2152However, \CC restricts the types, \eg @unsigned long long int@ and @long double@ to represent integral and floating literals.
2153After which, user literals must match (no conversions);
2154hence, it is necessary to overload the unit with all appropriate types.
2155
2156\begin{figure}
2157\centering
2158\lstset{language=CFA,moredelim=**[is][\color{red}]{|}{|},deletedelim=**[is][]{`}{`}}
2159\lstDeleteShortInline@%
2160\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
2161\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{\CC}}      \\
2162\begin{cfa}
2163struct W {
2164        double stones;
2165};
2166void ?{}( W & w ) { w.stones = 0; }
2167void ?{}( W & w, double w ) { w.stones = w; }
2168W ?+?( W l, W r ) {
2169        return (W){ l.stones + r.stones };
2170}
2171W |?`st|(double w) { return (W){ w }; }
2172W |?`lb|(double w) { return (W){ w/14.0 }; }
2173W |?`kg|(double w) { return (W){ w*0.16 }; }
2174
2175
2176
2177int main() {
2178        W w, heavy = { 20 };
2179        w = 155|`lb|;
2180        w = 0b_1111|`st|;
2181        w = 0_233|`lb|;
2182        w = 0x_9b_u|`kg|;
2183        w = 5.5|`st| + 8|`kg| + 25.01|`lb| + heavy;
2184}
2185\end{cfa}
2186&
2187\begin{cfa}
2188struct W {
2189        double stones;
2190        W() { stones = 0.0; }
2191        W( double w ) { stones = w; }
2192};
2193W operator+( W l, W r ) {
2194        return W( l.stones + r.stones );
2195}
2196W |operator""_st|(unsigned long long int w) {return W(w); }
2197W |operator""_lb|(unsigned long long int w) {return W(w/14.0); }
2198W |operator""_kg|(unsigned long long int w) {return W(w*0.16); }
2199W |operator""_st|(long double w ) { return W( w ); }
2200W |operator""_lb|(long double w ) { return W( w / 14.0 ); }
2201W |operator""_kg|(long double w ) { return W( w * 0.16 ); }
2202int main() {
2203        W w, heavy = { 20 };
2204        w = 155|_lb|;
2205        w = 0b1111|_lb|;       // error, binary unsupported
2206        w = 0${\color{red}\LstBasicStyle{'}}$233|_lb|;          // quote separator
2207        w = 0x9b|_kg|;
2208        w = 5.5d|_st| + 8|_kg| + 25.01|_lb| + heavy;
2209}
2210\end{cfa}
2211\end{tabular}
2212\lstMakeShortInline@%
2213\caption{User Literal}
2214\label{f:UserLiteral}
2215\end{figure}
2216
2217
2218\section{Libraries}
2219\label{sec:libraries}
2220
2221As 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.
2222\CFA has replacement libraries condensing hundreds of existing C names into tens of \CFA overloaded names, all without rewriting the actual computations.
2223In many cases, the interface is an inline wrapper providing overloading during compilation but zero cost at runtime.
2224The following sections give a glimpse of the interface reduction to many C libraries.
2225In 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.
2226
2227
2228\subsection{Limits}
2229
2230C library @limits.h@ provides lower and upper bound constants for the basic types.
2231\CFA name overloading is used to condense these typed constants, \eg:
2232\begin{cquote}
2233\lstDeleteShortInline@%
2234\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
2235\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{Definition}}      & \multicolumn{1}{c}{\textbf{Usage}}    \\
2236\begin{cfa}
2237const short int `MIN` = -32768;
2238const int `MIN` = -2147483648;
2239const long int `MIN` = -9223372036854775808L;
2240\end{cfa}
2241&
2242\begin{cfa}
2243short int si = `MIN`;
2244int i = `MIN`;
2245long int li = `MIN`;
2246\end{cfa}
2247\end{tabular}
2248\lstMakeShortInline@%
2249\end{cquote}
2250The result is a significant reduction in names to access typed constants, \eg:
2251\begin{cquote}
2252\lstDeleteShortInline@%
2253\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
2254\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
2255\begin{cfa}
2256MIN
2257
2258MAX
2259
2260PI
2261E
2262\end{cfa}
2263&
2264\begin{cfa}
2265SCHAR_MIN, CHAR_MIN, SHRT_MIN, INT_MIN, LONG_MIN,
2266        LLONG_MIN, FLT_MIN, DBL_MIN, LDBL_MIN
2267SCHAR_MAX, UCHAR_MAX, SHRT_MAX, INT_MAX, LONG_MAX,
2268        LLONG_MAX, FLT_MAX, DBL_MAX, LDBL_MAX
2269M_PI, M_PIl
2270M_E, M_El
2271\end{cfa}
2272\end{tabular}
2273\lstMakeShortInline@%
2274\end{cquote}
2275
2276
2277\subsection{Math}
2278
2279C library @math.h@ provides many mathematical functions.
