source: doc/generic_types/generic_types.tex @ 19b2133

aaron-thesisarm-ehcleanup-dtorsdeferred_resndemanglerjacob/cs343-translationjenkins-sandboxnew-astnew-ast-unique-exprnew-envno_listpersistent-indexerresolv-newwith_gc
Last change on this file since 19b2133 was 19b2133, checked in by Peter A. Buhr <pabuhr@…>, 5 years ago

fix citations

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47\makeatother
48
49% Useful macros
50\newcommand{\CFA}{C$\mathbf\forall$\xspace} % Cforall symbolic name
51\newcommand{\CC}{\rm C\kern-.1em\hbox{+\kern-.25em+}\xspace} % C++ symbolic name
52\newcommand{\CCeleven}{\rm C\kern-.1em\hbox{+\kern-.25em+}11\xspace} % C++11 symbolic name
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58\newcommand{\Textbf}[1]{{\color{red}\textbf{#1}}}
59
60% CFA programming language, based on ANSI C (with some gcc additions)
61\lstdefinelanguage{CFA}[ANSI]{C}{
62        morekeywords={_Alignas,_Alignof,__alignof,__alignof__,asm,__asm,__asm__,_At,_Atomic,__attribute,__attribute__,auto,
63                _Bool,catch,catchResume,choose,_Complex,__complex,__complex__,__const,__const__,disable,dtype,enable,__extension__,
64                fallthrough,fallthru,finally,forall,ftype,_Generic,_Imaginary,inline,__label__,lvalue,_Noreturn,one_t,otype,restrict,_Static_assert,
65                _Thread_local,throw,throwResume,trait,try,ttype,typeof,__typeof,__typeof__,zero_t},
66}%
67
68\lstset{
69language=CFA,
70columns=fullflexible,
71basicstyle=\linespread{0.9}\sf,                                                 % reduce line spacing and use sanserif font
72stringstyle=\tt,                                                                                % use typewriter font
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75%mathescape=true,                                                                               % LaTeX math escape in CFA code $...$
76escapechar=\$,                                                                                  % LaTeX escape in CFA code
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85        {<-}{$\leftarrow$}2 {=>}{$\Rightarrow$}2,
86moredelim=**[is][\color{red}]{`}{`},
87}% lstset
88
89% inline code @...@
90\lstMakeShortInline@%
91
92% ACM Information
93\citestyle{acmauthoryear}
94
95\acmJournal{PACMPL}
96
97\title{Generic and Tuple Types with Efficient Dynamic Layout in \CFA}
98
99\author{Aaron Moss}
100\email{a3moss@uwaterloo.ca}
101\author{Robert Schluntz}
102\email{rschlunt@uwaterloo.ca}
103\author{Peter Buhr}
104\email{pabuhr@uwaterloo.ca}
105\affiliation{%
106        \institution{University of Waterloo}
107        \department{David R. Cheriton School of Computer Science}
108        \streetaddress{Davis Centre, University of Waterloo}
109        \city{Waterloo}
110        \state{ON}
111        \postcode{N2L 3G1}
112        \country{Canada}
113}
114
115\terms{generic, tuple, variadic, types}
116\keywords{generic types, tuple types, variadic types, polymorphic functions, C, Cforall}
117
118\begin{CCSXML}
119<ccs2012>
120<concept>
121<concept_id>10011007.10011006.10011008.10011024.10011025</concept_id>
122<concept_desc>Software and its engineering~Polymorphism</concept_desc>
123<concept_significance>500</concept_significance>
124</concept>
125<concept>
126<concept_id>10011007.10011006.10011008.10011024.10011028</concept_id>
127<concept_desc>Software and its engineering~Data types and structures</concept_desc>
128<concept_significance>500</concept_significance>
129</concept>
130<concept>
131<concept_id>10011007.10011006.10011041.10011047</concept_id>
132<concept_desc>Software and its engineering~Source code generation</concept_desc>
133<concept_significance>300</concept_significance>
134</concept>
135</ccs2012>
136\end{CCSXML}
137
138\ccsdesc[500]{Software and its engineering~Polymorphism}
139\ccsdesc[500]{Software and its engineering~Data types and structures}
140\ccsdesc[300]{Software and its engineering~Source code generation}
141
142\begin{abstract}
143The 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.
144This installation base and the programmers producing it represent a massive software-engineering investment spanning decades and likely to continue for decades more.
145Nonetheless, C, first standardized over thirty years ago, lacks many features that make programming in more modern languages safer and more productive.
146The 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.
147Prior 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.
148Specifically, \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.
149This 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.
150\end{abstract}
151
152\begin{document}
153\maketitle
154
155
156\section{Introduction and Background}
157
158The 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.
159This installation base and the programmers producing it represent a massive software-engineering investment spanning decades and likely to continue for decades more.
160The \citet{TIOBE} ranks the top 5 most popular programming languages as: Java 16\%, \Textbf{C 7\%}, \Textbf{\CC 5\%}, \CS 4\%, Python 4\% = 36\%, where the next 50 languages are less than 3\% each with a long tail.
161The top 3 rankings over the past 30 years are:
162\lstDeleteShortInline@%
163\begin{center}
164\setlength{\tabcolsep}{10pt}
165\begin{tabular}{@{}r|c|c|c|c|c|c|c@{}}
166                & 2017  & 2012  & 2007  & 2002  & 1997  & 1992  & 1987          \\
167\hline
168Java    & 1             & 1             & 1             & 1             & 12    & -             & -                     \\
169\hline
170\Textbf{C}      & \Textbf{2}& \Textbf{2}& \Textbf{2}& \Textbf{2}& \Textbf{1}& \Textbf{1}& \Textbf{1}    \\
171\hline
172\CC             & 3             & 3             & 3             & 3             & 2             & 2             & 4                     \\
173\end{tabular}
174\end{center}
175\lstMakeShortInline@%
176Love it or hate it, C is extremely popular, highly used, and one of the few systems languages.
177In many cases, \CC is often used solely as a better C.
178Nonetheless, C, first standardized over thirty years ago, lacks many features that make programming in more modern languages safer and more productive.
179
180\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.
181The four key design goals for \CFA~\citep{Bilson03} are:
182(1) The behaviour of standard C code must remain the same when translated by a \CFA compiler as when translated by a C compiler;
183(2) Standard C code must be as fast and as small when translated by a \CFA compiler as when translated by a C compiler;
184(3) \CFA code must be at least as portable as standard C code;
185(4) Extensions introduced by \CFA must be translated in the most efficient way possible.
