source: doc/papers/general/Paper.tex @ 7ad6b6d

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 7ad6b6d was 7ad6b6d, checked in by Aaron Moss <a3moss@…>, 4 years ago

Add discussion of reference initialization to the paper, start reference conversions

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22% Names used in the document.
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24\newcommand{\CFAIcon}{\textsf{C}\raisebox{\depth}{\rotatebox{180}{\textsf{A}}}\xspace} % Cforall symbolic name
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95% CFA programming language, based on ANSI C (with some gcc additions)
96\lstdefinelanguage{CFA}[ANSI]{C}{
97        morekeywords={
98                _Alignas, _Alignof, __alignof, __alignof__, asm, __asm, __asm__, _At, __attribute,
99                __attribute__, auto, _Bool, catch, catchResume, choose, _Complex, __complex, __complex__,
100                __const, __const__, disable, dtype, enable, __extension__, fallthrough, fallthru,
101                finally, forall, ftype, _Generic, _Imaginary, inline, __label__, lvalue, _Noreturn, one_t,
102                otype, restrict, _Static_assert, throw, throwResume, trait, try, ttype, typeof, __typeof,
103                __typeof__, virtual, with, zero_t},
104        moredirectives={defined,include_next}%
105}%
106
107\lstset{
108language=CFA,
109columns=fullflexible,
110basicstyle=\linespread{0.9}\sf,                                                 % reduce line spacing and use sanserif font
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114%mathescape=true,                                                                               % LaTeX math escape in CFA code $...$
115escapechar=\$,                                                                                  % LaTeX escape in CFA code
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124        {<-}{$\leftarrow$}2 {=>}{$\Rightarrow$}2 {->}{\makebox[1ex][c]{\raisebox{0.4ex}{\rule{0.8ex}{0.075ex}}}\kern-0.2ex\textgreater}2,
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127
128% inline code @...@
129\lstMakeShortInline@%
130
131\lstnewenvironment{cfa}[1][]
132{\lstset{#1}}
133{}
134\lstnewenvironment{C++}[1][]                            % use C++ style
135{\lstset{language=C++,moredelim=**[is][\protect\color{red}]{`}{`},#1}\lstset{#1}}
136{}
137
138
139\title{Generic and Tuple Types with Efficient Dynamic Layout in \protect\CFA}
140
141\author{Aaron Moss, Robert Schluntz, Peter Buhr}
142% \email{a3moss@uwaterloo.ca}
143% \email{rschlunt@uwaterloo.ca}
144% \email{pabuhr@uwaterloo.ca}
145% \affiliation{%
146%       \institution{University of Waterloo}
147%       \department{David R. Cheriton School of Computer Science}
148%       \streetaddress{Davis Centre, University of Waterloo}
149%       \city{Waterloo}
150%       \state{ON}
151%       \postcode{N2L 3G1}
152%       \country{Canada}
153% }
154
155%\terms{generic, tuple, variadic, types}
156%\keywords{generic types, tuple types, variadic types, polymorphic functions, C, Cforall}
157
158\begin{document}
159\maketitle
160
161
162\begin{abstract}
163The 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.
164This installation base and the programmers producing it represent a massive software-engineering investment spanning decades and likely to continue for decades more.
165Nonetheless, C, first standardized over thirty years ago, lacks many features that make programming in more modern languages safer and more productive.
166The 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.
167Prior 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.
168Specifically, \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 engineers.
169This paper describes two \CFA extensions, generic and tuple types, details how their design avoids shortcomings of similar features in C and other C-like languages, and presents experimental results validating the design.
170\end{abstract}
171
172
173\section{Introduction and Background}
174
175The 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.
176This installation base and the programmers producing it represent a massive software-engineering investment spanning decades and likely to continue for decades more.
177The TIOBE~\cite{TIOBE} ranks the top 5 most popular programming languages as: Java 16\%, \Textbf{C 7\%}, \Textbf{\CC 5\%}, \Csharp 4\%, Python 4\% = 36\%, where the next 50 languages are less than 3\% each with a long tail.
178The top 3 rankings over the past 30 years are:
179\lstDeleteShortInline@%
180\begin{center}
181\setlength{\tabcolsep}{10pt}
182\begin{tabular}{@{}rccccccc@{}}
183                & 2017  & 2012  & 2007  & 2002  & 1997  & 1992  & 1987          \\ \hline
184Java    & 1             & 1             & 1             & 1             & 12    & -             & -                     \\
185\Textbf{C}      & \Textbf{2}& \Textbf{2}& \Textbf{2}& \Textbf{2}& \Textbf{1}& \Textbf{1}& \Textbf{1}    \\
186\CC             & 3             & 3             & 3             & 3             & 2             & 2             & 4                     \\
187\end{tabular}
188\end{center}
189\lstMakeShortInline@%
190Love it or hate it, C is extremely popular, highly used, and one of the few systems languages.
191In many cases, \CC is often used solely as a better C.
192Nonetheless, C, first standardized over thirty years ago, lacks many features that make programming in more modern languages safer and more productive.
193
194\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.
195The four key design goals for \CFA~\cite{Bilson03} are:
196(1) The behaviour of standard C code must remain the same when translated by a \CFA compiler as when translated by a C compiler;
197(2) Standard C code must be as fast and as small when translated by a \CFA compiler as when translated by a C compiler;
198(3) \CFA code must be at least as portable as standard C code;
199(4) Extensions introduced by \CFA must be translated in the most efficient way possible.
200These 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.
201\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.
202
203\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).
204Ultimately, a compiler is necessary for advanced features and optimal performance.
205
206This paper identifies shortcomings in existing approaches to generic and variadic data types in C-like languages and presents a design for generic and variadic types avoiding those shortcomings.
207Specifically, 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.
208The new constructs are empirically compared with both standard C and \CC; the results show the new design is comparable in performance.
209
210
211\subsection{Polymorphic Functions}
212\label{sec:poly-fns}
213
214\CFA{}\hspace{1pt}'s polymorphism was originally formalized by Ditchfield~\cite{Ditchfield92}, and first implemented by Bilson~\cite{Bilson03}.
215The 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):
216\begin{lstlisting}
217`forall( otype T )` T identity( T val ) { return val; }
218int forty_two = identity( 42 );                         $\C{// T is bound to int, forty\_two == 42}$
219\end{lstlisting}
220The @identity@ function above can be applied to any complete \emph{object type} (or @otype@).
221The 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.
222The \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.
223If this extra information is not needed, \eg for a pointer, the type parameter can be declared as a \emph{data type} (or @dtype@).
224
225In \CFA, the polymorphism runtime-cost is spread over each polymorphic call, due to passing more arguments to polymorphic functions;
226the experiments in Section~\ref{sec:eval} show this overhead is similar to \CC virtual-function calls.
227A design advantage is that, unlike \CC template-functions, \CFA polymorphic-functions are compatible with C \emph{separate compilation}, preventing compilation and code bloat.
228
229Since bare polymorphic-types provide a restricted set of available operations, \CFA provides a \emph{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.
230For example, the function @twice@ can be defined using the \CFA syntax for operator overloading:
231\begin{lstlisting}
232forall( otype T `| { T ?+?(T, T); }` ) T twice( T x ) { return x + x; } $\C{// ? denotes operands}$
233int val = twice( twice( 3.7 ) );
234\end{lstlisting}
235which works for any type @T@ with a matching addition operator.
236The 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@.
237There 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.
238The first approach has a late conversion from @double@ to @int@ on the final assignment, while the second has an eager conversion to @int@.
239\CFA minimizes the number of conversions and their potential to lose information, so it selects the first approach, which corresponds with C-programmer intuition.
240
241Crucial to the design of a new programming language are the libraries to access thousands of external software features.
242Like \CC, \CFA inherits a massive compatible library-base, where other programming languages must rewrite or provide fragile inter-language communication with C.
243A simple example is leveraging the existing type-unsafe (@void *@) C @bsearch@ to binary search a sorted floating-point array:
244\begin{lstlisting}
245void * bsearch( const void * key, const void * base, size_t nmemb, size_t size,
246                                int (* compar)( const void *, const void * ));
247int comp( const void * t1, const void * t2 ) { return *(double *)t1 < *(double *)t2 ? -1 :
248                                *(double *)t2 < *(double *)t1 ? 1 : 0; }
249double key = 5.0, vals[10] = { /* 10 sorted floating-point values */ };
250double * val = (double *)bsearch( &key, vals, 10, sizeof(vals[0]), comp );      $\C{// search sorted array}$
251\end{lstlisting}
252which can be augmented simply with a generalized, type-safe, \CFA-overloaded wrappers:
253\begin{lstlisting}
254forall( otype T | { int ?<?( T, T ); } ) T * bsearch( T key, const T * arr, size_t size ) {
255        int comp( const void * t1, const void * t2 ) { /* as above with double changed to T */ }
256        return (T *)bsearch( &key, arr, size, sizeof(T), comp ); }
257forall( otype T | { int ?<?( T, T ); } ) unsigned int bsearch( T key, const T * arr, size_t size ) {
258        T * result = bsearch( key, arr, size ); $\C{// call first version}$
259        return result ? result - arr : size; }  $\C{// pointer subtraction includes sizeof(T)}$
260double * val = bsearch( 5.0, vals, 10 );        $\C{// selection based on return type}$
261int posn = bsearch( 5.0, vals, 10 );
262\end{lstlisting}
263The nested function @comp@ provides the hidden interface from typed \CFA to untyped (@void *@) C, plus the cast of the result.
264Providing a hidden @comp@ function in \CC is awkward as lambdas do not use C calling-conventions and template declarations cannot appear at block scope.
265As well, an alternate kind of return is made available: position versus pointer to found element.
266\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@.
267
268\CFA has replacement libraries condensing hundreds of existing C functions into tens of \CFA overloaded functions, all without rewriting the actual computations.
