source: doc/papers/general/Paper.tex @ 7d94d805

aaron-thesisarm-ehcleanup-dtorsdeferred_resndemanglerjacob/cs343-translationjenkins-sandboxnew-astnew-ast-unique-exprnew-envno_listpersistent-indexerresolv-newwith_gc
Last change on this file since 7d94d805 was 7d94d805, checked in by Aaron Moss <a3moss@…>, 4 years ago

First draft of references section in paper

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103% CFA programming language, based on ANSI C (with some gcc additions)
104\lstdefinelanguage{CFA}[ANSI]{C}{
105        morekeywords={
106                _Alignas, _Alignof, __alignof, __alignof__, asm, __asm, __asm__, _At, __attribute,
107                __attribute__, auto, _Bool, catch, catchResume, choose, _Complex, __complex, __complex__,
108                __const, __const__, disable, dtype, enable, __extension__, fallthrough, fallthru,
109                finally, forall, ftype, _Generic, _Imaginary, inline, __label__, lvalue, _Noreturn, one_t,
110                otype, restrict, _Static_assert, throw, throwResume, trait, try, ttype, typeof, __typeof,
111                __typeof__, virtual, with, zero_t},
112        moredirectives={defined,include_next}%
113}%
114
115\lstset{
116language=CFA,
117columns=fullflexible,
118basicstyle=\linespread{0.9}\sf,                                                 % reduce line spacing and use sanserif font
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122%mathescape=true,                                                                               % LaTeX math escape in CFA code $...$
123escapechar=\$,                                                                                  % LaTeX escape in CFA code
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132        {<-}{$\leftarrow$}2 {=>}{$\Rightarrow$}2 {->}{\makebox[1ex][c]{\raisebox{0.4ex}{\rule{0.8ex}{0.075ex}}}\kern-0.2ex\textgreater}2,
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135
136% inline code @...@
137\lstMakeShortInline@%
138
139\lstnewenvironment{cfa}[1][]
140{\lstset{#1}}
141{}
142\lstnewenvironment{C++}[1][]                            % use C++ style
143{\lstset{language=C++,moredelim=**[is][\protect\color{red}]{`}{`},#1}\lstset{#1}}
144{}
145
146
147\title{Generic and Tuple Types with Efficient Dynamic Layout in \protect\CFA}
148
149\author{Aaron Moss, Robert Schluntz, Peter Buhr}
150% \email{a3moss@uwaterloo.ca}
151% \email{rschlunt@uwaterloo.ca}
152% \email{pabuhr@uwaterloo.ca}
153% \affiliation{%
154%       \institution{University of Waterloo}
155%       \department{David R. Cheriton School of Computer Science}
156%       \streetaddress{Davis Centre, University of Waterloo}
157%       \city{Waterloo}
158%       \state{ON}
159%       \postcode{N2L 3G1}
160%       \country{Canada}
161% }
162
163%\terms{generic, tuple, variadic, types}
164%\keywords{generic types, tuple types, variadic types, polymorphic functions, C, Cforall}
165
166\begin{document}
167\maketitle
168
169
170\begin{abstract}
171The 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.
172This installation base and the programmers producing it represent a massive software-engineering investment spanning decades and likely to continue for decades more.
173Nonetheless, C, first standardized over thirty years ago, lacks many features that make programming in more modern languages safer and more productive.
174The 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.
175Prior 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.
176Specifically, \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.
177This 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.
178\end{abstract}
179
180
181\section{Introduction and Background}
182
183The 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.
184This installation base and the programmers producing it represent a massive software-engineering investment spanning decades and likely to continue for decades more.
185The 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.
186The top 3 rankings over the past 30 years are:
187\lstDeleteShortInline@%
188\begin{center}
189\setlength{\tabcolsep}{10pt}
190\begin{tabular}{@{}rccccccc@{}}
191                & 2017  & 2012  & 2007  & 2002  & 1997  & 1992  & 1987          \\ \hline
192Java    & 1             & 1             & 1             & 1             & 12    & -             & -                     \\
193\Textbf{C}      & \Textbf{2}& \Textbf{2}& \Textbf{2}& \Textbf{2}& \Textbf{1}& \Textbf{1}& \Textbf{1}    \\
194\CC             & 3             & 3             & 3             & 3             & 2             & 2             & 4                     \\
195\end{tabular}
196\end{center}
197\lstMakeShortInline@%
198Love it or hate it, C is extremely popular, highly used, and one of the few systems languages.
199In many cases, \CC is often used solely as a better C.
200Nonetheless, C, first standardized over thirty years ago, lacks many features that make programming in more modern languages safer and more productive.
201
202\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.
203The four key design goals for \CFA~\cite{Bilson03} are:
204(1) The behaviour of standard C code must remain the same when translated by a \CFA compiler as when translated by a C compiler;
205(2) Standard C code must be as fast and as small when translated by a \CFA compiler as when translated by a C compiler;
206(3) \CFA code must be at least as portable as standard C code;
207(4) Extensions introduced by \CFA must be translated in the most efficient way possible.
208These 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.
209\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.
210
211\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).
212Ultimately, a compiler is necessary for advanced features and optimal performance.
213
214This 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.
215Specifically, 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.
216The new constructs are empirically compared with both standard C and \CC; the results show the new design is comparable in performance.
217
218
219\subsection{Polymorphic Functions}
220\label{sec:poly-fns}
221
222\CFA{}\hspace{1pt}'s polymorphism was originally formalized by Ditchfield~\cite{Ditchfield92}, and first implemented by Bilson~\cite{Bilson03}.
223The 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):
224\begin{lstlisting}
225`forall( otype T )` T identity( T val ) { return val; }
226int forty_two = identity( 42 );                         $\C{// T is bound to int, forty\_two == 42}$
227\end{lstlisting}
228The @identity@ function above can be applied to any complete \emph{object type} (or @otype@).
229The 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.
230The \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.
231If this extra information is not needed, \eg for a pointer, the type parameter can be declared as a \emph{data type} (or @dtype@).
232
233In \CFA, the polymorphism runtime-cost is spread over each polymorphic call, due to passing more arguments to polymorphic functions;
234the experiments in Section~\ref{sec:eval} show this overhead is similar to \CC virtual-function calls.
235A design advantage is that, unlike \CC template-functions, \CFA polymorphic-functions are compatible with C \emph{separate compilation}, preventing compilation and code bloat.
236
237Since 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.
238For example, the function @twice@ can be defined using the \CFA syntax for operator overloading:
239\begin{lstlisting}
240forall( otype T `| { T ?+?(T, T); }` ) T twice( T x ) { return x + x; } $\C{// ? denotes operands}$
241int val = twice( twice( 3.7 ) );
242\end{lstlisting}
243which works for any type @T@ with a matching addition operator.
244The 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@.
245There 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.
246The first approach has a late conversion from @double@ to @int@ on the final assignment, while the second has an eager conversion to @int@.
247\CFA minimizes the number of conversions and their potential to lose information, so it selects the first approach, which corresponds with C-programmer intuition.
248
249Crucial to the design of a new programming language are the libraries to access thousands of external software features.
250Like \CC, \CFA inherits a massive compatible library-base, where other programming languages must rewrite or provide fragile inter-language communication with C.
251A simple example is leveraging the existing type-unsafe (@void *@) C @bsearch@ to binary search a sorted floating-point array:
252\begin{lstlisting}
253void * bsearch( const void * key, const void * base, size_t nmemb, size_t size,
254                                int (* compar)( const void *, const void * ));
255int comp( const void * t1, const void * t2 ) { return *(double *)t1 < *(double *)t2 ? -1 :
256                                *(double *)t2 < *(double *)t1 ? 1 : 0; }
257double key = 5.0, vals[10] = { /* 10 sorted floating-point values */ };
258double * val = (double *)bsearch( &key, vals, 10, sizeof(vals[0]), comp );      $\C{// search sorted array}$
259\end{lstlisting}
260which can be augmented simply with a generalized, type-safe, \CFA-overloaded wrappers:
261\begin{lstlisting}
262forall( otype T | { int ?<?( T, T ); } ) T * bsearch( T key, const T * arr, size_t size ) {
263        int comp( const void * t1, const void * t2 ) { /* as above with double changed to T */ }
264        return (T *)bsearch( &key, arr, size, sizeof(T), comp ); }
265forall( otype T | { int ?<?( T, T ); } ) unsigned int bsearch( T key, const T * arr, size_t size ) {
266        T * result = bsearch( key, arr, size ); $\C{// call first version}$
267        return result ? result - arr : size; }  $\C{// pointer subtraction includes sizeof(T)}$
268double * val = bsearch( 5.0, vals, 10 );        $\C{// selection based on return type}$
269int posn = bsearch( 5.0, vals, 10 );
270\end{lstlisting}
271The nested function @comp@ provides the hidden interface from typed \CFA to untyped (@void *@) C, plus the cast of the result.
272Providing a hidden @comp@ function in \CC is awkward as lambdas do not use C calling-conventions and template declarations cannot appear at block scope.
273As well, an alternate kind of return is made available: position versus pointer to found element.
274\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@.
275
276\CFA has replacement libraries condensing hundreds of existing C functions into tens of \CFA overloaded functions, all without rewriting the actual computations.