186These 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.
187\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.
188
189\CFA is currently implemented as a source-to-source translator from \CFA to the GCC-dialect of C~\citep{GCCExtensions}, allowing it to leverage the portability and code optimizations provided by GCC, meeting goals (1)-(3).
190Ultimately, a compiler is necessary for advanced features and optimal performance.
191
192This 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.
193Specifically, 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.
194The new constructs are empirically compared with both standard C and \CC; the results show the new design is comparable in performance.
195
196
197\subsection{Polymorphic Functions}
198\label{sec:poly-fns}
199
200\CFA's polymorphism was originally formalized by \citet{Ditchfield92}, and first implemented by \citet{Bilson03}.
201The signature feature of \CFA is parametric-polymorphic functions~\citep{forceone:impl,Cormack90,Duggan96} with functions generalized using a @forall@ clause (giving the language its name):
202\begin{lstlisting}
203`forall( otype T )` T identity( T val ) { return val; }
204int forty_two = identity( 42 );                         $\C{// T is bound to int, forty\_two == 42}$
205\end{lstlisting}
206The @identity@ function above can be applied to any complete \emph{object type} (or @otype@).
207The 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.
208The \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.
209If this extra information is not needed, \eg for a pointer, the type parameter can be declared as a \emph{data type} (or @dtype@).
210
211In \CFA, the polymorphism runtime-cost is spread over each polymorphic call, due to passing more arguments to polymorphic functions;
212the experiments in Section~\ref{sec:eval} show this overhead is similar to \CC virtual-function calls.
213A design advantage is that, unlike \CC template-functions, \CFA polymorphic-functions are compatible with C \emph{separate compilation}, preventing compilation and code bloat.
214
215Since bare polymorphic-types provide a restricted set of available operations, \CFA provides a \emph{type assertion}~\cite{alphard} mechanism to provide further type information, where type assertions may be variable or function declarations that depend on a polymorphic type-variable.
216For example, the function @twice@ can be defined using the \CFA syntax for operator overloading:
217\newpage
218\begin{lstlisting}
219forall( otype T `| { T ?+?(T, T); }` ) T twice( T x ) { return x + x; } $\C{// ? denotes operands}$
220int val = twice( twice( 3.7 ) );
221\end{lstlisting}
222which works for any type @T@ with a matching addition operator.
223The 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@.
224There 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.
225The first approach has a late conversion from @double@ to @int@ on the final assignment, while the second has an eager conversion to @int@.
226\CFA minimizes the number of conversions and their potential to lose information, so it selects the first approach, which corresponds with C-programmer intuition.
227
228Crucial to the design of a new programming language are the libraries to access thousands of external software features.
229Like \CC, \CFA inherits a massive compatible library-base, where other programming languages must rewrite or provide fragile inter-language communication with C.
230A simple example is leveraging the existing type-unsafe (@void *@) C @bsearch@ to binary search a sorted floating-point array:
231\begin{lstlisting}
232void * bsearch( const void * key, const void * base, size_t nmemb, size_t size,
233                                int (* compar)( const void *, const void * ));
234int comp( const void * t1, const void * t2 ) { return *(double *)t1 < *(double *)t2 ? -1 :
235                                *(double *)t2 < *(double *)t1 ? 1 : 0; }
236double vals[10] = { /* 10 floating-point values */ };
237double key = 5.0;
238double * val = (double *)bsearch( &key, vals, 10, sizeof(vals[0]), comp );      $\C{// search sorted array}$
239\end{lstlisting}
240which can be augmented simply with a generalized, type-safe, \CFA-overloaded wrappers:
241\begin{lstlisting}
242forall( otype T | { int ?<?( T, T ); } ) T * bsearch( T key, const T * arr, size_t size ) {
243        int comp( const void * t1, const void * t2 ) { /* as above with double changed to T */ }
244        return (T *)bsearch( &key, arr, size, sizeof(T), comp ); }
245forall( otype T | { int ?<?( T, T ); } ) unsigned int bsearch( T key, const T * arr, size_t size ) {
246        T *result = bsearch( key, arr, size );  $\C{// call first version}$
247        return result ? result - arr : size; }  $\C{// pointer subtraction includes sizeof(T)}$
248double * val = bsearch( 5.0, vals, 10 );        $\C{// selection based on return type}$
249int posn = bsearch( 5.0, vals, 10 );
250\end{lstlisting}
251The nested function @comp@ provides the hidden interface from typed \CFA to untyped (@void *@) C, plus the cast of the result.
252Providing a hidden @comp@ function in \CC is awkward as lambdas do not use C calling-conventions and template declarations cannot appear at block scope.
253As well, an alternate kind of return is made available: position versus pointer to found element.
254\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@.
255
256\CFA has replacement libraries condensing hundreds of existing C functions into tens of \CFA overloaded functions, all without rewriting the actual computations.
257For example, it is possible to write a type-safe \CFA wrapper @malloc@ based on the C @malloc@:
258\begin{lstlisting}
259forall( dtype T | sized(T) ) T * malloc( void ) { return (T *)malloc( sizeof(T) ); }
260int * ip = malloc();                                            $\C{// select type and size from left-hand side}$
261double * dp = malloc();
262struct S {...} * sp = malloc();
263\end{lstlisting}
264where the return type supplies the type/size of the allocation, which is impossible in most type systems.
265
266Call-site inferencing and nested functions provide a localized form of inheritance.
267For example, the \CFA @qsort@ only sorts in ascending order using @<@.
268However, it is trivial to locally change this behaviour:
269\begin{lstlisting}
270forall( otype T | { int ?<?( T, T ); } ) void qsort( const T * arr, size_t size ) { /* use C qsort */ }
271{       int ?<?( double x, double y ) { return x `>` y; }       $\C{// locally override behaviour}$
272        qsort( vals, size );                                    $\C{// descending sort}$
273}
274\end{lstlisting}
275Within the block, the nested version of @<@ performs @>@ and this local version overrides the built-in @<@ so it is passed to @qsort@.
276Hence, programmers can easily form local environments, adding and modifying appropriate functions, to maximize reuse of other existing functions and types.
277
278Finally, \CFA allows variable overloading:
279\lstDeleteShortInline@%
280\par\smallskip
281\begin{tabular}{@{}l@{\hspace{\parindent}}|@{\hspace{\parindent}}l@{}}
282\begin{lstlisting}
283short int MAX = ...;
284int MAX = ...;
285double MAX = ...;
286\end{lstlisting}
287&
288\begin{lstlisting}
289short int s = MAX;  // select correct MAX
290int i = MAX;
291double d = MAX;
292\end{lstlisting}
293\end{tabular}
294\smallskip\par\noindent
295\lstMakeShortInline@%
296Here, the single name @MAX@ replaces all the C type-specific names: @SHRT_MAX@, @INT_MAX@, @DBL_MAX@.