2280\CFA function overloading is used to condense these mathematical 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}
2286float `log`( float x );
2287double `log`( double );
2288double _Complex `log`( double _Complex x );
2289\end{cfa}
2290&
2291\begin{cfa}
2292float f = `log`( 3.5 );
2293double d = `log`( 3.5 );
2294double _Complex dc = `log`( 3.5+0.5I );
2295\end{cfa}
2296\end{tabular}
2297\lstMakeShortInline@%
2298\end{cquote}
2299The result is a significant reduction in names to access math 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}
2305log
2306sqrt
2307sin
2308\end{cfa}
2309&
2310\begin{cfa}
2311logf, log, logl, clogf, clog, clogl
2312sqrtf, sqrt, sqrtl, csqrtf, csqrt, csqrtl
2313sinf, sin, sinl, csinf, csin, csinl
2314\end{cfa}
2315\end{tabular}
2316\lstMakeShortInline@%
2317\end{cquote}
2318While \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).
2319For example, it is impossible to overload @atan@ for both one and two arguments;
2320instead the names @atan@ and @atan2@ are required (see Section~\ref{s:NameOverloading}).
2321The 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.
2322
2323
2324\subsection{Standard}
2325
2326C library @stdlib.h@ provides many general functions.
2327\CFA function overloading is used to condense these utility functions, \eg:
2328\begin{cquote}
2329\lstDeleteShortInline@%
2330\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
2331\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{Definition}}      & \multicolumn{1}{c}{\textbf{Usage}}    \\
2332\begin{cfa}
2333unsigned int `abs`( int );
2334double `abs`( double );
2335double abs( double _Complex );
2336\end{cfa}
2337&
2338\begin{cfa}
2339unsigned int i = `abs`( -1 );
2340double d = `abs`( -1.5 );
2341double d = `abs`( -1.5+0.5I );
2342\end{cfa}
2343\end{tabular}
2344\lstMakeShortInline@%
2345\end{cquote}
2346The result is a significant reduction in names to access utility functions, \eg:
2347\begin{cquote}
2348\lstDeleteShortInline@%
2349\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
2350\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
2351\begin{cfa}
2352abs
2353strto
2354random
2355\end{cfa}
2356&
2357\begin{cfa}
2358abs, labs, llabs, fabsf, fabs, fabsl, cabsf, cabs, cabsl
2359strtol, strtoul, strtoll, strtoull, strtof, strtod, strtold
2360srand48, mrand48, lrand48, drand48
2361\end{cfa}
2362\end{tabular}
2363\lstMakeShortInline@%
2364\end{cquote}
2365In additon, there are polymorphic functions, like @min@ and @max@, that work on any type with operators @?<?@ or @?>?@.
2366
2367The following shows one example where \CFA \emph{extends} an existing standard C interface to reduce complexity and provide safety.
2368C/\Celeven provide a number of complex and overlapping storage-management operation to support the following capabilities:
2369\begin{description}%[topsep=3pt,itemsep=2pt,parsep=0pt]
2370\item[fill]
2371an allocation with a specified character.
2372\item[resize]
2373an existing allocation to decreased or increased its size.
2374In 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.
2375For an increase in storage size, new storage after the copied data may be filled.
2376\item[align]
2377an allocation on a specified memory boundary, \eg, an address multiple of 64 or 128 for cache-line purposes.
2378\item[array]
2379allocation with a specified number of elements.
2380An array may be filled, resized, or aligned.
2381\end{description}
2382Table~\ref{t:StorageManagementOperations} shows the capabilities provided by C/\Celeven allocation-functions and how all the capabilities can be combined into two \CFA functions.
2383\CFA storage-management functions extend the C equivalents by overloading, providing shallow type-safety, and removing the need to specify the base allocation-size.
2384Figure~\ref{f:StorageAllocation} contrasts \CFA and C storage-allocation performing the same operations with the same type safety.