277For example, it is possible to write a type-safe \CFA wrapper @malloc@ based on the C @malloc@:
278\begin{lstlisting}
279forall( dtype T | sized(T) ) T * malloc( void ) { return (T *)malloc( sizeof(T) ); }
280int * ip = malloc();                                            $\C{// select type and size from left-hand side}$
281double * dp = malloc();
282struct S {...} * sp = malloc();
283\end{lstlisting}
284where the return type supplies the type/size of the allocation, which is impossible in most type systems.
285
286Call-site inferencing and nested functions provide a localized form of inheritance.
287For example, the \CFA @qsort@ only sorts in ascending order using @<@.
288However, it is trivial to locally change this behaviour:
289\begin{lstlisting}
290forall( otype T | { int ?<?( T, T ); } ) void qsort( const T * arr, size_t size ) { /* use C qsort */ }
291{       int ?<?( double x, double y ) { return x `>` y; }       $\C{// locally override behaviour}$
292        qsort( vals, size );                                    $\C{// descending sort}$
293}
294\end{lstlisting}
295Within the block, the nested version of @?<?@ performs @?>?@ and this local version overrides the built-in @?<?@ so it is passed to @qsort@.
296Hence, programmers can easily form local environments, adding and modifying appropriate functions, to maximize reuse of other existing functions and types.
297
298Finally, \CFA allows variable overloading:
299\begin{lstlisting}
300short int MAX = ...;   int MAX = ...;  double MAX = ...;
301short int s = MAX;    int i = MAX;    double d = MAX;   $\C{// select correct MAX}$
302\end{lstlisting}
303Here, the single name @MAX@ replaces all the C type-specific names: @SHRT_MAX@, @INT_MAX@, @DBL_MAX@.
304As 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.
305In addition, several operations are defined in terms values @0@ and @1@, \eg:
306\begin{lstlisting}
307int x;
308if (x) x++                                                                      $\C{// if (x != 0) x += 1;}$
309\end{lstlisting}
310Every @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.
311Due 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.
312The 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.
313
314
315\subsection{Traits}
316
317\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:
318\begin{lstlisting}
319trait summable( otype T ) {
320        void ?{}( T *, zero_t );                                $\C{// constructor from 0 literal}$
321        T ?+?( T, T );                                                  $\C{// assortment of additions}$
322        T ?+=?( T *, T );
323        T ++?( T * );
324        T ?++( T * ); };
325forall( otype T `| summable( T )` ) T sum( T a[$\,$], size_t size ) {  // use trait
326        `T` total = { `0` };                                    $\C{// instantiate T from 0 by calling its constructor}$
327        for ( unsigned int i = 0; i < size; i += 1 ) total `+=` a[i]; $\C{// select appropriate +}$
328        return total; }
329\end{lstlisting}
330
331In 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:
332\begin{lstlisting}
333trait otype( dtype T | sized(T) ) {  // sized is a pseudo-trait for types with known size and alignment
334        void ?{}( T * );                                                $\C{// default constructor}$
335        void ?{}( T *, T );                                             $\C{// copy constructor}$
336        void ?=?( T *, T );                                             $\C{// assignment operator}$
337        void ^?{}( T * ); };                                    $\C{// destructor}$
338\end{lstlisting}
339Given 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.
340
341In 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.
342Hence, trait names play no part in type equivalence;
343the names are simply macros for a list of polymorphic assertions, which are expanded at usage sites.
344Nevertheless, trait names form a logical subtype-hierarchy with @dtype@ at the top, where traits often contain overlapping assertions, \eg operator @+@.
345Traits are used like interfaces in Java or abstract base-classes in \CC, but without the nominal inheritance-relationships.
346Instead, 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.
347Hence, 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.
348(Nominal inheritance can be approximated with traits using marker variables or functions, as is done in Go.)
349
350% Nominal inheritance can be simulated with traits using marker variables or functions:
351% \begin{lstlisting}
352% trait nominal(otype T) {
353%     T is_nominal;
354% };
355% int is_nominal;                                                               $\C{// int now satisfies the nominal trait}$
356% \end{lstlisting}
357%
358% 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:
359% \begin{lstlisting}
360% trait pointer_like(otype Ptr, otype El) {
361%     lvalue El *?(Ptr);                                                $\C{// Ptr can be dereferenced into a modifiable value of type El}$
362% }
363% struct list {
364%     int value;
365%     list * next;                                                              $\C{// may omit "struct" on type names as in \CC}$
366% };
367% typedef list * list_iterator;
368%
369% lvalue int *?( list_iterator it ) { return it->value; }
370% \end{lstlisting}
371% 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@).
372% 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.
373
374
375\section{Generic Types}
376
377One of the known shortcomings of standard C is that it does not provide reusable type-safe abstractions for generic data structures and algorithms.
378Broadly speaking, there are three approaches to implement abstract data-structures in C.
379One approach is to write bespoke data-structures for each context in which they are needed.
380While 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.
381A 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.
382However, 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.
383A 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.
384Furthermore, writing and using preprocessor macros can be unnatural and inflexible.
385
386\CC, Java, and other languages use \emph{generic types} to produce type-safe abstract data-types.
387\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.
388However, for known concrete parameters, the generic-type definition can be inlined, like \CC templates.
389
390A 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:
391\begin{lstlisting}
392forall( otype R, otype S ) struct pair {
393        R first;
394        S second;
395};
396forall( otype T ) T value( pair( const char *, T ) p ) { return p.second; }
397forall( dtype F, otype T ) T value_p( pair( F *, T * ) p ) { return * p.second; }
398pair( const char *, int ) p = { "magic", 42 };
399int magic = value( p );
400pair( void *, int * ) q = { 0, &p.second };
401magic = value_p( q );
402double d = 1.0;
403pair( double *, double * ) r = { &d, &d };
404d = value_p( r );
405\end{lstlisting}
406
407\CFA classifies generic types as either \emph{concrete} or \emph{dynamic}.
408Concrete types have a fixed memory layout regardless of type parameters, while dynamic types vary in memory layout depending on their type parameters.
409A type may have polymorphic parameters but still be concrete, called \emph{dtype-static}.
410Polymorphic 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.
411
412\CFA generic types also allow checked argument-constraints.
413For example, the following declaration of a sorted set-type ensures the set key supports equality and relational comparison:
414\begin{lstlisting}
415forall( otype Key | { _Bool ?==?(Key, Key); _Bool ?<?(Key, Key); } ) struct sorted_set;
416\end{lstlisting}
417
418
419\subsection{Concrete Generic-Types}
420
421The \CFA translator template-expands concrete generic-types into new structure types, affording maximal inlining.
422To 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.
423A 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.
424For example, the concrete instantiation for @pair( const char *, int )@ is:
425\begin{lstlisting}
426struct _pair_conc1 {
427        const char * first;
428        int second;
429};
430\end{lstlisting}
431
432A concrete generic-type with dtype-static parameters is also expanded to a structure type, but this type is used for all matching instantiations.
433In 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:
434\begin{lstlisting}
435struct _pair_conc0 {
436        void * first;
437        void * second;
438};
439\end{lstlisting}
440
441
442\subsection{Dynamic Generic-Types}
443
444Though \CFA implements concrete generic-types efficiently, it also has a fully general system for dynamic generic types.
445As 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.
446Dynamic generic-types also have an \emph{offset array} containing structure-member offsets.
447A dynamic generic-union needs no such offset array, as all members are at offset 0, but size and alignment are still necessary.
448Access 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.
449
450The offset arrays are statically generated where possible.
451If 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;
452if 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.
453As 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 )@.
454The offset array @_offsetof_pair@ is generated at the call site as @size_t _offsetof_pair[] = { offsetof(_pair_conc1, first), offsetof(_pair_conc1, second) }@.
455
456In some cases the offset arrays cannot be statically generated.
457For 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.
458\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.
459The \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.
460These 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).
461Results of these layout functions are cached so that they are only computed once per type per function. %, as in the example below for @pair@.
462Layout functions also allow generic types to be used in a function definition without reflecting them in the function signature.
463For 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.
464This function could acquire the layout for @set(T)@ by calling its layout function with the layout of @T@ implicitly passed into the function.
465
466Whether a type is concrete, dtype-static, or dynamic is decided solely on the @forall@'s type parameters.
467This 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.
468If 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.
469
470
471\subsection{Applications}
472\label{sec:generic-apps}
473
474The reuse of dtype-static structure instantiations enables useful programming patterns at zero runtime cost.
475The 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@:
476\begin{lstlisting}
477forall(dtype T) int lexcmp( pair( T *, T * ) * a, pair( T *, T * ) * b, int (* cmp)( T *, T * ) ) {
478        return cmp( a->first, b->first ) ? : cmp( a->second, b->second );
479}
480\end{lstlisting}
481Since @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.
482
483Another useful pattern enabled by reused dtype-static type instantiations is zero-cost \emph{tag-structures}.
484Sometimes information is only used for type-checking and can be omitted at runtime, \eg:
485\begin{lstlisting}
486forall(dtype Unit) struct scalar { unsigned long value; };
487struct metres {};
488struct litres {};
489
490forall(dtype U) scalar(U) ?+?( scalar(U) a, scalar(U) b ) {
491        return (scalar(U)){ a.value + b.value };
492}
493scalar(metres) half_marathon = { 21093 };
494scalar(litres) swimming_pool = { 2500000 };
495scalar(metres) marathon = half_marathon + half_marathon;
496scalar(litres) two_pools = swimming_pool + swimming_pool;
497marathon + swimming_pool;                                       $\C{// compilation ERROR}$
498\end{lstlisting}
499@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 @?+?@.
500These implementations may even be separately compiled, unlike \CC template functions.