297As 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.
298In addition, several operations are defined in terms values @0@ and @1@, \eg:
299\begin{lstlisting}
300int x;
301if (x) x++                                                                      $\C{// if (x != 0) x += 1;}$
302\end{lstlisting}
303Every 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.
304Due 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.
305The 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.
306
307
308\subsection{Traits}
309
310\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:
311\begin{lstlisting}
312trait summable( otype T ) {
313        void ?{}( T *, zero_t );                                $\C{// constructor from 0 literal}$
314        T ?+?( T, T );                                                  $\C{// assortment of additions}$
315        T ?+=?( T *, T );
316        T ++?( T * );
317        T ?++( T * ); };
318forall( otype T `| summable( T )` ) T sum( T a[$\,$], size_t size ) {  // use trait
319        `T` total = { `0` };                                    $\C{// instantiate T from 0 by calling its constructor}$
320        for ( unsigned int i = 0; i < size; i += 1 ) total `+=` a[i]; $\C{// select appropriate +}$
321        return total; }
322\end{lstlisting}
323
324In 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:
325\begin{lstlisting}
326trait otype( dtype T | sized(T) ) {  // sized is a pseudo-trait for types with known size and alignment
327        void ?{}( T * );                                                $\C{// default constructor}$
328        void ?{}( T *, T );                                             $\C{// copy constructor}$
329        void ?=?( T *, T );                                             $\C{// assignment operator}$
330        void ^?{}( T * ); };                                    $\C{// destructor}$
331\end{lstlisting}
332Given 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.
333
334In 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.
335Hence, trait names play no part in type equivalence;
336the names are simply macros for a list of polymorphic assertions, which are expanded at usage sites.
337Nevertheless, trait names form a logical subtype-hierarchy with @dtype@ at the top, where traits often contain overlapping assertions, \eg operator @+@.
338Traits are used like interfaces in Java or abstract base-classes in \CC, but without the nominal inheritance-relationships.
339Instead, 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~\citep{Go} interfaces.
340Hence, 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.
341(Nominal inheritance can be approximated with traits using marker variables or functions, as is done in Go.)
342
343% Nominal inheritance can be simulated with traits using marker variables or functions:
344% \begin{lstlisting}
345% trait nominal(otype T) {
346%     T is_nominal;
347% };
348% int is_nominal;                                                               $\C{// int now satisfies the nominal trait}$
349% \end{lstlisting}
350%
351% 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:
352% \begin{lstlisting}
353% trait pointer_like(otype Ptr, otype El) {
354%     lvalue El *?(Ptr);                                                $\C{// Ptr can be dereferenced into a modifiable value of type El}$
355% }
356% struct list {
357%     int value;
358%     list *next;                                                               $\C{// may omit "struct" on type names as in \CC}$
359% };
360% typedef list *list_iterator;
361%
362% lvalue int *?( list_iterator it ) { return it->value; }
363% \end{lstlisting}
364% 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@).
365% 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.
366
367
368\section{Generic Types}
369
370One of the known shortcomings of standard C is that it does not provide reusable type-safe abstractions for generic data structures and algorithms.
371Broadly speaking, there are three approaches to implement abstract data-structures in C.
372One approach is to write bespoke data structures for each context in which they are needed.
373While 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.
374A 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.
375However, 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.
376A 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.
377Furthermore, writing and using preprocessor macros can be unnatural and inflexible.
378
379\CC, Java, and other languages use \emph{generic types} to produce type-safe abstract data-types.
380\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.
381However, for known concrete parameters, the generic-type definition can be inlined, like \CC templates.
382
383A 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:
384\begin{lstlisting}
385forall( otype R, otype S ) struct pair {
386        R first;
387        S second;
388};
389forall( otype T ) T value( pair( const char *, T ) p ) { return p.second; }
390forall( dtype F, otype T ) T value_p( pair( F *, T * ) p ) { return *p.second; }
391pair( const char *, int ) p = { "magic", 42 };
392int magic = value( p );
393pair( void *, int * ) q = { 0, &p.second };
394magic = value_p( q );
395double d = 1.0;
396pair( double *, double * ) r = { &d, &d };
397d = value_p( r );
398\end{lstlisting}
399
400\CFA classifies generic types as either \emph{concrete} or \emph{dynamic}.
401Concrete types have a fixed memory layout regardless of type parameters, while dynamic types vary in memory layout depending on their type parameters.
402A type may have polymorphic parameters but still be concrete, called \emph{dtype-static}.
403Polymorphic 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.
404
405\CFA generic types also allow checked argument-constraints.
406For example, the following declaration of a sorted set-type ensures the set key supports equality and relational comparison:
407\begin{lstlisting}
408forall( otype Key | { _Bool ?==?(Key, Key); _Bool ?<?(Key, Key); } ) struct sorted_set;
409\end{lstlisting}
410
411
412\subsection{Concrete Generic-Types}
413
414The \CFA translator template-expands concrete generic-types into new structure types, affording maximal inlining.
415To 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.
416For example, a function declaration that accepts or returns a concrete generic-type produces a declaration for the instantiated struct in the same scope, which all callers may reuse.
417For example, the concrete instantiation for @pair( const char *, int )@ is:
418\begin{lstlisting}
419struct _pair_conc1 {
420        const char * first;
421        int second;
422};
423\end{lstlisting}
424
425A concrete generic-type with dtype-static parameters is also expanded to a structure type, but this type is used for all matching instantiations.
426In 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:
427\begin{lstlisting}
428struct _pair_conc0 {
429        void * first;
430        void * second;
431};
432\end{lstlisting}
433
434
435\subsection{Dynamic Generic-Types}
436
437Though \CFA implements concrete generic-types efficiently, it also has a fully general system for dynamic generic types.
438As 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.
439Dynamic generic-types also have an \emph{offset array} containing structure-member offsets.
440A dynamic generic-union needs no such offset array, as all members are at offset 0, but size and alignment are still necessary.
441Access 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.
442
443The offset arrays are statically generated where possible.
444If 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;
445if 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.
446As 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 )@.
447The offset array @_offsetof_pair@ is generated at the call site as @size_t _offsetof_pair[] = { offsetof(_pair_conc1, first), offsetof(_pair_conc1, second) }@.