2385
2386\begin{table}
2387\centering
2388\lstDeleteShortInline@%
2389\lstMakeShortInline~%
2390\begin{tabular}{@{}r|r|l|l|l|l@{}}
2391\multicolumn{1}{c}{}&           & \multicolumn{1}{c|}{fill}     & resize        & align & array \\
2392\hline
2393C               & ~malloc~                      & no                    & no            & no            & no    \\
2394                & ~calloc~                      & yes (0 only)  & no            & no            & yes   \\
2395                & ~realloc~                     & no/copy               & yes           & no            & no    \\
2396                & ~memalign~            & no                    & no            & yes           & no    \\
2397                & ~posix_memalign~      & no                    & no            & yes           & no    \\
2398\hline
2399C11             & ~aligned_alloc~       & no                    & no            & yes           & no    \\
2400\hline
2401\CFA    & ~alloc~                       & yes/copy              & no/yes        & no            & yes   \\
2402                & ~align_alloc~         & yes                   & no            & yes           & yes   \\
2403\end{tabular}
2404\lstDeleteShortInline~%
2405\lstMakeShortInline@%
2406\caption{Storage-Management Operations}
2407\label{t:StorageManagementOperations}
2408\end{table}
2409
2410\begin{figure}
2411\centering
2412\begin{cquote}
2413\begin{cfa}[aboveskip=0pt]
2414size_t  dim = 10;                                                       $\C{// array dimension}$
2415char fill = '\xff';                                                     $\C{// initialization fill value}$
2416int * ip;
2417\end{cfa}
2418\lstDeleteShortInline@%
2419\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
2420\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
2421\begin{cfa}
2422ip = alloc();
2423ip = alloc( fill );
2424ip = alloc( dim );
2425ip = alloc( dim, fill );
2426ip = alloc( ip, 2 * dim );
2427ip = alloc( ip, 4 * dim, fill );
2428
2429ip = align_alloc( 16 );
2430ip = align_alloc( 16, fill );
2431ip = align_alloc( 16, dim );
2432ip = align_alloc( 16, dim, fill );
2433\end{cfa}
2434&
2435\begin{cfa}
2436ip = (int *)malloc( sizeof( int ) );
2437ip = (int *)malloc( sizeof( int ) ); memset( ip, fill, sizeof( int ) );
2438ip = (int *)malloc( dim * sizeof( int ) );
2439ip = (int *)malloc( sizeof( int ) ); memset( ip, fill, dim * sizeof( int ) );
2440ip = (int *)realloc( ip, 2 * dim * sizeof( int ) );
2441ip = (int *)realloc( ip, 4 * dim * sizeof( int ) );
2442                        memset( ip, fill, 4 * dim * sizeof( int ) );
2443ip = memalign( 16, sizeof( int ) );
2444ip = memalign( 16, sizeof( int ) ); memset( ip, fill, sizeof( int ) );
2445ip = memalign( 16, dim * sizeof( int ) );
2446ip = memalign( 16, dim * sizeof( int ) ); memset( ip, fill, dim * sizeof( int ) );
2447\end{cfa}
2448\end{tabular}
2449\lstMakeShortInline@%
2450\end{cquote}
2451\caption{\CFA versus C Storage-Allocation}
2452\label{f:StorageAllocation}
2453\end{figure}
2454
2455Variadic @new@ (see Section~\ref{sec:variadic-tuples}) cannot support the same overloading because extra parameters are for initialization.
2456Hence, there are @new@ and @anew@ functions for single and array variables, and the fill value is the arguments to the constructor, \eg:
2457\begin{cfa}
2458struct S { int i, j; };
2459void ?{}( S & s, int i, int j ) { s.i = i; s.j = j; }
2460S * s = new( 2, 3 );                                            $\C{// allocate storage and run constructor}$
2461S * as = anew( dim, 2, 3 );                                     $\C{// each array element initialized to 2, 3}$
2462\end{cfa}
2463Note, \CC can only initialization array elements via the default constructor.
2464
2465Finally, the \CFA memory-allocator has \newterm{sticky properties} for dynamic storage: fill and alignment are remembered with an object's storage in the heap.
2466When a @realloc@ is performed, the sticky properties are respected, so that new storage is correctly aligned and initialized with the fill character.
2467
2468
2469\subsection{I/O}
2470\label{s:IOLibrary}
2471
2472The goal of \CFA I/O is to simplify the common cases, while fully supporting polymorphism and user defined types in a consistent way.
2473The approach combines ideas from \CC and Python.
2474The \CFA header file for the I/O library is @fstream@.
2475
2476The common case is printing out a sequence of variables separated by whitespace.
2477\begin{cquote}
2478\lstDeleteShortInline@%
2479\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
2480\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{\CC}}      \\
2481\begin{cfa}
2482int x = 1, y = 2, z = 3;
2483sout | x `|` y `|` z | endl;
2484\end{cfa}
2485&
2486\begin{cfa}
2487
2488cout << x `<< " "` << y `<< " "` << z << endl;
2489\end{cfa}
2490\\
2491\begin{cfa}[showspaces=true,aboveskip=0pt,belowskip=0pt]
24921` `2` `3
2493\end{cfa}
2494&
2495\begin{cfa}[showspaces=true,aboveskip=0pt,belowskip=0pt]
24961 2 3
2497\end{cfa}
2498\end{tabular}
2499\lstMakeShortInline@%
2500\end{cquote}
2501The \CFA form has half the characters of the \CC form, and is similar to Python I/O with respect to implicit separators.
2502Similar simplification occurs for tuple I/O, which prints all tuple values separated by ``\lstinline[showspaces=true]@, @''.