269For example, it is possible to write a type-safe \CFA wrapper @malloc@ based on the C @malloc@:
270\begin{lstlisting}
271forall( dtype T | sized(T) ) T * malloc( void ) { return (T *)malloc( sizeof(T) ); }
272int * ip = malloc();                                            $\C{// select type and size from left-hand side}$
273double * dp = malloc();
274struct S {...} * sp = malloc();
275\end{lstlisting}
276where the return type supplies the type/size of the allocation, which is impossible in most type systems.
277
278Call-site inferencing and nested functions provide a localized form of inheritance.
279For example, the \CFA @qsort@ only sorts in ascending order using @<@.
280However, it is trivial to locally change this behaviour:
281\begin{lstlisting}
282forall( otype T | { int ?<?( T, T ); } ) void qsort( const T * arr, size_t size ) { /* use C qsort */ }
283{       int ?<?( double x, double y ) { return x `>` y; }       $\C{// locally override behaviour}$
284        qsort( vals, size );                                    $\C{// descending sort}$
285}
286\end{lstlisting}
287Within the block, the nested version of @?<?@ performs @?>?@ and this local version overrides the built-in @?<?@ so it is passed to @qsort@.
288Hence, programmers can easily form local environments, adding and modifying appropriate functions, to maximize reuse of other existing functions and types.
289
290Finally, \CFA allows variable overloading:
291\begin{lstlisting}
292short int MAX = ...;   int MAX = ...;  double MAX = ...;
293short int s = MAX;    int i = MAX;    double d = MAX;   $\C{// select correct MAX}$
294\end{lstlisting}
295Here, the single name @MAX@ replaces all the C type-specific names: @SHRT_MAX@, @INT_MAX@, @DBL_MAX@.
296As well, restricted constant overloading is allowed for the values @0@ and @1@, which have special status in C, \eg the value @0@ is both an integer and a pointer literal, so its meaning depends on context.
297In addition, several operations are defined in terms values @0@ and @1@, \eg:
298\begin{lstlisting}
299int x;
300if (x) x++                                                                      $\C{// if (x != 0) x += 1;}$
301\end{lstlisting}
302Every @if@ and iteration statement in C compares the condition with @0@, and every increment and decrement operator is semantically equivalent to adding or subtracting the value @1@ and storing the result.
303Due to these rewrite rules, the values @0@ and @1@ have the types @zero_t@ and @one_t@ in \CFA, which allows overloading various operations for new types that seamlessly connect to all special @0@ and @1@ contexts.
304The types @zero_t@ and @one_t@ have special built in implicit conversions to the various integral types, and a conversion to pointer types for @0@, which allows standard C code involving @0@ and @1@ to work as normal.
305
306
307\subsection{Traits}
308
309\CFA provides \emph{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:
310\begin{lstlisting}
311trait summable( otype T ) {
312        void ?{}( T *, zero_t );                                $\C{// constructor from 0 literal}$
313        T ?+?( T, T );                                                  $\C{// assortment of additions}$
314        T ?+=?( T *, T );
315        T ++?( T * );
316        T ?++( T * ); };
317forall( otype T `| summable( T )` ) T sum( T a[$\,$], size_t size ) {  // use trait
318        `T` total = { `0` };                                    $\C{// instantiate T from 0 by calling its constructor}$
319        for ( unsigned int i = 0; i < size; i += 1 ) total `+=` a[i]; $\C{// select appropriate +}$
320        return total; }
321\end{lstlisting}
322
323In 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:
324\begin{lstlisting}
325trait otype( dtype T | sized(T) ) {  // sized is a pseudo-trait for types with known size and alignment
326        void ?{}( T * );                                                $\C{// default constructor}$
327        void ?{}( T *, T );                                             $\C{// copy constructor}$
328        void ?=?( T *, T );                                             $\C{// assignment operator}$
329        void ^?{}( T * ); };                                    $\C{// destructor}$
330\end{lstlisting}
331Given 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.
332
333In summation, the \CFA type-system uses \emph{nominal typing} for concrete types, matching with the C type-system, and \emph{structural typing} for polymorphic types.
334Hence, trait names play no part in type equivalence;
335the names are simply macros for a list of polymorphic assertions, which are expanded at usage sites.
336Nevertheless, trait names form a logical subtype-hierarchy with @dtype@ at the top, where traits often contain overlapping assertions, \eg operator @+@.
337Traits are used like interfaces in Java or abstract base-classes in \CC, but without the nominal inheritance-relationships.
338Instead, 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.
339Hence, 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.
340(Nominal inheritance can be approximated with traits using marker variables or functions, as is done in Go.)
341
342% Nominal inheritance can be simulated with traits using marker variables or functions:
343% \begin{lstlisting}
344% trait nominal(otype T) {
345%     T is_nominal;
346% };
347% int is_nominal;                                                               $\C{// int now satisfies the nominal trait}$
348% \end{lstlisting}
349%
350% 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:
351% \begin{lstlisting}
352% trait pointer_like(otype Ptr, otype El) {
353%     lvalue El *?(Ptr);                                                $\C{// Ptr can be dereferenced into a modifiable value of type El}$
354% }
355% struct list {
356%     int value;
357%     list * next;                                                              $\C{// may omit "struct" on type names as in \CC}$
358% };
359% typedef list * list_iterator;
360%
361% lvalue int *?( list_iterator it ) { return it->value; }
362% \end{lstlisting}
363% 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@).
364% 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.
365
366
367\section{Generic Types}
368
369One of the known shortcomings of standard C is that it does not provide reusable type-safe abstractions for generic data structures and algorithms.
370Broadly speaking, there are three approaches to implement abstract data-structures in C.
371One approach is to write bespoke data-structures for each context in which they are needed.
372While 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.
373A second approach is to use @void *@--based polymorphism, \eg the C standard-library functions @bsearch@ and @qsort@; an approach which does allow reuse of code for common functionality.
374However, 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 would not otherwise be needed.
375A 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.
376Furthermore, writing and using preprocessor macros can be unnatural and inflexible.
377
378\CC, Java, and other languages use \emph{generic types} to produce type-safe abstract data-types.
379\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.
380However, for known concrete parameters, the generic-type definition can be inlined, like \CC templates.
381
382A 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:
383\begin{lstlisting}
384forall( otype R, otype S ) struct pair {
385        R first;
386        S second;
387};
388forall( otype T ) T value( pair( const char *, T ) p ) { return p.second; }
389forall( dtype F, otype T ) T value_p( pair( F *, T * ) p ) { return * p.second; }
390pair( const char *, int ) p = { "magic", 42 };
391int magic = value( p );
392pair( void *, int * ) q = { 0, &p.second };
393magic = value_p( q );
394double d = 1.0;
395pair( double *, double * ) r = { &d, &d };
396d = value_p( r );
397\end{lstlisting}
398
399\CFA classifies generic types as either \emph{concrete} or \emph{dynamic}.
400Concrete types have a fixed memory layout regardless of type parameters, while dynamic types vary in memory layout depending on their type parameters.
401A type may have polymorphic parameters but still be concrete, called \emph{dtype-static}.
402Polymorphic 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.
403
404\CFA generic types also allow checked argument-constraints.
405For example, the following declaration of a sorted set-type ensures the set key supports equality and relational comparison:
406\begin{lstlisting}
407forall( otype Key | { _Bool ?==?(Key, Key); _Bool ?<?(Key, Key); } ) struct sorted_set;
408\end{lstlisting}
409
410
411\subsection{Concrete Generic-Types}
412
413The \CFA translator template-expands concrete generic-types into new structure types, affording maximal inlining.
414To 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.
415A 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.
416For example, the concrete instantiation for @pair( const char *, int )@ is:
417\begin{lstlisting}
418struct _pair_conc1 {
419        const char * first;
420        int second;
421};
422\end{lstlisting}
423
424A concrete generic-type with dtype-static parameters is also expanded to a structure type, but this type is used for all matching instantiations.
425In 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:
426\begin{lstlisting}
427struct _pair_conc0 {
428        void * first;
429        void * second;
430};
431\end{lstlisting}
432
433
434\subsection{Dynamic Generic-Types}
435
436Though \CFA implements concrete generic-types efficiently, it also has a fully general system for dynamic generic types.
437As 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.
438Dynamic generic-types also have an \emph{offset array} containing structure-member offsets.
439A dynamic generic-union needs no such offset array, as all members are at offset 0, but size and alignment are still necessary.
440Access 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.
441
442The offset arrays are statically generated where possible.
443If 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;
444if 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.
445As 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 )@.
446The offset array @_offsetof_pair@ is generated at the call site as @size_t _offsetof_pair[] = { offsetof(_pair_conc1, first), offsetof(_pair_conc1, second) }@.
447
448In some cases the offset arrays cannot be statically generated.
449For 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.
450\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.
451The \CFA translator automatically generates \emph{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.
452These 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).
453Results of these layout functions are cached so that they are only computed once per type per function. %, as in the example below for @pair@.
454Layout functions also allow generic types to be used in a function definition without reflecting them in the function signature.
455For 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.
456This function could acquire the layout for @set(T)@ by calling its layout function with the layout of @T@ implicitly passed into the function.
457
458Whether a type is concrete, dtype-static, or dynamic is decided solely on the @forall@'s type parameters.
459This 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.
460If 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.
461
462
463\subsection{Applications}
464\label{sec:generic-apps}
465
466The reuse of dtype-static structure instantiations enables useful programming patterns at zero runtime cost.
467The 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@:
468\begin{lstlisting}
469forall(dtype T) int lexcmp( pair( T *, T * ) * a, pair( T *, T * ) * b, int (* cmp)( T *, T * ) ) {
470        return cmp( a->first, b->first ) ? : cmp( a->second, b->second );
471}
472\end{lstlisting}
473Since @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.
474
475Another useful pattern enabled by reused dtype-static type instantiations is zero-cost \emph{tag-structures}.
