source: doc/papers/general/Paper.tex @ ea46db7

aaron-thesisarm-ehcleanup-dtorsdeferred_resndemanglerenumforall-pointer-decayjacob/cs343-translationjenkins-sandboxnew-astnew-ast-unique-exprnew-envno_listpersistent-indexerresolv-newwith_gc
Last change on this file since ea46db7 was ea46db7, checked in by Peter A. Buhr <pabuhr@…>, 4 years ago

updates, and extend section on user literals

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1\documentclass{article}
2
3\usepackage{fullpage}
4\usepackage{epic,eepic}
5\usepackage{xspace,calc,comment}
6\usepackage{upquote}                                            % switch curled `'" to straight
7\usepackage{listings}                                           % format program code
8\usepackage{enumitem}
9\setlist[itemize]{topsep=3pt,itemsep=2pt,parsep=0pt}% global
10\usepackage[flushmargin]{footmisc}                      % support label/reference in footnote
11\usepackage{rotating}
12\usepackage[usenames]{color}
13\usepackage{pslatex}                                            % reduce size of san serif font
14\usepackage[plainpages=false,pdfpagelabels,pdfpagemode=UseNone,pagebackref=true,breaklinks=true,colorlinks=true,linkcolor=blue,citecolor=blue,urlcolor=blue]{hyperref}
15\urlstyle{sf}
16\usepackage{breakurl}
17
18\setlength{\textheight}{9in}
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23\renewcommand{\textfraction}{0.0}                       % the entire page maybe devoted to floats with no text on the page at all
24
25\lefthyphenmin=4                                                        % hyphen only after 4 characters
26\righthyphenmin=4
27
28% Names used in the document.
29
30\newcommand{\CFAIcon}{\textsf{C}\raisebox{\depth}{\rotatebox{180}{\textsf{A}}}\xspace} % Cforall symbolic name
31\newcommand{\CFA}{\protect\CFAIcon}             % safe for section/caption
32\newcommand{\CFL}{\textrm{Cforall}\xspace}      % Cforall symbolic name
33\newcommand{\Celeven}{\textrm{C11}\xspace}      % C11 symbolic name
34\newcommand{\CC}{\textrm{C}\kern-.1em\hbox{+\kern-.25em+}\xspace} % C++ symbolic name
35\newcommand{\CCeleven}{\textrm{C}\kern-.1em\hbox{+\kern-.25em+}11\xspace} % C++11 symbolic name
36\newcommand{\CCfourteen}{\textrm{C}\kern-.1em\hbox{+\kern-.25em+}14\xspace} % C++14 symbolic name
37\newcommand{\CCseventeen}{\textrm{C}\kern-.1em\hbox{+\kern-.25em+}17\xspace} % C++17 symbolic name
38\newcommand{\CCtwenty}{\textrm{C}\kern-.1em\hbox{+\kern-.25em+}20\xspace} % C++20 symbolic name
39\newcommand{\CCV}{\rm C\kern-.1em\hbox{+\kern-.25em+}obj\xspace} % C++ virtual symbolic name
40\newcommand{\Csharp}{C\raisebox{-0.7ex}{\Large$^\sharp$}\xspace} % C# symbolic name
41
42%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
43
44\newcommand{\Textbf}[2][red]{{\color{#1}{\textbf{#2}}}}
45%\newcommand{\TODO}[1]{\textbf{TODO}: {\itshape #1}} % TODO included
46\newcommand{\TODO}[1]{} % TODO elided
47
48% Default underscore is too low and wide. Cannot use lstlisting "literate" as replacing underscore
49% removes it as a variable-name character so keywords in variables are highlighted. MUST APPEAR
50% AFTER HYPERREF.
51%\DeclareTextCommandDefault{\textunderscore}{\leavevmode\makebox[1.2ex][c]{\rule{1ex}{0.1ex}}}
52\renewcommand{\textunderscore}{\leavevmode\makebox[1.2ex][c]{\rule{1ex}{0.075ex}}}
53
54\makeatletter
55% parindent is relative, i.e., toggled on/off in environments like itemize, so store the value for
56% use rather than use \parident directly.
57\newlength{\parindentlnth}
58\setlength{\parindentlnth}{\parindent}
59
60\newcommand{\LstKeywordStyle}[1]{{\lst@basicstyle{\lst@keywordstyle{#1}}}}
61\newcommand{\LstCommentStyle}[1]{{\lst@basicstyle{\lst@commentstyle{#1}}}}
62
63\newlength{\gcolumnposn}                                        % temporary hack because lstlisting does not handle tabs correctly
64\newlength{\columnposn}
65\setlength{\gcolumnposn}{2.75in}
66\setlength{\columnposn}{\gcolumnposn}
67\newcommand{\C}[2][\@empty]{\ifx#1\@empty\else\global\setlength{\columnposn}{#1}\global\columnposn=\columnposn\fi\hfill\makebox[\textwidth-\columnposn][l]{\lst@basicstyle{\LstCommentStyle{#2}}}}
68\newcommand{\CRT}{\global\columnposn=\gcolumnposn}
69
70% Denote newterms in particular font and index them without particular font and in lowercase, e.g., \newterm{abc}.
71% The option parameter provides an index term different from the new term, e.g., \newterm[\texttt{abc}]{abc}
72% The star version does not lowercase the index information, e.g., \newterm*{IBM}.
73\newcommand{\newtermFontInline}{\emph}
74\newcommand{\newterm}{\@ifstar\@snewterm\@newterm}
75\newcommand{\@newterm}[2][\@empty]{\lowercase{\def\temp{#2}}{\newtermFontInline{#2}}\ifx#1\@empty\index{\temp}\else\index{#1@{\protect#2}}\fi}
76\newcommand{\@snewterm}[2][\@empty]{{\newtermFontInline{#2}}\ifx#1\@empty\index{#2}\else\index{#1@{\protect#2}}\fi}
77
78% Latin abbreviation
79\newcommand{\abbrevFont}{\textit}                       % set empty for no italics
80\newcommand{\EG}{\abbrevFont{e}.\abbrevFont{g}.}
81\newcommand*{\eg}{%
82        \@ifnextchar{,}{\EG}%
83                {\@ifnextchar{:}{\EG}%
84                        {\EG,\xspace}}%
85}%
86\newcommand{\IE}{\abbrevFont{i}.\abbrevFont{e}.}
87\newcommand*{\ie}{%
88        \@ifnextchar{,}{\IE}%
89                {\@ifnextchar{:}{\IE}%
90                        {\IE,\xspace}}%
91}%
92\newcommand{\ETC}{\abbrevFont{etc}}
93\newcommand*{\etc}{%
94        \@ifnextchar{.}{\ETC}%
95        {\ETC.\xspace}%
96}%
97\newcommand{\ETAL}{\abbrevFont{et}~\abbrevFont{al}}
98\newcommand*{\etal}{%
99        \@ifnextchar{.}{\protect\ETAL}%
100                {\protect\ETAL.\xspace}%
101}%
102\newcommand{\VIZ}{\abbrevFont{viz}}
103\newcommand*{\viz}{%
104        \@ifnextchar{.}{\VIZ}%
105                {\VIZ.\xspace}%
106}%
107\makeatother
108
109\newenvironment{cquote}{%
110        \list{}{\lstset{resetmargins=true,aboveskip=0pt,belowskip=0pt}\topsep=3pt\parsep=0pt\leftmargin=\parindentlnth\rightmargin\leftmargin}%
111        \item\relax
112}{%
113        \endlist
114}% cquote
115
116% CFA programming language, based on ANSI C (with some gcc additions)
117\lstdefinelanguage{CFA}[ANSI]{C}{
118        morekeywords={
119                _Alignas, _Alignof, __alignof, __alignof__, asm, __asm, __asm__, _At, __attribute,
120                __attribute__, auto, _Bool, catch, catchResume, choose, _Complex, __complex, __complex__,
121                __const, __const__, disable, dtype, enable, exception, __extension__, fallthrough, fallthru,
122                finally, forall, ftype, _Generic, _Imaginary, inline, __label__, lvalue, _Noreturn, one_t,
123                otype, restrict, _Static_assert, throw, throwResume, trait, try, ttype, typeof, __typeof,
124                __typeof__, virtual, with, zero_t},
125        morekeywords=[2]{
126                _Atomic, coroutine, is_coroutine, is_monitor, is_thread, monitor, mutex, nomutex, or,
127                resume, suspend, thread, _Thread_local, waitfor, when, yield},
128        moredirectives={defined,include_next}%
129}
130
131\lstset{
132language=CFA,
133columns=fullflexible,
134basicstyle=\linespread{0.9}\sf,                                                 % reduce line spacing and use sanserif font
135stringstyle=\tt,                                                                                % use typewriter font
136tabsize=5,                                                                                              % N space tabbing
137xleftmargin=\parindentlnth,                                                             % indent code to paragraph indentation
138%mathescape=true,                                                                               % LaTeX math escape in CFA code $...$
139escapechar=\$,                                                                                  % LaTeX escape in CFA code
140keepspaces=true,                                                                                %
141showstringspaces=false,                                                                 % do not show spaces with cup
142showlines=true,                                                                                 % show blank lines at end of code
143aboveskip=4pt,                                                                                  % spacing above/below code block
144belowskip=3pt,
145% replace/adjust listing characters that look bad in sanserif
146literate={-}{\makebox[1ex][c]{\raisebox{0.4ex}{\rule{0.8ex}{0.1ex}}}}1 {^}{\raisebox{0.6ex}{$\scriptscriptstyle\land\,$}}1
147        {~}{\raisebox{0.3ex}{$\scriptstyle\sim\,$}}1 {@}{\small{@}}1 % {`}{\ttfamily\upshape\hspace*{-0.1ex}`}1
148        {<-}{$\leftarrow$}2 {=>}{$\Rightarrow$}2 {->}{\makebox[1ex][c]{\raisebox{0.4ex}{\rule{0.8ex}{0.075ex}}}\kern-0.2ex\textgreater}2,
149moredelim=**[is][\color{red}]{`}{`},
150}% lstset
151
152% inline code @...@
153\lstMakeShortInline@%
154
155\lstnewenvironment{cfa}[1][]
156{\lstset{#1}}
157{}
158\lstnewenvironment{C++}[1][]                            % use C++ style
159{\lstset{language=C++,moredelim=**[is][\protect\color{red}]{`}{`},#1}\lstset{#1}}
160{}
161
162
163\title{\protect\CFA : Adding Modern Programming Language Features to C}
164
165\author{Aaron Moss, Robert Schluntz, Peter Buhr}
166% \email{a3moss@uwaterloo.ca}
167% \email{rschlunt@uwaterloo.ca}
168% \email{pabuhr@uwaterloo.ca}
169% \affiliation{%
170%       \institution{University of Waterloo}
171%       \department{David R. Cheriton School of Computer Science}
172%       \streetaddress{Davis Centre, University of Waterloo}
173%       \city{Waterloo}
174%       \state{ON}
175%       \postcode{N2L 3G1}
176%       \country{Canada}
177% }
178
179%\terms{generic, tuple, variadic, types}
180%\keywords{generic types, tuple types, variadic types, polymorphic functions, C, Cforall}
181
182\begin{document}
183\maketitle
184
185
186\begin{abstract}
187The 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.
188This installation base and the programmers producing it represent a massive software-engineering investment spanning decades and likely to continue for decades more.
189Nevertheless, C, first standardized over thirty years ago, lacks many features that make programming in more modern languages safer and more productive.
190
191The 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.
192Prior 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.
193Specifically, \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.
194This paper presents a quick tour of \CFA features showing how their design avoids shortcomings of similar features in C and other C-like languages.
195Finally, experimental results are presented to validate several of the new features.
196\end{abstract}
197
198
199\section{Introduction}
200
201The 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.
202This installation base and the programmers producing it represent a massive software-engineering investment spanning decades and likely to continue for decades more.
203The 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.
204The top 3 rankings over the past 30 years are:
205\begin{center}
206\setlength{\tabcolsep}{10pt}
207\lstDeleteShortInline@%
208\begin{tabular}{@{}rccccccc@{}}
209                & 2018  & 2013  & 2008  & 2003  & 1998  & 1993  & 1988  \\ \hline
210Java    & 1             & 2             & 1             & 1             & 18    & -             & -             \\
211\Textbf{C}& \Textbf{2} & \Textbf{1} & \Textbf{2} & \Textbf{2} & \Textbf{1} & \Textbf{1} & \Textbf{1} \\
212\CC             & 3             & 4             & 3             & 3             & 2             & 2             & 5             \\
213\end{tabular}
214\lstMakeShortInline@%
215\end{center}
216Love it or hate it, C is extremely popular, highly used, and one of the few systems languages.
217In many cases, \CC is often used solely as a better C.
218Nonetheless, C, first standardized over thirty years ago, lacks many features that make programming in more modern languages safer and more productive.
219
220\CFA (pronounced ``C-for-all'', and written \CFA or Cforall) is an evolutionary extension of the C programming language that aims to add modern language features to C while maintaining both source compatibility with C and a familiar programming model for programmers.
221The four key design goals for \CFA~\cite{Bilson03} are:
222(1) The behaviour of standard C code must remain the same when translated by a \CFA compiler as when translated by a C compiler;
223(2) Standard C code must be as fast and as small when translated by a \CFA compiler as when translated by a C compiler;
224(3) \CFA code must be at least as portable as standard C code;
225(4) Extensions introduced by \CFA must be translated in the most efficient way possible.
226These 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.
227\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.
228
229\CFA is currently implemented as a source-to-source translator from \CFA to the gcc-dialect of C~\cite{GCCExtensions}, allowing it to leverage the portability and code optimizations provided by gcc, meeting goals (1)--(3).
230Ultimately, a compiler is necessary for advanced features and optimal performance.
231All of the features discussed in this paper are working, unless a feature states it is a future feature for completion.
232
233
234\section{Polymorphic Functions}
235
236\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}.
237Shortcomings are identified in existing approaches to generic and variadic data types in C-like languages and how these shortcomings are avoided in \CFA.
238Specifically, 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.
239The new constructs are empirically compared with C and \CC approaches via performance experiments in Section~\ref{sec:eval}.
240
241
242\subsection{Name Overloading}
243\label{s:NameOverloading}
244
245\begin{quote}
246There are only two hard things in Computer Science: cache invalidation and \emph{naming things} -- Phil Karlton
247\end{quote}
248C 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.
249\CFA extends the built-in operator overloading by allowing users to define overloads for any function, not just operators, and even any variable;
250Section~\ref{sec:libraries} includes a number of examples of how this overloading simplifies \CFA programming relative to C.
251Code 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.
252As an example:
253
254\begin{cfa}
255int max = 2147483647;                                           $\C[3.75in]{// (1)}$
256double max = 1.7976931348623157E+308;   $\C{// (2)}$
257int max( int a, int b ) { return a < b ? b : a; }  $\C{// (3)}$
258double max( double a, double b ) { return a < b ? b : a; }  $\C{// (4)}\CRT$
259max( 7, -max );                                                         $\C{// uses (3) and (1), by matching int from constant 7}$
260max( max, 3.14 );                                                       $\C{// uses (4) and (2), by matching double from constant 3.14}$
261max( max, -max );                                                       $\C{// ERROR: ambiguous}$
262int m = max( max, -max );                                       $\C{// uses (3) and (1) twice, by matching return type}$
263\end{cfa}
264\CFA maximizes the ability to reuse names to aggressively address the naming problem.
265In some cases, hundreds of names can be reduced to tens, resulting in a significant cognitive reduction for a programmer.
266In the above, the name @max@ has a consistent meaning, and a programmer only needs to remember the single concept: maximum.
267To 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).
268As 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.
269
270\Celeven added @_Generic@ expressions, which can be used in preprocessor macros to provide a form of ad-hoc polymorphism; however, this polymorphism is both functionally and ergonomically inferior to \CFA name overloading.
271The macro wrapping the generic expression imposes some limitations; as an example, it could not implement the example above, because the variables @max@ would collide with the functions @max@.
272Ergonomic 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 functions dispatched to, which must all have distinct names.
273Though name-overloading removes a major use-case for @_Generic@ expressions, \CFA implements @_Generic@ for backwards-compatibility purposes. \TODO{actually implement that}
274
275% http://fanf.livejournal.com/144696.html
276% http://www.robertgamble.net/2012/01/c11-generic-selections.html
277% https://abissell.com/2014/01/16/c11s-_generic-keyword-macro-applications-and-performance-impacts/
278
279
280\subsection{\texorpdfstring{\LstKeywordStyle{forall} Functions}{forall Functions}}
281\label{sec:poly-fns}
282
283The 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):
284\begin{cfa}
285`forall( otype T )` T identity( T val ) { return val; }
286int forty_two = identity( 42 );                         $\C{// T is bound to int, forty\_two == 42}$
287\end{cfa}
288The @identity@ function above can be applied to any complete \newterm{object type} (or @otype@).
289The 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.
290The \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.
291If this extra information is not needed, \eg for a pointer, the type parameter can be declared as a \newterm{data type} (or @dtype@).
292
293In \CFA, the polymorphism runtime-cost is spread over each polymorphic call, due to passing more arguments to polymorphic functions;
294the experiments in Section~\ref{sec:eval} show this overhead is similar to \CC virtual-function calls.