2503\begin{cfa}
2504[int, [ int, int ] ] t1 = [ 1, [ 2, 3 ] ], t2 = [ 4, [ 5, 6 ] ];
2505sout | t1 | t2 | endl;                                  $\C{// print tuples}$
2506\end{cfa}
2507\begin{cfa}[showspaces=true,aboveskip=0pt]
25081`, `2`, `3 4`, `5`, `6
2509\end{cfa}
2510Finally, \CFA uses the logical-or operator for I/O as it is the lowest-priority overloadable operator, other than assignment.
2511Therefore, fewer output expressions require parenthesis.
2512\begin{cquote}
2513\lstDeleteShortInline@%
2514\begin{tabular}{@{}ll@{}}
2515\textbf{\CFA:}
2516&
2517\begin{cfa}
2518sout | x * 3 | y + 1 | z << 2 | x == y | (x | y) | (x || y) | (x > z ? 1 : 2) | endl;
2519\end{cfa}
2520\\
2521\textbf{\CC:}
2522&
2523\begin{cfa}
2524cout << x * 3 << y + 1 << `(`z << 2`)` << `(`x == y`)` << (x | y) << (x || y) << (x > z ? 1 : 2) << endl;
2525\end{cfa}
2526\\
2527&
2528\begin{cfa}[showspaces=true,aboveskip=0pt]
25293 3 12 0 3 1 2
2530\end{cfa}
2531\end{tabular}
2532\lstMakeShortInline@%
2533\end{cquote}
2534There 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.
2535
2536The implicit separator character (space/blank) is a separator not a terminator.
2537The rules for implicitly adding the separator are:
2538\begin{itemize}
2539\item
2540A separator does not appear at the start or end of a line.
2541\item
2542A separator does not appear before or after a character literal or variable.
2543\item
2544A separator does not appear before or after a null (empty) C string, which is a local mechanism to disable insertion of the separator character.
2545\item
2546A separator does not appear before a C string starting with the characters: \lstinline[mathescape=off,basicstyle=\tt]@([{=$@
2547\item
2548A separator does not appear after a C string ending with the characters: \lstinline[basicstyle=\tt]@,.;!?)]}%@
2549\item
2550{\lstset{language=CFA,deletedelim=**[is][]{`}{`}}
2551A 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@
2552}%
2553\end{itemize}
2554There are functions to set and get the separator string, and manipulators to toggle separation on and off in the middle of output.
2555
2556
2557\subsection{Multi-precision Integers}
2558\label{s:MultiPrecisionIntegers}
2559
2560\CFA has an interface to the GMP multi-precision signed-integers~\cite{GMP}, similar to the \CC interface provided by GMP.
2561The \CFA interface wraps GMP functions into operator functions to make programming with multi-precision integers identical to using fixed-sized integers.
2562The \CFA type name for multi-precision signed-integers is @Int@ and the header file is @gmp@.
2563Figure~\ref{f:GMPInterface} shows a multi-precision factorial-program contrasting the GMP interface in \CFA and C.
2564
2565\begin{figure}
2566\centering
2567\lstDeleteShortInline@%
2568\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}@{\hspace{2\parindentlnth}}l@{}}
2569\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{@{\hspace{2\parindentlnth}}c}{\textbf{C}}     \\
2570\begin{cfa}
2571#include <gmp>
2572int main( void ) {
2573        sout | "Factorial Numbers" | endl;
2574        Int fact = 1;
2575        sout | 0 | fact | endl;
2576        for ( unsigned int i = 1; i <= 40; i += 1 ) {
2577                fact *= i;
2578                sout | i | fact | endl;
2579        }
2580}
2581\end{cfa}
2582&
2583\begin{cfa}
2584#include <gmp.h>
2585int main( void ) {
2586        `gmp_printf`( "Factorial Numbers\n" );
2587        `mpz_t` fact;  `mpz_init_set_ui`( fact, 1 );
2588        `gmp_printf`( "%d %Zd\n", 0, fact );
2589        for ( unsigned int i = 1; i <= 40; i += 1 ) {
2590                `mpz_mul_ui`( fact, fact, i );
2591                `gmp_printf`( "%d %Zd\n", i, fact );
2592        }
2593}
2594\end{cfa}
2595\end{tabular}
2596\lstMakeShortInline@%
2597\caption{GMP Interface \CFA versus C}
2598\label{f:GMPInterface}
2599\end{figure}
2600
2601
2602\section{Evaluation}
2603\label{sec:eval}
2604
2605Though \CFA provides significant added functionality over C, these features have a low runtime penalty.
2606In fact, \CFA's features for generic programming can enable faster runtime execution than idiomatic @void *@-based C code.
2607This claim is demonstrated through a set of generic-code-based micro-benchmarks in C, \CFA, and \CC (see stack implementations in Appendix~\ref{sec:BenchmarkStackImplementations}).
2608Since 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.
2609A more illustrative comparison measures the costs of idiomatic usage of each language's features.