476Sometimes information is only used for type-checking and can be omitted at runtime, \eg:
477\begin{lstlisting}
478forall(dtype Unit) struct scalar { unsigned long value; };
479struct metres {};
480struct litres {};
481
482forall(dtype U) scalar(U) ?+?( scalar(U) a, scalar(U) b ) {
483        return (scalar(U)){ a.value + b.value };
484}
485scalar(metres) half_marathon = { 21093 };
486scalar(litres) swimming_pool = { 2500000 };
487scalar(metres) marathon = half_marathon + half_marathon;
488scalar(litres) two_pools = swimming_pool + swimming_pool;
489marathon + swimming_pool;                                       $\C{// compilation ERROR}$
490\end{lstlisting}
491@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 @?+?@.
492These implementations may even be separately compiled, unlike \CC template functions.
493However, the \CFA type-checker ensures matching types are used by all calls to @?+?@, preventing nonsensical computations like adding a length to a volume.
494
495
496\section{Tuples}
497\label{sec:tuples}
498
499In many languages, functions can return at most one value;
500however, many operations have multiple outcomes, some exceptional.
501Consider C's @div@ and @remquo@ functions, which return the quotient and remainder for a division of integer and floating-point values, respectively.
502\begin{lstlisting}
503typedef struct { int quo, rem; } div_t;         $\C{// from include stdlib.h}$
504div_t div( int num, int den );
505double remquo( double num, double den, int * quo );
506div_t qr = div( 13, 5 );                                        $\C{// return quotient/remainder aggregate}$
507int q;
508double r = remquo( 13.5, 5.2, &q );                     $\C{// return remainder, alias quotient}$
509\end{lstlisting}
510@div@ aggregates the quotient/remainder in a structure, while @remquo@ aliases a parameter to an argument.
511Both approaches are awkward.
512Alternatively, a programming language can directly support returning multiple values, \eg in \CFA:
513\begin{lstlisting}
514[ int, int ] div( int num, int den );           $\C{// return two integers}$
515[ double, double ] div( double num, double den ); $\C{// return two doubles}$
516int q, r;                                                                       $\C{// overloaded variable names}$
517double q, r;
518[ q, r ] = div( 13, 5 );                                        $\C{// select appropriate div and q, r}$
519[ q, r ] = div( 13.5, 5.2 );                            $\C{// assign into tuple}$
520\end{lstlisting}
521Clearly, this approach is straightforward to understand and use;
522therefore, why do few programming languages support this obvious feature or provide it awkwardly?
523The answer is that there are complex consequences that cascade through multiple aspects of the language, especially the type-system.
524This section show these consequences and how \CFA handles them.
525
526
527\subsection{Tuple Expressions}
528
529The addition of multiple-return-value functions (MRVF) are useless without a syntax for accepting multiple values at the call-site.
530The simplest mechanism for capturing the return values is variable assignment, allowing the values to be retrieved directly.
531As such, \CFA allows assigning multiple values from a function into multiple variables, using a square-bracketed list of lvalue expressions (as above), called a \emph{tuple}.
532
533However, functions also use \emph{composition} (nested calls), with the direct consequence that MRVFs must also support composition to be orthogonal with single-returning-value functions (SRVF), \eg:
534\begin{lstlisting}
535printf( "%d %d\n", div( 13, 5 ) );                      $\C{// return values seperated into arguments}$
536\end{lstlisting}
537Here, the values returned by @div@ are composed with the call to @printf@ by flattening the tuple into separate arguments.
538However, the \CFA type-system must support significantly more complex composition:
539\begin{lstlisting}
540[ int, int ] foo$\(_1\)$( int );                        $\C{// overloaded foo functions}$
541[ double ] foo$\(_2\)$( int );
542void bar( int, double, double );
543bar( foo( 3 ), foo( 3 ) );
544\end{lstlisting}
545The type-resolver only has the tuple return-types to resolve the call to @bar@ as the @foo@ parameters are identical, which involves unifying the possible @foo@ functions with @bar@'s parameter list.
546No combination of @foo@s are an exact match with @bar@'s parameters, so the resolver applies C conversions.
547The minimal cost is @bar( foo@$_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.
548
549
550\subsection{Tuple Variables}
551
552An important observation from function composition is that new variable names are not required to initialize parameters from an MRVF.
553\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:
554\begin{lstlisting}
555[ int, int ] qr = div( 13, 5 );                         $\C{// tuple-variable declaration and initialization}$
556[ double, double ] qr = div( 13.5, 5.2 );
557\end{lstlisting}
558where the tuple variable-name serves the same purpose as the parameter name(s).
559Tuple variables can be composed of any types, except for array types, since array sizes are generally unknown in C.
560
561One way to access the tuple-variable components is with assignment or composition:
562\begin{lstlisting}
563[ q, r ] = qr;                                                          $\C{// access tuple-variable components}$
564printf( "%d %d\n", qr );
565\end{lstlisting}
566\CFA also supports \emph{tuple indexing} to access single components of a tuple expression:
567\begin{lstlisting}
568[int, int] * p = &qr;                                           $\C{// tuple pointer}$
569int rem = qr`.1`;                                                       $\C{// access remainder}$
570int quo = div( 13, 5 )`.0`;                                     $\C{// access quotient}$
571p`->0` = 5;                                                                     $\C{// change quotient}$
572bar( qr`.1`, qr );                                                      $\C{// pass remainder and quotient/remainder}$
573rem = [div( 13, 5 ), 42]`.0.1`;                         $\C{// access 2nd component of 1st component of tuple expression}$
574\end{lstlisting}
575
576
577\subsection{Flattening and Restructuring}
578
579In function call contexts, tuples support implicit flattening and restructuring conversions.
580Tuple flattening recursively expands a tuple into the list of its basic components.
581Tuple structuring packages a list of expressions into a value of tuple type, \eg:
582%\lstDeleteShortInline@%
583%\par\smallskip
584%\begin{tabular}{@{}l@{\hspace{1.5\parindent}}||@{\hspace{1.5\parindent}}l@{}}
585\begin{lstlisting}
586int f( int, int );
587int g( [int, int] );
588int h( int, [int, int] );
589[int, int] x;
590int y;
591f( x );                 $\C{// flatten}$
592g( y, 10 );             $\C{// structure}$
593h( x, y );              $\C{// flatten and structure}$
594\end{lstlisting}
595%\end{lstlisting}
596%&
597%\begin{lstlisting}
598%\end{tabular}
599%\smallskip\par\noindent
600%\lstMakeShortInline@%
601In the call to @f@, @x@ is implicitly flattened so the components of @x@ are passed as the two arguments.
602In 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@.
603Finally, 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]@.
604The 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.
605
606
607\subsection{Tuple Assignment}
608
609An assignment where the left side is a tuple type is called \emph{tuple assignment}.
610There 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 \emph{multiple} and \emph{mass assignment}, respectively.
611%\lstDeleteShortInline@%
612%\par\smallskip
613%\begin{tabular}{@{}l@{\hspace{1.5\parindent}}||@{\hspace{1.5\parindent}}l@{}}
614\begin{lstlisting}
615int x = 10;
616double y = 3.5;
617[int, double] z;
618z = [x, y];                                                                     $\C{// multiple assignment}$
619[x, y] = z;                                                                     $\C{// multiple assignment}$
620z = 10;                                                                         $\C{// mass assignment}$
621[y, x] = 3.14;                                                          $\C{// mass assignment}$
622\end{lstlisting}
623%\end{lstlisting}
624%&
625%\begin{lstlisting}
626%\end{tabular}
627%\smallskip\par\noindent
628%\lstMakeShortInline@%
629Both kinds of tuple assignment have parallel semantics, so that each value on the left and right side is evaluated before any assignments occur.
630As 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]@.
631This 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.
632For example, @[y, x] = 3.14@ performs the assignments @y = 3.14@ and @x = 3.14@, yielding @y == 3.14@ and @x == 3@;
633whereas, C cascading assignment @y = x = 3.14@ performs the assignments @x = 3.14@ and @y = x@, yielding @3@ in @y@ and @x@.
634Finally, 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.
635This example shows mass, multiple, and cascading assignment used in one expression:
636\begin{lstlisting}
637void f( [int, int] );
638f( [x, y] = z = 1.5 );                                          $\C{// assignments in parameter list}$
639\end{lstlisting}
640
641
642\subsection{Member Access}
643
644It is also possible to access multiple fields from a single expression using a \emph{member-access}.
645The result is a single tuple-valued expression whose type is the tuple of the types of the members, \eg:
646\begin{lstlisting}
647struct S { int x; double y; char * z; } s;
648s.[x, y, z] = 0;
649\end{lstlisting}
650Here, the mass assignment sets all members of @s@ to zero.
651Since 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).
652%\lstDeleteShortInline@%
653%\par\smallskip
654%\begin{tabular}{@{}l@{\hspace{1.5\parindent}}||@{\hspace{1.5\parindent}}l@{}}
655\begin{lstlisting}
656[int, int, long, double] x;
657void f( double, long );
658x.[0, 1] = x.[1, 0];                                            $\C{// rearrange: [x.0, x.1] = [x.1, x.0]}$
659f( x.[0, 3] );                                                          $\C{// drop: f(x.0, x.3)}$
660[int, int, int] y = x.[2, 0, 2];                        $\C{// duplicate: [y.0, y.1, y.2] = [x.2, x.0.x.2]}$
661\end{lstlisting}
662%\end{lstlisting}
663%&
664%\begin{lstlisting}
665%\end{tabular}
666%\smallskip\par\noindent
667%\lstMakeShortInline@%
668It is also possible for a member access to contain other member accesses, \eg:
669\begin{lstlisting}
670struct A { double i; int j; };
671struct B { int * k; short l; };
672struct C { int x; A y; B z; } v;
673v.[x, y.[i, j], z.k];                                           $\C{// [v.x, [v.y.i, v.y.j], v.z.k]}$
674\end{lstlisting}
675
676
677\begin{comment}
678\subsection{Casting}
679
680In C, the cast operator is used to explicitly convert between types.