295A design advantage is that, unlike \CC template-functions, \CFA polymorphic-functions are compatible with C \emph{separate compilation}, preventing compilation and code bloat.
296
297Since 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.
298For example, the function @twice@ can be defined using the \CFA syntax for operator overloading:
299\begin{cfa}
300forall( otype T `| { T ?+?(T, T); }` ) T twice( T x ) { return x `+` x; }       $\C{// ? denotes operands}$
301int val = twice( twice( 3.7 ) );
302\end{cfa}
303which works for any type @T@ with a matching addition operator.
304The 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@.
305There 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.
306The first approach has a late conversion from @double@ to @int@ on the final assignment, while the second has an eager conversion to @int@.
307\CFA minimizes the number of conversions and their potential to lose information, so it selects the first approach, which corresponds with C-programmer intuition.
308
309Crucial to the design of a new programming language are the libraries to access thousands of external software features.
310Like \CC, \CFA inherits a massive compatible library-base, where other programming languages must rewrite or provide fragile inter-language communication with C.
311A simple example is leveraging the existing type-unsafe (@void *@) C @bsearch@ to binary search a sorted float array:
312\begin{cfa}
313void * bsearch( const void * key, const void * base, size_t nmemb, size_t size,
314                                int (* compar)( const void *, const void * ));
315
316int comp( const void * t1, const void * t2 ) { return *(double *)t1 < *(double *)t2 ? -1 :
317                                *(double *)t2 < *(double *)t1 ? 1 : 0; }
318
319double key = 5.0, vals[10] = { /* 10 sorted float values */ };
320double * val = (double *)bsearch( &key, vals, 10, sizeof(vals[0]), comp );      $\C{// search sorted array}$
321\end{cfa}
322which can be augmented simply with a generalized, type-safe, \CFA-overloaded wrappers:
323\begin{cfa}
324forall( otype T | { int ?<?( T, T ); } ) T * bsearch( T key, const T * arr, size_t size ) {
325        int comp( const void * t1, const void * t2 ) { /* as above with double changed to T */ }
326        return (T *)bsearch( &key, arr, size, sizeof(T), comp ); }
327
328forall( otype T | { int ?<?( T, T ); } ) unsigned int bsearch( T key, const T * arr, size_t size ) {
329        T * result = bsearch( key, arr, size ); $\C{// call first version}$
330        return result ? result - arr : size; }  $\C{// pointer subtraction includes sizeof(T)}$
331
332double * val = bsearch( 5.0, vals, 10 );        $\C{// selection based on return type}$
333int posn = bsearch( 5.0, vals, 10 );
334\end{cfa}
335The nested function @comp@ provides the hidden interface from typed \CFA to untyped (@void *@) C, plus the cast of the result.
336Providing a hidden @comp@ function in \CC is awkward as lambdas do not use C calling-conventions and template declarations cannot appear at block scope.
337As well, an alternate kind of return is made available: position versus pointer to found element.
338\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 templated @bsearch@.
339
340\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}).
341For example, it is possible to write a type-safe \CFA wrapper @malloc@ based on the C @malloc@:
342\begin{cfa}
343forall( dtype T | sized(T) ) T * malloc( void ) { return (T *)malloc( sizeof(T) ); }
344int * ip = malloc();                                            $\C{// select type and size from left-hand side}$
345double * dp = malloc();
346struct S {...} * sp = malloc();
347\end{cfa}
348where the return type supplies the type/size of the allocation, which is impossible in most type systems.
349
350Call-site inferencing and nested functions provide a localized form of inheritance.
351For example, the \CFA @qsort@ only sorts in ascending order using @<@.
352However, it is trivial to locally change this behaviour:
353\begin{cfa}
354forall( otype T | { int ?<?( T, T ); } ) void qsort( const T * arr, size_t size ) { /* use C qsort */ }
355{
356        int ?<?( double x, double y ) { return x `>` y; }       $\C{// locally override behaviour}$
357        qsort( vals, size );                                    $\C{// descending sort}$
358}
359\end{cfa}
360Within the block, the nested version of @?<?@ performs @?>?@ and this local version overrides the built-in @?<?@ so it is passed to @qsort@.
361Hence, programmers can easily form local environments, adding and modifying appropriate functions, to maximize reuse of other existing functions and types.
362
363
364\subsection{Traits}
365
366\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:
367\begin{cfa}
368trait `summable`( otype T ) {
369        void ?{}( T *, zero_t );                                $\C{// constructor from 0 literal}$
370        T ?+?( T, T );                                                  $\C{// assortment of additions}$
371        T ?+=?( T *, T );
372        T ++?( T * );
373        T ?++( T * ); };
374
375forall( otype T `| summable( T )` ) T sum( T a[$\,$], size_t size ) {  // use trait
376        `T` total = { `0` };                                    $\C{// instantiate T from 0 by calling its constructor}$
377        for ( unsigned int i = 0; i < size; i += 1 ) total `+=` a[i]; $\C{// select appropriate +}$
378        return total; }
379\end{cfa}
380
381In 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:
382\begin{cfa}
383trait otype( dtype T | sized(T) ) {  // sized is a pseudo-trait for types with known size and alignment
384        void ?{}( T * );                                                $\C{// default constructor}$
385        void ?{}( T *, T );                                             $\C{// copy constructor}$
386        void ?=?( T *, T );                                             $\C{// assignment operator}$
387        void ^?{}( T * ); };                                    $\C{// destructor}$
388\end{cfa}
389Given 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.
390
391In 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.
392Hence, trait names play no part in type equivalence;
393the names are simply macros for a list of polymorphic assertions, which are expanded at usage sites.
394Nevertheless, trait names form a logical subtype-hierarchy with @dtype@ at the top, where traits often contain overlapping assertions, \eg operator @+@.
395Traits are used like interfaces in Java or abstract base-classes in \CC, but without the nominal inheritance-relationships.
396Instead, 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.
397Hence, 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.
398(Nominal inheritance can be approximated with traits using marker variables or functions, as is done in Go.)
399
400% Nominal inheritance can be simulated with traits using marker variables or functions:
401% \begin{cfa}
402% trait nominal(otype T) {
403%     T is_nominal;
404% };
405% int is_nominal;                                                               $\C{// int now satisfies the nominal trait}$
406% \end{cfa}
407%
408% 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:
409% \begin{cfa}
410% trait pointer_like(otype Ptr, otype El) {
411%     lvalue El *?(Ptr);                                                $\C{// Ptr can be dereferenced into a modifiable value of type El}$
412% }
413% struct list {
414%     int value;
415%     list * next;                                                              $\C{// may omit "struct" on type names as in \CC}$
416% };
417% typedef list * list_iterator;
418%
419% lvalue int *?( list_iterator it ) { return it->value; }
420% \end{cfa}
421% 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@).
422% 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.
423
424
425\section{Generic Types}
426
427A significant shortcoming of standard C is the lack of reusable type-safe abstractions for generic data structures and algorithms.
428Broadly speaking, there are three approaches to implement abstract data-structures in C.
429One approach is to write bespoke data-structures for each context in which they are needed.
430While 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.
431A second approach is to use @void *@--based polymorphism, \eg the C standard-library functions @bsearch@ and @qsort@, which allows reuse of code with common functionality.
432However, 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.
433A 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.
434Furthermore, writing and using preprocessor macros can be unnatural and inflexible.
435
436\CC, Java, and other languages use \newterm{generic types} to produce type-safe abstract data-types.
437\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.
438However, for known concrete parameters, the generic-type definition can be inlined, like \CC templates.
439
440A 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:
441\begin{cfa}
442forall( otype R, otype S ) struct pair {
443        R first;
444        S second;
445};
446forall( otype T ) T value( pair( const char *, T ) p ) { return p.second; }
447forall( dtype F, otype T ) T value( pair( F *, T * ) p ) { return *p.second; }
448
449pair( const char *, int ) p = { "magic", 42 };
450int i = value( p );
451pair( void *, int * ) q = { 0, &p.second };
452i = value( q );
453double d = 1.0;
454pair( double *, double * ) r = { &d, &d };
455d = value( r );
456\end{cfa}
457
458\CFA classifies generic types as either \newterm{concrete} or \newterm{dynamic}.
459Concrete types have a fixed memory layout regardless of type parameters, while dynamic types vary in memory layout depending on their type parameters.
460A type may have polymorphic parameters but still be concrete, called \newterm{dtype-static}.
461Polymorphic 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.
462
463\CFA generic types also allow checked argument-constraints.
464For example, the following declaration of a sorted set-type ensures the set key supports equality and relational comparison:
465\begin{cfa}
466forall( otype Key | { _Bool ?==?(Key, Key); _Bool ?<?(Key, Key); } ) struct sorted_set;
467\end{cfa}
468
469
470\subsection{Concrete Generic-Types}
471
472The \CFA translator template-expands concrete generic-types into new structure types, affording maximal inlining.
473To 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.
474A 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.
475For example, the concrete instantiation for @pair( const char *, int )@ is:
476\begin{cfa}
477struct _pair_conc1 {
478        const char * first;
479        int second;
480};
481\end{cfa}
482
483A concrete generic-type with dtype-static parameters is also expanded to a structure type, but this type is used for all matching instantiations.
484In the above example, the @pair( F *, T * )@ parameter to @value_p@ 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:
485\begin{cfa}
486struct _pair_conc0 {
487        void * first;
488        void * second;
489};
490\end{cfa}
491
492
493\subsection{Dynamic Generic-Types}
494
495Though \CFA implements concrete generic-types efficiently, it also has a fully general system for dynamic generic types.
496As 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.
497Dynamic generic-types also have an \newterm{offset array} containing structure-member offsets.
498A dynamic generic-union needs no such offset array, as all members are at offset 0, but size and alignment are still necessary.
499Access 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.
500
501The offset arrays are statically generated where possible.
502If 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;
503if 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.
504As an example, @p.second@ in the @value@ function above is implemented as @*(p + _offsetof_pair[1])@, where @p@ is a @void *@, and @_offsetof_pair@ is the offset array passed into @value@ for @pair( const char *, T )@.
505The offset array @_offsetof_pair@ is generated at the call site as @size_t _offsetof_pair[] = { offsetof(_pair_conc1, first), offsetof(_pair_conc1, second) }@.
506
507In some cases the offset arrays cannot be statically generated.
508For 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.
509\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.
510The \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.
511These 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).
512Results of these layout functions are cached so that they are only computed once per type per function. %, as in the example below for @pair@.
513Layout functions also allow generic types to be used in a function definition without reflecting them in the function signature.
514For instance, a function that strips duplicate values from an unsorted @vector(T)@ would likely have a pointer to the vector as its only explicit parameter, but use some sort of @set(T)@ internally to test for duplicate values.
515This function could acquire the layout for @set(T)@ by calling its layout function with the layout of @T@ implicitly passed into the function.
516
517Whether a type is concrete, dtype-static, or dynamic is decided solely on the @forall@'s type parameters.
518This 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.
519If 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.
520
521
522\subsection{Applications}
523\label{sec:generic-apps}
524
525The reuse of dtype-static structure instantiations enables useful programming patterns at zero runtime cost.
526The 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@:
527\begin{cfa}
528forall(dtype T) int lexcmp( pair( T *, T * ) * a, pair( T *, T * ) * b, int (* cmp)( T *, T * ) ) {
529        return cmp( a->first, b->first ) ? : cmp( a->second, b->second );
530}
531\end{cfa}
532Since @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.
533
534Another useful pattern enabled by reused dtype-static type instantiations is zero-cost \newterm{tag-structures}.
535Sometimes information is only used for type-checking and can be omitted at runtime, \eg:
536\begin{cfa}
537forall(dtype Unit) struct scalar { unsigned long value; };
538struct metres {};
539struct litres {};
540
541forall(dtype U) scalar(U) ?+?( scalar(U) a, scalar(U) b ) {
542        return (scalar(U)){ a.value + b.value };
543}
544scalar(metres) half_marathon = { 21093 };
545scalar(litres) swimming_pool = { 2500000 };
546scalar(metres) marathon = half_marathon + half_marathon;
547scalar(litres) two_pools = swimming_pool + swimming_pool;
548marathon + swimming_pool;                                       $\C{// compilation ERROR}$
549\end{cfa}
550@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 @?+?@.
551These implementations may even be separately compiled, unlike \CC template functions.
552However, the \CFA type-checker ensures matching types are used by all calls to @?+?@, preventing nonsensical computations like adding a length to a volume.
553
554
555\section{Tuples}
556\label{sec:tuples}
557
558In many languages, functions can return at most one value;
559however, many operations have multiple outcomes, some exceptional.
560Consider C's @div@ and @remquo@ functions, which return the quotient and remainder for a division of integer and float values, respectively.
561\begin{cfa}
562typedef struct { int quo, rem; } div_t;         $\C{// from include stdlib.h}$
563div_t div( int num, int den );
564double remquo( double num, double den, int * quo );
565div_t qr = div( 13, 5 );                                        $\C{// return quotient/remainder aggregate}$
566int q;
567double r = remquo( 13.5, 5.2, &q );                     $\C{// return remainder, alias quotient}$
568\end{cfa}
569@div@ aggregates the quotient/remainder in a structure, while @remquo@ aliases a parameter to an argument.
570Both approaches are awkward.
571Alternatively, a programming language can directly support returning multiple values, \eg in \CFA:
572\begin{cfa}
573[ int, int ] div( int num, int den );           $\C{// return two integers}$
574[ double, double ] div( double num, double den ); $\C{// return two doubles}$
575int q, r;                                                                       $\C{// overloaded variable names}$
576double q, r;
577[ q, r ] = div( 13, 5 );                                        $\C{// select appropriate div and q, r}$
578[ q, r ] = div( 13.5, 5.2 );                            $\C{// assign into tuple}$
579\end{cfa}
580Clearly, this approach is straightforward to understand and use;
581therefore, why do few programming languages support this obvious feature or provide it awkwardly?
582The answer is that there are complex consequences that cascade through multiple aspects of the language, especially the type-system.
583This section show these consequences and how \CFA handles them.
584
585
586\subsection{Tuple Expressions}
587
588The addition of multiple-return-value functions (MRVF) are useless without a syntax for accepting multiple values at the call-site.
589The simplest mechanism for capturing the return values is variable assignment, allowing the values to be retrieved directly.
590As 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}.
591
592However, 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:
593\begin{cfa}
594printf( "%d %d\n", div( 13, 5 ) );                      $\C{// return values seperated into arguments}$
595\end{cfa}
596Here, the values returned by @div@ are composed with the call to @printf@ by flattening the tuple into separate arguments.
597However, the \CFA type-system must support significantly more complex composition:
598\begin{cfa}
599[ int, int ] foo$\(_1\)$( int );                        $\C{// overloaded foo functions}$
600[ double ] foo$\(_2\)$( int );
601void bar( int, double, double );
602`bar`( foo( 3 ), foo( 3 ) );
603\end{cfa}
604The type-resolver only has the tuple return-types to resolve the call to @bar@ as the @foo@ parameters are identical, which involves unifying the possible @foo@ functions with @bar@'s parameter list.
605No combination of @foo@s are an exact match with @bar@'s parameters, so the resolver applies C conversions.
606The minimal cost is @bar( foo@$_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.
607
608
609\subsection{Tuple Variables}
610
611An important observation from function composition is that new variable names are not required to initialize parameters from an MRVF.
612\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:
613\begin{cfa}
614[ int, int ] qr = div( 13, 5 );                         $\C{// tuple-variable declaration and initialization}$
615[ double, double ] qr = div( 13.5, 5.2 );
616\end{cfa}
617where the tuple variable-name serves the same purpose as the parameter name(s).
618Tuple variables can be composed of any types, except for array types, since array sizes are generally unknown in C.
619
620One way to access the tuple-variable components is with assignment or composition:
621\begin{cfa}
622[ q, r ] = qr;                                                          $\C{// access tuple-variable components}$
623printf( "%d %d\n", qr );
624\end{cfa}
625\CFA also supports \newterm{tuple indexing} to access single components of a tuple expression:
626\begin{cfa}
627[int, int] * p = &qr;                                           $\C{// tuple pointer}$
628int rem = qr`.1`;                                                       $\C{// access remainder}$
629int quo = div( 13, 5 )`.0`;                                     $\C{// access quotient}$
630p`->0` = 5;                                                                     $\C{// change quotient}$
631bar( qr`.1`, qr );                                                      $\C{// pass remainder and quotient/remainder}$
632rem = [div( 13, 5 ), 42]`.0.1`;                         $\C{// access 2nd component of 1st component of tuple expression}$
633\end{cfa}
634
635
636\subsection{Flattening and Restructuring}
637
638In function call contexts, tuples support implicit flattening and restructuring conversions.
639Tuple flattening recursively expands a tuple into the list of its basic components.
640Tuple structuring packages a list of expressions into a value of tuple type, \eg:
641%\lstDeleteShortInline@%
642%\par\smallskip
643%\begin{tabular}{@{}l@{\hspace{1.5\parindent}}||@{\hspace{1.5\parindent}}l@{}}
644\begin{cfa}
645int f( int, int );
646int g( [int, int] );
647int h( int, [int, int] );
648[int, int] x;
649int y;
650f( x );                 $\C{// flatten}$
651g( y, 10 );             $\C{// structure}$
652h( x, y );              $\C{// flatten and structure}$
653\end{cfa}
654%\end{cfa}
655%&
656%\begin{cfa}
657%\end{tabular}
658%\smallskip\par\noindent
659%\lstMakeShortInline@%
660In the call to @f@, @x@ is implicitly flattened so the components of @x@ are passed as the two arguments.