501However, the \CFA type-checker ensures matching types are used by all calls to @?+?@, preventing nonsensical computations like adding a length to a volume.
502
503
504\section{Tuples}
505\label{sec:tuples}
506
507In many languages, functions can return at most one value;
508however, many operations have multiple outcomes, some exceptional.
509Consider C's @div@ and @remquo@ functions, which return the quotient and remainder for a division of integer and floating-point values, respectively.
510\begin{lstlisting}
511typedef struct { int quo, rem; } div_t;         $\C{// from include stdlib.h}$
512div_t div( int num, int den );
513double remquo( double num, double den, int * quo );
514div_t qr = div( 13, 5 );                                        $\C{// return quotient/remainder aggregate}$
515int q;
516double r = remquo( 13.5, 5.2, &q );                     $\C{// return remainder, alias quotient}$
517\end{lstlisting}
518@div@ aggregates the quotient/remainder in a structure, while @remquo@ aliases a parameter to an argument.
519Both approaches are awkward.
520Alternatively, a programming language can directly support returning multiple values, \eg in \CFA:
521\begin{lstlisting}
522[ int, int ] div( int num, int den );           $\C{// return two integers}$
523[ double, double ] div( double num, double den ); $\C{// return two doubles}$
524int q, r;                                                                       $\C{// overloaded variable names}$
525double q, r;
526[ q, r ] = div( 13, 5 );                                        $\C{// select appropriate div and q, r}$
527[ q, r ] = div( 13.5, 5.2 );                            $\C{// assign into tuple}$
528\end{lstlisting}
529Clearly, this approach is straightforward to understand and use;
530therefore, why do few programming languages support this obvious feature or provide it awkwardly?
531The answer is that there are complex consequences that cascade through multiple aspects of the language, especially the type-system.
532This section show these consequences and how \CFA handles them.
533
534
535\subsection{Tuple Expressions}
536
537The addition of multiple-return-value functions (MRVF) are useless without a syntax for accepting multiple values at the call-site.
538The simplest mechanism for capturing the return values is variable assignment, allowing the values to be retrieved directly.
539As 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}.
540
541However, 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:
542\begin{lstlisting}
543printf( "%d %d\n", div( 13, 5 ) );                      $\C{// return values seperated into arguments}$
544\end{lstlisting}
545Here, the values returned by @div@ are composed with the call to @printf@ by flattening the tuple into separate arguments.
546However, the \CFA type-system must support significantly more complex composition:
547\begin{lstlisting}
548[ int, int ] foo$\(_1\)$( int );                        $\C{// overloaded foo functions}$
549[ double ] foo$\(_2\)$( int );
550void bar( int, double, double );
551bar( foo( 3 ), foo( 3 ) );
552\end{lstlisting}
553The type-resolver only has the tuple return-types to resolve the call to @bar@ as the @foo@ parameters are identical, which involves unifying the possible @foo@ functions with @bar@'s parameter list.
554No combination of @foo@s are an exact match with @bar@'s parameters, so the resolver applies C conversions.
555The minimal cost is @bar( foo@$_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.
556
557
558\subsection{Tuple Variables}
559
560An important observation from function composition is that new variable names are not required to initialize parameters from an MRVF.
561\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:
562\begin{lstlisting}
563[ int, int ] qr = div( 13, 5 );                         $\C{// tuple-variable declaration and initialization}$
564[ double, double ] qr = div( 13.5, 5.2 );
565\end{lstlisting}
566where the tuple variable-name serves the same purpose as the parameter name(s).
567Tuple variables can be composed of any types, except for array types, since array sizes are generally unknown in C.
568
569One way to access the tuple-variable components is with assignment or composition:
570\begin{lstlisting}
571[ q, r ] = qr;                                                          $\C{// access tuple-variable components}$
572printf( "%d %d\n", qr );
573\end{lstlisting}
574\CFA also supports \emph{tuple indexing} to access single components of a tuple expression:
575\begin{lstlisting}
576[int, int] * p = &qr;                                           $\C{// tuple pointer}$
577int rem = qr`.1`;                                                       $\C{// access remainder}$
578int quo = div( 13, 5 )`.0`;                                     $\C{// access quotient}$
579p`->0` = 5;                                                                     $\C{// change quotient}$
580bar( qr`.1`, qr );                                                      $\C{// pass remainder and quotient/remainder}$
581rem = [div( 13, 5 ), 42]`.0.1`;                         $\C{// access 2nd component of 1st component of tuple expression}$
582\end{lstlisting}
583
584
585\subsection{Flattening and Restructuring}
586
587In function call contexts, tuples support implicit flattening and restructuring conversions.
588Tuple flattening recursively expands a tuple into the list of its basic components.
589Tuple structuring packages a list of expressions into a value of tuple type, \eg:
590%\lstDeleteShortInline@%
591%\par\smallskip
592%\begin{tabular}{@{}l@{\hspace{1.5\parindent}}||@{\hspace{1.5\parindent}}l@{}}
593\begin{lstlisting}
594int f( int, int );
595int g( [int, int] );
596int h( int, [int, int] );
597[int, int] x;
598int y;
599f( x );                 $\C{// flatten}$
600g( y, 10 );             $\C{// structure}$
601h( x, y );              $\C{// flatten and structure}$
602\end{lstlisting}
603%\end{lstlisting}
604%&
605%\begin{lstlisting}
606%\end{tabular}
607%\smallskip\par\noindent
608%\lstMakeShortInline@%
609In the call to @f@, @x@ is implicitly flattened so the components of @x@ are passed as the two arguments.
610In 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@.
611Finally, 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]@.
612The 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.
613
614
615\subsection{Tuple Assignment}
616
617An assignment where the left side is a tuple type is called \emph{tuple assignment}.
618There 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.
619%\lstDeleteShortInline@%
620%\par\smallskip
621%\begin{tabular}{@{}l@{\hspace{1.5\parindent}}||@{\hspace{1.5\parindent}}l@{}}
622\begin{lstlisting}
623int x = 10;
624double y = 3.5;
625[int, double] z;
626z = [x, y];                                                                     $\C{// multiple assignment}$
627[x, y] = z;                                                                     $\C{// multiple assignment}$
628z = 10;                                                                         $\C{// mass assignment}$
629[y, x] = 3.14;                                                          $\C{// mass assignment}$
630\end{lstlisting}
631%\end{lstlisting}
632%&
633%\begin{lstlisting}
634%\end{tabular}
635%\smallskip\par\noindent
636%\lstMakeShortInline@%
637Both kinds of tuple assignment have parallel semantics, so that each value on the left and right side is evaluated before any assignments occur.
638As 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]@.
639This 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.
640For example, @[y, x] = 3.14@ performs the assignments @y = 3.14@ and @x = 3.14@, yielding @y == 3.14@ and @x == 3@;
641whereas, C cascading assignment @y = x = 3.14@ performs the assignments @x = 3.14@ and @y = x@, yielding @3@ in @y@ and @x@.
642Finally, 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.
643This example shows mass, multiple, and cascading assignment used in one expression:
644\begin{lstlisting}
645void f( [int, int] );
646f( [x, y] = z = 1.5 );                                          $\C{// assignments in parameter list}$
647\end{lstlisting}
648
649
650\subsection{Member Access}
651
652It is also possible to access multiple fields from a single expression using a \emph{member-access}.
653The result is a single tuple-valued expression whose type is the tuple of the types of the members, \eg:
654\begin{lstlisting}
655struct S { int x; double y; char * z; } s;
656s.[x, y, z] = 0;
657\end{lstlisting}
658Here, the mass assignment sets all members of @s@ to zero.
659Since 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).
660%\lstDeleteShortInline@%
661%\par\smallskip
662%\begin{tabular}{@{}l@{\hspace{1.5\parindent}}||@{\hspace{1.5\parindent}}l@{}}
663\begin{lstlisting}
664[int, int, long, double] x;
665void f( double, long );
666x.[0, 1] = x.[1, 0];                                            $\C{// rearrange: [x.0, x.1] = [x.1, x.0]}$
667f( x.[0, 3] );                                                          $\C{// drop: f(x.0, x.3)}$
668[int, int, int] y = x.[2, 0, 2];                        $\C{// duplicate: [y.0, y.1, y.2] = [x.2, x.0.x.2]}$
669\end{lstlisting}
670%\end{lstlisting}
671%&
672%\begin{lstlisting}
673%\end{tabular}
674%\smallskip\par\noindent
675%\lstMakeShortInline@%
676It is also possible for a member access to contain other member accesses, \eg:
677\begin{lstlisting}
678struct A { double i; int j; };
679struct B { int * k; short l; };
680struct C { int x; A y; B z; } v;
681v.[x, y.[i, j], z.k];                                           $\C{// [v.x, [v.y.i, v.y.j], v.z.k]}$
682\end{lstlisting}
683
684
685\begin{comment}
686\subsection{Casting}
687
688In C, the cast operator is used to explicitly convert between types.
689In \CFA, the cast operator has a secondary use as type ascription.
690That 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:
691\begin{lstlisting}
692int f();     // (1)
693double f()// (2)
694
695f();       // ambiguous - (1),(2) both equally viable
696(int)f()// choose (2)
697\end{lstlisting}
698
699Since casting is a fundamental operation in \CFA, casts should be given a meaningful interpretation in the context of tuples.
700Taking a look at standard C provides some guidance with respect to the way casts should work with tuples:
701\begin{lstlisting}
702int f();
703void g();
704
705(void)f()// (1)
706(int)g()// (2)
707\end{lstlisting}
708In C, (1) is a valid cast, which calls @f@ and discards its result.