681In \CFA, the cast operator has a secondary use as type ascription.
682That 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:
683\begin{lstlisting}
684int f();     // (1)
685double f()// (2)
686
687f();       // ambiguous - (1),(2) both equally viable
688(int)f()// choose (2)
689\end{lstlisting}
690
691Since casting is a fundamental operation in \CFA, casts should be given a meaningful interpretation in the context of tuples.
692Taking a look at standard C provides some guidance with respect to the way casts should work with tuples:
693\begin{lstlisting}
694int f();
695void g();
696
697(void)f()// (1)
698(int)g()// (2)
699\end{lstlisting}
700In C, (1) is a valid cast, which calls @f@ and discards its result.
701On the other hand, (2) is invalid, because @g@ does not produce a result, so requesting an @int@ to materialize from nothing is nonsensical.
702Generalizing 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.
703
704Formally, 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 $T_i$.
705Excess 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.
706This approach follows naturally from the way that a cast to @void@ works in C.
707
708For example, in
709\begin{lstlisting}
710[int, int, int] f();
711[int, [int, int], int] g();
712
713([int, double])f();           $\C{// (1)}$
714([int, int, int])g();         $\C{// (2)}$
715([void, [int, int]])g();      $\C{// (3)}$
716([int, int, int, int])g();    $\C{// (4)}$
717([int, [int, int, int]])g()$\C{// (5)}$
718\end{lstlisting}
719
720(1) discards the last element of the return value and converts the second element to @double@.
721Since @int@ is effectively a 1-element tuple, (2) discards the second component of the second element of the return value of @g@.
722If @g@ is free of side effects, this expression is equivalent to @[(int)(g().0), (int)(g().1.0), (int)(g().2)]@.
723Since @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)]@).
724
725Note 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.}.
726As such, (4) is invalid because the cast target type contains 4 components, while the source type contains only 3.
727Similarly, (5) is invalid because the cast @([int, int, int])(g().1)@ is invalid.
728That is, it is invalid to cast @[int, int]@ to @[int, int, int]@.
729\end{comment}
730
731
732\subsection{Polymorphism}
733
734Tuples also integrate with \CFA polymorphism as a kind of generic type.
735Due 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:
736\begin{lstlisting}
737forall(otype T, dtype U) void f( T x, U * y );
738f( [5, "hello"] );
739\end{lstlisting}
740where @[5, "hello"]@ is flattened, giving argument list @5, "hello"@, and @T@ binds to @int@ and @U@ binds to @const char@.
741Tuples, however, may contain polymorphic components.
742For example, a plus operator can be written to add two triples together.
743\begin{lstlisting}
744forall(otype T | { T ?+?( T, T ); }) [T, T, T] ?+?( [T, T, T] x, [T, T, T] y ) {
745        return [x.0 + y.0, x.1 + y.1, x.2 + y.2];
746}
747[int, int, int] x;
748int i1, i2, i3;
749[i1, i2, i3] = x + ([10, 20, 30]);
750\end{lstlisting}
751
752Flattening and restructuring conversions are also applied to tuple types in polymorphic type assertions.
753\begin{lstlisting}
754int f( [int, double], double );
755forall(otype T, otype U | { T f( T, U, U ); }) void g( T, U );
756g( 5, 10.21 );
757\end{lstlisting}
758Hence, function parameter and return lists are flattened for the purposes of type unification allowing the example to pass expression resolution.
759This relaxation is possible by extending the thunk scheme described by Bilson~\cite{Bilson03}.
760Whenever 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:
761\begin{lstlisting}
762int _thunk( int _p0, double _p1, double _p2 ) { return f( [_p0, _p1], _p2 ); }
763\end{lstlisting}
764so the thunk provides flattening and structuring conversions to inferred functions, improving the compatibility of tuples and polymorphism.
765These thunks take advantage of GCC C nested-functions to produce closures that have the usual function-pointer signature.
766
767
768\subsection{Variadic Tuples}
769\label{sec:variadic-tuples}
770
771To define variadic functions, \CFA adds a new kind of type parameter, @ttype@ (tuple type).
772Matching against a @ttype@ parameter consumes all remaining argument components and packages them into a tuple, binding to the resulting tuple of types.
773In 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.
774As such, @ttype@ variables are also called \emph{argument packs}.
775
776Like variadic templates, the main way to manipulate @ttype@ polymorphic functions is via recursion.
777Since nothing is known about a parameter pack by default, assertion parameters are key to doing anything meaningful.
778Unlike variadic templates, @ttype@ polymorphic functions can be separately compiled.
779For example, a generalized @sum@ function written using @ttype@:
780\begin{lstlisting}
781int sum$\(_0\)$() { return 0; }
782forall(ttype Params | { int sum( Params ); } ) int sum$\(_1\)$( int x, Params rest ) {
783        return x + sum( rest );
784}
785sum( 10, 20, 30 );
786\end{lstlisting}
787Since @sum@\(_0\) does not accept any arguments, it is not a valid candidate function for the call @sum(10, 20, 30)@.
788In 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]@.
789The process continues unitl @Params@ is bound to @[]@, requiring an assertion @int sum()@, which matches @sum@\(_0\) and terminates the recursion.
790Effectively, 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))@.
791
792It is reasonable to take the @sum@ function a step further to enforce a minimum number of arguments:
793\begin{lstlisting}
794int sum( int x, int y ) { return x + y; }
795forall(ttype Params | { int sum( int, Params ); } ) int sum( int x, int y, Params rest ) {
796        return sum( x + y, rest );
797}
798\end{lstlisting}
799One more step permits the summation of any summable type with all arguments of the same type:
800\begin{lstlisting}
801trait summable(otype T) {
802        T ?+?( T, T );
803};
804forall(otype R | summable( R ) ) R sum( R x, R y ) {
805        return x + y;
806}
807forall(otype R, ttype Params | summable(R) | { R sum(R, Params); } ) R sum(R x, R y, Params rest) {
808        return sum( x + y, rest );
809}
810\end{lstlisting}
811Unlike C variadic functions, it is unnecessary to hard code the number and expected types.
812Furthermore, this code is extendable for any user-defined type with a @?+?@ operator.
813Summing arbitrary heterogeneous lists is possible with similar code by adding the appropriate type variables and addition operators.
814
815It is also possible to write a type-safe variadic print function to replace @printf@:
816\begin{lstlisting}
817struct S { int x, y; };
818forall(otype T, ttype Params | { void print(T); void print(Params); }) void print(T arg, Params rest) {
819        print(arg);  print(rest);
820}
821void print( char * x ) { printf( "%s", x ); }
822void print( int x ) { printf( "%d", x ); }
823void print( S s ) { print( "{ ", s.x, ",", s.y, " }" ); }
824print( "s = ", (S){ 1, 2 }, "\n" );
825\end{lstlisting}
826This example showcases a variadic-template-like decomposition of the provided argument list.
827The individual @print@ functions allow printing a single element of a type.
828The polymorphic @print@ allows printing any list of types, where as each individual type has a @print@ function.
829The individual print functions can be used to build up more complicated @print@ functions, such as @S@, which cannot be done with @printf@ in C.
830
831Finally, it is possible to use @ttype@ polymorphism to provide arbitrary argument forwarding functions.
832For example, it is possible to write @new@ as a library function:
833\begin{lstlisting}
834forall( otype R, otype S ) void ?{}( pair(R, S) *, R, S );
835forall( dtype T, ttype Params | sized(T) | { void ?{}( T *, Params ); } ) T * new( Params p ) {
836        return ((T *)malloc()){ p };                    $\C{// construct into result of malloc}$
837}
838pair( int, char ) * x = new( 42, '!' );
839\end{lstlisting}
840The @new@ function provides the combination of type-safe @malloc@ with a \CFA constructor call, making it impossible to forget constructing dynamically allocated objects.
841This function provides the type-safety of @new@ in \CC, without the need to specify the allocated type again, thanks to return-type inference.
842
843
844\subsection{Implementation}
845
846Tuples are implemented in the \CFA translator via a transformation into \emph{generic types}.
847For each $N$, the first time an $N$-tuple is seen in a scope a generic type with $N$ type parameters is generated, \eg:
848\begin{lstlisting}
849[int, int] f() {
850        [double, double] x;
851        [int, double, int] y;
852}
853\end{lstlisting}
854is transformed into:
855\begin{lstlisting}
856forall(dtype T0, dtype T1 | sized(T0) | sized(T1)) struct _tuple2 {
857        T0 field_0;                                                             $\C{// generated before the first 2-tuple}$
858        T1 field_1;
859};
860_tuple2(int, int) f() {
861        _tuple2(double, double) x;
862        forall(dtype T0, dtype T1, dtype T2 | sized(T0) | sized(T1) | sized(T2)) struct _tuple3 {
863                T0 field_0;                                                     $\C{// generated before the first 3-tuple}$
864                T1 field_1;
865                T2 field_2;
866        };
867        _tuple3(int, double, int) y;
868}
869\end{lstlisting}
870\begin{sloppypar}
871Tuple expressions are then simply converted directly into compound literals, \eg @[5, 'x', 1.24]@ becomes @(_tuple3(int, char, double)){ 5, 'x', 1.24 }@.
872\end{sloppypar}
873
874\begin{comment}
875Since tuples are essentially structures, tuple indexing expressions are just field accesses:
876\begin{lstlisting}
877void f(int, [double, char]);
878[int, double] x;
879
880x.0+x.1;
881printf("%d %g\n", x);
882f(x, 'z');
883\end{lstlisting}
884Is transformed into:
885\begin{lstlisting}
886void f(int, _tuple2(double, char));
887_tuple2(int, double) x;
888
889x.field_0+x.field_1;
890printf("%d %g\n", x.field_0, x.field_1);
891f(x.field_0, (_tuple2){ x.field_1, 'z' });
892\end{lstlisting}
893Note that due to flattening, @x@ used in the argument position is converted into the list of its fields.