661In 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@.
662Finally, 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]@.
663The 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.
664
665
666\subsection{Tuple Assignment}
667
668An assignment where the left side is a tuple type is called \newterm{tuple assignment}.
669There 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.
670%\lstDeleteShortInline@%
671%\par\smallskip
672%\begin{tabular}{@{}l@{\hspace{1.5\parindent}}||@{\hspace{1.5\parindent}}l@{}}
673\begin{cfa}
674int x = 10;
675double y = 3.5;
676[int, double] z;
677z = [x, y];                                                                     $\C{// multiple assignment}$
678[x, y] = z;                                                                     $\C{// multiple assignment}$
679z = 10;                                                                         $\C{// mass assignment}$
680[y, x] = 3.14;                                                          $\C{// mass assignment}$
681\end{cfa}
682%\end{cfa}
683%&
684%\begin{cfa}
685%\end{tabular}
686%\smallskip\par\noindent
687%\lstMakeShortInline@%
688Both kinds of tuple assignment have parallel semantics, so that each value on the left and right side is evaluated before any assignments occur.
689As 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]@.
690This 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.
691For example, @[y, x] = 3.14@ performs the assignments @y = 3.14@ and @x = 3.14@, yielding @y == 3.14@ and @x == 3@;
692whereas, C cascading assignment @y = x = 3.14@ performs the assignments @x = 3.14@ and @y = x@, yielding @3@ in @y@ and @x@.
693Finally, 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.
694This example shows mass, multiple, and cascading assignment used in one expression:
695\begin{cfa}
696void f( [int, int] );
697f( [x, y] = z = 1.5 );                                          $\C{// assignments in parameter list}$
698\end{cfa}
699
700
701\subsection{Member Access}
702
703It is also possible to access multiple fields from a single expression using a \newterm{member-access}.
704The result is a single tuple-valued expression whose type is the tuple of the types of the members, \eg:
705\begin{cfa}
706struct S { int x; double y; char * z; } s;
707s.[x, y, z] = 0;
708\end{cfa}
709Here, the mass assignment sets all members of @s@ to zero.
710Since 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).
711%\lstDeleteShortInline@%
712%\par\smallskip
713%\begin{tabular}{@{}l@{\hspace{1.5\parindent}}||@{\hspace{1.5\parindent}}l@{}}
714\begin{cfa}
715[int, int, long, double] x;
716void f( double, long );
717x.[0, 1] = x.[1, 0];                                            $\C{// rearrange: [x.0, x.1] = [x.1, x.0]}$
718f( x.[0, 3] );                                                          $\C{// drop: f(x.0, x.3)}$
719[int, int, int] y = x.[2, 0, 2];                        $\C{// duplicate: [y.0, y.1, y.2] = [x.2, x.0.x.2]}$
720\end{cfa}
721%\end{cfa}
722%&
723%\begin{cfa}
724%\end{tabular}
725%\smallskip\par\noindent
726%\lstMakeShortInline@%
727It is also possible for a member access to contain other member accesses, \eg:
728\begin{cfa}
729struct A { double i; int j; };
730struct B { int * k; short l; };
731struct C { int x; A y; B z; } v;
732v.[x, y.[i, j], z.k];                                           $\C{// [v.x, [v.y.i, v.y.j], v.z.k]}$
733\end{cfa}
734
735
736\begin{comment}
737\subsection{Casting}
738
739In C, the cast operator is used to explicitly convert between types.
740In \CFA, the cast operator has a secondary use as type ascription.
741That 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:
742\begin{cfa}
743int f();     // (1)
744double f()// (2)
745
746f();       // ambiguous - (1),(2) both equally viable
747(int)f()// choose (2)
748\end{cfa}
749
750Since casting is a fundamental operation in \CFA, casts should be given a meaningful interpretation in the context of tuples.
751Taking a look at standard C provides some guidance with respect to the way casts should work with tuples:
752\begin{cfa}
753int f();
754void g();
755
756(void)f()// (1)
757(int)g()// (2)
758\end{cfa}
759In C, (1) is a valid cast, which calls @f@ and discards its result.
760On the other hand, (2) is invalid, because @g@ does not produce a result, so requesting an @int@ to materialize from nothing is nonsensical.
761Generalizing 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.
762
763Formally, 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 $T_i$.
764Excess 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.
765This approach follows naturally from the way that a cast to @void@ works in C.
766
767For example, in
768\begin{cfa}
769[int, int, int] f();
770[int, [int, int], int] g();
771
772([int, double])f();           $\C{// (1)}$
773([int, int, int])g();         $\C{// (2)}$
774([void, [int, int]])g();      $\C{// (3)}$
775([int, int, int, int])g();    $\C{// (4)}$
776([int, [int, int, int]])g()$\C{// (5)}$
777\end{cfa}
778
779(1) discards the last element of the return value and converts the second element to @double@.
780Since @int@ is effectively a 1-element tuple, (2) discards the second component of the second element of the return value of @g@.
781If @g@ is free of side effects, this expression is equivalent to @[(int)(g().0), (int)(g().1.0), (int)(g().2)]@.
782Since @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)]@).
783
784Note 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 would require more precise matching of types than allowed for function arguments and parameters.}.
785As such, (4) is invalid because the cast target type contains 4 components, while the source type contains only 3.
786Similarly, (5) is invalid because the cast @([int, int, int])(g().1)@ is invalid.
787That is, it is invalid to cast @[int, int]@ to @[int, int, int]@.
788\end{comment}
789
790
791\subsection{Polymorphism}
792
793Tuples also integrate with \CFA polymorphism as a kind of generic type.
794Due 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:
795\begin{cfa}
796forall(otype T, dtype U) void f( T x, U * y );
797f( [5, "hello"] );
798\end{cfa}
799where @[5, "hello"]@ is flattened, giving argument list @5, "hello"@, and @T@ binds to @int@ and @U@ binds to @const char@.
800Tuples, however, may contain polymorphic components.
801For example, a plus operator can be written to add two triples together.
802\begin{cfa}
803forall(otype T | { T ?+?( T, T ); }) [T, T, T] ?+?( [T, T, T] x, [T, T, T] y ) {
804        return [x.0 + y.0, x.1 + y.1, x.2 + y.2];
805}
806[int, int, int] x;
807int i1, i2, i3;
808[i1, i2, i3] = x + ([10, 20, 30]);
809\end{cfa}
810
811Flattening and restructuring conversions are also applied to tuple types in polymorphic type assertions.
812\begin{cfa}
813int f( [int, double], double );
814forall(otype T, otype U | { T f( T, U, U ); }) void g( T, U );
815g( 5, 10.21 );
816\end{cfa}
817Hence, function parameter and return lists are flattened for the purposes of type unification allowing the example to pass expression resolution.
818This relaxation is possible by extending the thunk scheme described by Bilson~\cite{Bilson03}.
819Whenever 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:
820\begin{cfa}
821int _thunk( int _p0, double _p1, double _p2 ) { return f( [_p0, _p1], _p2 ); }
822\end{cfa}
823so the thunk provides flattening and structuring conversions to inferred functions, improving the compatibility of tuples and polymorphism.
824These thunks take advantage of gcc C nested-functions to produce closures that have the usual function-pointer signature.
825
826
827\subsection{Variadic Tuples}
828\label{sec:variadic-tuples}
829
830To define variadic functions, \CFA adds a new kind of type parameter, @ttype@ (tuple type).
831Matching against a @ttype@ parameter consumes all remaining argument components and packages them into a tuple, binding to the resulting tuple of types.
832In 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.
833As such, @ttype@ variables are also called \newterm{argument packs}.
834
835Like variadic templates, the main way to manipulate @ttype@ polymorphic functions is via recursion.
836Since nothing is known about a parameter pack by default, assertion parameters are key to doing anything meaningful.
837Unlike variadic templates, @ttype@ polymorphic functions can be separately compiled.
838For example, a generalized @sum@ function written using @ttype@:
839\begin{cfa}
840int sum$\(_0\)$() { return 0; }
841forall(ttype Params | { int sum( Params ); } ) int sum$\(_1\)$( int x, Params rest ) {
842        return x + sum( rest );
843}
844sum( 10, 20, 30 );
845\end{cfa}
846Since @sum@\(_0\) does not accept any arguments, it is not a valid candidate function for the call @sum(10, 20, 30)@.
847In 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]@.
848The process continues until @Params@ is bound to @[]@, requiring an assertion @int sum()@, which matches @sum@\(_0\) and terminates the recursion.
849Effectively, 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))@.
850
851It is reasonable to take the @sum@ function a step further to enforce a minimum number of arguments:
852\begin{cfa}
853int sum( int x, int y ) { return x + y; }
854forall(ttype Params | { int sum( int, Params ); } ) int sum( int x, int y, Params rest ) {
855        return sum( x + y, rest );
856}
857\end{cfa}
858One more step permits the summation of any summable type with all arguments of the same type:
859\begin{cfa}
860trait summable(otype T) {
861        T ?+?( T, T );
862};
863forall(otype R | summable( R ) ) R sum( R x, R y ) {
864        return x + y;
865}
866forall(otype R, ttype Params | summable(R) | { R sum(R, Params); } ) R sum(R x, R y, Params rest) {
867        return sum( x + y, rest );
868}
869\end{cfa}
870Unlike C variadic functions, it is unnecessary to hard code the number and expected types.
871Furthermore, this code is extendable for any user-defined type with a @?+?@ operator.
872Summing arbitrary heterogeneous lists is possible with similar code by adding the appropriate type variables and addition operators.
873
874It is also possible to write a type-safe variadic print function to replace @printf@:
875\begin{cfa}
876struct S { int x, y; };
877forall(otype T, ttype Params | { void print(T); void print(Params); }) void print(T arg, Params rest) {
878        print(arg);  print(rest);
879}
880void print( char * x ) { printf( "%s", x ); }
881void print( int x ) { printf( "%d", x ); }
882void print( S s ) { print( "{ ", s.x, ",", s.y, " }" ); }
883print( "s = ", (S){ 1, 2 }, "\n" );
884\end{cfa}
885This example showcases a variadic-template-like decomposition of the provided argument list.
886The individual @print@ functions allow printing a single element of a type.
887The polymorphic @print@ allows printing any list of types, where as each individual type has a @print@ function.
888The individual print functions can be used to build up more complicated @print@ functions, such as @S@, which cannot be done with @printf@ in C.
889
890Finally, it is possible to use @ttype@ polymorphism to provide arbitrary argument forwarding functions.
891For example, it is possible to write @new@ as a library function:
892\begin{cfa}
893forall( otype R, otype S ) void ?{}( pair(R, S) *, R, S );
894forall( dtype T, ttype Params | sized(T) | { void ?{}( T *, Params ); } ) T * new( Params p ) {
895        return ((T *)malloc()){ p };                    $\C{// construct into result of malloc}$
896}
897pair( int, char ) * x = new( 42, '!' );
898\end{cfa}
899The @new@ function provides the combination of type-safe @malloc@ with a \CFA constructor call, making it impossible to forget constructing dynamically allocated objects.
900This function provides the type-safety of @new@ in \CC, without the need to specify the allocated type again, thanks to return-type inference.
901
902
903\subsection{Implementation}
904
905Tuples are implemented in the \CFA translator via a transformation into \newterm{generic types}.
906For each $N$, the first time an $N$-tuple is seen in a scope a generic type with $N$ type parameters is generated, \eg:
907\begin{cfa}
908[int, int] f() {
909        [double, double] x;
910        [int, double, int] y;
911}
912\end{cfa}
913is transformed into:
914\begin{cfa}
915forall(dtype T0, dtype T1 | sized(T0) | sized(T1)) struct _tuple2 {
916        T0 field_0;                                                             $\C{// generated before the first 2-tuple}$
917        T1 field_1;
918};
919_tuple2(int, int) f() {
920        _tuple2(double, double) x;
921        forall(dtype T0, dtype T1, dtype T2 | sized(T0) | sized(T1) | sized(T2)) struct _tuple3 {
922                T0 field_0;                                                     $\C{// generated before the first 3-tuple}$
923                T1 field_1;
924                T2 field_2;
925        };
926        _tuple3(int, double, int) y;
927}
928\end{cfa}
929\begin{sloppypar}
930Tuple expressions are then simply converted directly into compound literals, \eg @[5, 'x', 1.24]@ becomes @(_tuple3(int, char, double)){ 5, 'x', 1.24 }@.
931\end{sloppypar}
932
933\begin{comment}
934Since tuples are essentially structures, tuple indexing expressions are just field accesses:
935\begin{cfa}
936void f(int, [double, char]);
937[int, double] x;
938
939x.0+x.1;
940printf("%d %g\n", x);
941f(x, 'z');
942\end{cfa}
943Is transformed into:
944\begin{cfa}
945void f(int, _tuple2(double, char));
946_tuple2(int, double) x;
947
948x.field_0+x.field_1;
949printf("%d %g\n", x.field_0, x.field_1);
950f(x.field_0, (_tuple2){ x.field_1, 'z' });
951\end{cfa}
952Note that due to flattening, @x@ used in the argument position is converted into the list of its fields.
953In the call to @f@, the second and third argument components are structured into a tuple argument.
954Similarly, tuple member expressions are recursively expanded into a list of member access expressions.
955
956Expressions that may contain side effects are made into \newterm{unique expressions} before being expanded by the flattening conversion.
957Each unique expression is assigned an identifier and is guaranteed to be executed exactly once:
958\begin{cfa}
959void g(int, double);
960[int, double] h();
961g(h());
962\end{cfa}
963Internally, this expression is converted to two variables and an expression:
964\begin{cfa}
965void g(int, double);
966[int, double] h();
967
968_Bool _unq0_finished_ = 0;
969[int, double] _unq0;
970g(
971        (_unq0_finished_ ? _unq0 : (_unq0 = f(), _unq0_finished_ = 1, _unq0)).0,
972        (_unq0_finished_ ? _unq0 : (_unq0 = f(), _unq0_finished_ = 1, _unq0)).1,
973);
974\end{cfa}
975Since argument evaluation order is not specified by the C programming language, this scheme is built to work regardless of evaluation order.
976The first time a unique expression is executed, the actual expression is evaluated and the accompanying boolean is set to true.
977Every subsequent evaluation of the unique expression then results in an access to the stored result of the actual expression.
978Tuple member expressions also take advantage of unique expressions in the case of possible impurity.
979
980Currently, the \CFA translator has a very broad, imprecise definition of impurity, where any function call is assumed to be impure.
981This 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.
982
983The various kinds of tuple assignment, constructors, and destructors generate GNU C statement expressions.
984A 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.
985The 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.
986However, 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.
987\end{comment}
988
989
990\section{Control Structures}
991
992\CFA identifies inconsistent, problematic, and missing control structures in C, and extends, modifies, and adds to control structures to increase functionality and safety.
993
994
995\subsection{\texorpdfstring{\LstKeywordStyle{if} Statement}{if Statement}}
996
997The @if@ expression allows declarations, similar to @for@ declaration expression:
998\begin{cfa}
999if ( int x = f() ) ...                                          $\C{// x != 0}$
1000if ( int x = f(), y = g() ) ...                         $\C{// x != 0 \&\& y != 0}$
1001if ( int x = f(), y = g(); `x < y` ) ...        $\C{// relational expression}$
1002\end{cfa}
1003Unless 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.}
1004The scope of the declaration(s) is local to the @if@ statement but exist within both the ``then'' and ``else'' clauses.
1005
1006
1007\subsection{\texorpdfstring{\LstKeywordStyle{switch} Statement}{switch Statement}}
1008
1009There 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.
1010
1011C 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.}.
1012\CFA provides a shorthand for a non-contiguous list:
1013\begin{cquote}
1014\lstDeleteShortInline@%
1015\begin{tabular}{@{}l@{\hspace{\parindentlnth}}l@{}}
1016\multicolumn{1}{c@{\hspace{\parindentlnth}}}{\textbf{\CFA}}     & \multicolumn{1}{c}{\textbf{C}}        \\
1017\begin{cfa}
1018case 2, 10, 34, 42:
1019\end{cfa}
1020&
1021\begin{cfa}
1022case 2: case 10: case 34: case 42:
1023\end{cfa}
1024\end{tabular}
1025\lstMakeShortInline@%
1026\end{cquote}
1027for a contiguous list:\footnote{gcc provides the same mechanism with awkward syntax, \lstinline@2 ... 42@, where spaces are required around the ellipse.}
1028\begin{cquote}
1029\lstDeleteShortInline@%
1030\begin{tabular}{@{}l@{\hspace{\parindentlnth}}l@{}}
1031\multicolumn{1}{c@{\hspace{\parindentlnth}}}{\textbf{\CFA}}     & \multicolumn{1}{c}{\textbf{C}}        \\
1032\begin{cfa}
1033case 2~42:
1034\end{cfa}
1035&
1036\begin{cfa}
1037case 2: case 3: ... case 41: case 42:
1038\end{cfa}
1039\end{tabular}
1040\lstMakeShortInline@%
1041\end{cquote}
1042and a combination:
1043\begin{cfa}
1044case -12~-4, -1~5, 14~21, 34~42:
1045\end{cfa}
1046
1047C allows placement of @case@ clauses \emph{within} statements nested in the @switch@ body (see Duff's device~\cite{Duff83});
1048\begin{cfa}
1049switch ( i ) {
1050  case 0:
1051        for ( int i = 0; i < 10; i += 1 ) {
1052                ...