2610Figure~\ref{fig:BenchmarkTest} shows the \CFA benchmark tests for a generic stack based on a singly linked-list.
2611The benchmark test is similar for the other languages.
2612The 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.
2613
2614\begin{figure}
2615\begin{cfa}[xleftmargin=3\parindentlnth,aboveskip=0pt,belowskip=0pt]
2616int main() {
2617        int max = 0, val = 42;
2618        stack( int ) si, ti;
2619
2620        REPEAT_TIMED( "push_int", N, push( si, val ); )
2621        TIMED( "copy_int", ti{ si }; )
2622        TIMED( "clear_int", clear( si ); )
2623        REPEAT_TIMED( "pop_int", N, int x = pop( ti ); if ( x > max ) max = x; )
2624
2625        pair( short, char ) max = { 0h, '\0' }, val = { 42h, 'a' };
2626        stack( pair( short, char ) ) sp, tp;
2627
2628        REPEAT_TIMED( "push_pair", N, push( sp, val ); )
2629        TIMED( "copy_pair", tp{ sp }; )
2630        TIMED( "clear_pair", clear( sp ); )
2631        REPEAT_TIMED( "pop_pair", N, pair(short, char) x = pop( tp ); if ( x > max ) max = x; )
2632}
2633\end{cfa}
2634\caption{\protect\CFA Benchmark Test}
2635\label{fig:BenchmarkTest}
2636\end{figure}
2637
2638The 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.
2639The \CCV variant illustrates an alternative object-oriented idiom where all objects inherit from a base @object@ class, mimicking a Java-like interface;
2640hence runtime checks are necessary to safely down-cast objects.
2641The 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.
2642Note 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.
2643
2644Figure~\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.
2645The graph plots the median of 5 consecutive runs of each program, with an initial warm-up run omitted.
2646All code is compiled at \texttt{-O2} by gcc or g++ 6.4.0, with all \CC code compiled as \CCfourteen.
2647The 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.
2648
2649\begin{figure}
2650\centering
2651\input{timing}
2652\caption{Benchmark Timing Results (smaller is better)}
2653\label{fig:eval}
2654\end{figure}
2655
2656\begin{table}
2657\centering
2658\caption{Properties of benchmark code}
2659\label{tab:eval}
2660\newcommand{\CT}[1]{\multicolumn{1}{c}{#1}}
2661\begin{tabular}{rrrrr}
2662                                                                        & \CT{C}        & \CT{\CFA}     & \CT{\CC}      & \CT{\CCV}             \\ \hline
2663maximum memory usage (MB)                       & 10,001        & 2,502         & 2,503         & 11,253                \\
2664source code size (lines)                        & 201           & 191           & 125           & 294                   \\
2665redundant type annotations (lines)      & 27            & 0                     & 2                     & 16                    \\
2666binary size (KB)                                        & 14            & 257           & 14            & 37                    \\
2667\end{tabular}
2668\end{table}
2669
2670The 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;
2671this inefficiency is exacerbated by the second level of generic types in the pair benchmarks.
2672By 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.
2673\CCV is slower than C largely due to the cost of runtime type-checking of down-casts (implemented with @dynamic_cast@);
2674The outlier in the graph for \CFA, pop @pair@, results from the complexity of the generated-C polymorphic code.
2675The gcc compiler is unable to optimize some dead code and condense nested calls; a compiler designed for \CFA could easily perform these optimizations.
2676Finally, the binary size for \CFA is larger because of static linking with the \CFA libraries.
2677
2678\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.
2679The 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.
2680On 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.
2681\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;
2682with their omission, the \CCV line count is similar to C.
2683We 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.
2684
2685Line-count is a fairly rough measure of code complexity;
2686another important factor is how much type information the programmer must specify manually, especially where that information is not compiler-checked.
2687Such 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.
2688To 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.
2689The \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.
2690The \CFA benchmark is able to eliminate all redundant type annotations through use of the polymorphic @alloc@ function discussed in Section~\ref{sec:libraries}.
2691
2692
2693\section{Related Work}
2694
2695
2696\subsection{Polymorphism}
2697
2698\CC provides three disjoint polymorphic extensions to C: overloading, inheritance, and templates.
2699The 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.
2700In 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.
2701The key mechanism to support separate compilation is \CFA's \emph{explicit} use of assumed type properties.
2702Until \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;
2703furthermore, \CC concepts are restricted to template polymorphism.
2704
2705Cyclone~\cite{Grossman06} also provides capabilities for polymorphic functions and existential types, similar to \CFA's @forall@ functions and generic types.
2706Cyclone 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.
2707Furthermore, 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@.
2708In \CFA terms, all Cyclone polymorphism must be dtype-static.
2709While 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.
2710Smith 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.
2711
2712Objective-C~\cite{obj-c-book} is an industrially successful extension to C.