894In the call to @f@, the second and third argument components are structured into a tuple argument.
895Similarly, tuple member expressions are recursively expanded into a list of member access expressions.
896
897Expressions that may contain side effects are made into \emph{unique expressions} before being expanded by the flattening conversion.
898Each unique expression is assigned an identifier and is guaranteed to be executed exactly once:
899\begin{lstlisting}
900void g(int, double);
901[int, double] h();
902g(h());
903\end{lstlisting}
904Internally, this expression is converted to two variables and an expression:
905\begin{lstlisting}
906void g(int, double);
907[int, double] h();
908
909_Bool _unq0_finished_ = 0;
910[int, double] _unq0;
911g(
912        (_unq0_finished_ ? _unq0 : (_unq0 = f(), _unq0_finished_ = 1, _unq0)).0,
913        (_unq0_finished_ ? _unq0 : (_unq0 = f(), _unq0_finished_ = 1, _unq0)).1,
914);
915\end{lstlisting}
916Since argument evaluation order is not specified by the C programming language, this scheme is built to work regardless of evaluation order.
917The first time a unique expression is executed, the actual expression is evaluated and the accompanying boolean is set to true.
918Every subsequent evaluation of the unique expression then results in an access to the stored result of the actual expression.
919Tuple member expressions also take advantage of unique expressions in the case of possible impurity.
920
921Currently, the \CFA translator has a very broad, imprecise definition of impurity, where any function call is assumed to be impure.
922This 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.
923
924The various kinds of tuple assignment, constructors, and destructors generate GNU C statement expressions.
925A 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.
926The 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.
927However, 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.
928\end{comment}
929
930
931\section{Control Structures}
932
933
934\subsection{\texorpdfstring{Labelled \LstKeywordStyle{continue} / \LstKeywordStyle{break}}{Labelled continue / break}}
935
936While C provides @continue@ and @break@ statements for altering control flow, both are restricted to one level of nesting for a particular control structure.
937Unfortunately, this restriction forces programmers to use @goto@ to achieve the equivalent control-flow for more than one level of nesting.
938To 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.
939For both @continue@ and @break@, the target label must be directly associated with a @for@, @while@ or @do@ statement;
940for @break@, the target label can also be associated with a @switch@, @if@ or compound (@{}@) statement.
941Figure~\ref{f:MultiLevelExit} shows @continue@ and @break@ indicating the specific control structure, and the corresponding C program using only @goto@ and labels.
942The innermost loop has 7 exit points, which cause continuation or termination of one or more of the 7 nested control-structures.
943
944\begin{figure}
945\lstDeleteShortInline@%
946\begin{tabular}{@{\hspace{\parindentlnth}}l@{\hspace{\parindentlnth}}l@{\hspace{\parindentlnth}}l@{}}
947\multicolumn{1}{@{\hspace{\parindentlnth}}c@{\hspace{\parindentlnth}}}{\textbf{\CFA}}   & \multicolumn{1}{@{\hspace{\parindentlnth}}c}{\textbf{C}}      \\
948\begin{cfa}
949`LC:` {
950        ... $declarations$ ...
951        `LS:` switch ( ... ) {
952          case 3:
953                `LIF:` if ( ... ) {
954                        `LF:` for ( ... ) {
955                                `LW:` while ( ... ) {
956                                        ... break `LC`; ...
957                                        ... break `LS`; ...
958                                        ... break `LIF`; ...
959                                        ... continue `LF;` ...
960                                        ... break `LF`; ...
961                                        ... continue `LW`; ...
962                                        ... break `LW`; ...
963                                } // while
964                        } // for
965                } else {
966                        ... break `LIF`; ...
967                } // if
968        } // switch
969} // compound
970\end{cfa}
971&
972\begin{cfa}
973{
974        ... $declarations$ ...
975        switch ( ... ) {
976          case 3:
977                if ( ... ) {
978                        for ( ... ) {
979                                while ( ... ) {
980                                        ... goto `LC`; ...
981                                        ... goto `LS`; ...
982                                        ... goto `LIF`; ...
983                                        ... goto `LFC`; ...
984                                        ... goto `LFB`; ...
985                                        ... goto `LWC`; ...
986                                        ... goto `LWB`; ...
987                                  `LWC`: ; } `LWB:` ;
988                          `LFC:` ; } `LFB:` ;
989                } else {
990                        ... goto `LIF`; ...
991                } `L3:` ;
992        } `LS:` ;
993} `LC:` ;
994\end{cfa}
995&
996\begin{cfa}
997
998
999
1000
1001
1002
1003
1004// terminate compound
1005// terminate switch
1006// terminate if
1007// continue loop
1008// terminate loop
1009// continue loop
1010// terminate loop
1011
1012
1013
1014// terminate if
1015
1016
1017
1018\end{cfa}
1019\end{tabular}
1020\lstMakeShortInline@%
1021\caption{Multi-level Exit}
1022\label{f:MultiLevelExit}
1023\end{figure}
1024
1025Both labelled @continue@ and @break@ are a @goto@ restricted in the following ways:
1026\begin{itemize}
1027\item
1028They cannot create a loop, which means only the looping constructs cause looping.
1029This restriction means all situations resulting in repeated execution are clearly delineated.
1030\item
1031They cannot branch into a control structure.
1032This restriction prevents missing declarations and/or initializations at the start of a control structure resulting in undefined behaviour.
1033\end{itemize}
1034The 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.
1035Furthermore, 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.
1036With @goto@, the label is at the end of the control structure, which fails to convey this important clue early enough to the reader.
1037Finally, using an explicit target for the transfer instead of an implicit target allows new constructs to be added or removed without affecting existing constructs.
1038The implicit targets of the current @continue@ and @break@, \ie the closest enclosing loop or @switch@, change as certain constructs are added or removed.
1039
1040\TODO{choose and fallthrough here as well?}
1041
1042\subsection{\texorpdfstring{\LstKeywordStyle{with} Clause / Statement}{with Clause / Statement}}
1043\label{s:WithClauseStatement}
1044
1045In any programming language, some functions have a naturally close relationship with a particular data type.
1046Object-oriented programming allows this close relationship to be codified in the language by making such functions \emph{class methods} of their related data type.
1047Class methods have certain privileges with respect to their associated data type, notably un-prefixed access to the fields of that data type.
1048When writing C functions in an object-oriented style, this un-prefixed access is swiftly missed, as access to fields of a @Foo* f@ requires an extra three characters @f->@ every time, which disrupts coding flow and clutters the produced code.
1049
1050\TODO{Fill out section. Be sure to mention arbitrary expressions in with-blocks, recent change driven by Thierry to prioritize field name over parameters.}
1051
1052
1053In object-oriented programming, there is an implicit first parameter, often names @self@ or @this@, which is elided.
1054\begin{C++}
1055class C {
1056        int i, j;
1057        int mem() {                                     $\C{\color{red}// implicit "this" parameter}$
1058                i = 1;                                  $\C{\color{red}// this-{\textgreater}i}$
1059                j = 2;                                  $\C{\color{red}// this-{\textgreater}j}$
1060        }
1061}
1062\end{C++}
1063Since \CFA is non-object-oriented, the equivalent object-oriented program looks like:
1064\begin{cfa}
1065struct S { int i, j; };
1066int mem( S & `this` ) {                 $\C{// explicit "this" parameter}$
1067        `this.`i = 1;                           $\C{// "this" is not elided}$
1068        `this.`j = 2;
1069}
1070\end{cfa}
1071but it is cumbersome having to write "this." many times in a member.
1072
1073\CFA provides a @with@ clause/statement (see Pascal~\cite[\S~4.F]{Pascal}) to elided the "@this.@" by opening a scope containing field identifiers, changing the qualified fields into variables and giving an opportunity for optimizing qualified references.
1074\begin{cfa}
1075int mem( S &this ) `with this` { $\C{// with clause}$
1076        i = 1;                                          $\C{\color{red}// this.i}$
1077        j = 2;                                          $\C{\color{red}// this.j}$
1078}
1079\end{cfa}
1080which extends to multiple routine parameters:
1081\begin{cfa}
1082struct T { double m, n; };
1083int mem2( S & this1, T & this2 ) `with this1, this2` {
1084        i = 1; j = 2;
1085        m = 1.0; n = 2.0;
1086}
1087\end{cfa}
1088
1089The statement form is used within a block:
1090\begin{cfa}
1091int foo() {
1092        struct S1 { ... } s1;
1093        struct S2 { ... } s2;
1094        `with s1` {                                     $\C{// with statement}$
1095                // access fields of s1 without qualification
1096                `with s2` {                             $\C{// nesting}$
1097                        // access fields of s1 and s2 without qualification
1098                }
1099        }
1100        `with s1, s2` {
1101                // access unambiguous fields of s1 and s2 without qualification
1102        }
1103}
1104\end{cfa}
1105
1106When opening multiple structures, fields with the same name and type are ambiguous and must be fully qualified.
1107For fields with the same name but different type, context/cast can be used to disambiguate.
1108\begin{cfa}
1109struct S { int i; int j; double m; } a, c;
1110struct T { int i; int k; int m } b, c;
1111`with a, b` {
1112        j + k;                                          $\C{// unambiguous, unique names define unique types}$
1113        i;                                                      $\C{// ambiguous, same name and type}$
1114        a.i + b.i;                                      $\C{// unambiguous, qualification defines unique names}$
1115        m;                                                      $\C{// ambiguous, same name and no context to define unique type}$
1116        m = 5.0;                                        $\C{// unambiguous, same name and context defines unique type}$
1117        m = 1;                                          $\C{// unambiguous, same name and context defines unique type}$
1118}
1119`with c` { ... }                                $\C{// ambiguous, same name and no context}$
1120`with (S)c` { ... }                             $\C{// unambiguous, same name and cast defines unique type}$
1121\end{cfa}
1122
1123The components in the "with" clause
1124
1125  with a, b, c { ... }
1126
1127serve 2 purposes: each component provides a type and object. The type must be a
1128structure type. Enumerations are already opened, and I think a union is opened
1129to some extent, too. (Or is that just unnamed unions?) The object is the target
1130that the naked structure-fields apply to. The components are open in "parallel"
1131at the scope of the "with" clause/statement, so opening "a" does not affect
1132opening "b", etc. This semantic is different from Pascal, which nests the
1133openings.