1053  `case 1:`             // no initialization of loop index
1054                ...
1055        }
1056}
1057\end{cfa}
1058\CFA precludes this form of transfer into a control structure because it causes undefined behaviour, especially with respect to missed initialization, and provides very limited functionality.
1059
1060C allows placement of declaration within the @switch@ body and unreachable code at the start, resulting in undefined behaviour:
1061\begin{cfa}
1062switch ( x ) {
1063        `int y = 1;`                                                    $\C{// unreachable initialization}$
1064        `x = 7;`                                                                $\C{// unreachable code without label/branch}$
1065  case 0:
1066        ...
1067        `int z = 0;`                                                    $\C{// unreachable initialization, cannot appear after case}$
1068        z = 2;
1069  case 1:
1070        `x = z;`                                                                $\C{// without fall through, z is undefined}$
1071}
1072\end{cfa}
1073\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.
1074\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.
1075
1076C @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};
1077@case@ clauses are made disjoint by the @break@ statement.
1078While the ability to fall through \emph{is} a useful form of control flow, it does not match well with programmer intuition, resulting in many errors from missing @break@ statements.
1079For 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}).
1080Collectively, these enhancements reduce programmer burden and increase readability and safety.
1081
1082\begin{figure}
1083\centering
1084\lstDeleteShortInline@%
1085\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
1086\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
1087\begin{cfa}
1088`choose` ( day ) {
1089  case Mon~Thu:  // program
1090
1091  case Fri:  // program
1092        wallet += pay;
1093        `fallthrough;`
1094  case Sat:  // party
1095        wallet -= party;
1096
1097  case Sun:  // rest
1098
1099  default:  // error
1100}
1101\end{cfa}
1102&
1103\begin{cfa}
1104switch ( day ) {
1105  case Mon: case Tue: case Wed: case Thu:  // program
1106        `break;`
1107  case Fri:  // program
1108        wallet += pay;
1109
1110  case Sat:  // party
1111        wallet -= party;
1112        `break;`
1113  case Sun:  // rest
1114        `break;`
1115  default:  // error
1116}
1117\end{cfa}
1118\end{tabular}
1119\lstMakeShortInline@%
1120\caption{\lstinline|choose| versus \lstinline|switch| Statements}
1121\label{f:ChooseSwitchStatements}
1122\end{figure}
1123
1124\begin{comment}
1125Forgotten @break@ statements at the end of @switch@ cases are a persistent sort of programmer error in C, and the @break@ statements themselves introduce visual clutter and an un-C-like keyword-based block delimiter.
1126\CFA addresses this error by introducing a @choose@ statement, which works identically to a @switch@ except that its default end-of-case behaviour is to break rather than to fall through for all non-empty cases.
1127Since empty cases like @case 7:@ in @case 7: case 11:@ still have fall-through semantics and explicit @break@ is still allowed at the end of a @choose@ case, many idiomatic uses of @switch@ in standard C can be converted to @choose@ statements by simply changing the keyword.
1128Where fall-through is desired for a non-empty case, it can be specified with the new @fallthrough@ statement, making @choose@ equivalently powerful to @switch@, but more concise in the common case where most non-empty cases end with a @break@ statement, as in the example below:
1129
1130\begin{cfa}
1131choose( i ) {
1132        case 2:
1133                printf("even ");
1134                fallthrough;
1135        case 3: case 5: case 7:
1136                printf("small prime\n");
1137        case 4,6,8,9:
1138                printf("small composite\n");
1139        case 13~19:
1140                printf("teen\n");
1141        default:
1142                printf("something else\n");
1143}
1144\end{cfa}
1145\end{comment}
1146
1147
1148\subsection{\texorpdfstring{Labelled \LstKeywordStyle{continue} / \LstKeywordStyle{break}}{Labelled continue / break}}
1149
1150While C provides @continue@ and @break@ statements for altering control flow, both are restricted to one level of nesting for a particular control structure.
1151Unfortunately, this restriction forces programmers to use @goto@ to achieve the equivalent control-flow for more than one level of nesting.
1152To 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.
1153For both @continue@ and @break@, the target label must be directly associated with a @for@, @while@ or @do@ statement;
1154for @break@, the target label can also be associated with a @switch@, @if@ or compound (@{}@) statement.
1155Figure~\ref{f:MultiLevelExit} shows @continue@ and @break@ indicating the specific control structure, and the corresponding C program using only @goto@ and labels.
1156The innermost loop has 7 exit points, which cause continuation or termination of one or more of the 7 nested control-structures.
1157
1158\begin{figure}
1159\lstDeleteShortInline@%
1160\begin{tabular}{@{\hspace{\parindentlnth}}l@{\hspace{\parindentlnth}}l@{\hspace{\parindentlnth}}l@{}}
1161\multicolumn{1}{@{\hspace{\parindentlnth}}c@{\hspace{\parindentlnth}}}{\textbf{\CFA}}   & \multicolumn{1}{@{\hspace{\parindentlnth}}c}{\textbf{C}}      \\
1162\begin{cfa}
1163`LC:` {
1164        ... $declarations$ ...
1165        `LS:` switch ( ... ) {
1166          case 3:
1167                `LIF:` if ( ... ) {
1168                        `LF:` for ( ... ) {
1169                                `LW:` while ( ... ) {
1170                                        ... break `LC`; ...
1171                                        ... break `LS`; ...
1172                                        ... break `LIF`; ...
1173                                        ... continue `LF;` ...
1174                                        ... break `LF`; ...
1175                                        ... continue `LW`; ...
1176                                        ... break `LW`; ...
1177                                } // while
1178                        } // for
1179                } else {
1180                        ... break `LIF`; ...
1181                } // if
1182        } // switch
1183} // compound
1184\end{cfa}
1185&
1186\begin{cfa}
1187{
1188        ... $declarations$ ...
1189        switch ( ... ) {
1190          case 3:
1191                if ( ... ) {
1192                        for ( ... ) {
1193                                while ( ... ) {
1194                                        ... goto `LC`; ...
1195                                        ... goto `LS`; ...
1196                                        ... goto `LIF`; ...
1197                                        ... goto `LFC`; ...
1198                                        ... goto `LFB`; ...
1199                                        ... goto `LWC`; ...
1200                                        ... goto `LWB`; ...
1201                                  `LWC`: ; } `LWB:` ;
1202                          `LFC:` ; } `LFB:` ;
1203                } else {
1204                        ... goto `LIF`; ...
1205                } `LIF:` ;
1206        } `LS:` ;
1207} `LC:` ;
1208\end{cfa}
1209&
1210\begin{cfa}
1211
1212
1213
1214
1215
1216
1217
1218// terminate compound
1219// terminate switch
1220// terminate if
1221// continue loop
1222// terminate loop
1223// continue loop
1224// terminate loop
1225
1226
1227
1228// terminate if
1229
1230
1231
1232\end{cfa}
1233\end{tabular}
1234\lstMakeShortInline@%
1235\caption{Multi-level Exit}
1236\label{f:MultiLevelExit}
1237\end{figure}
1238
1239Both labelled @continue@ and @break@ are a @goto@ restricted in the following ways:
1240\begin{itemize}
1241\item
1242They cannot create a loop, which means only the looping constructs cause looping.
1243This restriction means all situations resulting in repeated execution are clearly delineated.
1244\item
1245They cannot branch into a control structure.
1246This restriction prevents missing declarations and/or initializations at the start of a control structure resulting in undefined behaviour.
1247\end{itemize}
1248The 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.
1249Furthermore, 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.
1250With @goto@, the label is at the end of the control structure, which fails to convey this important clue early enough to the reader.
1251Finally, using an explicit target for the transfer instead of an implicit target allows new constructs to be added or removed without affecting existing constructs.
1252The implicit targets of the current @continue@ and @break@, \ie the closest enclosing loop or @switch@, change as certain constructs are added or removed.
1253
1254
1255\subsection{Exception Handling}
1256
1257The following framework for \CFA exception handling is in place, excluding a run-time type information and dynamic casts.
1258\CFA provides two forms of exception handling: \newterm{fix-up} and \newterm{recovery} (see Figure~\ref{f:CFAExceptionHandling}).
1259Both 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.
1260\CFA restricts exception types to those defined by aggregate type @exception@.
1261The 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@).
1262If @resume@ or @throw@ have no exception type, it is a reresume/rethrow, meaning the currently exception continues propagation.
1263If there is no current exception, the reresume/rethrow results in a runtime error.
1264
1265\begin{figure}
1266\begin{cquote}
1267\lstDeleteShortInline@%
1268\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
1269\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{Resumption}}      & \multicolumn{1}{c}{\textbf{Termination}}      \\
1270\begin{cfa}
1271`exception R { int fix; };`
1272void f() {
1273        R r;
1274        ... `resume( r );` ...
1275        ... r.fix // control does return here after handler
1276}
1277`try` {
1278        ... f(); ...
1279} `catchResume( R r )` {
1280        ... r.fix = ...; // return correction to raise
1281} // dynamic return to _Resume
1282\end{cfa}
1283&
1284\begin{cfa}
1285`exception T {};`
1286void f() {
1287
1288        ... `throw( T{} );` ...
1289        // control does NOT return here after handler
1290}
1291`try` {
1292        ... f(); ...
1293} `catch( T t )` {
1294        ... // recover and continue
1295} // static return to next statement
1296\end{cfa}
1297\end{tabular}
1298\lstMakeShortInline@%
1299\end{cquote}
1300\caption{\CFA Exception Handling}
1301\label{f:CFAExceptionHandling}
1302\end{figure}
1303
1304The set of exception types in a list of catch clause may include both a resumption and termination handler:
1305\begin{cfa}
1306try {
1307        ... resume( `R{}` ); ...
1308} catchResume( `R` r ) { ... throw( R{} ); ... } $\C{\color{red}// H1}$
1309   catch( `R` r ) { ... }                                       $\C{\color{red}// H2}$
1310
1311\end{cfa}
1312The resumption propagation raises @R@ and the stack is not unwound;
1313the exception is caught by the @catchResume@ clause and handler H1 is invoked.
1314The termination propagation in handler H1 raises @R@ and the stack is unwound;
1315the exception is caught by the @catch@ clause and handler H2 is invoked.
1316The termination handler is available because the resumption propagation did not unwind the stack.
1317
1318An additional feature is conditional matching in a catch clause:
1319\begin{cfa}
1320try {
1321        ... write( `datafile`, ... ); ...               $\C{// may throw IOError}$
1322        ... write( `logfile`, ... ); ...
1323} catch ( IOError err; `err.file == datafile` ) { ... } $\C{// handle datafile error}$
1324   catch ( IOError err; `err.file == logfile` ) { ... } $\C{// handle logfile error}$
1325   catch ( IOError err ) { ... }                        $\C{// handler error from other files}$
1326\end{cfa}
1327where the throw inserts the failing file-handle in the I/O exception.
1328Conditional catch cannot be trivially mimicked by other mechanisms because once an exception is caught, handler clauses in that @try@ statement are no longer eligible..
1329
1330The resumption raise can specify an alternate stack on which to raise an exception, called a \newterm{nonlocal raise}:
1331\begin{cfa}
1332resume( $\emph{exception-type}$, $\emph{alternate-stack}$ )
1333resume( $\emph{alternate-stack}$ )
1334\end{cfa}
1335These overloads of @resume@ raise the specified exception or the currently propagating exception (reresume) at another coroutine or task~\cite{Delisle18}.
1336Nonlocal 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 handle returns.
1337
1338To facilitate nonlocal exception, \CFA provides dynamic enabling and disabling of nonlocal exception-propagation.
1339The constructs for controlling propagation of nonlocal exceptions are the @enable@ and the @disable@ blocks:
1340\begin{cquote}
1341\lstDeleteShortInline@%
1342\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
1343\begin{cfa}
1344enable $\emph{exception-type-list}$ {
1345        // allow non-local resumption
1346}
1347\end{cfa}
1348&
1349\begin{cfa}
1350disable $\emph{exception-type-list}$ {
1351        // disallow non-local resumption
1352}
1353\end{cfa}
1354\end{tabular}
1355\lstMakeShortInline@%
1356\end{cquote}
1357The arguments for @enable@/@disable@ specify the exception types allowed to be propagated or postponed, respectively.
1358Specifying no exception type is shorthand for specifying all exception types.
1359Both @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.
1360
1361Finally, \CFA provides a Java like  @finally@ clause after the catch clauses:
1362\begin{cfa}
1363try {
1364        ... f(); ...
1365// catchResume or catch clauses
1366} `finally` {
1367        // house keeping
1368}
1369\end{cfa}
1370The finally clause is always executed, i.e., if the try block ends normally or if an exception is raised.
1371If an exception is raised and caught, the handler is run before the finally clause.
1372Like a destructor (see Section~\ref{s:ConstructorsDestructors}), a finally clause can raise an exception but not if there is an exception being propagated.
1373Mimicking the @finally@ clause with mechanisms like RAII is non-trivially when there are multiple types and local accesses.
1374
1375
1376\subsection{\texorpdfstring{\LstKeywordStyle{with} Clause / Statement}{with Clause / Statement}}
1377\label{s:WithClauseStatement}
1378
1379Grouping heterogeneous data into \newterm{aggregate}s (structure/union) is a common programming practice, and an aggregate can be further organized into more complex structures, such as arrays and containers:
1380\begin{cfa}
1381struct S {                                                                      $\C{// aggregate}$
1382        char c;                                                                 $\C{// fields}$
1383        int i;
1384        double d;
1385};
1386S s, as[10];
1387\end{cfa}
1388However, functions manipulating aggregates must repeat the aggregate name to access its containing fields:
1389\begin{cfa}
1390void f( S s ) {
1391        `s.`c; `s.`i; `s.`d;                                    $\C{// access containing fields}$
1392}
1393\end{cfa}
1394which extends to multiple levels of qualification for nested aggregates.
1395A similar situation occurs in object-oriented programming, \eg \CC:
1396\begin{C++}
1397class C {
1398        char c;                                                                 $\C{// fields}$
1399        int i;
1400        double d;
1401        int f() {                                                               $\C{// implicit ``this'' aggregate}$
1402                `this->`c; `this->`i; `this->`d;        $\C{// access containing fields}$
1403        }
1404}
1405\end{C++}
1406Object-oriented nesting of member functions in a \lstinline[language=C++]@class@ allows eliding \lstinline[language=C++]@this->@ because of lexical scoping.
1407However, for other aggregate parameters, qualification is necessary:
1408\begin{cfa}
1409struct T { double m, n; };
1410int C::f( T & t ) {                                                     $\C{// multiple aggregate parameters}$
1411        c; i; d;                                                                $\C{\color{red}// this-\textgreater.c, this-\textgreater.i, this-\textgreater.d}$
1412        `t.`m; `t.`n;                                                   $\C{// must qualify}$
1413}
1414\end{cfa}
1415
1416To simplify the programmer experience, \CFA provides a @with@ statement (see Pascal~\cite[\S~4.F]{Pascal}) to elide aggregate qualification to fields by opening a scope containing the field identifiers.
1417Hence, the qualified fields become variables with the side-effect that it is easier to optimizing field references in a block.
1418\begin{cfa}
1419void f( S & this ) `with ( this )` {            $\C{// with statement}$
1420        c; i; d;                                                                $\C{\color{red}// this.c, this.i, this.d}$
1421}
1422\end{cfa}
1423with the generality of opening multiple aggregate-parameters:
1424\begin{cfa}
1425int f( S & s, T & t ) `with ( s, t )` {         $\C{// multiple aggregate parameters}$
1426        c; i; d;                                                                $\C{\color{red}// s.c, s.i, s.d}$
1427        m; n;                                                                   $\C{\color{red}// t.m, t.n}$
1428}
1429\end{cfa}
1430
1431In detail, the @with@ statement has the form:
1432\begin{cfa}
1433$\emph{with-statement}$:
1434        'with' '(' $\emph{expression-list}$ ')' $\emph{compound-statement}$
1435\end{cfa}
1436and may appear as the body of a function or nested within a function body.
1437Each expression in the expression-list provides a type and object.
1438The type must be an aggregate type.
1439(Enumerations are already opened.)
1440The object is the implicit qualifier for the open structure-fields.
1441
1442All expressions in the expression list are open in parallel within the compound statement.
1443This semantic is different from Pascal, which nests the openings from left to right.