448
449In some cases the offset arrays cannot be statically generated.
450For 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.
451\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.
452The \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.
453These 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).
454Results of these layout functions are cached so that they are only computed once per type per function. %, as in the example below for @pair@.
455Layout functions also allow generic types to be used in a function definition without reflecting them in the function signature.
456For 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.
457This function could acquire the layout for @set(T)@ by calling its layout function with the layout of @T@ implicitly passed into the function.
458
459Whether a type is concrete, dtype-static, or dynamic is decided solely on the type parameters and @forall@ clause on a declaration.
460This 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.
461If 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.
462
463
464\subsection{Applications}
465\label{sec:generic-apps}
466
467The reuse of dtype-static structure instantiations enables useful programming patterns at zero runtime cost.
468The 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@:
469\begin{lstlisting}
470forall(dtype T) int lexcmp( pair( T *, T * ) * a, pair( T *, T * ) * b, int (* cmp)( T *, T * ) ) {
471        return cmp( a->first, b->first ) ? : cmp( a->second, b->second );
472}
473\end{lstlisting}
474%       int c = cmp( a->first, b->first );
475%       if ( c == 0 ) c = cmp( a->second, b->second );
476%       return c;
477Since @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.
478
479Another useful pattern enabled by reused dtype-static type instantiations is zero-cost \emph{tag-structures}.
480Sometimes information is only used for type-checking and can be omitted at runtime, \eg:
481\begin{lstlisting}
482forall(dtype Unit) struct scalar { unsigned long value; };
483struct metres {};
484struct litres {};
485
486forall(dtype U) scalar(U) ?+?( scalar(U) a, scalar(U) b ) {
487        return (scalar(U)){ a.value + b.value };
488}
489scalar(metres) half_marathon = { 21093 };
490scalar(litres) swimming_pool = { 2500000 };
491scalar(metres) marathon = half_marathon + half_marathon;
492scalar(litres) two_pools = swimming_pool + swimming_pool;
493marathon + swimming_pool;                                       $\C{// compilation ERROR}$
494\end{lstlisting}
495@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 @?+?@.
496These implementations may even be separately compiled, unlike \CC template functions.
497However, the \CFA type-checker ensures matching types are used by all calls to @?+?@, preventing nonsensical computations like adding a length to a volume.
498
499
500\section{Tuples}
501\label{sec:tuples}
502
503In many languages, functions can return at most one value;
504however, many operations have multiple outcomes, some exceptional.
505Consider C's @div@ and @remquo@ functions, which return the quotient and remainder for a division of integer and floating-point values, respectively.
506\begin{lstlisting}
507typedef struct { int quo, rem; } div_t;         $\C{// from include stdlib.h}$
508div_t div( int num, int den );
509double remquo( double num, double den, int * quo );
510div_t qr = div( 13, 5 );                                        $\C{// return quotient/remainder aggregate}$
511int q;
512double r = remquo( 13.5, 5.2, &q );                     $\C{// return remainder, alias quotient}$
513\end{lstlisting}
514@div@ aggregates the quotient/remainder in a structure, while @remquo@ aliases a parameter to an argument.
515Both approaches are awkward.
516Alternatively, a programming language can directly support returning multiple values, \eg in \CFA:
517\begin{lstlisting}
518[ int, int ] div( int num, int den );           $\C{// return two integers}$
519[ double, double ] div( double num, double den ); $\C{// return two doubles}$
520int q, r;                                                                       $\C{// overloaded variable names}$
521double q, r;
522[ q, r ] = div( 13, 5 );                                        $\C{// select appropriate div and q, r}$
523[ q, r ] = div( 13.5, 5.2 );                            $\C{// assign into tuple}$
524\end{lstlisting}
525Clearly, this approach is straightforward to understand and use;
526therefore, why do few programming languages support this obvious feature or provide it awkwardly?
527The answer is that there are complex consequences that cascade through multiple aspects of the language, especially the type-system.
528This section show these consequences and how \CFA handles them.
529
530
531\subsection{Tuple Expressions}
532
533The addition of multiple-return-value functions (MRVF) are useless without a syntax for accepting multiple values at the call-site.
534The simplest mechanism for capturing the return values is variable assignment, allowing the values to be retrieved directly.
535As 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}.
536
537However, 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:
538\begin{lstlisting}
539printf( "%d %d\n", div( 13, 5 ) );                      $\C{// return values seperated into arguments}$
540\end{lstlisting}
541Here, the values returned by @div@ are composed with the call to @printf@ by flattening the tuple into separate arguments.
542However, the \CFA type-system must support significantly more complex composition:
543\begin{lstlisting}
544[ int, int ] foo$\(_1\)$( int );
545[ double ] foo$\(_2\)$( int );
546void bar( int, double, double );
547bar( foo( 3 ), foo( 3 ) );
548\end{lstlisting}
549The type-resolver only has the tuple return-types to resolve the call to @bar@ as the @foo@ parameters are identical, which involves unifying the possible @foo@ functions with @bar@'s parameter list.
550No combination of @foo@s are an exact match with @bar@'s parameters, so the resolver applies C conversions.
551The minimal cost is @bar( foo@$_1$@( 3 ), foo@$_2$@( 3 ) )@, giving (@int@, {\color{green}@int@}, @double@) to (@int@, {\color{green}@double@}, @double@) with one {\color{green}safe} (widening) conversion from @int@ to @double@ versus ({\color{red}@double@}, {\color{green}@int@}, {\color{green}@int@}) to ({\color{red}@int@}, {\color{green}@double@}, {\color{green}@double@}) with one {\color{red}unsafe} (narrowing) conversion from @double@ to @int@ and two safe conversions.
552
553
554\subsection{Tuple Variables}
555
556An important observation from function composition is that new variable names are not required to initialize parameters from an MRVF.
557\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:
558\begin{lstlisting}
559[ int, int ] qr = div( 13, 5 );                         $\C{// tuple-variable declaration and initialization}$
560[ double, double ] qr = div( 13.5, 5.2 );
561\end{lstlisting}
562where the tuple variable-name serves the same purpose as the parameter name(s).
563Tuple variables can be composed of any types, except for array types, since array sizes are generally unknown.