1134
1135Having said the above, it seems reasonable to allow a "with" component to be an
1136expression. The type is the static expression-type and the object is the result
1137of the expression. Again, the type must be an aggregate. Expressions require
1138parenthesis around the components.
1139
1140  with( a, b, c ) { ... }
1141
1142Does this now make sense?
1143
1144Having written more CFA code, it is becoming clear to me that I *really* want
1145the "with" to be implemented because I hate having to type all those object
1146names for fields. It's a great way to drive people away from the language.
1147
1148
1149\subsection{Exception Handling ???}
1150
1151
1152\section{Declarations}
1153
1154It is important to the design team that \CFA subjectively ``feel like'' C to user programmers.
1155An important part of this subjective feel is maintaining C's procedural programming paradigm, as opposed to the object-oriented paradigm of other systems languages such as \CC and Rust.
1156Maintaining this procedural paradigm means that coding patterns that work in C will remain not only functional but idiomatic in \CFA, reducing the mental burden of retraining C programmers and switching between C and \CFA development.
1157Nonetheless, some features of object-oriented languages are undeniably convienient, and the \CFA design team has attempted to adapt them to a procedural paradigm so as to incorporate their benefits into \CFA; two of these features are resource management and name scoping.
1158
1159
1160\subsection{Alternative Declaration Syntax}
1161
1162
1163\subsection{References}
1164
1165All variables in C have an \emph{address}, a \emph{value}, and a \emph{type}; at 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.
1166The C type system does not always track the relationship between a value and its address; a value that does not have a corresponding address is called a \emph{rvalue} (for ``right-hand value''), while a value that does have an address is called a \emph{lvalue} (for ``left-hand value''); 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.
1167Which address a value is located at is sometimes significant; the imperative programming paradigm of C relies on the mutation of values at specific addresses.
1168Within a lexical scope, lvalue exressions can be used in either their \emph{address interpretation} to determine where a mutated value should be stored or in their \emph{value interpretation} to refer to their stored value; in @x = y;@ in @{ int x, y = 7; x = y; }@, @x@ is used in its address interpretation, while y is used in its value interpretation.
1169Though this duality of interpretation is useful, C lacks a direct mechanism to pass lvalues between contexts, instead relying on \emph{pointer types} to serve a similar purpose.
1170In C, for any type @T@ there is a pointer type @T*@, the value of which is the address of a value of type @T@; a pointer rvalue can be explicitly \emph{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 @&?@.
1171
1172\begin{cfa}
1173int x = 1, y = 2, * p1, * p2, ** p3;
1174p1 = &x;  $\C{// p1 points to x}$
1175p2 = &y;  $\C{// p2 points to y}$
1176p3 = &p1;  $\C{// p3 points to p1}$
1177\end{cfa}
1178
1179Unfortunately, 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.
1180It would be desirable to have the compiler figure out how to elide the dereference operators in a complex expression such as @*p2 = ((*p1 + *p2) * (**p3 - *p1)) / (**p3 - 15);@, for both brevity and clarity.
1181However, since C defines a number of forms of \emph{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 user programmer may write one when they mean the other, and precluding any simple algorithm for elision of dereference operators.
1182To solve these problems, \CFA introduces reference types @T&@; a @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:
1183
1184\begin{cfa}
1185inx x = 1, y = 2, & r1, & r2, && r3;
1186&r1 = &x;  $\C{// r1 points to x}$
1187&r2 = &y;  $\C{// r2 points to y}$
1188&&r3 = &&r1;  $\C{// r3 points to r2}$
1189r2 = ((r1 + r2) * (r3 - r1)) / (r3 - 15);  $\C{// implicit dereferencing}$
1190\end{cfa}
1191
1192Except for auto-dereferencing by the compiler, this reference example is exactly the same as the previous pointer example.
1193Hence, 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.
1194One 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:
1195
1196\begin{cfa}
1197`*`r2 = ((`*`r1 + `*`r2) * (`**`r3 - `*`r1)) / (`**`r3 - 15);
1198\end{cfa}
1199
1200References in \CFA are similar to those in \CC, but with a couple important improvements, both of which can be seen in the example above.
1201Firstly, \CFA does not forbid references to references, unlike \CC.
1202This provides a much more orthogonal design for library implementors, obviating the need for workarounds such as @std::reference_wrapper@.
1203
1204Secondly, unlike the references in \CC which always point to a fixed address, \CFA references are rebindable.
1205This allows \CFA references to be default-initialized (to a null pointer), and also to point to different addresses throughout their lifetime.
1206This rebinding is accomplished without adding any new syntax to \CFA, but simply by extending the existing semantics of the address-of operator in C.
1207In 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.
1208In \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.
1209The 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.
1210This rebinding can occur to an arbitrary depth of reference nesting; $n$ address-of operators applied to a reference nested $m$ times will produce an lvalue pointer nested $n$ times if $n \le m$ (note that $n = m+1$ is simply the usual C rvalue address-of operator applied to the $n = m$ case).
1211The 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@.
1212
1213Since 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 in user code can be made based solely on convenience.
1214By analogy to pointers, \CFA references also allow cv-qualifiers:
1215
1216\begin{cfa}
1217const int cx = 5;               $\C{// cannot change cx}$
1218const int & cr = cx;    $\C{// cannot change cr's referred value}$
1219&cr = &cx;                              $\C{// rebinding cr allowed}$
1220cr = 7;                                 $\C{// ERROR, cannot change cr}$
1221int & const rc = x;             $\C{// must be initialized, like in \CC}$
1222&rc = &x;                               $\C{// ERROR, cannot rebind rc}$
1223rc = 7;                                 $\C{// x now equal to 7}$
1224\end{cfa}
1225
1226Given that a reference is meant to represent a lvalue, \CFA provides some syntactic shortcuts when initializing references.
1227There are three initialization contexts in \CFA: declaration initialization, argument/parameter binding, and return/temporary binding.
1228In each of these contexts, the address-of operator on the target lvalue may (in fact, must) be elided.
1229The syntactic motivation for this 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@.
1230
1231This initialization of references from lvalues rather than pointers can be considered a ``lvalue-to-reference'' conversion rather than an elision of the address-of operator; similarly, use of a the value pointed to by a reference in an rvalue context can be thought of as a ``reference-to-rvalue'' conversion.
1232\CFA includes one more reference conversion, an ``rvalue-to-reference'' conversion.
1233
1234\TODO{finish reference conversions; look at user manual}
1235
1236\subsection{Constructors and Destructors}
1237
1238One of the strengths of C is the control over memory management it gives programmers, allowing resource release to be more consistent and precisely timed than is possible with garbage-collected memory management.
1239However, this manual approach to memory management is often verbose, and it is useful to manage resources other than memory (\eg file handles) using the same mechanism as memory.
1240\CC is well-known for an approach to manual memory management that addresses both these issues, Resource Allocation Is Initialization (RAII), implemented by means of special \emph{constructor} and \emph{destructor} functions; we have implemented a similar feature in \CFA.
1241
1242\TODO{Fill out section. Mention field-constructors and at-equal escape hatch to C-style initialization. Probably pull some text from Rob's thesis for first draft.}
1243
1244
1245\subsection{Default Parameters}
1246
1247
1248\section{Literals}
1249
1250
1251\subsection{0/1}
1252
1253\TODO{Some text already at the end of Section~\ref{sec:poly-fns}}
1254
1255\subsection{Units}
1256
1257Alternative call syntax (literal argument before routine name) to convert basic literals into user literals.
1258
1259{\lstset{language=CFA,deletedelim=**[is][]{`}{`},moredelim=**[is][\color{red}]{@}{@}}
1260\begin{cfa}
1261struct Weight { double stones; };
1262
1263void ?{}( Weight & w ) { w.stones = 0; } $\C{// operations}$
1264void ?{}( Weight & w, double w ) { w.stones = w; }
1265Weight ?+?( Weight l, Weight r ) { return (Weight){ l.stones + r.stones }; }
1266
1267Weight @?`st@( double w ) { return (Weight){ w }; } $\C{// backquote for units}$
1268Weight @?`lb@( double w ) { return (Weight){ w / 14.0 }; }
1269Weight @?`kg@( double w ) { return (Weight) { w * 0.1575}; }
1270
1271int main() {
1272        Weight w, hw = { 14 };                  $\C{// 14 stone}$
1273        w = 11@`st@ + 1@`lb@;
1274        w = 70.3@`kg@;
1275        w = 155@`lb@;
1276        w = 0x_9b_u@`lb@;                               $\C{// hexadecimal unsigned weight (155)}$
1277        w = 0_233@`lb@;                                 $\C{// octal weight (155)}$
1278        w = 5@`st@ + 8@`kg@ + 25@`lb@ + hw;
1279}
1280\end{cfa}
1281}%
1282
1283
1284\section{Evaluation}
1285\label{sec:eval}
1286
1287Though \CFA provides significant added functionality over C, these features have a low runtime penalty.
1288In fact, \CFA's features for generic programming can enable faster runtime execution than idiomatic @void *@-based C code.
1289This 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}).
1290Since 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.
1291A more illustrative benchmark measures the costs of idiomatic usage of each language's features.
1292Figure~\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@ routine similar to that in Section~\ref{sec:variadic-tuples}.
1293The benchmark test is similar for C and \CC.
1294The 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.