1444The difference between parallel and nesting occurs for fields with the same name and type:
1445\begin{cfa}
1446struct S { int `i`; int j; double m; } s, w;
1447struct T { int `i`; int k; int m; } t, w;
1448with ( s, t ) {
1449        j + k;                                                                  $\C{// unambiguous, s.j + t.k}$
1450        m = 5.0;                                                                $\C{// unambiguous, t.m = 5.0}$
1451        m = 1;                                                                  $\C{// unambiguous, s.m = 1}$
1452        int a = m;                                                              $\C{// unambiguous, a = s.i }$
1453        double b = m;                                                   $\C{// unambiguous, b = t.m}$
1454        int c = s.i + t.i;                                              $\C{// unambiguous, qualification}$
1455        (double)m;                                                              $\C{// unambiguous, cast}$
1456}
1457\end{cfa}
1458For parallel semantics, both @s.i@ and @t.i@ are visible, so @i@ is ambiguous without qualification;
1459for nested semantics, @t.i@ hides @s.i@, so @i@ implies @t.i@.
1460\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.
1461Qualification or a cast is used to disambiguate.
1462
1463There is an interesting problem between parameters and the function @with@, \eg:
1464\begin{cfa}
1465void ?{}( S & s, int i ) with ( s ) {           $\C{// constructor}$
1466        `s.i = i;`  j = 3;  m = 5.5;                    $\C{// initialize fields}$
1467}
1468\end{cfa}
1469Here, 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 @with@.
1470To solve this problem, parameters are treated like an initialized aggregate:
1471\begin{cfa}
1472struct Params {
1473        S & s;
1474        int i;
1475} params;
1476\end{cfa}
1477and implicitly opened \emph{after} a function open, to give them higher priority:
1478\begin{cfa}
1479void ?{}( S & s, int i ) with ( s ) `with( $\emph{\color{red}params}$ )` {
1480        s.i = i; j = 3; m = 5.5;
1481}
1482\end{cfa}
1483Finally, a cast may be used to disambiguate among overload variables in a @with@ expression:
1484\begin{cfa}
1485with ( w ) { ... }                                                      $\C{// ambiguous, same name and no context}$
1486with ( (S)w ) { ... }                                           $\C{// unambiguous, cast}$
1487\end{cfa}
1488and @with@ expressions may be complex expressions with type reference (see Section~\ref{s:References}) to aggregate:
1489\begin{cfa}
1490struct S { int i, j; } sv;
1491with ( sv ) {                                                           $\C{implicit reference}$
1492        S & sr = sv;
1493        with ( sr ) {                                                   $\C{explicit reference}$
1494                S * sp = &sv;
1495                with ( *sp ) {                                          $\C{computed reference}$
1496                        i = 3; j = 4;                                   $\C{\color{red}// sp-{\textgreater}i, sp-{\textgreater}j}$
1497                }
1498                i = 2; j = 3;                                           $\C{\color{red}// sr.i, sr.j}$
1499        }
1500        i = 1; j = 2;                                                   $\C{\color{red}// sv.i, sv.j}$
1501}
1502\end{cfa}
1503
1504
1505\section{Declarations}
1506
1507Declarations in C have weaknesses and omissions.
1508\CFA attempts to correct and add to C declarations, while ensuring \CFA subjectively ``feels like'' C.
1509An 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.
1510Maintaining 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.
1511Nevertheless, some features from other approaches are undeniably convenient;
1512\CFA attempts to adapt these features to the C paradigm.
1513
1514
1515\subsection{Alternative Declaration Syntax}
1516
1517C declaration syntax is notoriously confusing and error prone.
1518For example, many C programmers are confused by a declaration as simple as:
1519\begin{cquote}
1520\lstDeleteShortInline@%
1521\begin{tabular}{@{}ll@{}}
1522\begin{cfa}
1523int * x[5]
1524\end{cfa}
1525&
1526\raisebox{-0.75\totalheight}{\input{Cdecl}}
1527\end{tabular}
1528\lstMakeShortInline@%
1529\end{cquote}
1530Is this an array of 5 pointers to integers or a pointer to an array of 5 integers?
1531If there is any doubt, it implies productivity and safety issues even for basic programs.
1532Another 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.
1533For example, a function returning a pointer to an array of integers is defined and used in the following way:
1534\begin{cfa}
1535int `(*`f`())[`5`]` {...};                                      $\C{// definition}$
1536 ... `(*`f`())[`3`]` += 1;                                      $\C{// usage}$
1537\end{cfa}
1538Essentially, the return type is wrapped around the function name in successive layers (like an onion).
1539While attempting to make the two contexts consistent is a laudable goal, it has not worked out in practice.
1540
1541\CFA provides its own type, variable and function declarations, using a different syntax.
1542The new declarations place qualifiers to the left of the base type, while C declarations place qualifiers to the right.
1543The qualifiers have the same meaning but are ordered left to right to specify a variable's type.
1544\begin{cquote}
1545\lstDeleteShortInline@%
1546\begin{tabular}{@{}l@{\hspace{\parindentlnth}}l@{\hspace{\parindentlnth}}l@{}}
1547\multicolumn{1}{c@{\hspace{\parindentlnth}}}{\textbf{\CFA}}     & \multicolumn{1}{c}{\textbf{C}}        \\
1548\begin{cfa}
1549`[5] *` int x1;
1550`* [5]` int x2;
1551`[* [5] int]` f( int p );
1552\end{cfa}
1553&
1554\begin{cfa}
1555int `*` x1 `[5]`;
1556int `(*`x2`)[5]`;
1557`int (*`f( int p )`)[5]`;
1558\end{cfa}
1559&
1560\begin{cfa}
1561// array of 5 pointers to int
1562// pointer to an array of 5 int
1563// function returning pointer to an array of 5 int and taking an int
1564\end{cfa}
1565\end{tabular}
1566\lstMakeShortInline@%
1567\end{cquote}
1568The only exception is bit field specification, which always appear to the right of the base type.
1569% 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.
1570However, unlike C, \CFA type declaration tokens are distributed across all variables in the declaration list.
1571For instance, variables @x@ and @y@ of type pointer to integer are defined in \CFA as follows:
1572\begin{cquote}
1573\lstDeleteShortInline@%
1574\begin{tabular}{@{}l@{\hspace{\parindentlnth}}l@{}}
1575\multicolumn{1}{c@{\hspace{\parindentlnth}}}{\textbf{\CFA}}     & \multicolumn{1}{c}{\textbf{C}}        \\
1576\begin{cfa}
1577`*` int x, y;
1578int y;
1579\end{cfa}
1580&
1581\begin{cfa}
1582int `*`x, `*`y;
1583
1584\end{cfa}
1585\end{tabular}
1586\lstMakeShortInline@%
1587\end{cquote}
1588The downside of the \CFA semantics is the need to separate regular and pointer declarations.
1589
1590\begin{comment}
1591Other examples are:
1592\begin{cquote}
1593\lstDeleteShortInline@%
1594\begin{tabular}{@{}l@{\hspace{\parindentlnth}}l@{\hspace{\parindentlnth}}l@{}}
1595\multicolumn{1}{c@{\hspace{\parindentlnth}}}{\textbf{\CFA}}     & \multicolumn{1}{c@{\hspace{\parindentlnth}}}{\textbf{C}}      \\
1596\begin{cfa}
1597[ 5 ] int z;
1598[ 5 ] * char w;
1599* [ 5 ] double v;
1600struct s {
1601        int f0:3;
1602        * int f1;
1603        [ 5 ] * int f2;
1604};
1605\end{cfa}
1606&
1607\begin{cfa}
1608int z[ 5 ];
1609char * w[ 5 ];
1610double (* v)[ 5 ];
1611struct s {
1612        int f0:3;
1613        int * f1;
1614        int * f2[ 5 ]
1615};
1616\end{cfa}
1617&
1618\begin{cfa}
1619// array of 5 integers
1620// array of 5 pointers to char
1621// pointer to array of 5 doubles
1622
1623// common bit field syntax
1624
1625
1626
1627\end{cfa}
1628\end{tabular}
1629\lstMakeShortInline@%
1630\end{cquote}
1631\end{comment}
1632
1633All 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:
1634\begin{cquote}
1635\lstDeleteShortInline@%
1636\begin{tabular}{@{}l@{\hspace{1em}}l@{\hspace{1em}}l@{}}
1637\multicolumn{1}{c@{\hspace{1em}}}{\textbf{\CFA}}        & \multicolumn{1}{c@{\hspace{1em}}}{\textbf{C}} \\
1638\begin{cfa}
1639extern const * const int x;
1640static const * [ 5 ] const int y;
1641\end{cfa}
1642&
1643\begin{cfa}
1644int extern const * const x;
1645static const int (* const y)[ 5 ]
1646\end{cfa}
1647&
1648\begin{cfa}
1649// external const pointer to const int
1650// internal const pointer to array of 5 const int
1651\end{cfa}
1652\end{tabular}
1653\lstMakeShortInline@%
1654\end{cquote}
1655Specifiers must appear at the start of a \CFA function declaration\footnote{\label{StorageClassSpecifier}
1656The 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}}.
1657
1658The new declaration syntax can be used in other contexts where types are required, \eg casts and the pseudo-function @sizeof@:
1659\begin{cquote}
1660\lstDeleteShortInline@%
1661\begin{tabular}{@{}l@{\hspace{\parindentlnth}}l@{}}
1662\multicolumn{1}{c@{\hspace{\parindentlnth}}}{\textbf{\CFA}}     & \multicolumn{1}{c}{\textbf{C}}        \\
1663\begin{cfa}
1664y = (* int)x;
1665i = sizeof([ 5 ] * int);
1666\end{cfa}
1667&
1668\begin{cfa}
1669y = (int *)x;
1670i = sizeof(int * [ 5 ]);
1671\end{cfa}
1672\end{tabular}
1673\lstMakeShortInline@%
1674\end{cquote}
1675
1676The syntax of the new function-prototype declaration follows directly from the new function-definition syntax;
1677as well, parameter names are optional, \eg:
1678\begin{cfa}
1679[ int x ] f ( /* void */ );                                     $\C{// returning int with no parameters}$
1680[ int x ] f (...);                                                      $\C{// returning int with unknown parameters}$
1681[ * int ] g ( int y );                                          $\C{// returning pointer to int with int parameter}$
1682[ void ] h ( int, char );                                       $\C{// returning no result with int and char parameters}$
1683[ * int, int ] j ( int );                                       $\C{// returning pointer to int and int, with int parameter}$
1684\end{cfa}
1685This syntax allows a prototype declaration to be created by cutting and pasting source text from the function-definition header (or vice versa).
1686Like 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:
1687\begin{cquote}
1688\lstDeleteShortInline@%
1689\begin{tabular}{@{}l@{\hspace{\parindentlnth}}l@{}}
1690\multicolumn{1}{c@{\hspace{\parindentlnth}}}{\textbf{\CFA}}     & \multicolumn{1}{c}{\textbf{C}}        \\
1691\begin{cfa}
1692[double] foo(), foo( int ), foo( double ) {...}
1693\end{cfa}
1694&
1695\begin{cfa}
1696double foo1( void ), foo2( int ), foo3( double );
1697\end{cfa}
1698\end{tabular}
1699\lstMakeShortInline@%
1700\end{cquote}
1701where \CFA allows the last function in the list to define its body.
1702
1703The syntax for pointers to \CFA functions specifies the pointer name on the right, \eg:
1704\begin{cfa}
1705* [ int x ] () fp;                                                      $\C{// pointer to function returning int with no parameters}$
1706* [ * int ] ( int y ) gp;                                       $\C{// pointer to function returning pointer to int with int parameter}$
1707* [ ] ( int, char ) hp;                                         $\C{// pointer to function returning no result with int and char parameters}$
1708* [ * int, int ] ( int ) jp;                            $\C{// pointer to function returning pointer to int and int, with int parameter}$
1709\end{cfa}
1710Note, a function name cannot be specified:
1711\begin{cfa}
1712* [ int x ] f () fp;                                            $\C{// function name "f" is disallowed}$
1713\end{cfa}
1714
1715Finally, new \CFA declarations may appear together with C declarations in the same program block, but cannot be mixed within a specific declaration.
1716Therefore, a programmer has the option of either continuing to use traditional C declarations or take advantage of the new style.
1717Clearly, both styles need to be supported for some time due to existing C-style header-files, particularly for UNIX-like systems.
1718
1719
1720\subsection{References}
1721\label{s:References}
1722
1723All variables in C have an \newterm{address}, a \newterm{value}, and a \newterm{type};
1724at 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.
1725The C type-system does not always track the relationship between a value and its address;
1726a 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'').
1727For 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.
1728Despite 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.
1729
1730Within a lexical scope, lvalue expressions have an \newterm{address interpretation} for writing a value or a \newterm{value interpretation} to read a value.
1731For example, in @x = y@, @x@ has an address interpretation, while @y@ has a value interpretation.
1732While 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.
1733In C, for any type @T@ there is a pointer type @T *@, the value of which is the address of a value of type @T@.
1734A 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 @&?@.
1735
1736\begin{cfa}
1737int x = 1, y = 2, * p1, * p2, ** p3;
1738p1 = &x;                                                                        $\C{// p1 points to x}$
1739p2 = &y;                                                                        $\C{// p2 points to y}$
1740p3 = &p1;                                                                       $\C{// p3 points to p1}$
1741*p2 = ((*p1 + *p2) * (**p3 - *p1)) / (**p3 - 15);
1742\end{cfa}
1743
1744Unfortunately, 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.
1745For 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.
1746However, 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.
1747To solve these problems, \CFA introduces reference types @T &@;
1748a @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:
1749
1750\begin{cfa}
1751int x = 1, y = 2, & r1, & r2, && r3;
1752&r1 = &x;                                                                       $\C{// r1 points to x}$
1753&r2 = &y;                                                                       $\C{// r2 points to y}$
1754&&r3 = &&r1;                                                            $\C{// r3 points to r2}$
1755r2 = ((r1 + r2) * (r3 - r1)) / (r3 - 15);       $\C{// implicit dereferencing}$
1756\end{cfa}
1757
1758Except for auto-dereferencing by the compiler, this reference example is exactly the same as the previous pointer example.
1759Hence, 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.
1760One 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:
1761
1762\begin{cfa}
1763`*`r2 = ((`*`r1 + `*`r2) * (`**`r3 - `*`r1)) / (`**`r3 - 15);
1764\end{cfa}
1765
1766References in \CFA are similar to those in \CC, with important improvements, which can be seen in the example above.
1767Firstly, \CFA does not forbid references to references.
1768This provides a much more orthogonal design for library implementors, obviating the need for workarounds such as @std::reference_wrapper@.
1769Secondly, \CFA references are rebindable, whereas \CC references have a fixed address.
1770\newsavebox{\LstBox}
1771\begin{lrbox}{\LstBox}
1772\lstset{basicstyle=\footnotesize\linespread{0.9}\sf}
1773\begin{cfa}
1774int & r = *new( int );
1775...                                                                                     $\C{// non-null reference}$
1776delete &r;
1777r += 1;                                                                         $\C{// undefined reference}$
1778\end{cfa}
1779\end{lrbox}
1780Rebinding allows \CFA references to be default-initialized (\eg to a null pointer\footnote{
1781While 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:
1782\begin{cquote}
1783\usebox{\LstBox}
1784\end{cquote}
1785}%
1786) and point to different addresses throughout their lifetime, like pointers.
1787Rebinding is accomplished by extending the existing syntax and semantics of the address-of operator in C.
1788
1789In 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.
1790In \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.
1791The 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.
1792This rebinding occurs to an arbitrary depth of reference nesting;
1793loosely speaking, nested address-of operators produce a nested lvalue pointer up to the depth of the reference.
1794These 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@.
1795More precisely:
1796\begin{itemize}
1797\item
1798if @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).
1799       
1800\item
1801if @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).
1802\end{itemize}
1803Since 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.
1804
1805By analogy to pointers, \CFA references also allow cv-qualifiers such as @const@:
1806\begin{cfa}
1807const int cx = 5;                                                       $\C{// cannot change cx}$
1808const int & cr = cx;                                            $\C{// cannot change cr's referred value}$
1809&cr = &cx;                                                                      $\C{// rebinding cr allowed}$
1810cr = 7;                                                                         $\C{// ERROR, cannot change cr}$
1811int & const rc = x;                                                     $\C{// must be initialized, like in \CC}$
1812&rc = &x;                                                                       $\C{// ERROR, cannot rebind rc}$
1813rc = 7;                                                                         $\C{// x now equal to 7}$
1814\end{cfa}
1815Given that a reference is meant to represent a lvalue, \CFA provides some syntactic shortcuts when initializing references.
1816There are three initialization contexts in \CFA: declaration initialization, argument/parameter binding, and return/temporary binding.
1817In each of these contexts, the address-of operator on the target lvalue is elided.
1818The 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@.
1819
1820More 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;
1821this conversion is used in any context in \CFA where an implicit conversion is allowed.
1822Similarly, 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.
1823The final reference conversion included in \CFA is ``rvalue-to-reference'' conversion, implemented by means of an implicit temporary.
1824When 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.
1825\begin{cfa}
1826struct S { double x, y; };
1827int i, j;
1828void f( int & i, int & j, S & s, int v[] );
1829f( 3, i + j, (S){ 1.0, 7.0 }, (int [3]){ 1, 2, 3 } );   $\C{// pass rvalue to lvalue \(\Rightarrow\) implicit temporary}$
1830\end{cfa}
1831This 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.
1832\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.
1833
1834
1835\subsection{Type Nesting}
1836
1837Nested 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@).
1838Java 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.