2713However, Objective-C is a radical departure from C, using an object-oriented model with message-passing.
2714Objective-C did not support type-checked generics until recently \cite{xcode7}, historically using less-efficient runtime checking of object types.
2715The GObject~\cite{GObject} framework also adds object-oriented programming with runtime type-checking and reference-counting garbage-collection to C;
2716these features are more intrusive additions than those provided by \CFA, in addition to the runtime overhead of reference-counting.
2717Vala~\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.
2718Java~\cite{Java8} included generic types in Java~5, which are type-checked at compilation and type-erased at runtime, similar to \CFA's.
2719However, in Java, each object carries its own table of method pointers, while \CFA passes the method pointers separately to maintain a C-compatible layout.
2720Java is also a garbage-collected, object-oriented language, with the associated resource usage and C-interoperability burdens.
2721
2722D~\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.
2723However, 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.
2724D and Go are garbage-collected languages, imposing the associated runtime overhead.
2725The necessity of accounting for data transfer between managed runtimes and the unmanaged C runtime complicates foreign-function interfaces to C.
2726Furthermore, 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.
2727D 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.
2728Rust also possesses much more powerful abstraction capabilities for writing generic code than Go.
2729On 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.
2730\CFA, with its more modest safety features, allows direct ports of C code while maintaining the idiomatic style of the original source.
2731
2732
2733\subsection{Tuples/Variadics}
2734
2735Many programming languages have some form of tuple construct and/or variadic functions, \eg SETL, C, KW-C, \CC, D, Go, Java, ML, and Scala.
2736SETL~\cite{SETL} is a high-level mathematical programming language, with tuples being one of the primary data types.
2737Tuples in SETL allow subscripting, dynamic expansion, and multiple assignment.
2738C 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.
2739KW-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.
2740The main contributions of that work were adding MRVF, tuple mass and multiple assignment, and record-field access.
2741\CCeleven introduced @std::tuple@ as a library variadic template structure.
2742Tuples are a generalization of @std::pair@, in that they allow for arbitrary length, fixed-size aggregation of heterogeneous values.
2743Operations include @std::get<N>@ to extract values, @std::tie@ to create a tuple of references used for assignment, and lexicographic comparisons.
2744\CCseventeen proposes \emph{structured bindings}~\cite{Sutter15} to eliminate pre-declaring variables and use of @std::tie@ for binding the results.
2745This 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.
2746Furthermore, structured bindings are not a full replacement for @std::tie@, as it always declares new variables.
2747Like \CC, D provides tuples through a library variadic-template structure.
2748Go does not have tuples but supports MRVF.
2749Java'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.
2750Tuples are a fundamental abstraction in most functional programming languages, such as Standard ML~\cite{sml} and~\cite{Scala}, which decompose tuples using pattern matching.
2751
2752
2753\subsection{C Extensions}
2754
2755\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.
2756Specific 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.
2757The 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.
2758\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.
2759As a result, \CC has a steep learning curve for even experienced C programmers, especially when attempting to maintain performance equivalent to C legacy-code.
2760
2761There are several other C extension-languages with less usage and even more dramatic changes than \CC.
2762Objective-C and Cyclone are two other extensions to C with different design goals than \CFA, as discussed above.
2763Other languages extend C with more focused features.
2764$\mu$\CC~\cite{uC++book}, CUDA~\cite{Nickolls08}, ispc~\cite{Pharr12}, and Sierra~\cite{Leissa14} add concurrent or data-parallel primitives to C or \CC;
2765data-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}.
2766Finally, 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.
2767
2768
2769\begin{comment}
2770\subsection{Control Structures / Declarations / Literals}
2771
2772Java has default fall through like C/\CC.
2773Pascal/Ada/Go/Rust do not have default fall through.
2774\Csharp does not have fall through but still requires a break.
2775Python uses dictionary mapping. \\
2776\CFA choose is like Rust match.
2777
2778Java has labelled break/continue. \\
2779Languages with and without exception handling.
2780
2781Alternative C declarations. \\
2782Different references \\
2783Constructors/destructors
2784
27850/1 Literals \\
2786user defined: D, Objective-C
2787\end{comment}
2788
2789
2790\section{Conclusion and Future Work}
2791
2792The 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.
2793While 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.
2794The 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.
2795The 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.
2796The work is a challenging design, engineering, and implementation exercise.
2797On the surface, the project may appear as a rehash of similar mechanisms in \CC.
2798However, 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.
2799All of these new features are being used by the \CFA development-team to build the \CFA runtime-system.
2800Finally, we demonstrate that \CFA performance for some idiomatic cases is better than C and close to \CC, showing the design is practically applicable.
2801
2802There 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.
2803While all examples in the paper compile and run, a public beta-release of \CFA will take another 8--12 months to finalize these extensions.
2804There are also interesting future directions for the polymorphism design.