709On the other hand, (2) is invalid, because @g@ does not produce a result, so requesting an @int@ to materialize from nothing is nonsensical.
710Generalizing 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.
711
712Formally, 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 $T_i$.
713Excess 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.
714This approach follows naturally from the way that a cast to @void@ works in C.
715
716For example, in
717\begin{lstlisting}
718[int, int, int] f();
719[int, [int, int], int] g();
720
721([int, double])f();           $\C{// (1)}$
722([int, int, int])g();         $\C{// (2)}$
723([void, [int, int]])g();      $\C{// (3)}$
724([int, int, int, int])g();    $\C{// (4)}$
725([int, [int, int, int]])g()$\C{// (5)}$
726\end{lstlisting}
727
728(1) discards the last element of the return value and converts the second element to @double@.
729Since @int@ is effectively a 1-element tuple, (2) discards the second component of the second element of the return value of @g@.
730If @g@ is free of side effects, this expression is equivalent to @[(int)(g().0), (int)(g().1.0), (int)(g().2)]@.
731Since @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)]@).
732
733Note 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.}.
734As such, (4) is invalid because the cast target type contains 4 components, while the source type contains only 3.
735Similarly, (5) is invalid because the cast @([int, int, int])(g().1)@ is invalid.
736That is, it is invalid to cast @[int, int]@ to @[int, int, int]@.
737\end{comment}
738
739
740\subsection{Polymorphism}
741
742Tuples also integrate with \CFA polymorphism as a kind of generic type.
743Due 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:
744\begin{lstlisting}
745forall(otype T, dtype U) void f( T x, U * y );
746f( [5, "hello"] );
747\end{lstlisting}
748where @[5, "hello"]@ is flattened, giving argument list @5, "hello"@, and @T@ binds to @int@ and @U@ binds to @const char@.
749Tuples, however, may contain polymorphic components.
750For example, a plus operator can be written to add two triples together.
751\begin{lstlisting}
752forall(otype T | { T ?+?( T, T ); }) [T, T, T] ?+?( [T, T, T] x, [T, T, T] y ) {
753        return [x.0 + y.0, x.1 + y.1, x.2 + y.2];
754}
755[int, int, int] x;
756int i1, i2, i3;
757[i1, i2, i3] = x + ([10, 20, 30]);
758\end{lstlisting}
759
760Flattening and restructuring conversions are also applied to tuple types in polymorphic type assertions.
761\begin{lstlisting}
762int f( [int, double], double );
763forall(otype T, otype U | { T f( T, U, U ); }) void g( T, U );
764g( 5, 10.21 );
765\end{lstlisting}
766Hence, function parameter and return lists are flattened for the purposes of type unification allowing the example to pass expression resolution.
767This relaxation is possible by extending the thunk scheme described by Bilson~\cite{Bilson03}.
768Whenever 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:
769\begin{lstlisting}
770int _thunk( int _p0, double _p1, double _p2 ) { return f( [_p0, _p1], _p2 ); }
771\end{lstlisting}
772so the thunk provides flattening and structuring conversions to inferred functions, improving the compatibility of tuples and polymorphism.
773These thunks take advantage of GCC C nested-functions to produce closures that have the usual function-pointer signature.
774
775
776\subsection{Variadic Tuples}
777\label{sec:variadic-tuples}
778
779To define variadic functions, \CFA adds a new kind of type parameter, @ttype@ (tuple type).
780Matching against a @ttype@ parameter consumes all remaining argument components and packages them into a tuple, binding to the resulting tuple of types.
781In 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.
782As such, @ttype@ variables are also called \emph{argument packs}.
783
784Like variadic templates, the main way to manipulate @ttype@ polymorphic functions is via recursion.
785Since nothing is known about a parameter pack by default, assertion parameters are key to doing anything meaningful.
786Unlike variadic templates, @ttype@ polymorphic functions can be separately compiled.
787For example, a generalized @sum@ function written using @ttype@:
788\begin{lstlisting}
789int sum$\(_0\)$() { return 0; }
790forall(ttype Params | { int sum( Params ); } ) int sum$\(_1\)$( int x, Params rest ) {
791        return x + sum( rest );
792}
793sum( 10, 20, 30 );
794\end{lstlisting}
795Since @sum@\(_0\) does not accept any arguments, it is not a valid candidate function for the call @sum(10, 20, 30)@.
796In 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]@.
797The process continues unitl @Params@ is bound to @[]@, requiring an assertion @int sum()@, which matches @sum@\(_0\) and terminates the recursion.
798Effectively, 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))@.
799
800It is reasonable to take the @sum@ function a step further to enforce a minimum number of arguments:
801\begin{lstlisting}
802int sum( int x, int y ) { return x + y; }
803forall(ttype Params | { int sum( int, Params ); } ) int sum( int x, int y, Params rest ) {
804        return sum( x + y, rest );
805}
806\end{lstlisting}
807One more step permits the summation of any summable type with all arguments of the same type:
808\begin{lstlisting}
809trait summable(otype T) {
810        T ?+?( T, T );
811};
812forall(otype R | summable( R ) ) R sum( R x, R y ) {
813        return x + y;
814}
815forall(otype R, ttype Params | summable(R) | { R sum(R, Params); } ) R sum(R x, R y, Params rest) {
816        return sum( x + y, rest );
817}
818\end{lstlisting}
819Unlike C variadic functions, it is unnecessary to hard code the number and expected types.
820Furthermore, this code is extendable for any user-defined type with a @?+?@ operator.
821Summing arbitrary heterogeneous lists is possible with similar code by adding the appropriate type variables and addition operators.
822
823It is also possible to write a type-safe variadic print function to replace @printf@:
824\begin{lstlisting}
825struct S { int x, y; };
826forall(otype T, ttype Params | { void print(T); void print(Params); }) void print(T arg, Params rest) {
827        print(arg);  print(rest);
828}
829void print( char * x ) { printf( "%s", x ); }
830void print( int x ) { printf( "%d", x ); }
831void print( S s ) { print( "{ ", s.x, ",", s.y, " }" ); }
832print( "s = ", (S){ 1, 2 }, "\n" );
833\end{lstlisting}
834This example showcases a variadic-template-like decomposition of the provided argument list.
835The individual @print@ functions allow printing a single element of a type.
836The polymorphic @print@ allows printing any list of types, where as each individual type has a @print@ function.
837The individual print functions can be used to build up more complicated @print@ functions, such as @S@, which cannot be done with @printf@ in C.
838
839Finally, it is possible to use @ttype@ polymorphism to provide arbitrary argument forwarding functions.
840For example, it is possible to write @new@ as a library function:
841\begin{lstlisting}
842forall( otype R, otype S ) void ?{}( pair(R, S) *, R, S );
843forall( dtype T, ttype Params | sized(T) | { void ?{}( T *, Params ); } ) T * new( Params p ) {
844        return ((T *)malloc()){ p };                    $\C{// construct into result of malloc}$
845}
846pair( int, char ) * x = new( 42, '!' );
847\end{lstlisting}
848The @new@ function provides the combination of type-safe @malloc@ with a \CFA constructor call, making it impossible to forget constructing dynamically allocated objects.
849This function provides the type-safety of @new@ in \CC, without the need to specify the allocated type again, thanks to return-type inference.
850
851
852\subsection{Implementation}
853
854Tuples are implemented in the \CFA translator via a transformation into \emph{generic types}.
855For each $N$, the first time an $N$-tuple is seen in a scope a generic type with $N$ type parameters is generated, \eg:
856\begin{lstlisting}
857[int, int] f() {
858        [double, double] x;
859        [int, double, int] y;
860}
861\end{lstlisting}
862is transformed into:
863\begin{lstlisting}
864forall(dtype T0, dtype T1 | sized(T0) | sized(T1)) struct _tuple2 {
865        T0 field_0;                                                             $\C{// generated before the first 2-tuple}$
866        T1 field_1;
867};
868_tuple2(int, int) f() {
869        _tuple2(double, double) x;
870        forall(dtype T0, dtype T1, dtype T2 | sized(T0) | sized(T1) | sized(T2)) struct _tuple3 {
871                T0 field_0;                                                     $\C{// generated before the first 3-tuple}$
872                T1 field_1;
873                T2 field_2;
874        };
875        _tuple3(int, double, int) y;
876}
877\end{lstlisting}
878\begin{sloppypar}
879Tuple expressions are then simply converted directly into compound literals, \eg @[5, 'x', 1.24]@ becomes @(_tuple3(int, char, double)){ 5, 'x', 1.24 }@.
880\end{sloppypar}
881
882\begin{comment}
883Since tuples are essentially structures, tuple indexing expressions are just field accesses:
884\begin{lstlisting}
885void f(int, [double, char]);
886[int, double] x;
887
888x.0+x.1;
889printf("%d %g\n", x);
890f(x, 'z');
891\end{lstlisting}
892Is transformed into:
893\begin{lstlisting}
894void f(int, _tuple2(double, char));
895_tuple2(int, double) x;
896
897x.field_0+x.field_1;
898printf("%d %g\n", x.field_0, x.field_1);
899f(x.field_0, (_tuple2){ x.field_1, 'z' });
900\end{lstlisting}
901Note that due to flattening, @x@ used in the argument position is converted into the list of its fields.
902In the call to @f@, the second and third argument components are structured into a tuple argument.