1839Since \CFA in not object-oriented, adopting dynamic scoping does not make sense;
1840instead \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}).
1841\begin{figure}
1842\centering
1843\lstDeleteShortInline@%
1844\begin{tabular}{@{}l@{\hspace{3em}}l|l@{}}
1845\multicolumn{1}{c@{\hspace{3em}}}{\textbf{C Type Nesting}}      & \multicolumn{1}{c}{\textbf{C Implicit Hoisting}}      & \multicolumn{1}{|c}{\textbf{\CFA}}    \\
1846\hline
1847\begin{cfa}
1848struct S {
1849        enum C { R, G, B };
1850        struct T {
1851                union U { int i, j; };
1852                enum C c;
1853                short int i, j;
1854        };
1855        struct T t;
1856} s;
1857
1858int rtn() {
1859        s.t.c = R;
1860        struct T t = { R, 1, 2 };
1861        enum C c;
1862        union U u;
1863}
1864\end{cfa}
1865&
1866\begin{cfa}
1867enum C { R, G, B };
1868union U { int i, j; };
1869struct T {
1870        enum C c;
1871        short int i, j;
1872};
1873struct S {
1874        struct T t;
1875} s;
1876       
1877
1878
1879
1880
1881
1882
1883\end{cfa}
1884&
1885\begin{cfa}
1886struct S {
1887        enum C { R, G, B };
1888        struct T {
1889                union U { int i, j; };
1890                enum C c;
1891                short int i, j;
1892        };
1893        struct T t;
1894} s;
1895
1896int rtn() {
1897        s.t.c = `S.`R;  // type qualification
1898        struct `S.`T t = { `S.`R, 1, 2 };
1899        enum `S.`C c;
1900        union `S.T.`U u;
1901}
1902\end{cfa}
1903\end{tabular}
1904\lstMakeShortInline@%
1905\caption{Type Nesting / Qualification}
1906\label{f:TypeNestingQualification}
1907\end{figure}
1908In the C left example, types @C@, @U@ and @T@ are implicitly hoisted outside of type @S@ into the containing block scope.
1909In the \CFA right example, the types are not hoisted and accessible.
1910
1911
1912\subsection{Constructors and Destructors}
1913\label{s:ConstructorsDestructors}
1914
1915One 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.
1916However, this manual approach is often verbose, and it is useful to manage resources other than memory (\eg file handles) using the same mechanism as memory.
1917\CC addresses these issues using Resource Aquisition Is Initialization (RAII), implemented by means of \newterm{constructor} and \newterm{destructor} functions;
1918\CFA adopts constructors and destructors (and @finally@) to facilitate RAII.
1919While 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.
1920Specifically, \CFA constructors and destructors are denoted by name and first parameter-type versus name and nesting in an aggregate type.
1921Constructor 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.
1922
1923In \CFA, a constructor is named @?{}@ and a destructor is named @^?{}@.
1924The name @{}@ comes from the syntax for the initializer: @struct S { int i, j; } s = `{` 2, 3 `}`@\footnote{%
1925The symbol \lstinline+^+ is used for the destructor name because it was the last binary operator that could be used in a unary context.}.
1926Like other \CFA operators, these names represent the syntax used to call the constructor or destructor, \eg @?{}(x, ...)@ or @^{}(x, ...)@.
1927The constructor and destructor have return type @void@, and the first parameter is a reference to the object type to be constructed or destructed.
1928While the first parameter is informally called the @this@ parameter, as in object-oriented languages, any variable name may be used.
1929Both constructors and destructors allow additional parametes after the @this@ parameter for specifying values for initialization/de-initialization\footnote{
1930Destruction parameters are useful for specifying storage-management actions, such as de-initialize but not deallocate.}.
1931\begin{cfa}
1932struct VLA { int len, * data; };
1933void ?{}( VLA & vla ) with ( vla ) { len = 10;  data = alloc( len ); }  $\C{// default constructor}$
1934void ^?{}( VLA & vla ) with ( vla ) { free( data ); } $\C{// destructor}$
1935{
1936        VLA x;                                                                  $\C{// implicit:  ?\{\}( x );}$
1937}                                                                                       $\C{// implicit:  ?\^{}\{\}( x );}$
1938\end{cfa}
1939@VLA@ is a \newterm{managed type}\footnote{
1940A 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.
1941A 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.
1942For details of the code-generation placement of implicit constructor and destructor calls among complex executable statements see~\cite[\S~2.2]{Schluntz17}.
1943
1944\CFA also provides syntax for \newterm{initialization} and \newterm{copy}:
1945\begin{cfa}
1946void ?{}( VLA & vla, int size, char fill ) with ( vla ) {  $\C{// initialization}$
1947        len = size;  data = alloc( len, fill );
1948}
1949void ?{}( VLA & vla, VLA other ) {                      $\C{// copy, shallow}$
1950        vla.len = other.len;  vla.data = other.data;
1951}
1952\end{cfa}
1953(Note, the example is purposely kept simple by using shallow-copy semantics.)
1954An 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).
1955\begin{cfa}
1956VLA va = `{` 20, 0 `}`,  * arr = alloc()`{` 5, 0 `}`;
1957\end{cfa}
1958Note, the use of a \newterm{constructor expression} to initialize the storage from the dynamic storage-allocation.
1959Like \CC, the copy constructor has two parameters, the second of which is a value parameter with the same type as the first parameter;
1960appropriate care is taken to not recursively call the copy constructor when initializing the second parameter.
1961
1962\CFA constructors may be explicitly call, like Java, and destructors may be explicitly called, like \CC.
1963Explicit 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.
1964While existing call syntax works for explicit calls to constructors and destructors, \CFA also provides a more concise \newterm{operator syntax} for both:
1965\begin{cfa}
1966{
1967        VLA  x,            y = { 20, 0x01 },     z = y; $\C{// z points to y}$
1968        //      ?{}( x );  ?{}( y, 20, 0x01 );  ?{}( z, y );
1969        ^x{};                                                                   $\C{// deallocate x}$
1970        x{};                                                                    $\C{// reallocate x}$
1971        z{ 5, 0xff };                                                   $\C{// reallocate z, not pointing to y}$
1972        ^y{};                                                                   $\C{// deallocate y}$
1973        y{ x };                                                                 $\C{// reallocate y, points to x}$
1974        x{};                                                                    $\C{// reallocate x, not pointing to y}$
1975        // ^?{}(z);  ^?{}(y);  ^?{}(x);
1976}
1977\end{cfa}
1978
1979To 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.
1980These default functions can be overridden by user-generated versions.
1981For 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;
1982if default zero-initialization is desired, the default constructors can be overridden.
1983For user-generated types, the four functions are also automatically generated.
1984@enum@ types are handled the same as their underlying integral type, and unions are also bitwise copied and no-op initialized and destructed.
1985For compatibility with C, a copy constructor from the first union member type is also defined.
1986For @struct@ types, each of the four functions are implicitly defined to call their corresponding functions on each member of the struct.
1987To better simulate the behaviour of C initializers, a set of \newterm{field constructors} is also generated for structures.
1988A 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.
1989To 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;
1990similarly, the generated default constructor is hidden upon declaration of any constructor.
1991These semantics closely mirror the rule for implicit declaration of constructors in \CC\cite[p.~186]{ANSI98:C++}.
1992
1993In some circumstance programmers may not wish to have constructor and destructor calls.
1994In these cases, \CFA provides the initialization syntax \lstinline|S x @= {}|, and the object becomes unmanaged, so implicit constructor and destructor calls are not generated.
1995Any C initializer can be the right-hand side of an \lstinline|@=| initializer, \eg \lstinline|VLA a @= { 0, 0x0 }|, with the usual C initialization semantics.
1996The 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.
1997
1998
1999% \subsection{Default Parameters}
2000
2001
2002\section{Literals}
2003
2004C 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.
2005In 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.
2006A trivial 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@.
2007
2008
2009\subsection{Integral Suffixes}
2010
2011Additional integral suffixes are added to cover all the integral types and lengths.
2012\begin{cquote}
2013\lstDeleteShortInline@%
2014\begin{tabular}{@{}l@{\hspace{\parindentlnth}}l@{\hspace{\parindentlnth}}l@{}}
2015\begin{cfa}
201620`_hh`     // signed char
201721`_hhu`   // unsigned char
201822`_h`       // signed short int
201923`_uh`     // unsigned short int
202024`z`         // size_t
2021\end{cfa}
2022&
2023\begin{cfa}
202420`_L8`      // int8_t
202521`_ul8`     // uint8_t
202622`_l16`     // int16_t
202723`_ul16`   // uint16_t
202824`_l32`     // int32_t
2029\end{cfa}
2030&
2031\begin{cfa}
203225`_ul32`      // uint32_t
203326`_l64`        // int64_t
203427`_l64u`      // uint64_t
203526`_L128`     // int128
203627`_L128u`   // unsigned int128
2037\end{cfa}
2038\end{tabular}
2039\lstMakeShortInline@%
2040\end{cquote}
2041
2042
2043\subsection{0/1}
2044
2045In C, @0@ has the special property that it is the only ``false'' value; by the standard, any value which compares equal to @0@ is false, while any value that compares unequal to @0@ is true.
2046As 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.
2047The operator overloading feature of \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.
2048To provide this precision, \CFA introduces a new type @zero_t@ as type type of literal @0@ (somewhat analagous to @nullptr_t@ and @nullptr@ in \CCeleven); @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 properly.
2049With this addition, the \CFA compiler rewrites @if (x)@ and similar expressions to @if ((x) != 0)@ or the appropriate analogue, and any type @T@ can be made ``truthy'' by defining an operator overload @int ?!=?(T, zero_t)@.
2050\CC makes types truthy by adding a conversion to @bool@; prior to the addition of explicit cast operators in \CCeleven this approach had the pitfall of making truthy types transitively convertable to any numeric type; our design for \CFA avoids this issue.
2051
2052\CFA also includes a special type for @1@, @one_t@; like @zero_t@, @one_t@ has built-in implicit conversions to the various integral types so that @1@ maintains its expected semantics in legacy code.
2053The addition of @one_t@ allows generic algorithms to handle the unit value uniformly for types where that is meaningful.
2054\TODO{Make this sentence true} In 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)@; analogous overloads for the decrement operators are present as well.
2055
2056
2057\subsection{User Literals}
2058
2059For readability, it is useful to associate units to scale literals, \eg weight (stone, pound, kilogram) or time (seconds, minutes, hours).
2060The left of Figure~\ref{f:UserLiteral} shows the \CFA alternative call-syntax (literal argument before function name), using the backquote, to convert basic literals into user literals.
2061The backquote is a small character, making the unit (function name) predominate.
2062For examples, the multi-precision integers in Section~\ref{s:MultiPrecisionIntegers} make use of user literals:
2063{\lstset{language=CFA,moredelim=**[is][\color{red}]{|}{|},deletedelim=**[is][]{`}{`}}
2064\begin{cfa}
2065y = 9223372036854775807L|`mp| * 18446744073709551615UL|`mp|;
2066y = "12345678901234567890123456789"|`mp| + "12345678901234567890123456789"|`mp|;
2067\end{cfa}
2068Because \CFA uses a standard function, all types and literals are applicable, as well as overloading and conversions.
2069}%
2070
2071The right of Figure~\ref{f:UserLiteral} shows the equivalent \CC version using the underscore for the call-syntax.
2072However, \CC restricts the types, \eg @unsigned long long int@ and @long double@ to represent integral and floating literals.
2073After which, user literals must match (no conversions);
2074hence, it is necessary to overload the unit with all appropriate types.
2075Finally, the use of the single quote as a separator is restricted to digits, precluding its use in the literal prefix or suffix, and causes problems with most IDEs, which must be extended to deal with this alternate use of the single quote.
2076
2077\begin{figure}
2078\centering
2079\lstset{language=CFA,moredelim=**[is][\color{red}]{|}{|},deletedelim=**[is][]{`}{`}}
2080\lstDeleteShortInline@%
2081\begin{tabular}{@{}l@{\hspace{\parindentlnth}}l@{}}
2082\multicolumn{1}{c@{\hspace{\parindentlnth}}}{\textbf{\CFA}}     & \multicolumn{1}{c}{\textbf{\CC}}      \\
2083\begin{cfa}
2084struct W {
2085        double stones;
2086};
2087void ?{}( W & w ) { w.stones = 0; }
2088void ?{}( W & w, double w ) { w.stones = w; }
2089W ?+?( W l, W r ) {
2090        return (W){ l.stones + r.stones };
2091}
2092W |?`st|( double w ) { return (W){ w }; }
2093W |?`lb|( double w ) { return (W){ w / 14.0 }; }
2094W |?`kg|( double w ) { return (W) { w * 0.16 }; }
2095
2096
2097
2098int main() {
2099        W w, heavy = { 20 };
2100        w = 155|`lb|;
2101        w = 0b_1111|`st|;
2102        w = 0_233|`lb|;
2103        w = 0x_9b_u|`kg|;
2104        w = 5.5|`st| + 8|`kg| + 25.01|`lb| + heavy;
2105}
2106\end{cfa}
2107&
2108\begin{cfa}
2109struct W {
2110    double stones;
2111    W() { stones = 0.0; }
2112    W( double w ) { stones = w; }
2113};
2114W operator+( W l, W r ) {
2115        return W( l.stones + r.stones );
2116}
2117W |operator"" _st|( unsigned long long int w ) { return W( w ); }
2118W |operator"" _lb|( unsigned long long int w ) { return W( w / 14.0 ); }
2119W |operator"" _kg|( unsigned long long int w ) { return W( w * 0.16 ); }
2120W |operator"" _st|( long double w ) { return W( w ); }
2121W |operator"" _lb|( long double w ) { return W( w / 14.0 ); }
2122W |operator"" _kg|( long double w ) { return W( w * 0.16 ); }
2123int main() {
2124        W w, heavy = { 20 };
2125        w = 155|_lb|;
2126        w = 0b1111|_lb|;       // error, binary unsupported
2127        w = 0${\color{red}'}$233|_lb|;          // quote separator
2128        w = 0x9b|_kg|;
2129        w = 5.5d|_st| + 8|_kg| + 25.01|_lb| + heavy;
2130}
2131\end{cfa}
2132\end{tabular}
2133\lstMakeShortInline@%
2134\caption{User Literal}
2135\label{f:UserLiteral}
2136\end{figure}
2137
2138
2139\section{Libraries}
2140\label{sec:libraries}
2141
2142As 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.
2143\CFA has replacement libraries condensing hundreds of existing C names into tens of \CFA overloaded names, all without rewriting the actual computations.
2144In many cases, the interface is an inline wrapper providing overloading during compilation but zero cost at runtime.
2145The following sections give a glimpse of the interface reduction to many C libraries.
2146In 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.
2147
2148
2149\subsection{Limits}
2150
2151C library @limits.h@ provides lower and upper bound constants for the basic types.
2152\CFA name overloading is used to condense these typed constants, \eg:
2153\begin{cquote}
2154\lstDeleteShortInline@%
2155\begin{tabular}{@{}l@{\hspace{\parindentlnth}}l@{}}
2156\multicolumn{1}{c@{\hspace{\parindentlnth}}}{\textbf{Definition}}       & \multicolumn{1}{c}{\textbf{Usage}}    \\
2157\begin{cfa}
2158const short int `MIN` = -32768;
2159const int `MIN` = -2147483648;
2160const long int `MIN` = -9223372036854775808L;
2161\end{cfa}
2162&
2163\begin{cfa}
2164short int si = `MIN`;
2165int i = `MIN`;
2166long int li = `MIN`;
2167\end{cfa}
2168\end{tabular}
2169\lstMakeShortInline@%
2170\end{cquote}
2171The result is a significant reduction in names to access typed constants, \eg:
2172\begin{cquote}
2173\lstDeleteShortInline@%
2174\lstset{basicstyle=\linespread{0.9}\sf\small}
2175\begin{tabular}{@{}l@{\hspace{0.5\parindentlnth}}l@{}}
2176\multicolumn{1}{c@{\hspace{0.5\parindentlnth}}}{\textbf{\CFA}}  & \multicolumn{1}{c}{\textbf{C}}        \\
2177\begin{cfa}
2178MIN
2179MAX
2180PI
2181E
2182\end{cfa}
2183&
2184\begin{cfa}
2185SCHAR_MIN, CHAR_MIN, SHRT_MIN, INT_MIN, LONG_MIN, LLONG_MIN, FLT_MIN, DBL_MIN, LDBL_MIN
2186SCHAR_MAX, UCHAR_MAX, SHRT_MAX, INT_MAX, LONG_MAX, LLONG_MAX, FLT_MAX, DBL_MAX, LDBL_MAX
2187M_PI, M_PIl
2188M_E, M_El
2189\end{cfa}
2190\end{tabular}
2191\lstMakeShortInline@%
2192\end{cquote}
2193
2194
2195\subsection{Math}
2196
2197C library @math.h@ provides many mathematical functions.