2805Notably, \CC template functions trade compile time and code bloat for optimal runtime of individual instantiations of polymorphic functions.
2806\CFA polymorphic functions use dynamic virtual-dispatch;
2807the 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.
2808Two 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).
2809These approaches are not mutually exclusive and allow performance optimizations to be applied only when necessary, without suffering global code-bloat.
2810In general, we believe separate compilation, producing smaller code, works well with loaded hardware-caches, which may offset the benefit of larger inlined-code.
2811
2812
2813\section{Acknowledgments}
2814
2815The 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.
2816This 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.
2817
2818
2819\bibliography{pl}
2820
2821
2822\appendix
2823
2824\section{Benchmark Stack Implementations}
2825\label{sec:BenchmarkStackImplementations}
2826
2827Throughout, @/***/@ designates a counted redundant type annotation; code reformatted slightly for brevity.
2828
2829
2830\subsection{C}
2831
2832\begin{flushleft}
2833\lstDeleteShortInline@%
2834\begin{tabular}{@{}l@{\hspace{1.8\parindentlnth}}|@{\hspace{\parindentlnth}}l@{}}
2835\begin{cfa}[xleftmargin=0pt,aboveskip=0pt,belowskip=0pt]
2836typedef struct node {
2837        void * value;
2838        struct node * next;
2839} node;
2840typedef struct stack {
2841        struct node * head;
2842} stack;
2843void copy_stack( stack * s, const stack * t,
2844                                void * (*copy)( const void * ) ) {
2845        node ** cr = &s->head;
2846        for (node * nx = t->head; nx; nx = nx->next) {
2847                *cr = malloc( sizeof(node) ); /***/
2848                (*cr)->value = copy( nx->value );
2849                cr = &(*cr)->next;
2850        }
2851        *cr = NULL;
2852}
2853void clear_stack( stack * s, void (* free_el)( void * ) ) {
2854        for ( node * nx = s->head; nx; ) {
2855                node * cr = nx;
2856                nx = cr->next;
2857                free_el( cr->value );
2858                free( cr );
2859        }
2860        s->head = NULL;
2861}
2862\end{cfa}
2863&
2864\begin{cfa}[xleftmargin=0pt,aboveskip=0pt,belowskip=0pt]
2865stack new_stack() {
2866        return (stack){ NULL }; /***/
2867}
2868stack * assign_stack( stack * s, const stack * t,
2869                                void * (*copy_el)( const void * ),
2870                                void (*free_el)( void * ) ) {
2871        if ( s->head == t->head ) return s;
2872        clear_stack( s, free_el ); /***/
2873        copy_stack( s, t, copy_el ); /***/
2874        return s;
2875}
2876_Bool stack_empty( const stack * s ) {
2877        return s->head == NULL;
2878}
2879void push_stack( stack * s, void * v ) {
2880        node * n = malloc( sizeof(node) ); /***/
2881        *n = (node){ v, s->head }; /***/
2882        s->head = n;
2883}
2884void * pop_stack( stack * s ) {
2885        node * n = s->head;
2886        s->head = n->next;
2887        void * v = n->value;
2888        free( n );
2889        return v;
2890}
2891\end{cfa}
2892\end{tabular}
2893\lstMakeShortInline@%
2894\end{flushleft}
2895
2896
2897\subsection{\CFA}
2898\label{s:CforallStack}
2899
2900\begin{flushleft}
2901\lstDeleteShortInline@%
2902\begin{tabular}{@{}l|@{\hspace{\parindentlnth}}l@{}}
2903\begin{cfa}[xleftmargin=0pt,aboveskip=0pt,belowskip=0pt]
2904forall( otype T ) {
2905        struct node {
2906                T value;
2907                node(T) * next;
2908        };
2909        struct stack { node(T) * head; };
2910        void ?{}( stack(T) & s, stack(T) t ) { // copy
2911                node(T) ** cr = &s.head;
2912                for ( node(T) * nx = t.head; nx; nx = nx->next ) {
2913                        *cr = alloc();
2914                        ((*cr)->value){ nx->value };
2915                        cr = &(*cr)->next;
2916                }
2917                *cr = 0;
2918        }
2919        void clear( stack(T) & s ) with( s ) {
2920                for ( node(T) * nx = head; nx; ) {
2921                        node(T) * cr = nx;
2922                        nx = cr->next;
2923                        ^(*cr){};
2924                        free( cr );
2925                }
2926                head = 0;
2927        }
2928
2929\end{cfa}
2930&
2931\begin{cfa}[xleftmargin=0pt,aboveskip=0pt,belowskip=0pt]
2932        void ?{}( stack(T) & s ) { (s.head){ 0 }; }
2933        void ^?{}( stack(T) & s) { clear( s ); }
2934        stack(T) ?=?( stack(T) & s, stack(T) t ) {
2935                if ( s.head == t.head ) return s;
2936                clear( s );
2937                s{ t };
2938                return s;
2939        }
2940        _Bool empty( const stack(T) & s ) {
2941                return s.head == 0;