903Similarly, tuple member expressions are recursively expanded into a list of member access expressions.
904
905Expressions that may contain side effects are made into \emph{unique expressions} before being expanded by the flattening conversion.
906Each unique expression is assigned an identifier and is guaranteed to be executed exactly once:
907\begin{lstlisting}
908void g(int, double);
909[int, double] h();
910g(h());
911\end{lstlisting}
912Internally, this expression is converted to two variables and an expression:
913\begin{lstlisting}
914void g(int, double);
915[int, double] h();
916
917_Bool _unq0_finished_ = 0;
918[int, double] _unq0;
919g(
920        (_unq0_finished_ ? _unq0 : (_unq0 = f(), _unq0_finished_ = 1, _unq0)).0,
921        (_unq0_finished_ ? _unq0 : (_unq0 = f(), _unq0_finished_ = 1, _unq0)).1,
922);
923\end{lstlisting}
924Since argument evaluation order is not specified by the C programming language, this scheme is built to work regardless of evaluation order.
925The first time a unique expression is executed, the actual expression is evaluated and the accompanying boolean is set to true.
926Every subsequent evaluation of the unique expression then results in an access to the stored result of the actual expression.
927Tuple member expressions also take advantage of unique expressions in the case of possible impurity.
928
929Currently, the \CFA translator has a very broad, imprecise definition of impurity, where any function call is assumed to be impure.
930This 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.
931
932The various kinds of tuple assignment, constructors, and destructors generate GNU C statement expressions.
933A 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.
934The 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.
935However, 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.
936\end{comment}
937
938
939\section{Control Structures}
940
941
942\subsection{\texorpdfstring{Labelled \LstKeywordStyle{continue} / \LstKeywordStyle{break}}{Labelled continue / break}}
943
944While C provides @continue@ and @break@ statements for altering control flow, both are restricted to one level of nesting for a particular control structure.
945Unfortunately, this restriction forces programmers to use @goto@ to achieve the equivalent control-flow for more than one level of nesting.
946To 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.
947For both @continue@ and @break@, the target label must be directly associated with a @for@, @while@ or @do@ statement;
948for @break@, the target label can also be associated with a @switch@, @if@ or compound (@{}@) statement.
949Figure~\ref{f:MultiLevelExit} shows @continue@ and @break@ indicating the specific control structure, and the corresponding C program using only @goto@ and labels.
950The innermost loop has 7 exit points, which cause continuation or termination of one or more of the 7 nested control-structures.
951
952\begin{figure}
953\lstDeleteShortInline@%
954\begin{tabular}{@{\hspace{\parindentlnth}}l@{\hspace{\parindentlnth}}l@{\hspace{\parindentlnth}}l@{}}
955\multicolumn{1}{@{\hspace{\parindentlnth}}c@{\hspace{\parindentlnth}}}{\textbf{\CFA}}   & \multicolumn{1}{@{\hspace{\parindentlnth}}c}{\textbf{C}}      \\
956\begin{cfa}
957`LC:` {
958        ... $declarations$ ...
959        `LS:` switch ( ... ) {
960          case 3:
961                `LIF:` if ( ... ) {
962                        `LF:` for ( ... ) {
963                                `LW:` while ( ... ) {
964                                        ... break `LC`; ...
965                                        ... break `LS`; ...
966                                        ... break `LIF`; ...
967                                        ... continue `LF;` ...
968                                        ... break `LF`; ...
969                                        ... continue `LW`; ...
970                                        ... break `LW`; ...
971                                } // while
972                        } // for
973                } else {
974                        ... break `LIF`; ...
975                } // if
976        } // switch
977} // compound
978\end{cfa}
979&
980\begin{cfa}
981{
982        ... $declarations$ ...
983        switch ( ... ) {
984          case 3:
985                if ( ... ) {
986                        for ( ... ) {
987                                while ( ... ) {
988                                        ... goto `LC`; ...
989                                        ... goto `LS`; ...
990                                        ... goto `LIF`; ...
991                                        ... goto `LFC`; ...
992                                        ... goto `LFB`; ...
993                                        ... goto `LWC`; ...
994                                        ... goto `LWB`; ...
995                                  `LWC`: ; } `LWB:` ;
996                          `LFC:` ; } `LFB:` ;
997                } else {
998                        ... goto `LIF`; ...
999                } `L3:` ;
1000        } `LS:` ;
1001} `LC:` ;
1002\end{cfa}
1003&
1004\begin{cfa}
1005
1006
1007
1008
1009
1010
1011
1012// terminate compound
1013// terminate switch
1014// terminate if
1015// continue loop
1016// terminate loop
1017// continue loop
1018// terminate loop
1019
1020
1021
1022// terminate if
1023
1024
1025
1026\end{cfa}
1027\end{tabular}
1028\lstMakeShortInline@%
1029\caption{Multi-level Exit}
1030\label{f:MultiLevelExit}
1031\end{figure}
1032
1033Both labelled @continue@ and @break@ are a @goto@ restricted in the following ways:
1034\begin{itemize}
1035\item
1036They cannot create a loop, which means only the looping constructs cause looping.
1037This restriction means all situations resulting in repeated execution are clearly delineated.
1038\item
1039They cannot branch into a control structure.
1040This restriction prevents missing declarations and/or initializations at the start of a control structure resulting in undefined behaviour.
1041\end{itemize}
1042The 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.
1043Furthermore, 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.
1044With @goto@, the label is at the end of the control structure, which fails to convey this important clue early enough to the reader.
1045Finally, using an explicit target for the transfer instead of an implicit target allows new constructs to be added or removed without affecting existing constructs.
1046The implicit targets of the current @continue@ and @break@, \ie the closest enclosing loop or @switch@, change as certain constructs are added or removed.
1047
1048\TODO{choose and fallthrough here as well?}
1049
1050
1051\subsection{\texorpdfstring{\LstKeywordStyle{with} Clause / Statement}{with Clause / Statement}}
1052\label{s:WithClauseStatement}
1053
1054Grouping heterogenous data into \newterm{aggregate}s is a common programming practice, and an aggregate can be further organized into more complex structures, such as arrays and containers:
1055\begin{cfa}
1056struct S {                                                              $\C{// aggregate}$
1057        char c;                                                         $\C{// fields}$
1058        int i;
1059        double d;
1060};
1061S s, as[10];
1062\end{cfa}
1063However, routines manipulating aggregates have repeition of the aggregate name to access its containing fields:
1064\begin{cfa}
1065void f( S s ) {
1066        `s.`c; `s.`i; `s.`d;                            $\C{// access containing fields}$
1067}
1068\end{cfa}
1069A similar situation occurs in object-oriented programming, \eg \CC:
1070\begin{C++}
1071class C {
1072        char c;                                                         $\C{// fields}$
1073        int i;
1074        double d;
1075        int mem() {                                                     $\C{// implicit "this" parameter}$
1076                `this->`c; `this->`i; `this->`d;$\C{// access containing fields}$
1077        }
1078}
1079\end{C++}
1080Nesting of member routines in a \lstinline[language=C++]@class@ allows eliding \lstinline[language=C++]@this->@ because of nested lexical-scoping.
1081
1082% In object-oriented programming, there is an implicit first parameter, often names @self@ or @this@, which is elided.
1083% In any programming language, some functions have a naturally close relationship with a particular data type.
1084% Object-oriented programming allows this close relationship to be codified in the language by making such functions \emph{class methods} of their related data type.
1085% Class methods have certain privileges with respect to their associated data type, notably un-prefixed access to the fields of that data type.
1086% When 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.
1087%
1088% \TODO{Fill out section. Be sure to mention arbitrary expressions in with-blocks, recent change driven by Thierry to prioritize field name over parameters.}
1089
1090\CFA provides a @with@ clause/statement (see Pascal~\cite[\S~4.F]{Pascal}) to elided aggregate qualification to fields by opening a scope containing field identifiers.
1091Hence, the qualified fields become variables, and making it easier to optimizing field references in a block.
1092\begin{cfa}
1093void f( S s ) `with s` {                                $\C{// with clause}$
1094        c; i; d;                                                        $\C{\color{red}// s.c, s.i, s.d}$
1095}
1096\end{cfa}
1097and the equivalence for object-style programming is:
1098\begin{cfa}
1099int mem( S & this ) `with this` {               $\C{// with clause}$
1100        c; i; d;                                                        $\C{\color{red}// this.c, this.i, this.d}$
1101}
1102\end{cfa}
1103The key generality over the object-oriented approach is that one aggregate parameter \lstinline[language=C++]@this@ is not treated specially over other aggregate parameters:
1104\begin{cfa}
1105struct T { double m, n; };
1106int mem( S & s, T & t ) `with s, t` {   $\C{// multiple aggregate parameters}$
1107        c; i; d;                                                        $\C{\color{red}// s.c, s.i, s.d}$
1108        m; n;                                                           $\C{\color{red}// t.m, t.n}$
1109}
1110\end{cfa}
1111The equivalent object-oriented style is:
1112\begin{cfa}
1113int S::mem( T & t ) {                                   $\C{// multiple aggregate parameters}$
1114        c; i; d;                                                        $\C{\color{red}// this-\textgreater.c, this-\textgreater.i, this-\textgreater.d}$
1115        `t.`m; `t.`n;
1116}
1117\end{cfa}
1118
1119The statement form is used within a block:
1120\begin{cfa}
1121int foo() {
1122        struct S1 { ... } s1;
1123        struct S2 { ... } s2;
1124        `with s1` {                                             $\C{// with statement}$
1125                // access fields of s1 without qualification
1126                `with s2` {                                     $\C{// nesting}$
1127                        // access fields of s1 and s2 without qualification
1128                }
1129        }
1130        `with s1, s2` {
1131                // access unambiguous fields of s1 and s2 without qualification
1132        }
1133}
1134\end{cfa}
1135
1136When opening multiple structures, fields with the same name and type are ambiguous and must be fully qualified.