2198\CFA function overloading is used to condense these mathematical functions, \eg:
2199\begin{cquote}
2200\lstDeleteShortInline@%
2201\begin{tabular}{@{}l@{\hspace{\parindentlnth}}l@{}}
2202\multicolumn{1}{c@{\hspace{\parindentlnth}}}{\textbf{Definition}}       & \multicolumn{1}{c}{\textbf{Usage}}    \\
2203\begin{cfa}
2204float `log`( float x );
2205double `log`( double );
2206double _Complex `log`( double _Complex x );
2207\end{cfa}
2208&
2209\begin{cfa}
2210float f = `log`( 3.5 );
2211double d = `log`( 3.5 );
2212double _Complex dc = `log`( 3.5+0.5I );
2213\end{cfa}
2214\end{tabular}
2215\lstMakeShortInline@%
2216\end{cquote}
2217The result is a significant reduction in names to access math functions, \eg:
2218\begin{cquote}
2219\lstDeleteShortInline@%
2220\begin{tabular}{@{}l@{\hspace{\parindentlnth}}l@{}}
2221\multicolumn{1}{c@{\hspace{\parindentlnth}}}{\textbf{\CFA}}     & \multicolumn{1}{c}{\textbf{C}}        \\
2222\begin{cfa}
2223log
2224sqrt
2225sin
2226\end{cfa}
2227&
2228\begin{cfa}
2229logf, log, logl, clogf, clog, clogl
2230sqrtf, sqrt, sqrtl, csqrtf, csqrt, csqrtl
2231sinf, sin, sinl, csinf, csin, csinl
2232\end{cfa}
2233\end{tabular}
2234\lstMakeShortInline@%
2235\end{cquote}
2236While \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).
2237For example, it is impossible to overload @atan@ for both one and two arguments;
2238instead the names @atan@ and @atan2@ are required (see Section~\ref{s:NameOverloading}).
2239The 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.
2240
2241
2242\subsection{Standard}
2243
2244C library @stdlib.h@ provides many general functions.
2245\CFA function overloading is used to condense these utility functions, \eg:
2246\begin{cquote}
2247\lstDeleteShortInline@%
2248\begin{tabular}{@{}l@{\hspace{\parindentlnth}}l@{}}
2249\multicolumn{1}{c@{\hspace{\parindentlnth}}}{\textbf{Definition}}       & \multicolumn{1}{c}{\textbf{Usage}}    \\
2250\begin{cfa}
2251unsigned int `abs`( int );
2252double `abs`( double );
2253double abs( double _Complex );
2254\end{cfa}
2255&
2256\begin{cfa}
2257unsigned int i = `abs`( -1 );
2258double d = `abs`( -1.5 );
2259double d = `abs`( -1.5+0.5I );
2260\end{cfa}
2261\end{tabular}
2262\lstMakeShortInline@%
2263\end{cquote}
2264The result is a significant reduction in names to access utility functions, \eg:
2265\begin{cquote}
2266\lstDeleteShortInline@%
2267\begin{tabular}{@{}l@{\hspace{\parindentlnth}}l@{}}
2268\multicolumn{1}{c@{\hspace{\parindentlnth}}}{\textbf{\CFA}}     & \multicolumn{1}{c}{\textbf{C}}        \\
2269\begin{cfa}
2270abs
2271strto
2272random
2273\end{cfa}
2274&
2275\begin{cfa}
2276abs, labs, llabs, fabsf, fabs, fabsl, cabsf, cabs, cabsl
2277strtol, strtoul, strtoll, strtoull, strtof, strtod, strtold
2278srand48, mrand48, lrand48, drand48
2279\end{cfa}
2280\end{tabular}
2281\lstMakeShortInline@%
2282\end{cquote}
2283In additon, there are polymorphic functions, like @min@ and @max@, which work on any type with operators @?<?@ or @?>?@.
2284
2285The following shows one example where \CFA \emph{extends} an existing standard C interface to reduce complexity and provide safety.
2286C/\Celeven provide a number of complex and overlapping storage-management operation to support the following capabilities:
2287\begin{description}[topsep=3pt,itemsep=2pt,parsep=0pt]
2288\item[fill]
2289after allocation the storage is filled with a specified character.
2290\item[resize]
2291an existing allocation is decreased or increased in size.
2292In 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.
2293For an increase in storage size, new storage after the copied data may be filled.
2294\item[alignment]
2295an allocation starts on a specified memory boundary, \eg, an address multiple of 64 or 128 for cache-line purposes.
2296\item[array]
2297the allocation size is scaled to the specified number of array elements.
2298An array may be filled, resized, or aligned.
2299\end{description}
2300Table~\ref{t:StorageManagementOperations} shows the capabilities provided by C/\Celeven allocation-functions and how all the capabilities can be combined into two \CFA functions.
2301\CFA storage-management functions extend the C equivalents by overloading, providing shallow type-safety, and removing the need to specify the base allocation-size.
2302Figure~\ref{f:StorageAllocation} contrasts \CFA and C storage-allocation operation performing the same operations with the same type safety.
2303
2304\begin{table}
2305\centering
2306\lstDeleteShortInline@%
2307\lstMakeShortInline~%
2308\begin{tabular}{@{}r|r|l|l|l|l@{}}
2309\multicolumn{1}{c}{}&           & \multicolumn{1}{c|}{fill}     & resize        & alignment     & array \\
2310\hline
2311C               & ~malloc~                      & no                    & no            & no            & no    \\
2312                & ~calloc~                      & yes (0 only)  & no            & no            & yes   \\
2313                & ~realloc~                     & no/copy               & yes           & no            & no    \\
2314                & ~memalign~            & no                    & no            & yes           & no    \\
2315                & ~posix_memalign~      & no                    & no            & yes           & no    \\
2316\hline
2317C11             & ~aligned_alloc~       & no                    & no            & yes           & no    \\
2318\hline
2319\CFA    & ~alloc~                       & yes/copy              & no/yes        & no            & yes   \\
2320                & ~align_alloc~         & yes                   & no            & yes           & yes   \\
2321\end{tabular}
2322\lstDeleteShortInline~%
2323\lstMakeShortInline@%
2324\caption{Storage-Management Operations}
2325\label{t:StorageManagementOperations}
2326\end{table}
2327
2328\begin{figure}
2329\centering
2330\begin{cquote}
2331\begin{cfa}[aboveskip=0pt]
2332size_t  dim = 10;                                                       $\C{// array dimension}$
2333char fill = '\xff';                                                     $\C{// initialization fill value}$
2334int * ip;
2335\end{cfa}
2336\lstDeleteShortInline@%
2337\begin{tabular}{@{}l@{\hspace{\parindentlnth}}l@{}}
2338\multicolumn{1}{c@{\hspace{\parindentlnth}}}{\textbf{\CFA}}     & \multicolumn{1}{c}{\textbf{C}}        \\
2339\begin{cfa}
2340ip = alloc();
2341ip = alloc( fill );
2342ip = alloc( dim );
2343ip = alloc( dim, fill );
2344ip = alloc( ip, 2 * dim );
2345ip = alloc( ip, 4 * dim, fill );
2346
2347ip = align_alloc( 16 );
2348ip = align_alloc( 16, fill );
2349ip = align_alloc( 16, dim );
2350ip = align_alloc( 16, dim, fill );
2351\end{cfa}
2352&
2353\begin{cfa}
2354ip = (int *)malloc( sizeof( int ) );
2355ip = (int *)malloc( sizeof( int ) ); memset( ip, fill, sizeof( int ) );
2356ip = (int *)malloc( dim * sizeof( int ) );
2357ip = (int *)malloc( sizeof( int ) ); memset( ip, fill, dim * sizeof( int ) );
2358ip = (int *)realloc( ip, 2 * dim * sizeof( int ) );
2359ip = (int *)realloc( ip, 4 * dim * sizeof( int ) ); memset( ip, fill, 4 * dim * sizeof( int ) );
2360
2361ip = memalign( 16, sizeof( int ) );
2362ip = memalign( 16, sizeof( int ) ); memset( ip, fill, sizeof( int ) );
2363ip = memalign( 16, dim * sizeof( int ) );
2364ip = memalign( 16, dim * sizeof( int ) ); memset( ip, fill, dim * sizeof( int ) );
2365\end{cfa}
2366\end{tabular}
2367\lstMakeShortInline@%
2368\end{cquote}
2369\caption{\CFA versus C Storage-Allocation}
2370\label{f:StorageAllocation}
2371\end{figure}
2372
2373Variadic @new@ (see Section~\ref{sec:variadic-tuples}) cannot support the same overloading because extra parameters are for initialization.
2374Hence, there are @new@ and @anew@ functions for single and array variables, and the fill value is the arguments to the constructor, \eg:
2375\begin{cfa}
2376struct S { int i, j; };
2377void ?{}( S & s, int i, int j ) { s.i = i; s.j = j; }
2378S * s = new( 2, 3 );                                            $\C{// allocate storage and run constructor}$
2379S * as = anew( dim, 2, 3 );                                     $\C{// each array element initialized to 2, 3}$
2380\end{cfa}
2381Note, \CC can only initialization array elements via the default constructor.
2382
2383Finally, the \CFA memory-allocator has \newterm{sticky properties} for dynamic storage: fill and alignment are remembered with an object's storage in the heap.
2384When a @realloc@ is performed, the sticky properties are respected, so that new storage is correctly aligned and initialized with the fill character.
2385
2386
2387\subsection{I/O}
2388\label{s:IOLibrary}
2389
2390The goal of \CFA I/O is to simplify the common cases, while fully supporting polymorphism and user defined types in a consistent way.
2391The approach combines ideas from \CC and Python.
2392The \CFA header file for the I/O library is @fstream@.
2393
2394The common case is printing out a sequence of variables separated by whitespace.
2395\begin{cquote}
2396\lstDeleteShortInline@%
2397\begin{tabular}{@{}l@{\hspace{\parindentlnth}}l@{}}
2398\multicolumn{1}{c@{\hspace{\parindentlnth}}}{\textbf{\CFA}}     & \multicolumn{1}{c}{\textbf{\CC}}      \\
2399\begin{cfa}
2400int x = 1, y = 2, z = 3;
2401sout | x `|` y `|` z | endl;
2402\end{cfa}
2403&
2404\begin{cfa}
2405
2406cout << x `<< " "` << y `<< " "` << z << endl;
2407\end{cfa}
2408\\
2409\begin{cfa}[showspaces=true,aboveskip=0pt,belowskip=0pt]
24101` `2` `3
2411\end{cfa}
2412&
2413\begin{cfa}[showspaces=true,aboveskip=0pt,belowskip=0pt]
24141 2 3
2415\end{cfa}
2416\end{tabular}
2417\lstMakeShortInline@%
2418\end{cquote}
2419The \CFA form has half the characters of the \CC form, and is similar to Python I/O with respect to implicit separators.
2420Similar simplification occurs for tuple I/O, which prints all tuple values separated by ``\lstinline[showspaces=true]@, @''.
2421\begin{cfa}
2422[int, [ int, int ] ] t1 = [ 1, [ 2, 3 ] ], t2 = [ 4, [ 5, 6 ] ];
2423sout | t1 | t2 | endl;                                  $\C{// print tuples}$
2424\end{cfa}
2425\begin{cfa}[showspaces=true,aboveskip=0pt]
24261`, `2`, `3 4`, `5`, `6
2427\end{cfa}
2428Finally, \CFA uses the logical-or operator for I/O as it is the lowest-priority overloadable operator, other than assignment.
2429Therefore, fewer output expressions require parenthesis.
2430\begin{cquote}
2431\lstDeleteShortInline@%
2432\begin{tabular}{@{}ll@{}}
2433\textbf{\CFA:}
2434&
2435\begin{cfa}
2436sout | x * 3 | y + 1 | z << 2 | x == y | (x | y) | (x || y) | (x > z ? 1 : 2) | endl;
2437\end{cfa}
2438\\
2439\textbf{\CC:}
2440&
2441\begin{cfa}
2442cout << x * 3 << y + 1 << `(`z << 2`)` << `(`x == y`)` << (x | y) << (x || y) << (x > z ? 1 : 2) << endl;
2443\end{cfa}
2444\\
2445\textbf{output:}
2446&
2447\begin{cfa}[showspaces=true,aboveskip=0pt]
24483 3 12 0 3 1 2
2449\end{cfa}
2450\end{tabular}
2451\lstMakeShortInline@%
2452\end{cquote}
2453There 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.
2454
2455The implicit separator character (space/blank) is a separator not a terminator.
2456The rules for implicitly adding the separator are:
2457\begin{itemize}
2458\item
2459A separator does not appear at the start or end of a line.
2460\item
2461A separator does not appear before or after a character literal or variable.
2462\item
2463A separator does not appear before or after a null (empty) C string, which is a local mechanism to disable insertion of the separator character.
2464\item
2465A separator does not appear before a C string starting with the characters: \lstinline[mathescape=off,basicstyle=\tt]@([{=$@
2466\item
2467A separator does not appear after a C string ending with the characters: \lstinline[basicstyle=\tt]@,.;!?)]}%@
2468\item
2469{\lstset{language=CFA,deletedelim=**[is][]{`}{`}}
2470A 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@
2471}%
2472\end{itemize}
2473There are functions to set and get the separator string, and manipulators to toggle separation on and off in the middle of output.
2474
2475
2476\subsection{Multi-precision Integers}
2477\label{s:MultiPrecisionIntegers}
2478
2479\CFA has an interface to the GMP multi-precision signed-integers~\cite{GMP}, similar to the \CC interface provided by GMP.
2480The \CFA interface wraps GMP functions into operator functions to make programming with multi-precision integers identical to using fixed-sized integers.
2481The \CFA type name for multi-precision signed-integers is @Int@ and the header file is @gmp@.
2482The following multi-precision factorial programs contrast using GMP with the \CFA and C interfaces.
2483\begin{cquote}
2484\lstDeleteShortInline@%
2485\begin{tabular}{@{}l@{\hspace{\parindentlnth}}@{\hspace{\parindentlnth}}l@{}}
2486\multicolumn{1}{c@{\hspace{\parindentlnth}}}{\textbf{\CFA}}     & \multicolumn{1}{@{\hspace{\parindentlnth}}c}{\textbf{C}}      \\
2487\begin{cfa}
2488#include <gmp>
2489int main( void ) {
2490        sout | "Factorial Numbers" | endl;
2491        Int fact = 1;
2492        sout | 0 | fact | endl;
2493        for ( unsigned int i = 1; i <= 40; i += 1 ) {
2494                fact *= i;
2495                sout | i | fact | endl;
2496        }
2497}
2498\end{cfa}
2499&
2500\begin{cfa}
2501#include <gmp.h>
2502int main( void ) {
2503        `gmp_printf`( "Factorial Numbers\n" );
2504        `mpz_t` fact;  `mpz_init_set_ui`( fact, 1 );
2505        `gmp_printf`( "%d %Zd\n", 0, fact );
2506        for ( unsigned int i = 1; i <= 40; i += 1 ) {
2507                `mpz_mul_ui`( fact, fact, i );
2508                `gmp_printf`( "%d %Zd\n", i, fact );
2509        }
2510}
2511\end{cfa}
2512\end{tabular}
2513\lstMakeShortInline@%
2514\end{cquote}
2515
2516
2517\section{Evaluation}
2518\label{sec:eval}
2519
2520Though \CFA provides significant added functionality over C, these features have a low runtime penalty.
2521In fact, \CFA's features for generic programming can enable faster runtime execution than idiomatic @void *@-based C code.
2522This claim is demonstrated through a set of generic-code-based micro-benchmarks in C, \CFA, and \CC (see stack implementations in Appendix~\ref{sec:BenchmarkStackImplementation}).
2523Since all these languages share a subset essentially comprising standard C, maximal-performance benchmarks would show little runtime variance, other than in length and clarity of source code.
2524A more illustrative benchmark measures the costs of idiomatic usage of each language's features.
2525Figure~\ref{fig:BenchmarkTest} shows the \CFA benchmark tests for a generic stack based on a singly linked-list, a generic pair-data-structure, and a variadic @print@ function similar to that in Section~\ref{sec:variadic-tuples}.
2526The benchmark test is similar for C and \CC.
2527The experiment uses element types @int@ and @pair(_Bool, char)@, and pushes $N=40M$ elements on a generic stack, copies the stack, clears one of the stacks, finds the maximum value in the other stack, and prints $N/2$ (to reduce graph height) constants.
2528
2529\begin{figure}
2530\begin{cfa}[xleftmargin=3\parindentlnth,aboveskip=0pt,belowskip=0pt]
2531int main( int argc, char * argv[] ) {
2532        ofstream out = { "cfa-out.txt" };
2533        int max = 0, val = 42;
2534        stack( int ) s, t;
2535
2536        REPEAT_TIMED( "push_int", N, push( s, val ); )
2537        TIMED( "copy_int", t = s; )
2538        TIMED( "clear_int", clear( s ); )
2539        REPEAT_TIMED( "pop_int", N, int v = pop( t ); max = max( v, max ); )
2540        REPEAT_TIMED( "print_int", N/2, out | val | ':' | val | endl; )
2541
2542        pair( _Bool, char ) max = { false, '\0' }, val = { true, 'a' };
2543        stack( pair( _Bool, char ) ) s, t;
2544
2545        REPEAT_TIMED( "push_pair", N, push( s, val ); )
2546        TIMED( "copy_pair", t = s; )
2547        TIMED( "clear_pair", clear( s ); )
2548        REPEAT_TIMED( "pop_pair", N, pair(_Bool, char) v = pop( t ); max = max( v, max ); )
2549        REPEAT_TIMED( "print_pair", N/2, out | val | ':' | val | endl; )
2550}
2551\end{cfa}
2552\caption{\protect\CFA Benchmark Test}
2553\label{fig:BenchmarkTest}
2554\end{figure}
2555
2556The 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.