1295
1296\begin{figure}
1297\begin{lstlisting}[xleftmargin=3\parindentlnth,aboveskip=0pt,belowskip=0pt]
1298int main( int argc, char * argv[] ) {
1299        FILE * out = fopen( "cfa-out.txt", "w" );
1300        int maxi = 0, vali = 42;
1301        stack(int) si, ti;
1302
1303        REPEAT_TIMED( "push_int", N, push( &si, vali ); )
1304        TIMED( "copy_int", ti = si; )
1305        TIMED( "clear_int", clear( &si ); )
1306        REPEAT_TIMED( "pop_int", N,
1307                int xi = pop( &ti ); if ( xi > maxi ) { maxi = xi; } )
1308        REPEAT_TIMED( "print_int", N/2, print( out, vali, ":", vali, "\n" ); )
1309
1310        pair(_Bool, char) maxp = { (_Bool)0, '\0' }, valp = { (_Bool)1, 'a' };
1311        stack(pair(_Bool, char)) sp, tp;
1312
1313        REPEAT_TIMED( "push_pair", N, push( &sp, valp ); )
1314        TIMED( "copy_pair", tp = sp; )
1315        TIMED( "clear_pair", clear( &sp ); )
1316        REPEAT_TIMED( "pop_pair", N,
1317                pair(_Bool, char) xp = pop( &tp ); if ( xp > maxp ) { maxp = xp; } )
1318        REPEAT_TIMED( "print_pair", N/2, print( out, valp, ":", valp, "\n" ); )
1319        fclose(out);
1320}
1321\end{lstlisting}
1322\caption{\protect\CFA Benchmark Test}
1323\label{fig:BenchmarkTest}
1324\end{figure}
1325
1326The 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.
1327The \CCV variant illustrates an alternative object-oriented idiom where all objects inherit from a base @object@ class, mimicking a Java-like interface;
1328hence runtime checks are necessary to safely down-cast objects.
1329The 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.
1330For 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.
1331Note, the C benchmark uses unchecked casts as there is no runtime mechanism to perform such checks, while \CFA and \CC provide type-safety statically.
1332
1333Figure~\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.
1334The graph plots the median of 5 consecutive runs of each program, with an initial warm-up run omitted.
1335All code is compiled at \texttt{-O2} by GCC or G++ 6.2.0, with all \CC code compiled as \CCfourteen.
1336The 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.
1337
1338\begin{figure}
1339\centering
1340\input{timing}
1341\caption{Benchmark Timing Results (smaller is better)}
1342\label{fig:eval}
1343\end{figure}
1344
1345\begin{table}
1346\caption{Properties of benchmark code}
1347\label{tab:eval}
1348\newcommand{\CT}[1]{\multicolumn{1}{c}{#1}}
1349\begin{tabular}{rrrrr}
1350                                                                        & \CT{C}        & \CT{\CFA}     & \CT{\CC}      & \CT{\CCV}             \\ \hline
1351maximum memory usage (MB)                       & 10001         & 2502          & 2503          & 11253                 \\
1352source code size (lines)                        & 247           & 222           & 165           & 339                   \\
1353redundant type annotations (lines)      & 39            & 2                     & 2                     & 15                    \\
1354binary size (KB)                                        & 14            & 229           & 18            & 38                    \\
1355\end{tabular}
1356\end{table}
1357
1358The 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;
1359this inefficiency is exacerbated by the second level of generic types in the pair-based benchmarks.
1360By 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.
1361\CCV is slower than C largely due to the cost of runtime type-checking of down-casts (implemented with @dynamic_cast@);
1362There are two outliers in the graph for \CFA: all prints and pop of @pair@.
1363Both 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.
1364A compiler designed for \CFA could easily perform these optimizations.
1365Finally, the binary size for \CFA is larger because of static linking with the \CFA libraries.
1366
1367\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.
1368On 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.
1369\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;
1370with their omission, the \CCV line count is similar to C.
1371We 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.
1372
1373Raw line-count, however, is a fairly rough measure of code complexity;
1374another important factor is how much type information the programmer must manually specify, especially where that information is not checked by the compiler.
1375Such 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@).
1376To 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.
1377The \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.
1378The 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).
1379These uses are similar to the @new@ expressions in \CC, though the \CFA compiler's type resolver should shortly render even these type casts superfluous.
1380
1381
1382\section{Related Work}
1383
1384
1385\subsection{Polymorphism}
1386
1387\CC is the most similar language to \CFA;
1388both are extensions to C with source and runtime backwards compatibility.
1389The fundamental difference is in their engineering approach to C compatibility and programmer expectation.
1390While \CC provides good backwards compatibility with C, it has a steep learning curve for many of its extensions.
1391For example, polymorphism is provided via three disjoint mechanisms: overloading, inheritance, and templates.
1392The 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.
1393In 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.
1394The key mechanism to support separate compilation is \CFA's \emph{explicit} use of assumed properties for a type.
1395Until \CC concepts~\cite{C++Concepts} are standardized (anticipated for \CCtwenty), \CC provides no way to specify the requirements of a generic function in code beyond compilation errors during template expansion;
1396furthermore, \CC concepts are restricted to template polymorphism.
1397
1398Cyclone~\cite{Grossman06} also provides capabilities for polymorphic functions and existential types, similar to \CFA's @forall@ functions and generic types.
1399Cyclone 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.
1400Furthermore, 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@.
1401In \CFA terms, all Cyclone polymorphism must be dtype-static.
1402While 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.
1403Smith 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.
1404
1405Objective-C~\cite{obj-c-book} is an industrially successful extension to C.
1406However, Objective-C is a radical departure from C, using an object-oriented model with message-passing.
1407Objective-C did not support type-checked generics until recently \cite{xcode7}, historically using less-efficient runtime checking of object types.
1408The GObject~\cite{GObject} framework also adds object-oriented programming with runtime type-checking and reference-counting garbage-collection to C;
1409these features are more intrusive additions than those provided by \CFA, in addition to the runtime overhead of reference-counting.
1410Vala~\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.
1411Java~\cite{Java8} included generic types in Java~5, which are type-checked at compilation and type-erased at runtime, similar to \CFA's.
1412However, in Java, each object carries its own table of method pointers, while \CFA passes the method pointers separately to maintain a C-compatible layout.
1413Java is also a garbage-collected, object-oriented language, with the associated resource usage and C-interoperability burdens.
1414
1415D~\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.
1416However, 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.
1417D and Go are garbage-collected languages, imposing the associated runtime overhead.
1418The necessity of accounting for data transfer between managed runtimes and the unmanaged C runtime complicates foreign-function interfaces to C.
1419Furthermore, 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.
1420D 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.
1421Rust also possesses much more powerful abstraction capabilities for writing generic code than Go.
1422On 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.
1423\CFA, with its more modest safety features, allows direct ports of C code while maintaining the idiomatic style of the original source.
1424
1425
1426\subsection{Tuples/Variadics}
1427
1428Many programming languages have some form of tuple construct and/or variadic functions, \eg SETL, C, KW-C, \CC, D, Go, Java, ML, and Scala.
1429SETL~\cite{SETL} is a high-level mathematical programming language, with tuples being one of the primary data types.
1430Tuples in SETL allow subscripting, dynamic expansion, and multiple assignment.
1431C 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.
1432KW-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.
1433The main contributions of that work were adding MRVF, tuple mass and multiple assignment, and record-field access.
1434\CCeleven introduced @std::tuple@ as a library variadic template structure.
1435Tuples are a generalization of @std::pair@, in that they allow for arbitrary length, fixed-size aggregation of heterogeneous values.
1436Operations include @std::get<N>@ to extract values, @std::tie@ to create a tuple of references used for assignment, and lexicographic comparisons.
1437\CCseventeen proposes \emph{structured bindings}~\cite{Sutter15} to eliminate pre-declaring variables and use of @std::tie@ for binding the results.
1438This 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.
1439Furthermore, structured bindings are not a full replacement for @std::tie@, as it always declares new variables.
1440Like \CC, D provides tuples through a library variadic-template structure.
1441Go does not have tuples but supports MRVF.
1442Java'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.
1443Tuples are a fundamental abstraction in most functional programming languages, such as Standard ML~\cite{sml} and~\cite{Scala}, which decompose tuples using pattern matching.
1444
1445
1446\section{Conclusion and Future Work}
1447
1448The 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.
1449While 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.
1450The 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.
1451The contributions are a powerful type-system using parametric polymorphism and overloading, generic types, and tuples, which all have complex interactions.
1452The work is a challenging design, engineering, and implementation exercise.
1453On the surface, the project may appear as a rehash of similar mechanisms in \CC.
1454However, 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.
1455All of these new features are being used by the \CFA development-team to build the \CFA runtime-system.
1456Finally, we demonstrate that \CFA performance for some idiomatic cases is better than C and close to \CC, showing the design is practically applicable.
1457
1458There is ongoing work on a wide range of \CFA feature extensions, including reference types, arrays with size, exceptions, concurrent primitives and modules.
1459(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.)
1460In addition, there are interesting future directions for the polymorphism design.
1461Notably, \CC template functions trade compile time and code bloat for optimal runtime of individual instantiations of polymorphic functions.
1462\CFA polymorphic functions use dynamic virtual-dispatch;
1463the 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.
1464Two 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).
1465These approaches are not mutually exclusive and allow performance optimizations to be applied only when necessary, without suffering global code-bloat.
1466In general, we believe separate compilation, producing smaller code, works well with loaded hardware-caches, which may offset the benefit of larger inlined-code.
1467
1468
1469\section{Acknowledgments}
1470
1471The 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 and the three anonymous reviewers for valuable feedback.
1472%This work is supported in part by a corporate partnership with \grantsponsor{Huawei}{Huawei Ltd.}{http://www.huawei.com}, and Aaron Moss and Peter Buhr are funded by the \grantsponsor{Natural Sciences and Engineering Research Council} of Canada.
1473% 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.
1474
1475
1476\bibliographystyle{plain}
1477\bibliography{pl}
1478
1479
1480\appendix
1481
1482\section{Benchmark Stack Implementation}
1483\label{sec:BenchmarkStackImplementation}
1484
1485\lstset{basicstyle=\linespread{0.9}\sf\small}
1486
1487Throughout, @/***/@ designates a counted redundant type annotation.