1137For fields with the same name but different type, context/cast can be used to disambiguate.
1138\begin{cfa}
1139struct S { int i; int j; double m; } a, c;
1140struct T { int i; int k; int m } b, c;
1141`with a, b` {
1142        j + k;                                                  $\C{// unambiguous, unique names define unique types}$
1143        i;                                                              $\C{// ambiguous, same name and type}$
1144        a.i + b.i;                                              $\C{// unambiguous, qualification defines unique names}$
1145        m;                                                              $\C{// ambiguous, same name and no context to define unique type}$
1146        m = 5.0;                                                $\C{// unambiguous, same name and context defines unique type}$
1147        m = 1;                                                  $\C{// unambiguous, same name and context defines unique type}$
1148}
1149`with c` { ... }                                        $\C{// ambiguous, same name and no context}$
1150`with (S)c` { ... }                                     $\C{// unambiguous, same name and cast defines unique type}$
1151\end{cfa}
1152
1153The components in the "with" clause
1154
1155  with a, b, c { ... }
1156
1157serve 2 purposes: each component provides a type and object. The type must be a
1158structure type. Enumerations are already opened, and I think a union is opened
1159to some extent, too. (Or is that just unnamed unions?) The object is the target
1160that the naked structure-fields apply to. The components are open in "parallel"
1161at the scope of the "with" clause/statement, so opening "a" does not affect
1162opening "b", etc. This semantic is different from Pascal, which nests the
1163openings.
1164
1165Having said the above, it seems reasonable to allow a "with" component to be an
1166expression. The type is the static expression-type and the object is the result
1167of the expression. Again, the type must be an aggregate. Expressions require
1168parenthesis around the components.
1169
1170  with( a, b, c ) { ... }
1171
1172Does this now make sense?
1173
1174Having written more CFA code, it is becoming clear to me that I *really* want
1175the "with" to be implemented because I hate having to type all those object
1176names for fields. It's a great way to drive people away from the language.
1177
1178
1179\subsection{Exception Handling ???}
1180
1181
1182\section{Declarations}
1183
1184It is important to the design team that \CFA subjectively ``feel like'' C to user programmers.
1185An 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.
1186Maintaining 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.
1187Nonetheless, 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.
1188
1189
1190\subsection{Alternative Declaration Syntax}
1191
1192
1193\subsection{References}
1194
1195All 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.
1196The 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.
1197Which address a value is located at is sometimes significant; the imperative programming paradigm of C relies on the mutation of values at specific addresses.
1198Within 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.
1199Though 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.
1200In 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 @&?@.
1201
1202\begin{cfa}
1203int x = 1, y = 2, * p1, * p2, ** p3;
1204p1 = &x;  $\C{// p1 points to x}$
1205p2 = &y;  $\C{// p2 points to y}$
1206p3 = &p1;  $\C{// p3 points to p1}$
1207\end{cfa}
1208
1209Unfortunately, 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.
1210It 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.
1211However, 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.
1212To 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:
1213
1214\begin{cfa}
1215inx x = 1, y = 2, & r1, & r2, && r3;
1216&r1 = &x;  $\C{// r1 points to x}$
1217&r2 = &y;  $\C{// r2 points to y}$
1218&&r3 = &&r1;  $\C{// r3 points to r2}$
1219r2 = ((r1 + r2) * (r3 - r1)) / (r3 - 15);  $\C{// implicit dereferencing}$
1220\end{cfa}
1221
1222Except for auto-dereferencing by the compiler, this reference example is exactly the same as the previous pointer example.
1223Hence, 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.
1224One 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:
1225
1226\begin{cfa}
1227`*`r2 = ((`*`r1 + `*`r2) * (`**`r3 - `*`r1)) / (`**`r3 - 15);
1228\end{cfa}
1229
1230References in \CFA are similar to those in \CC, but with a couple important improvements, both of which can be seen in the example above.
1231Firstly, \CFA does not forbid references to references, unlike \CC.
1232This provides a much more orthogonal design for library implementors, obviating the need for workarounds such as @std::reference_wrapper@.
1233
1234Secondly, unlike the references in \CC which always point to a fixed address, \CFA references are rebindable.
1235This allows \CFA references to be default-initialized (to a null pointer), and also to point to different addresses throughout their lifetime.
1236This rebinding is accomplished without adding any new syntax to \CFA, but simply by extending the existing semantics of the address-of operator in C.
1237In 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.
1238In \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.
1239The 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.
1240This 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).
1241The 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@.
1242
1243Since 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.
1244By analogy to pointers, \CFA references also allow cv-qualifiers:
1245
1246\begin{cfa}
1247const int cx = 5;               $\C{// cannot change cx}$
1248const int & cr = cx;    $\C{// cannot change cr's referred value}$
1249&cr = &cx;                              $\C{// rebinding cr allowed}$
1250cr = 7;                                 $\C{// ERROR, cannot change cr}$
1251int & const rc = x;             $\C{// must be initialized, like in \CC}$
1252&rc = &x;                               $\C{// ERROR, cannot rebind rc}$
1253rc = 7;                                 $\C{// x now equal to 7}$
1254\end{cfa}
1255
1256Given that a reference is meant to represent a lvalue, \CFA provides some syntactic shortcuts when initializing references.
1257There are three initialization contexts in \CFA: declaration initialization, argument/parameter binding, and return/temporary binding.
1258In each of these contexts, the address-of operator on the target lvalue may (in fact, must) be elided.
1259The 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@.
1260
1261This 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.
1262\CFA includes one more reference conversion, an ``rvalue-to-reference'' conversion, implemented by means of an implicit temporary.
1263When an rvalue is used to initialize a reference, it is instead used to initialize a hidden temporary value with the same lexical scope as the reference, and the reference is initialized to the address of this temporary.
1264This allows complex values to be succinctly and efficiently passed to functions, without the syntactic overhead of explicit definition of a temporary variable or the runtime cost of pass-by-value.
1265\CC allows a similar binding, but only for @const@ references; the more general semantics of \CFA are an attempt to avoid the \emph{const hell} problem, in which addition of a @const@ qualifier to one reference requires a cascading chain of added qualifiers.
1266
1267\subsection{Constructors and Destructors}
1268
1269One 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.
1270However, 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.
1271\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.
1272
1273\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.}
1274
1275
1276\subsection{Default Parameters}
1277
1278
1279\section{Literals}
1280
1281
1282\subsection{0/1}
1283
1284\TODO{Some text already at the end of Section~\ref{sec:poly-fns}}
1285
1286
1287\subsection{Units}
1288
1289Alternative call syntax (literal argument before routine name) to convert basic literals into user literals.
1290
1291{\lstset{language=CFA,deletedelim=**[is][]{`}{`},moredelim=**[is][\color{red}]{@}{@}}
1292\begin{cfa}
1293struct Weight { double stones; };
1294
1295void ?{}( Weight & w ) { w.stones = 0; } $\C{// operations}$
1296void ?{}( Weight & w, double w ) { w.stones = w; }
1297Weight ?+?( Weight l, Weight r ) { return (Weight){ l.stones + r.stones }; }
1298
1299Weight @?`st@( double w ) { return (Weight){ w }; } $\C{// backquote for units}$
1300Weight @?`lb@( double w ) { return (Weight){ w / 14.0 }; }
1301Weight @?`kg@( double w ) { return (Weight) { w * 0.1575}; }
1302
1303int main() {
1304        Weight w, hw = { 14 };                  $\C{// 14 stone}$
1305        w = 11@`st@ + 1@`lb@;
1306        w = 70.3@`kg@;
1307        w = 155@`lb@;
1308        w = 0x_9b_u@`lb@;                               $\C{// hexadecimal unsigned weight (155)}$
1309        w = 0_233@`lb@;                                 $\C{// octal weight (155)}$
1310        w = 5@`st@ + 8@`kg@ + 25@`lb@ + hw;
1311}
1312\end{cfa}
1313}%
1314
1315
1316\section{Evaluation}
1317\label{sec:eval}
1318
1319Though \CFA provides significant added functionality over C, these features have a low runtime penalty.
1320In fact, \CFA's features for generic programming can enable faster runtime execution than idiomatic @void *@-based C code.
1321This 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}).
1322Since 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.
1323A more illustrative benchmark measures the costs of idiomatic usage of each language's features.
1324Figure~\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}.
1325The benchmark test is similar for C and \CC.
1326The 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.