564
565One way to access the tuple-variable components is with assignment or composition:
566\begin{lstlisting}
567[ q, r ] = qr;                                                          $\C{// access tuple-variable components}$
568printf( "%d %d\n", qr );
569\end{lstlisting}
570\CFA also supports \emph{tuple indexing} to access single components of a tuple expression:
571\begin{lstlisting}
572[int, int] * p = &qr;                                           $\C{// tuple pointer}$
573int rem = qr.1;                                                         $\C{// access remainder}$
574int quo = div( 13, 5 ).0;                                       $\C{// access quotient}$
575p->0 = 5;                                                                       $\C{// change quotient}$
576bar( qr.1, qr );                                                        $\C{// pass remainder and quotient/remainder}$
577rem = [42, div( 13, 5 )].0.1;                           $\C{// access 2nd component of 1st component of tuple expression}$
578\end{lstlisting}
579
580
581\subsection{Flattening and Restructuring}
582
583In function call contexts, tuples support implicit flattening and restructuring conversions.
584Tuple flattening recursively expands a tuple into the list of its basic components.
585Tuple structuring packages a list of expressions into a value of tuple type, \eg:
586\lstDeleteShortInline@%
587\par\smallskip
588\begin{tabular}{@{}l@{\hspace{\parindent}}|@{\hspace{\parindent}}l@{}}
589\begin{lstlisting}
590int f( int, int );
591int g( [int, int] );
592int h( int, [int, int] );
593[int, int] x;
594\end{lstlisting}
595&
596\begin{lstlisting}
597int y;
598f( x );                 $\C[1in]{// flatten}$
599g( y, 10 );             $\C{// structure}$
600h( x, y );              $\C{// flatten and structure}\CRT{}$
601\end{lstlisting}
602\end{tabular}
603\smallskip\par\noindent
604\lstMakeShortInline@%
605In the call to @f@, @x@ is implicitly flattened so the components of @x@ are passed as the two arguments.
606In 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@.
607Finally, 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]@.
608The 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.
609
610
611\subsection{Tuple Assignment}
612
613An assignment where the left side is a tuple type is called \emph{tuple assignment}.
614There 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.
615\lstDeleteShortInline@%
616\par\smallskip
617\begin{tabular}{@{}l@{\hspace{\parindent}}|@{\hspace{\parindent}}l@{}}
618\begin{lstlisting}
619int x = 10;
620double y = 3.5;
621[int, double] z;
622
623\end{lstlisting}
624&
625\begin{lstlisting}
626z = [x, y];             $\C[1in]{// multiple assignment}$
627[x, y] = z;             $\C{// multiple assignment}$
628z = 10;                 $\C{// mass assignment}$
629[y, x] = 3.14$\C{// mass assignment}\CRT{}$
630\end{lstlisting}
631\end{tabular}
632\smallskip\par\noindent
633\lstMakeShortInline@%
634Both kinds of tuple assignment have parallel semantics, so that each value on the left and right side is evaluated before any assignments occur.
635As 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]@.
636This 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.
637For example, @[y, x] = 3.14@ performs the assignments @y = 3.14@ and @x = 3.14@, yielding @y == 3.14@ and @x == 3@;
638whereas C cascading assignment @y = x = 3.14@ performs the assignments @x = 3.14@ and @y = x@, yielding @3@ in @y@ and @x@.
639Finally, 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.
640This example shows mass, multiple, and cascading assignment used in one expression:
641\begin{lstlisting}
642void f( [int, int] );
643f( [x, y] = z = 1.5 );                                          $\C{// assignments in parameter list}$
644\end{lstlisting}
645
646
647\subsection{Member Access}
648
649It is also possible to access multiple fields from a single expression using a \emph{member-access}.
650The result is a single tuple-valued expression whose type is the tuple of the types of the members, \eg:
651\begin{lstlisting}
652struct S { int x; double y; char * z; } s;
653s.[x, y, z] = 0;
654\end{lstlisting}
655Here, the mass assignment sets all members of @s@ to zero.
656Since 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).
657\lstDeleteShortInline@%
658\par\smallskip
659\begin{tabular}{@{}l@{\hspace{\parindent}}|@{\hspace{\parindent}}l@{}}
660\begin{lstlisting}
661[int, int, long, double] x;
662void f( double, long );
663
664\end{lstlisting}
665&
666\begin{lstlisting}
667x.[0, 1] = x.[1, 0];    $\C[1in]{// rearrange: [x.0, x.1] = [x.1, x.0]}$
668f( x.[0, 3] );            $\C{// drop: f(x.0, x.3)}\CRT{}$
669[int, int, int] y = x.[2, 0, 2]; // duplicate: [y.0, y.1, y.2] = [x.2, x.0.x.2]
670\end{lstlisting}
671\end{tabular}
672\smallskip\par\noindent
673\lstMakeShortInline@%
674It is also possible for a member access to contain other member accesses, \eg:
675\begin{lstlisting}
676struct A { double i; int j; };
677struct B { int * k; short l; };
678struct C { int x; A y; B z; } v;
679v.[x, y.[i, j], z.k];                                           $\C{// [v.x, [v.y.i, v.y.j], v.z.k]}$
680\end{lstlisting}
681
682
683\begin{comment}
684\subsection{Casting}
685
686In C, the cast operator is used to explicitly convert between types.
687In \CFA, the cast operator has a secondary use as type ascription.
688That 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:
689\begin{lstlisting}
690int f();     // (1)
691double f()// (2)
692
693f();       // ambiguous - (1),(2) both equally viable
694(int)f()// choose (2)
695\end{lstlisting}
696
697Since casting is a fundamental operation in \CFA, casts should be given a meaningful interpretation in the context of tuples.
698Taking a look at standard C provides some guidance with respect to the way casts should work with tuples:
699\begin{lstlisting}
700int f();
701void g();
702
703(void)f()// (1)
704(int)g()// (2)
705\end{lstlisting}
706In C, (1) is a valid cast, which calls @f@ and discards its result.
707On the other hand, (2) is invalid, because @g@ does not produce a result, so requesting an @int@ to materialize from nothing is nonsensical.
708Generalizing 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.
709
710Formally, 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 $T_i$.
711Excess 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.
712This approach follows naturally from the way that a cast to @void@ works in C.
713
714For example, in
715\begin{lstlisting}
716[int, int, int] f();
717[int, [int, int], int] g();
718
719([int, double])f();           $\C{// (1)}$
720([int, int, int])g();         $\C{// (2)}$
721([void, [int, int]])g();      $\C{// (3)}$
722([int, int, int, int])g();    $\C{// (4)}$
723([int, [int, int, int]])g()$\C{// (5)}$
724\end{lstlisting}
725
726(1) discards the last element of the return value and converts the second element to @double@.
727Since @int@ is effectively a 1-element tuple, (2) discards the second component of the second element of the return value of @g@.