1488
1489\smallskip\noindent
1490\CFA
1491\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1492forall(otype T) struct stack_node {
1493        T value;
1494        stack_node(T) * next;
1495};
1496forall(otype T) void ?{}(stack(T) * s) { (&s->head){ 0 }; }
1497forall(otype T) void ?{}(stack(T) * s, stack(T) t) {
1498        stack_node(T) ** crnt = &s->head;
1499        for ( stack_node(T) * next = t.head; next; next = next->next ) {
1500                *crnt = ((stack_node(T) *)malloc()){ next->value }; /***/
1501                stack_node(T) * acrnt = *crnt;
1502                crnt = &acrnt->next;
1503        }
1504        *crnt = 0;
1505}
1506forall(otype T) stack(T) ?=?(stack(T) * s, stack(T) t) {
1507        if ( s->head == t.head ) return *s;
1508        clear(s);
1509        s{ t };
1510        return *s;
1511}
1512forall(otype T) void ^?{}(stack(T) * s) { clear(s); }
1513forall(otype T) _Bool empty(const stack(T) * s) { return s->head == 0; }
1514forall(otype T) void push(stack(T) * s, T value) {
1515        s->head = ((stack_node(T) *)malloc()){ value, s->head }; /***/
1516}
1517forall(otype T) T pop(stack(T) * s) {
1518        stack_node(T) * n = s->head;
1519        s->head = n->next;
1520        T x = n->value;
1521        ^n{};
1522        free(n);
1523        return x;
1524}
1525forall(otype T) void clear(stack(T) * s) {
1526        for ( stack_node(T) * next = s->head; next; ) {
1527                stack_node(T) * crnt = next;
1528                next = crnt->next;
1529                delete(crnt);
1530        }
1531        s->head = 0;
1532}
1533\end{lstlisting}
1534
1535\medskip\noindent
1536\CC
1537\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1538template<typename T> class stack {
1539        struct node {
1540                T value;
1541                node * next;
1542                node( const T & v, node * n = nullptr ) : value(v), next(n) {}
1543        };
1544        node * head;
1545        void copy(const stack<T>& o) {
1546                node ** crnt = &head;
1547                for ( node * next = o.head;; next; next = next->next ) {
1548                        *crnt = new node{ next->value }; /***/
1549                        crnt = &(*crnt)->next;
1550                }
1551                *crnt = nullptr;
1552        }
1553  public:
1554        stack() : head(nullptr) {}
1555        stack(const stack<T>& o) { copy(o); }
1556        stack(stack<T> && o) : head(o.head) { o.head = nullptr; }
1557        ~stack() { clear(); }
1558        stack & operator= (const stack<T>& o) {
1559                if ( this == &o ) return *this;
1560                clear();
1561                copy(o);
1562                return *this;
1563        }
1564        stack & operator= (stack<T> && o) {
1565                if ( this == &o ) return *this;
1566                head = o.head;
1567                o.head = nullptr;
1568                return *this;
1569        }
1570        bool empty() const { return head == nullptr; }
1571        void push(const T & value) { head = new node{ value, head };  /***/ }
1572        T pop() {
1573                node * n = head;
1574                head = n->next;
1575                T x = std::move(n->value);
1576                delete n;
1577                return x;
1578        }
1579        void clear() {
1580                for ( node * next = head; next; ) {
1581                        node * crnt = next;
1582                        next = crnt->next;
1583                        delete crnt;
1584                }
1585                head = nullptr;
1586        }
1587};
1588\end{lstlisting}
1589
1590\medskip\noindent
1591C
1592\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1593struct stack_node {
1594        void * value;
1595        struct stack_node * next;
1596};
1597struct stack new_stack() { return (struct stack){ NULL }; /***/ }
1598void copy_stack(struct stack * s, const struct stack * t, void * (*copy)(const void *)) {
1599        struct stack_node ** crnt = &s->head;
1600        for ( struct stack_node * next = t->head; next; next = next->next ) {
1601                *crnt = malloc(sizeof(struct stack_node)); /***/
1602                **crnt = (struct stack_node){ copy(next->value) }; /***/
1603                crnt = &(*crnt)->next;
1604        }
1605        *crnt = 0;
1606}
1607_Bool stack_empty(const struct stack * s) { return s->head == NULL; }
1608void push_stack(struct stack * s, void * value) {
1609        struct stack_node * n = malloc(sizeof(struct stack_node)); /***/
1610        *n = (struct stack_node){ value, s->head }; /***/
1611        s->head = n;
1612}
1613void * pop_stack(struct stack * s) {
1614        struct stack_node * n = s->head;
1615        s->head = n->next;
1616        void * x = n->value;
1617        free(n);
1618        return x;
1619}
1620void clear_stack(struct stack * s, void (*free_el)(void *)) {
1621        for ( struct stack_node * next = s->head; next; ) {
1622                struct stack_node * crnt = next;
1623                next = crnt->next;
1624                free_el(crnt->value);
1625                free(crnt);
1626        }
1627        s->head = NULL;
1628}
1629\end{lstlisting}
1630
1631\medskip\noindent
1632\CCV
1633\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1634stack::node::node( const object & v, node * n ) : value( v.new_copy() ), next( n ) {}
1635void stack::copy(const stack & o) {
1636        node ** crnt = &head;
1637        for ( node * next = o.head; next; next = next->next ) {
1638                *crnt = new node{ *next->value };
1639                crnt = &(*crnt)->next;
1640        }
1641        *crnt = nullptr;
1642}
1643stack::stack() : head(nullptr) {}
1644stack::stack(const stack & o) { copy(o); }
1645stack::stack(stack && o) : head(o.head) { o.head = nullptr; }
1646stack::~stack() { clear(); }
1647stack & stack::operator= (const stack & o) {
1648        if ( this == &o ) return *this;
1649        clear();
1650        copy(o);
1651        return *this;
1652}
1653stack & stack::operator= (stack && o) {
1654        if ( this == &o ) return *this;
1655        head = o.head;
1656        o.head = nullptr;
1657        return *this;
1658}
1659bool stack::empty() const { return head == nullptr; }
1660void stack::push(const object & value) { head = new node{ value, head }; /***/ }
1661ptr<object> stack::pop() {
1662        node * n = head;
1663        head = n->next;
1664        ptr<object> x = std::move(n->value);
1665        delete n;
1666        return x;
1667}
1668void stack::clear() {
1669        for ( node * next = head; next; ) {
1670                node * crnt = next;
1671                next = crnt->next;
1672                delete crnt;
1673        }
1674        head = nullptr;
1675}
1676\end{lstlisting}
1677
1678
1679\begin{comment}
1680
1681\subsubsection{bench.h}
1682(\texttt{bench.hpp} is similar.)
1683
1684\lstinputlisting{evaluation/bench.h}
1685
1686\subsection{C}
1687
1688\subsubsection{c-stack.h} ~
1689
1690\lstinputlisting{evaluation/c-stack.h}
1691
1692\subsubsection{c-stack.c} ~
1693
1694\lstinputlisting{evaluation/c-stack.c}
1695
1696\subsubsection{c-pair.h} ~
1697
1698\lstinputlisting{evaluation/c-pair.h}
1699
1700\subsubsection{c-pair.c} ~
1701
1702\lstinputlisting{evaluation/c-pair.c}
1703
1704\subsubsection{c-print.h} ~
1705
1706\lstinputlisting{evaluation/c-print.h}
1707
1708\subsubsection{c-print.c} ~
1709
1710\lstinputlisting{evaluation/c-print.c}
1711
1712\subsubsection{c-bench.c} ~
1713
1714\lstinputlisting{evaluation/c-bench.c}
1715
1716\subsection{\CFA}
1717
1718\subsubsection{cfa-stack.h} ~
1719
1720\lstinputlisting{evaluation/cfa-stack.h}
1721
1722\subsubsection{cfa-stack.c} ~
1723
1724\lstinputlisting{evaluation/cfa-stack.c}
1725
1726\subsubsection{cfa-print.h} ~
1727
1728\lstinputlisting{evaluation/cfa-print.h}
1729
1730\subsubsection{cfa-print.c} ~
1731
1732\lstinputlisting{evaluation/cfa-print.c}
1733
1734\subsubsection{cfa-bench.c} ~
1735
1736\lstinputlisting{evaluation/cfa-bench.c}
1737
1738\subsection{\CC}
1739
1740\subsubsection{cpp-stack.hpp} ~
1741
1742\lstinputlisting[language=c++]{evaluation/cpp-stack.hpp}
1743
1744\subsubsection{cpp-print.hpp} ~
1745
1746\lstinputlisting[language=c++]{evaluation/cpp-print.hpp}
1747
1748\subsubsection{cpp-bench.cpp} ~
1749
1750\lstinputlisting[language=c++]{evaluation/cpp-bench.cpp}
1751
1752\subsection{\CCV}
1753
1754\subsubsection{object.hpp} ~
1755
1756\lstinputlisting[language=c++]{evaluation/object.hpp}
1757
1758\subsubsection{cpp-vstack.hpp} ~
1759
1760\lstinputlisting[language=c++]{evaluation/cpp-vstack.hpp}
1761
1762\subsubsection{cpp-vstack.cpp} ~
1763
1764\lstinputlisting[language=c++]{evaluation/cpp-vstack.cpp}
1765
1766\subsubsection{cpp-vprint.hpp} ~
1767
1768\lstinputlisting[language=c++]{evaluation/cpp-vprint.hpp}
1769
1770\subsubsection{cpp-vbench.cpp} ~
1771
1772\lstinputlisting[language=c++]{evaluation/cpp-vbench.cpp}
1773\end{comment}
1774
1775\end{document}
1776
1777% Local Variables: %
1778% tab-width: 4 %
1779% compile-command: "make" %
1780% End: %
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