1327
1328\begin{figure}
1329\begin{lstlisting}[xleftmargin=3\parindentlnth,aboveskip=0pt,belowskip=0pt]
1330int main( int argc, char * argv[] ) {
1331        FILE * out = fopen( "cfa-out.txt", "w" );
1332        int maxi = 0, vali = 42;
1333        stack(int) si, ti;
1334
1335        REPEAT_TIMED( "push_int", N, push( &si, vali ); )
1336        TIMED( "copy_int", ti = si; )
1337        TIMED( "clear_int", clear( &si ); )
1338        REPEAT_TIMED( "pop_int", N,
1339                int xi = pop( &ti ); if ( xi > maxi ) { maxi = xi; } )
1340        REPEAT_TIMED( "print_int", N/2, print( out, vali, ":", vali, "\n" ); )
1341
1342        pair(_Bool, char) maxp = { (_Bool)0, '\0' }, valp = { (_Bool)1, 'a' };
1343        stack(pair(_Bool, char)) sp, tp;
1344
1345        REPEAT_TIMED( "push_pair", N, push( &sp, valp ); )
1346        TIMED( "copy_pair", tp = sp; )
1347        TIMED( "clear_pair", clear( &sp ); )
1348        REPEAT_TIMED( "pop_pair", N,
1349                pair(_Bool, char) xp = pop( &tp ); if ( xp > maxp ) { maxp = xp; } )
1350        REPEAT_TIMED( "print_pair", N/2, print( out, valp, ":", valp, "\n" ); )
1351        fclose(out);
1352}
1353\end{lstlisting}
1354\caption{\protect\CFA Benchmark Test}
1355\label{fig:BenchmarkTest}
1356\end{figure}
1357
1358The 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.
1359The \CCV variant illustrates an alternative object-oriented idiom where all objects inherit from a base @object@ class, mimicking a Java-like interface;
1360hence runtime checks are necessary to safely down-cast objects.
1361The 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.
1362For 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.
1363Note, the C benchmark uses unchecked casts as there is no runtime mechanism to perform such checks, while \CFA and \CC provide type-safety statically.
1364
1365Figure~\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.
1366The graph plots the median of 5 consecutive runs of each program, with an initial warm-up run omitted.
1367All code is compiled at \texttt{-O2} by GCC or G++ 6.2.0, with all \CC code compiled as \CCfourteen.
1368The 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.
1369
1370\begin{figure}
1371\centering
1372\input{timing}
1373\caption{Benchmark Timing Results (smaller is better)}
1374\label{fig:eval}
1375\end{figure}
1376
1377\begin{table}
1378\caption{Properties of benchmark code}
1379\label{tab:eval}
1380\newcommand{\CT}[1]{\multicolumn{1}{c}{#1}}
1381\begin{tabular}{rrrrr}
1382                                                                        & \CT{C}        & \CT{\CFA}     & \CT{\CC}      & \CT{\CCV}             \\ \hline
1383maximum memory usage (MB)                       & 10001         & 2502          & 2503          & 11253                 \\
1384source code size (lines)                        & 247           & 222           & 165           & 339                   \\
1385redundant type annotations (lines)      & 39            & 2                     & 2                     & 15                    \\
1386binary size (KB)                                        & 14            & 229           & 18            & 38                    \\
1387\end{tabular}
1388\end{table}
1389
1390The 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;
1391this inefficiency is exacerbated by the second level of generic types in the pair-based benchmarks.
1392By 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.
1393\CCV is slower than C largely due to the cost of runtime type-checking of down-casts (implemented with @dynamic_cast@);
1394There are two outliers in the graph for \CFA: all prints and pop of @pair@.
1395Both 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.
1396A compiler designed for \CFA could easily perform these optimizations.
1397Finally, the binary size for \CFA is larger because of static linking with the \CFA libraries.
1398
1399\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.
1400On 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.
1401\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;
1402with their omission, the \CCV line count is similar to C.
1403We 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.
1404
1405Raw line-count, however, is a fairly rough measure of code complexity;
1406another important factor is how much type information the programmer must manually specify, especially where that information is not checked by the compiler.
1407Such 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@).
1408To 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.
1409The \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.
1410The 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).
1411These uses are similar to the @new@ expressions in \CC, though the \CFA compiler's type resolver should shortly render even these type casts superfluous.
1412
1413
1414\section{Related Work}
1415
1416
1417\subsection{Polymorphism}
1418
1419\CC is the most similar language to \CFA;
1420both are extensions to C with source and runtime backwards compatibility.
1421The fundamental difference is in their engineering approach to C compatibility and programmer expectation.
1422While \CC provides good backwards compatibility with C, it has a steep learning curve for many of its extensions.
1423For example, polymorphism is provided via three disjoint mechanisms: overloading, inheritance, and templates.
1424The 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.
1425In 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.
1426The key mechanism to support separate compilation is \CFA's \emph{explicit} use of assumed properties for a type.
1427Until \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;
1428furthermore, \CC concepts are restricted to template polymorphism.
1429
1430Cyclone~\cite{Grossman06} also provides capabilities for polymorphic functions and existential types, similar to \CFA's @forall@ functions and generic types.
1431Cyclone 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.
1432Furthermore, 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@.
1433In \CFA terms, all Cyclone polymorphism must be dtype-static.
1434While 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.
1435Smith 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.
1436
1437Objective-C~\cite{obj-c-book} is an industrially successful extension to C.
1438However, Objective-C is a radical departure from C, using an object-oriented model with message-passing.
1439Objective-C did not support type-checked generics until recently \cite{xcode7}, historically using less-efficient runtime checking of object types.
1440The GObject~\cite{GObject} framework also adds object-oriented programming with runtime type-checking and reference-counting garbage-collection to C;
1441these features are more intrusive additions than those provided by \CFA, in addition to the runtime overhead of reference-counting.
1442Vala~\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.
1443Java~\cite{Java8} included generic types in Java~5, which are type-checked at compilation and type-erased at runtime, similar to \CFA's.
1444However, in Java, each object carries its own table of method pointers, while \CFA passes the method pointers separately to maintain a C-compatible layout.
1445Java is also a garbage-collected, object-oriented language, with the associated resource usage and C-interoperability burdens.
1446
1447D~\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.
1448However, 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.
1449D and Go are garbage-collected languages, imposing the associated runtime overhead.
1450The necessity of accounting for data transfer between managed runtimes and the unmanaged C runtime complicates foreign-function interfaces to C.
1451Furthermore, 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.
1452D 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.
1453Rust also possesses much more powerful abstraction capabilities for writing generic code than Go.
1454On 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.
1455\CFA, with its more modest safety features, allows direct ports of C code while maintaining the idiomatic style of the original source.
1456
1457
1458\subsection{Tuples/Variadics}
1459
1460Many programming languages have some form of tuple construct and/or variadic functions, \eg SETL, C, KW-C, \CC, D, Go, Java, ML, and Scala.
1461SETL~\cite{SETL} is a high-level mathematical programming language, with tuples being one of the primary data types.
1462Tuples in SETL allow subscripting, dynamic expansion, and multiple assignment.
1463C 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.
1464KW-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.
1465The main contributions of that work were adding MRVF, tuple mass and multiple assignment, and record-field access.
1466\CCeleven introduced @std::tuple@ as a library variadic template structure.
1467Tuples are a generalization of @std::pair@, in that they allow for arbitrary length, fixed-size aggregation of heterogeneous values.
1468Operations include @std::get<N>@ to extract values, @std::tie@ to create a tuple of references used for assignment, and lexicographic comparisons.
1469\CCseventeen proposes \emph{structured bindings}~\cite{Sutter15} to eliminate pre-declaring variables and use of @std::tie@ for binding the results.
1470This 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.
1471Furthermore, structured bindings are not a full replacement for @std::tie@, as it always declares new variables.
1472Like \CC, D provides tuples through a library variadic-template structure.
1473Go does not have tuples but supports MRVF.
1474Java'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.
1475Tuples are a fundamental abstraction in most functional programming languages, such as Standard ML~\cite{sml} and~\cite{Scala}, which decompose tuples using pattern matching.
1476
1477
1478\section{Conclusion and Future Work}
1479
1480The 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.
1481While 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.
1482The 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.
1483The contributions are a powerful type-system using parametric polymorphism and overloading, generic types, and tuples, which all have complex interactions.
1484The work is a challenging design, engineering, and implementation exercise.
1485On the surface, the project may appear as a rehash of similar mechanisms in \CC.
1486However, 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.
1487All of these new features are being used by the \CFA development-team to build the \CFA runtime-system.
1488Finally, we demonstrate that \CFA performance for some idiomatic cases is better than C and close to \CC, showing the design is practically applicable.
1489
1490There is ongoing work on a wide range of \CFA feature extensions, including reference types, arrays with size, exceptions, concurrent primitives and modules.
1491(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.)
1492In addition, there are interesting future directions for the polymorphism design.
1493Notably, \CC template functions trade compile time and code bloat for optimal runtime of individual instantiations of polymorphic functions.
1494\CFA polymorphic functions use dynamic virtual-dispatch;
1495the 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.
1496Two 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).
1497These approaches are not mutually exclusive and allow performance optimizations to be applied only when necessary, without suffering global code-bloat.
1498In general, we believe separate compilation, producing smaller code, works well with loaded hardware-caches, which may offset the benefit of larger inlined-code.
1499
1500
1501\section{Acknowledgments}
1502
1503The 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.
1504%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.
1505% 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.
1506
1507
1508\bibliographystyle{plain}
1509\bibliography{pl}
1510
1511
1512\appendix
1513
1514\section{Benchmark Stack Implementation}
1515\label{sec:BenchmarkStackImplementation}
1516
1517\lstset{basicstyle=\linespread{0.9}\sf\small}
1518
1519Throughout, @/***/@ designates a counted redundant type annotation.