728If @g@ is free of side effects, this expression is equivalent to @[(int)(g().0), (int)(g().1.0), (int)(g().2)]@.
729Since @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)]@).
730
731Note 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.}.
732As such, (4) is invalid because the cast target type contains 4 components, while the source type contains only 3.
733Similarly, (5) is invalid because the cast @([int, int, int])(g().1)@ is invalid.
734That is, it is invalid to cast @[int, int]@ to @[int, int, int]@.
735\end{comment}
736
737
738\subsection{Polymorphism}
739
740Tuples also integrate with \CFA polymorphism as a kind of generic type.
741Due 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:
742\begin{lstlisting}
743forall(otype T, dtype U) void f( T x, U * y );
744f( [5, "hello"] );
745\end{lstlisting}
746where @[5, "hello"]@ is flattened, giving argument list @5, "hello"@, and @T@ binds to @int@ and @U@ binds to @const char@.
747Tuples, however, may contain polymorphic components.
748For example, a plus operator can be written to add two triples together.
749\begin{lstlisting}
750forall(otype T | { T ?+?( T, T ); }) [T, T, T] ?+?( [T, T, T] x, [T, T, T] y ) {
751        return [x.0 + y.0, x.1 + y.1, x.2 + y.2];
752}
753[int, int, int] x;
754int i1, i2, i3;
755[i1, i2, i3] = x + ([10, 20, 30]);
756\end{lstlisting}
757
758Flattening and restructuring conversions are also applied to tuple types in polymorphic type assertions.
759\begin{lstlisting}
760int f( [int, double], double );
761forall(otype T, otype U | { T f( T, U, U ); }) void g( T, U );
762g( 5, 10.21 );
763\end{lstlisting}
764Hence, function parameter and return lists are flattened for the purposes of type unification allowing the example to pass expression resolution.
765This relaxation is possible by extending the thunk scheme described by \citet{Bilson03}.
766Whenever 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:
767\begin{lstlisting}
768int _thunk( int _p0, double _p1, double _p2 ) { return f( [_p0, _p1], _p2 ); }
769\end{lstlisting}
770so the thunk provides flattening and structuring conversions to inferred functions, improving the compatibility of tuples and polymorphism.
771These thunks take advantage of GCC C nested-functions to produce closures that have the usual function pointer signature.
772
773
774\subsection{Variadic Tuples}
775\label{sec:variadic-tuples}
776
777To define variadic functions, \CFA adds a new kind of type parameter, @ttype@ (tuple type).
778Matching against a @ttype@ parameter consumes all remaining argument components and packages them into a tuple, binding to the resulting tuple of types.
779In 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.
780As such, @ttype@ variables are also called \emph{argument packs}.
781
782Like variadic templates, the main way to manipulate @ttype@ polymorphic functions is via recursion.
783Since nothing is known about a parameter pack by default, assertion parameters are key to doing anything meaningful.
784Unlike variadic templates, @ttype@ polymorphic functions can be separately compiled.
785For example, a generalized @sum@ function written using @ttype@:
786\begin{lstlisting}
787int sum$\(_0\)$() { return 0; }
788forall(ttype Params | { int sum( Params ); } ) int sum$\(_1\)$( int x, Params rest ) {
789        return x + sum( rest );
790}
791sum( 10, 20, 30 );
792\end{lstlisting}
793Since @sum@\(_0\) does not accept any arguments, it is not a valid candidate function for the call @sum(10, 20, 30)@.
794In 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]@.
795The process continues, @Params@ is bound to @[]@, requiring an assertion @int sum()@, which matches @sum@\(_0\) and terminates the recursion.
796Effectively, 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))@.
797
798It is reasonable to take the @sum@ function a step further to enforce a minimum number of arguments:
799\begin{lstlisting}
800int sum( int x, int y ) { return x + y; }
801forall(ttype Params | { int sum( int, Params ); } ) int sum( int x, int y, Params rest ) {
802        return sum( x + y, rest );
803}
804\end{lstlisting}
805One more step permits the summation of any summable type with all arguments of the same type:
806\begin{lstlisting}
807trait summable(otype T) {
808        T ?+?( T, T );
809};
810forall(otype R | summable( R ) ) R sum( R x, R y ) {
811        return x + y;
812}
813forall(otype R, ttype Params | summable(R) | { R sum(R, Params); } ) R sum(R x, R y, Params rest) {
814        return sum( x + y, rest );
815}
816\end{lstlisting}
817Unlike C variadic functions, it is unnecessary to hard code the number and expected types.
818Furthermore, this code is extendable so any user-defined type with a @?+?@ operator.
819Summing arbitrary heterogeneous lists is possible with similar code by adding the appropriate type variables and addition operators.
820
821It is also possible to write a type-safe variadic print function to replace @printf@:
822\begin{lstlisting}
823struct S { int x, y; };
824forall(otype T, ttype Params | { void print(T); void print(Params); }) void print(T arg, Params rest) {
825        print(arg);  print(rest);
826}
827void print( char * x ) { printf( "%s", x ); }
828void print( int x ) { printf( "%d", x ); }
829void print( S s ) { print( "{ ", s.x, ",", s.y, " }" ); }
830print( "s = ", (S){ 1, 2 }, "\n" );
831\end{lstlisting}
832This example showcases a variadic-template-like decomposition of the provided argument list.
833The individual @print@ functions allow printing a single element of a type.
834The polymorphic @print@ allows printing any list of types, as long as each individual type has a @print@ function.
835The individual print functions can be used to build up more complicated @print@ functions, such as for @S@, which is something that cannot be done with @printf@ in C.
836
837Finally, it is possible to use @ttype@ polymorphism to provide arbitrary argument forwarding functions.
838For example, it is possible to write @new@ as a library function:
839\begin{lstlisting}
840forall( otype R, otype S ) void ?{}( pair(R, S) *, R, S );
841forall( dtype T, ttype Params | sized(T) | { void ?{}( T *, Params ); } ) T * new( Params p ) {
842        return ((T *)malloc()){ p };                    $\C{// construct into result of malloc}$
843}
844pair( int, char ) * x = new( 42, '!' );
845\end{lstlisting}
846The @new@ function provides the combination of type-safe @malloc@ with a \CFA constructor call, making it impossible to forget constructing dynamically allocated objects.
847This function provides the type-safety of @new@ in \CC, without the need to specify the allocated type again, thanks to return-type inference.
848
849
850\subsection{Implementation}
851
852Tuples are implemented in the \CFA translator via a transformation into generic types.