2942        }
2943        void push( stack(T) & s, T value ) with( s ) {
2944                node(T) * n = alloc();
2945                (*n){ value, head };
2946                head = n;
2947        }
2948        T pop( stack(T) & s ) with( s ) {
2949                node(T) * n = head;
2950                head = n->next;
2951                T v = n->value;
2952                ^(*n){};
2953                free( n );
2954                return v;
2955        }
2956}
2957\end{cfa}
2958\end{tabular}
2959\lstMakeShortInline@%
2960\end{flushleft}
2961
2962
2963\subsection{\CC}
2964
2965\begin{flushleft}
2966\lstDeleteShortInline@%
2967\begin{tabular}{@{}l|@{\hspace{\parindentlnth}}l@{}}
2968\begin{cfa}[xleftmargin=0pt,aboveskip=0pt,belowskip=0pt]
2969template<typename T> struct stack {
2970        struct node {
2971                T value;
2972                node * next;
2973                node( const T & v, node * n = nullptr ) :
2974                        value( v ), next( n ) {}
2975        };
2976        node * head;
2977        void copy( const stack<T> & o ) {
2978                node ** cr = &head;
2979                for ( node * nx = o.head; nx; nx = nx->next ) {
2980                        *cr = new node{ nx->value }; /***/
2981                        cr = &(*cr)->next;
2982                }
2983                *cr = nullptr;
2984        }
2985        void clear() {
2986                for ( node * nx = head; nx; ) {
2987                        node * cr = nx;
2988                        nx = cr->next;
2989                        delete cr;
2990                }
2991                head = nullptr;
2992        }
2993\end{cfa}
2994&
2995\begin{cfa}[xleftmargin=0pt,aboveskip=0pt,belowskip=0pt]
2996        stack() : head( nullptr ) {}
2997        stack( const stack<T> & o ) { copy( o ); }
2998        ~stack() { clear(); }
2999        stack & operator=( const stack<T> & o ) {
3000                if ( this == &o ) return *this;
3001                clear();
3002                copy( o );
3003                return *this;
3004        }
3005        bool empty() const {
3006                return head == nullptr;
3007        }
3008        void push( const T & value ) {
3009                head = new node{ value, head };  /***/
3010        }
3011        T pop() {
3012                node * n = head;
3013                head = n->next;
3014                T v = std::move( n->value );
3015                delete n;
3016                return v;
3017        }
3018};
3019
3020\end{cfa}
3021\end{tabular}
3022\lstMakeShortInline@%
3023\end{flushleft}
3024
3025
3026\subsection{\CCV}
3027
3028\begin{flushleft}
3029\lstDeleteShortInline@%
3030\begin{tabular}{@{}l|@{\hspace{\parindentlnth}}l@{}}
3031\begin{cfa}[xleftmargin=0pt,aboveskip=0pt,belowskip=0pt]
3032struct stack {
3033        struct node {
3034                ptr<object> value;
3035                node * next;
3036                node( const object & v, node * n = nullptr ) :
3037                                value( v.new_copy() ), next( n ) {}
3038        };
3039        node * head;
3040        void copy( const stack & o ) {
3041                node ** cr = &head;
3042                for ( node * nx = o.head; nx; nx = nx->next ) {
3043                        *cr = new node{ *nx->value }; /***/
3044                        cr = &(*cr)->next;
3045                }
3046                *cr = nullptr;
3047        }
3048        void clear() {
3049                for ( node * nx = head; nx; ) {
3050                        node * cr = nx;
3051                        nx = cr->next;
3052                        delete cr;
3053                }
3054                head = nullptr;
3055        }
3056\end{cfa}
3057&
3058\begin{cfa}[xleftmargin=0pt,aboveskip=0pt,belowskip=0pt]
3059        stack() : head( nullptr ) {}
3060        stack( const stack & o ) { copy( o ); }
3061        ~stack() { clear(); }
3062        stack & operator=( const stack & o ) {
3063                if ( this == &o ) return *this;
3064                clear();
3065                copy( o );
3066                return *this;
3067        }
3068        bool empty() const {
3069                return head == nullptr;
3070        }
3071        void push( const object & value ) {
3072                head = new node{ value, head }; /***/
3073        }
3074        ptr<object> pop() {
3075                node * n = head;
3076                head = n->next;
3077                ptr<object> v = std::move( n->value );
3078                delete n;
3079                return v;
3080        }
3081};
3082
3083\end{cfa}
3084\end{tabular}
3085\lstMakeShortInline@%
3086\end{flushleft}
3087
3088
3089\end{document}
3090
3091% Local Variables: %
3092% tab-width: 4 %
3093% compile-command: "make" %
3094% End: %
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