1520
1521\smallskip\noindent
1522\CFA
1523\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1524forall(otype T) struct stack_node {
1525        T value;
1526        stack_node(T) * next;
1527};
1528forall(otype T) void ?{}(stack(T) * s) { (&s->head){ 0 }; }
1529forall(otype T) void ?{}(stack(T) * s, stack(T) t) {
1530        stack_node(T) ** crnt = &s->head;
1531        for ( stack_node(T) * next = t.head; next; next = next->next ) {
1532                *crnt = ((stack_node(T) *)malloc()){ next->value }; /***/
1533                stack_node(T) * acrnt = *crnt;
1534                crnt = &acrnt->next;
1535        }
1536        *crnt = 0;
1537}
1538forall(otype T) stack(T) ?=?(stack(T) * s, stack(T) t) {
1539        if ( s->head == t.head ) return *s;
1540        clear(s);
1541        s{ t };
1542        return *s;
1543}
1544forall(otype T) void ^?{}(stack(T) * s) { clear(s); }
1545forall(otype T) _Bool empty(const stack(T) * s) { return s->head == 0; }
1546forall(otype T) void push(stack(T) * s, T value) {
1547        s->head = ((stack_node(T) *)malloc()){ value, s->head }; /***/
1548}
1549forall(otype T) T pop(stack(T) * s) {
1550        stack_node(T) * n = s->head;
1551        s->head = n->next;
1552        T x = n->value;
1553        ^n{};
1554        free(n);
1555        return x;
1556}
1557forall(otype T) void clear(stack(T) * s) {
1558        for ( stack_node(T) * next = s->head; next; ) {
1559                stack_node(T) * crnt = next;
1560                next = crnt->next;
1561                delete(crnt);
1562        }
1563        s->head = 0;
1564}
1565\end{lstlisting}
1566
1567\medskip\noindent
1568\CC
1569\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1570template<typename T> class stack {
1571        struct node {
1572                T value;
1573                node * next;
1574                node( const T & v, node * n = nullptr ) : value(v), next(n) {}
1575        };
1576        node * head;
1577        void copy(const stack<T>& o) {
1578                node ** crnt = &head;
1579                for ( node * next = o.head;; next; next = next->next ) {
1580                        *crnt = new node{ next->value }; /***/
1581                        crnt = &(*crnt)->next;
1582                }
1583                *crnt = nullptr;
1584        }
1585  public:
1586        stack() : head(nullptr) {}
1587        stack(const stack<T>& o) { copy(o); }
1588        stack(stack<T> && o) : head(o.head) { o.head = nullptr; }
1589        ~stack() { clear(); }
1590        stack & operator= (const stack<T>& o) {
1591                if ( this == &o ) return *this;
1592                clear();
1593                copy(o);
1594                return *this;
1595        }
1596        stack & operator= (stack<T> && o) {
1597                if ( this == &o ) return *this;
1598                head = o.head;
1599                o.head = nullptr;
1600                return *this;
1601        }
1602        bool empty() const { return head == nullptr; }
1603        void push(const T & value) { head = new node{ value, head };  /***/ }
1604        T pop() {
1605                node * n = head;
1606                head = n->next;
1607                T x = std::move(n->value);
1608                delete n;
1609                return x;
1610        }
1611        void clear() {
1612                for ( node * next = head; next; ) {
1613                        node * crnt = next;
1614                        next = crnt->next;
1615                        delete crnt;
1616                }
1617                head = nullptr;
1618        }
1619};
1620\end{lstlisting}
1621
1622\medskip\noindent
1623C
1624\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1625struct stack_node {
1626        void * value;
1627        struct stack_node * next;
1628};
1629struct stack new_stack() { return (struct stack){ NULL }; /***/ }
1630void copy_stack(struct stack * s, const struct stack * t, void * (*copy)(const void *)) {
1631        struct stack_node ** crnt = &s->head;
1632        for ( struct stack_node * next = t->head; next; next = next->next ) {
1633                *crnt = malloc(sizeof(struct stack_node)); /***/
1634                **crnt = (struct stack_node){ copy(next->value) }; /***/
1635                crnt = &(*crnt)->next;
1636        }
1637        *crnt = 0;
1638}
1639_Bool stack_empty(const struct stack * s) { return s->head == NULL; }
1640void push_stack(struct stack * s, void * value) {
1641        struct stack_node * n = malloc(sizeof(struct stack_node)); /***/
1642        *n = (struct stack_node){ value, s->head }; /***/
1643        s->head = n;
1644}
1645void * pop_stack(struct stack * s) {
1646        struct stack_node * n = s->head;
1647        s->head = n->next;
1648        void * x = n->value;
1649        free(n);
1650        return x;
1651}
1652void clear_stack(struct stack * s, void (*free_el)(void *)) {
1653        for ( struct stack_node * next = s->head; next; ) {
1654                struct stack_node * crnt = next;
1655                next = crnt->next;
1656                free_el(crnt->value);
1657                free(crnt);
1658        }
1659        s->head = NULL;
1660}
1661\end{lstlisting}
1662
1663\medskip\noindent
1664\CCV
1665\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1666stack::node::node( const object & v, node * n ) : value( v.new_copy() ), next( n ) {}
1667void stack::copy(const stack & o) {
1668        node ** crnt = &head;
1669        for ( node * next = o.head; next; next = next->next ) {
1670                *crnt = new node{ *next->value };
1671                crnt = &(*crnt)->next;
1672        }
1673        *crnt = nullptr;
1674}
1675stack::stack() : head(nullptr) {}
1676stack::stack(const stack & o) { copy(o); }
1677stack::stack(stack && o) : head(o.head) { o.head = nullptr; }
1678stack::~stack() { clear(); }
1679stack & stack::operator= (const stack & o) {
1680        if ( this == &o ) return *this;
1681        clear();
1682        copy(o);
1683        return *this;
1684}
1685stack & stack::operator= (stack && o) {
1686        if ( this == &o ) return *this;
1687        head = o.head;
1688        o.head = nullptr;
1689        return *this;
1690}
1691bool stack::empty() const { return head == nullptr; }
1692void stack::push(const object & value) { head = new node{ value, head }; /***/ }
1693ptr<object> stack::pop() {
1694        node * n = head;
1695        head = n->next;
1696        ptr<object> x = std::move(n->value);
1697        delete n;
1698        return x;
1699}
1700void stack::clear() {
1701        for ( node * next = head; next; ) {
1702                node * crnt = next;
1703                next = crnt->next;
1704                delete crnt;
1705        }
1706        head = nullptr;
1707}
1708\end{lstlisting}
1709
1710
1711\begin{comment}
1712
1713\subsubsection{bench.h}
1714(\texttt{bench.hpp} is similar.)
1715
1716\lstinputlisting{evaluation/bench.h}
1717
1718\subsection{C}
1719
1720\subsubsection{c-stack.h} ~
1721
1722\lstinputlisting{evaluation/c-stack.h}
1723
1724\subsubsection{c-stack.c} ~
1725
1726\lstinputlisting{evaluation/c-stack.c}
1727
1728\subsubsection{c-pair.h} ~
1729
1730\lstinputlisting{evaluation/c-pair.h}
1731
1732\subsubsection{c-pair.c} ~
1733
1734\lstinputlisting{evaluation/c-pair.c}
1735
1736\subsubsection{c-print.h} ~
1737
1738\lstinputlisting{evaluation/c-print.h}
1739
1740\subsubsection{c-print.c} ~
1741
1742\lstinputlisting{evaluation/c-print.c}
1743
1744\subsubsection{c-bench.c} ~
1745
1746\lstinputlisting{evaluation/c-bench.c}
1747
1748\subsection{\CFA}
1749
1750\subsubsection{cfa-stack.h} ~
1751
1752\lstinputlisting{evaluation/cfa-stack.h}
1753
1754\subsubsection{cfa-stack.c} ~
1755
1756\lstinputlisting{evaluation/cfa-stack.c}
1757
1758\subsubsection{cfa-print.h} ~
1759
1760\lstinputlisting{evaluation/cfa-print.h}
1761
1762\subsubsection{cfa-print.c} ~
1763
1764\lstinputlisting{evaluation/cfa-print.c}
1765
1766\subsubsection{cfa-bench.c} ~
1767
1768\lstinputlisting{evaluation/cfa-bench.c}
1769
1770\subsection{\CC}
1771
1772\subsubsection{cpp-stack.hpp} ~
1773
1774\lstinputlisting[language=c++]{evaluation/cpp-stack.hpp}
1775
1776\subsubsection{cpp-print.hpp} ~
1777
1778\lstinputlisting[language=c++]{evaluation/cpp-print.hpp}
1779
1780\subsubsection{cpp-bench.cpp} ~
1781
1782\lstinputlisting[language=c++]{evaluation/cpp-bench.cpp}
1783
1784\subsection{\CCV}
1785
1786\subsubsection{object.hpp} ~
1787
1788\lstinputlisting[language=c++]{evaluation/object.hpp}
1789
1790\subsubsection{cpp-vstack.hpp} ~
1791
1792\lstinputlisting[language=c++]{evaluation/cpp-vstack.hpp}
1793
1794\subsubsection{cpp-vstack.cpp} ~
1795
1796\lstinputlisting[language=c++]{evaluation/cpp-vstack.cpp}
1797
1798\subsubsection{cpp-vprint.hpp} ~
1799
1800\lstinputlisting[language=c++]{evaluation/cpp-vprint.hpp}
1801
1802\subsubsection{cpp-vbench.cpp} ~
1803
1804\lstinputlisting[language=c++]{evaluation/cpp-vbench.cpp}
1805\end{comment}
1806
1807\end{document}
1808
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1810% tab-width: 4 %
1811% compile-command: "make" %
1812% End: %
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