853For each $N$, the first time an $N$-tuple is seen in a scope a generic type with $N$ type parameters is generated, \eg:
854\begin{lstlisting}
855[int, int] f() {
856        [double, double] x;
857        [int, double, int] y;
858}
859\end{lstlisting}
860is transformed into:
861\begin{lstlisting}
862// generated before the first 2-tuple
863forall(dtype T0, dtype T1 | sized(T0) | sized(T1)) struct _tuple2 {
864        T0 field_0;
865        T1 field_1;
866};
867_tuple2(int, int) f() {
868        _tuple2(double, double) x;
869        // generated before the first 3-tuple
870        forall(dtype T0, dtype T1, dtype T2 | sized(T0) | sized(T1) | sized(T2)) struct _tuple3 {
871                T0 field_0;
872                T1 field_1;
873                T2 field_2;
874        };
875        _tuple3(int, double, int) y;
876}
877\end{lstlisting}
878Tuple expressions are then simply converted directly into compound literals:
879\begin{lstlisting}
880[5, 'x', 1.24];
881\end{lstlisting}
882becomes:
883\begin{lstlisting}
884(_tuple3(int, char, double)){ 5, 'x', 1.24 };
885\end{lstlisting}
886
887\begin{comment}
888Since tuples are essentially structures, tuple indexing expressions are just field accesses:
889\begin{lstlisting}
890void f(int, [double, char]);
891[int, double] x;
892
893x.0+x.1;
894printf("%d %g\n", x);
895f(x, 'z');
896\end{lstlisting}
897Is transformed into:
898\begin{lstlisting}
899void f(int, _tuple2(double, char));
900_tuple2(int, double) x;
901
902x.field_0+x.field_1;
903printf("%d %g\n", x.field_0, x.field_1);
904f(x.field_0, (_tuple2){ x.field_1, 'z' });
905\end{lstlisting}
906Note that due to flattening, @x@ used in the argument position is converted into the list of its fields.
907In the call to @f@, the second and third argument components are structured into a tuple argument.
908Similarly, tuple member expressions are recursively expanded into a list of member access expressions.
909
910Expressions that may contain side effects are made into \emph{unique expressions} before being expanded by the flattening conversion.
911Each unique expression is assigned an identifier and is guaranteed to be executed exactly once:
912\begin{lstlisting}
913void g(int, double);
914[int, double] h();
915g(h());
916\end{lstlisting}
917Internally, this expression is converted to two variables and an expression:
918\begin{lstlisting}
919void g(int, double);
920[int, double] h();
921
922_Bool _unq0_finished_ = 0;
923[int, double] _unq0;
924g(
925        (_unq0_finished_ ? _unq0 : (_unq0 = f(), _unq0_finished_ = 1, _unq0)).0,
926        (_unq0_finished_ ? _unq0 : (_unq0 = f(), _unq0_finished_ = 1, _unq0)).1,
927);
928\end{lstlisting}
929Since argument evaluation order is not specified by the C programming language, this scheme is built to work regardless of evaluation order.
930The first time a unique expression is executed, the actual expression is evaluated and the accompanying boolean is set to true.
931Every subsequent evaluation of the unique expression then results in an access to the stored result of the actual expression.
932Tuple member expressions also take advantage of unique expressions in the case of possible impurity.
933
934Currently, the \CFA translator has a very broad, imprecise definition of impurity, where any function call is assumed to be impure.
935This 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.
936
937The various kinds of tuple assignment, constructors, and destructors generate GNU C statement expressions.
938A 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.
939The 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.
940However, 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.
941\end{comment}
942
943
944\section{Evaluation}
945\label{sec:eval}
946
947Though \CFA provides significant added functionality over C, these features have a low runtime penalty.
948In fact, \CFA's features for generic programming can enable faster runtime execution than idiomatic @void *@-based C code.
949This claim is demonstrated through a set of generic-code-based micro-benchmarks in C, \CFA, and \CC (see source-code interfaces in Appendix~\ref{sec:BenchmarkInterfaces}).
950Since all these languages share a subset comprising standard C, maximal-performance benchmarks would show little runtime variance, other than in length and clarity of source code.
951A more illustrative benchmark is to show the costs of idiomatic use of each language's features covering common usage.
952Figure~\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}.
953The benchmark test is similar for C and \CC.
954The 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 $N$ constant values.
955
956The 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.
957The \CCV variant illustrates an alternative object-oriented idiom where all objects inherit from a base @object@ class, mimicking a Java-like interface;
958hence runtime checks are necessary to safely down-cast objects.
959The 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.
960For 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 little runtime impact.
961Note, the C benchmark uses unchecked casts as there is no runtime mechanism to perform such checks, while \CFA and \CC provide type-safety statically.
962
963\begin{figure}
964\begin{lstlisting}[xleftmargin=3\parindentlnth,aboveskip=0pt,belowskip=0pt]
965int main( int argc, char *argv[] ) {
966        FILE * out = fopen( "cfa-out.txt", "w" );
967        int max = 0, vali = 42;
968        stack(int) si, ti;
969
970        REPEAT_TIMED( "push_int", push( &si, vali ); )
971        TIMED( "copy_int", ti = si; )
972        TIMED( "clear_int", clear( &si ); )
973        REPEAT_TIMED( "pop_int", max = max( max, pop( &ti ) ); )
974        REPEAT_TIMED( "print_int", print( out, vali, ":", vali, "\n" ); )
975
976        pair(_Bool, char) maxp  = { (_Bool)0, '\0' }, valp = { (_Bool)0, 'a' };
977        stack(pair(_Bool, char)) sp, tp;
978
979        REPEAT_TIMED( "push_pair", push( &sp, valp ); )
980        TIMED( "copy_pair", tp = sp; )
981        TIMED( "clear_pair", clear( &sp ); )
982        REPEAT_TIMED( "pop_pair", maxp = max( maxp, pop( &tp ) ); )
983        REPEAT_TIMED( "print_pair", print( out, valp, ":", valp, "\n" ); )
984        fclose(out);
985}
986\end{lstlisting}
987\caption{\CFA Benchmark Test}
988\label{fig:BenchmarkTest}
989\end{figure}
990
991Figure~\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.
992The graph plots the median of 5 consecutive runs of each program, with an initial warm-up run omitted.
993All code is compiled at \texttt{-O2} by GCC or G++ 6.2.0, with all \CC code compiled as \CCfourteen.
994The 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.