2557The \CCV variant illustrates an alternative object-oriented idiom where all objects inherit from a base @object@ class, mimicking a Java-like interface;
2558hence runtime checks are necessary to safely down-cast objects.
2559The 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.
2560For the print benchmark, idiomatic printing is used: the C and \CFA variants used @stdio.h@, while the \CC and \CCV variants used @iostream@; preliminary tests show this distinction has negligible runtime impact.
2561Note, the C benchmark uses unchecked casts as there is no runtime mechanism to perform such checks, while \CFA and \CC provide type-safety statically.
2562
2563Figure~\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.
2564The graph plots the median of 5 consecutive runs of each program, with an initial warm-up run omitted.
2565All code is compiled at \texttt{-O2} by gcc or g++ 6.2.0, with all \CC code compiled as \CCfourteen.
2566The 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.
2567
2568\begin{figure}
2569\centering
2570\input{timing}
2571\caption{Benchmark Timing Results (smaller is better)}
2572\label{fig:eval}
2573\end{figure}
2574
2575\begin{table}
2576\centering
2577\caption{Properties of benchmark code}
2578\label{tab:eval}
2579\newcommand{\CT}[1]{\multicolumn{1}{c}{#1}}
2580\begin{tabular}{rrrrr}
2581                                                                        & \CT{C}        & \CT{\CFA}     & \CT{\CC}      & \CT{\CCV}             \\ \hline
2582maximum memory usage (MB)                       & 10001         & 2502          & 2503          & 11253                 \\
2583source code size (lines)                        & 247           & 222           & 165           & 339                   \\
2584redundant type annotations (lines)      & 39            & 2                     & 2                     & 15                    \\
2585binary size (KB)                                        & 14            & 229           & 18            & 38                    \\
2586\end{tabular}
2587\end{table}
2588
2589The 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;
2590this inefficiency is exacerbated by the second level of generic types in the pair-based benchmarks.
2591By contrast, the \CFA and \CC variants run in roughly equivalent time for both the integer and pair of @_Bool@ 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.
2592\CCV is slower than C largely due to the cost of runtime type-checking of down-casts (implemented with @dynamic_cast@);
2593There are two outliers in the graph for \CFA: all prints and pop of @pair@.
2594Both of these cases result from the complexity of the C-generated polymorphic code, so that the gcc compiler is unable to optimize some dead code and condense nested calls.
2595A compiler designed for \CFA could easily perform these optimizations.
2596Finally, the binary size for \CFA is larger because of static linking with the \CFA libraries.
2597
2598\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 73 and 54 lines, respectively.
2599On 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.
2600\CCV does not use the \CC standard template library by construction, and in fact includes the definition of @object@ and wrapper classes for @bool@, @char@, @int@, and @const char *@ in its line count, which inflates this count somewhat, as an actual object-oriented language would include these in the standard library;
2601with their omission, the \CCV line count is similar to C.
2602We 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.
2603
2604Raw line-count, however, is a fairly rough measure of code complexity;
2605another important factor is how much type information the programmer must manually specify, especially where that information is not checked by the compiler.
2606Such 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 pointers arguments and format codes, or \CCV, with its extensive use of un-type-checked downcasts (\eg @object@ to @integer@ when popping a stack, or @object@ to @printable@ when printing the elements of a @pair@).
2607To quantify this, the ``redundant type annotations'' line in Table~\ref{tab:eval} counts the number of lines on which the type of a known variable is re-specified, either as a format specifier, explicit downcast, type-specific function, or by name in a @sizeof@, struct literal, or @new@ expression.
2608The \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.
2609The two instances in which the \CFA benchmark still uses redundant type specifiers are to cast the result of a polymorphic @malloc@ call (the @sizeof@ argument is inferred by the compiler).
2610These uses are similar to the @new@ expressions in \CC, though the \CFA compiler's type resolver should shortly render even these type casts superfluous.
2611
2612
2613\section{Related Work}
2614
2615
2616\subsection{Polymorphism}
2617
2618\CC is the most similar language to \CFA;
2619both are extensions to C with source and runtime backwards compatibility.
2620The fundamental difference is the engineering approach to maintain C compatibility and programmer expectation.
2621While \CC provides good compatibility with C, it has a steep learning curve for many of its extensions.
2622For example, polymorphism is provided via three disjoint mechanisms: overloading, inheritance, and templates.
2623The 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.
2624In 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.
2625The key mechanism to support separate compilation is \CFA's \emph{explicit} use of assumed type properties.
2626Until \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;
2627furthermore, \CC concepts are restricted to template polymorphism.
2628
2629Cyclone~\cite{Grossman06} also provides capabilities for polymorphic functions and existential types, similar to \CFA's @forall@ functions and generic types.
2630Cyclone 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.
2631Furthermore, 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@.
2632In \CFA terms, all Cyclone polymorphism must be dtype-static.
2633While 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.
2634Smith 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.
2635
2636Objective-C~\cite{obj-c-book} is an industrially successful extension to C.
2637However, Objective-C is a radical departure from C, using an object-oriented model with message-passing.
2638Objective-C did not support type-checked generics until recently \cite{xcode7}, historically using less-efficient runtime checking of object types.
2639The GObject~\cite{GObject} framework also adds object-oriented programming with runtime type-checking and reference-counting garbage-collection to C;
2640these features are more intrusive additions than those provided by \CFA, in addition to the runtime overhead of reference-counting.
2641Vala~\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.
2642Java~\cite{Java8} included generic types in Java~5, which are type-checked at compilation and type-erased at runtime, similar to \CFA's.
2643However, in Java, each object carries its own table of method pointers, while \CFA passes the method pointers separately to maintain a C-compatible layout.
2644Java is also a garbage-collected, object-oriented language, with the associated resource usage and C-interoperability burdens.
2645
2646D~\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.
2647However, 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.
2648D and Go are garbage-collected languages, imposing the associated runtime overhead.
2649The necessity of accounting for data transfer between managed runtimes and the unmanaged C runtime complicates foreign-function interfaces to C.
2650Furthermore, 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.
2651D 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.
2652Rust also possesses much more powerful abstraction capabilities for writing generic code than Go.
2653On 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.
2654\CFA, with its more modest safety features, allows direct ports of C code while maintaining the idiomatic style of the original source.
2655
2656
2657\subsection{Tuples/Variadics}
2658
2659Many programming languages have some form of tuple construct and/or variadic functions, \eg SETL, C, KW-C, \CC, D, Go, Java, ML, and Scala.
2660SETL~\cite{SETL} is a high-level mathematical programming language, with tuples being one of the primary data types.
2661Tuples in SETL allow subscripting, dynamic expansion, and multiple assignment.
2662C 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.
2663KW-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.
2664The main contributions of that work were adding MRVF, tuple mass and multiple assignment, and record-field access.
2665\CCeleven introduced @std::tuple@ as a library variadic template structure.
2666Tuples are a generalization of @std::pair@, in that they allow for arbitrary length, fixed-size aggregation of heterogeneous values.
2667Operations include @std::get<N>@ to extract values, @std::tie@ to create a tuple of references used for assignment, and lexicographic comparisons.
2668\CCseventeen proposes \emph{structured bindings}~\cite{Sutter15} to eliminate pre-declaring variables and use of @std::tie@ for binding the results.
2669This 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.
2670Furthermore, structured bindings are not a full replacement for @std::tie@, as it always declares new variables.
2671Like \CC, D provides tuples through a library variadic-template structure.
2672Go does not have tuples but supports MRVF.
2673Java'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.
2674Tuples are a fundamental abstraction in most functional programming languages, such as Standard ML~\cite{sml} and~\cite{Scala}, which decompose tuples using pattern matching.
2675
2676
2677\subsection{Control Structures / Declarations / Literals}
2678
2679
2680\section{Conclusion and Future Work}
2681
2682The 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.
2683While 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.
2684The 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.
2685The contributions are a powerful type-system using parametric polymorphism and overloading, generic types, and tuples, which all have complex interactions.
2686The work is a challenging design, engineering, and implementation exercise.
2687On the surface, the project may appear as a rehash of similar mechanisms in \CC.
2688However, 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.
2689All of these new features are being used by the \CFA development-team to build the \CFA runtime-system.
2690Finally, we demonstrate that \CFA performance for some idiomatic cases is better than C and close to \CC, showing the design is practically applicable.
2691
2692There is ongoing work on a wide range of \CFA feature extensions, including arrays with size, exceptions, concurrent primitives, modules, and user-defined conversions.
2693(While all examples in the paper compile and run, a public beta-release of \CFA will take another 8--12 months to finalize these additional extensions.)
2694In addition, there are interesting future directions for the polymorphism design.
2695Notably, \CC template functions trade compile time and code bloat for optimal runtime of individual instantiations of polymorphic functions.
2696\CFA polymorphic functions use dynamic virtual-dispatch;
2697the 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.
2698Two 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).
2699These approaches are not mutually exclusive and allow performance optimizations to be applied only when necessary, without suffering global code-bloat.
2700In general, we believe separate compilation, producing smaller code, works well with loaded hardware-caches, which may offset the benefit of larger inlined-code.
2701
2702
2703\section{Acknowledgments}
2704
2705The authors would like to recognize the design assistance of Glen Ditchfield, Richard Bilson, and Thierry Delisle on the features described in this paper, and thank Magnus Madsen for feedback in the writing.
2706This work is supported through a corporate partnership with Huawei Ltd.\ (\url{http://www.huawei.com}), and Aaron Moss and Peter Buhr are funded by the Natural Sciences and Engineering Research Council of Canada.
2707
2708% the first author's \grantsponsor{NSERC-PGS}{NSERC PGS D}{http://www.nserc-crsng.gc.ca/Students-Etudiants/PG-CS/BellandPostgrad-BelletSuperieures_eng.asp} scholarship.
2709
2710
2711\bibliographystyle{plain}
2712\bibliography{pl}
2713
2714
2715\appendix
2716
2717\section{Benchmark Stack Implementation}
2718\label{sec:BenchmarkStackImplementation}
2719
2720\lstset{basicstyle=\linespread{0.9}\sf\small}
2721
2722Throughout, @/***/@ designates a counted redundant type annotation.
2723
2724\smallskip\noindent
2725\CFA
2726\begin{cfa}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
2727forall(otype T) struct stack_node;
2728forall(otype T) struct stack {
2729        stack_node(T) * head;
2730};
2731forall(otype T) struct stack_node {
2732        T value;
2733        stack_node(T) * next;
2734};
2735forall(otype T) void ?{}( stack(T) & s ) { (s.head){ 0 }; }
2736forall(otype T) void ?{}( stack(T) & s, stack(T) t ) {
2737        stack_node(T) ** crnt = &s.head;
2738        for ( stack_node(T) * next = t.head; next; next = next->next ) {
2739                stack_node(T) * new_node = ((stack_node(T)*)malloc());
2740                (*new_node){ next->value }; /***/
2741                *crnt = new_node;
2742                stack_node(T) * acrnt = *crnt;
2743                crnt = &acrnt->next;
2744        }
2745        *crnt = 0;
2746}
2747forall(otype T) stack(T) ?=?( stack(T) & s, stack(T) t ) {
2748        if ( s.head == t.head ) return s;
2749        clear( s );
2750        s{ t };
2751        return s;
2752}
2753forall(otype T) void ^?{}( stack(T) & s) { clear( s ); }
2754forall(otype T) _Bool empty( const stack(T) & s ) { return s.head == 0; }
2755forall(otype T) void push( stack(T) & s, T value ) {
2756        stack_node(T) * new_node = ((stack_node(T)*)malloc());
2757        (*new_node){ value, s.head }; /***/
2758        s.head = new_node;
2759}
2760forall(otype T) T pop( stack(T) & s ) {
2761        stack_node(T) * n = s.head;
2762        s.head = n->next;
2763        T v = n->value;
2764        delete( n );
2765        return v;
2766}
2767forall(otype T) void clear( stack(T) & s ) {
2768        for ( stack_node(T) * next = s.head; next; ) {
2769                stack_node(T) * crnt = next;
2770                next = crnt->next;
2771                delete( crnt );
2772        }
2773        s.head = 0;
2774}
2775\end{cfa}
2776
2777\medskip\noindent
2778\CC
2779\begin{cfa}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
2780template<typename T> class stack {
2781        struct node {
2782                T value;
2783                node * next;
2784                node( const T & v, node * n = nullptr ) : value(v), next(n) {}
2785        };
2786        node * head;
2787        void copy(const stack<T>& o) {
2788                node ** crnt = &head;
2789                for ( node * next = o.head;; next; next = next->next ) {
2790                        *crnt = new node{ next->value }; /***/
2791                        crnt = &(*crnt)->next;
2792                }
2793                *crnt = nullptr;
2794        }
2795  public:
2796        stack() : head(nullptr) {}
2797        stack(const stack<T>& o) { copy(o); }
2798        stack(stack<T> && o) : head(o.head) { o.head = nullptr; }
2799        ~stack() { clear(); }
2800        stack & operator= (const stack<T>& o) {
2801                if ( this == &o ) return *this;
2802                clear();
2803                copy(o);
2804                return *this;
2805        }
2806        stack & operator= (stack<T> && o) {
2807                if ( this == &o ) return *this;
2808                head = o.head;
2809                o.head = nullptr;
2810                return *this;
2811        }
2812        bool empty() const { return head == nullptr; }
2813        void push(const T & value) { head = new node{ value, head };  /***/ }
2814        T pop() {
2815                node * n = head;
2816                head = n->next;
2817                T x = std::move(n->value);
2818                delete n;
2819                return x;
2820        }
2821        void clear() {
2822                for ( node * next = head; next; ) {
2823                        node * crnt = next;
2824                        next = crnt->next;
2825                        delete crnt;
2826                }
2827                head = nullptr;
2828        }
2829};
2830\end{cfa}
2831
2832\medskip\noindent
2833C
2834\begin{cfa}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
2835struct stack_node {
2836        void * value;
2837        struct stack_node * next;
2838};
2839struct stack new_stack() { return (struct stack){ NULL }; /***/ }
2840void copy_stack(struct stack * s, const struct stack * t, void * (*copy)(const void *)) {
2841        struct stack_node ** crnt = &s->head;
2842        for ( struct stack_node * next = t->head; next; next = next->next ) {
2843                *crnt = malloc(sizeof(struct stack_node)); /***/
2844                **crnt = (struct stack_node){ copy(next->value) }; /***/
2845                crnt = &(*crnt)->next;
2846        }
2847        *crnt = 0;
2848}
2849_Bool stack_empty(const struct stack * s) { return s->head == NULL; }
2850void push_stack(struct stack * s, void * value) {
2851        struct stack_node * n = malloc(sizeof(struct stack_node)); /***/
2852        *n = (struct stack_node){ value, s->head }; /***/
2853        s->head = n;
2854}
2855void * pop_stack(struct stack * s) {
2856        struct stack_node * n = s->head;
2857        s->head = n->next;
2858        void * x = n->value;
2859        free(n);
2860        return x;
2861}
2862void clear_stack(struct stack * s, void (*free_el)(void *)) {
2863        for ( struct stack_node * next = s->head; next; ) {
2864                struct stack_node * crnt = next;
2865                next = crnt->next;
2866                free_el(crnt->value);
2867                free(crnt);
2868        }
2869        s->head = NULL;
2870}
2871\end{cfa}
2872
2873\medskip\noindent
2874\CCV
2875\begin{cfa}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
2876stack::node::node( const object & v, node * n ) : value( v.new_copy() ), next( n ) {}
2877void stack::copy(const stack & o) {
2878        node ** crnt = &head;
2879        for ( node * next = o.head; next; next = next->next ) {
2880                *crnt = new node{ *next->value };
2881                crnt = &(*crnt)->next;
2882        }
2883        *crnt = nullptr;
2884}
2885stack::stack() : head(nullptr) {}
2886stack::stack(const stack & o) { copy(o); }
2887stack::stack(stack && o) : head(o.head) { o.head = nullptr; }
2888stack::~stack() { clear(); }
2889stack & stack::operator= (const stack & o) {
2890        if ( this == &o ) return *this;
2891        clear();
2892        copy(o);
2893        return *this;
2894}
2895stack & stack::operator= (stack && o) {
2896        if ( this == &o ) return *this;
2897        head = o.head;
2898        o.head = nullptr;
2899        return *this;
2900}
2901bool stack::empty() const { return head == nullptr; }
2902void stack::push(const object & value) { head = new node{ value, head }; /***/ }
2903ptr<object> stack::pop() {
2904        node * n = head;
2905        head = n->next;
2906        ptr<object> x = std::move(n->value);
2907        delete n;
2908        return x;
2909}
2910void stack::clear() {
2911        for ( node * next = head; next; ) {
2912                node * crnt = next;
2913                next = crnt->next;
2914                delete crnt;
2915        }
2916        head = nullptr;
2917}
2918\end{cfa}
2919
2920
2921\end{document}
2922
2923% Local Variables: %
2924% tab-width: 4 %
2925% compile-command: "make" %
2926% End: %
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