995
996\begin{figure}
997\centering
998\input{timing}
999\caption{Benchmark Timing Results (smaller is better)}
1000\label{fig:eval}
1001\end{figure}
1002
1003\begin{table}
1004\caption{Properties of benchmark code}
1005\label{tab:eval}
1006\newcommand{\CT}[1]{\multicolumn{1}{c}{#1}}
1007\begin{tabular}{rrrrr}
1008                                                                        & \CT{C}        & \CT{\CFA}     & \CT{\CC}      & \CT{\CCV}             \\ \hline
1009maximum memory usage (MB)                       & 10001         & 2501          & 2503          & 11253                 \\
1010source code size (lines)                        & 301           & 224           & 188           & 437                   \\
1011redundant type annotations (lines)      & 46            & 3                     & 2                     & 15                    \\
1012binary size (KB)                                        & 18            & 234           & 18            & 42                    \\
1013\end{tabular}
1014\end{table}
1015
1016The C and \CCV variants are generally the slowest with the largest memory footprint, because to their less-efficient memory layout and the pointer-indirection necessary to implement generic types;
1017this inefficiency is exacerbated by the second level of generic types in the pair-based benchmarks.
1018By 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.
1019\CCV is slower than C largely due to the cost of runtime type-checking of down-casts (implemented with @dynamic_cast@);
1020There are two outliers in the graph for \CFA: all prints and pop of @pair@.
1021Both 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.
1022A compiler for \CFA could easily perform these optimizations.
1023Finally, the binary size for \CFA is larger because of static linking with the \CFA libraries.
1024
1025\CC performs best because it uses header-only inlined libraries (\ie no separate compilation).
1026\CFA and \CC have the advantage of a pre-written generic @pair@ and @stack@ type to reduce line count, while C and \CCV require it to written by the programmer, as C does not have a generic collections-library and \CCV does not use the \CC standard template library by construction.
1027For \CCV, the definition of @object@ and wrapper classes for @bool@, @char@, @int@, and @const char *@ are included in the line count, which inflates its line count, as an actual object-oriented language would include these in the standard library;
1028with their omission the \CCV line count is similar to C.
1029We 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.
1030
1031Raw line-count, however, is a fairly rough measure of code complexity;
1032another important factor is how much type information the programmer must manually specify, especially where that information is not checked by the compiler.
1033Such 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@).
1034To 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.
1035The \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.
1036The three 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).
1037These uses are similar to the @new@ expressions in \CC, though ongoing work on the \CFA compiler's type resolver should shortly render even these type casts superfluous.
1038
1039
1040\section{Related Work}
1041
1042
1043\subsection{Polymorphism}
1044
1045\CC is the most similar language to \CFA;
1046both are extensions to C with source and runtime backwards compatibility.
1047The fundamental difference is in their engineering approach to C compatibility and programmer expectation.
1048While \CC provides good backwards compatibility with C, it has a steep learning curve for many of its extensions.
1049For example, polymorphism is provided via three disjoint mechanisms: overloading, inheritance, and templates.
1050The overloading is restricted because resolution does not using 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.
1051In 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.
1052The key mechanism to support separate compilation is \CFA's \emph{explicit} use of assumed properties for a type.
1053Until \CC~\citep{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;
1054furthermore, \CC concepts are restricted to template polymorphism.
1055
1056Cyclone~\citep{Grossman06} also provides capabilities for polymorphic functions and existential types, similar to \CFA's @forall@ functions and generic types.
1057Cyclone 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.
1058Furthermore, 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@.
1059In \CFA terms, all Cyclone polymorphism must be dtype-static.
1060While 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.
1061
1062\citet{obj-c-book} is an industrially successful extension to C.
1063However, Objective-C is a radical departure from C, using an object-oriented model with message-passing.
1064Objective-C did not support type-checked generics until recently~\citet{xcode7}, historically using less-efficient and more error-prone runtime checking of object types.
1065The~\citet{GObject} framework also adds object-oriented programming with runtime type-checking and reference-counting garbage-collection to C;
1066these features are more intrusive additions than those provided by \CFA, in addition to the runtime overhead of reference-counting.
1067\citet{Vala} compiles to GObject-based C, and so adds the burden of learning a separate language syntax to the aforementioned demerits of GObject as a modernization path for the existing C code-bases.
1068Java~\citep{Java8} included generic types in Java~5;
1069Java's generic types are type-checked at compilation and type-erased at runtime, similar to \CFA's.
1070However, in Java, each object carries its own table of method pointers, while \CFA passes the method pointers separately to maintain a C-compatible layout.
1071Java is also a garbage-collected, object-oriented language, with the associated resource usage and C-interoperability burdens.
1072
1073D~\citep{D}, Go, and~\citet{Rust} are modern, compiled languages with abstraction features similar to \CFA traits, \emph{interfaces} in D and Go and \emph{traits} in Rust.
1074However, 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.
1075D and Go are garbage-collected languages, imposing the associated runtime overhead.
1076The necessity of accounting for data transfer between managed runtimes and the unmanaged C runtime complicates foreign-function interfaces to C.
1077Furthermore, 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.
1078D 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.
1079Rust also possesses much more powerful abstraction capabilities for writing generic code than Go.
1080On 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.
1081\CFA, with its more modest safety features, allows direct ports of C code while maintaining the idiomatic style of the original source.
1082
1083
1084\subsection{Tuples/Variadics}
1085
1086Many programming languages have some form of tuple construct and/or variadic functions, \eg SETL, C, KW-C, \CC, D, Go, Java, ML, and Scala.
1087SETL~\cite{SETL} is a high-level mathematical programming language, with tuples being one of the primary data types.
1088Tuples in SETL allow subscripting, dynamic expansion, and multiple assignment.
1089C 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.
1090KW-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.
1091The main contributions of that work were adding MRVF, tuple mass and multiple assignment, and record-field access.
1092\CCeleven introduced @std::tuple@ as a library variadic template structure.
1093Tuples are a generalization of @std::pair@, in that they allow for arbitrary length, fixed-size aggregation of heterogeneous values.
1094Operations include @std::get<N>@ to extract vales, @std::tie@ to create a tuple of references used for assignment, and lexicographic comparisons.
1095\CCseventeen proposes \emph{structured bindings}~\cite{Sutter15} to eliminate pre-declaring variables and use of @std::tie@ for binding the results.
1096This 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.
1097Furthermore, structured bindings are not a full replacement for @std::tie@, as it always declares new variables.
1098Like \CC, D provides tuples through a library variadic-template structure.
1099Go does not have tuples but supports MRVF.
1100Java'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.
1101Tuples are a fundamental abstraction in most functional programming languages, such as Standard ML~\cite{sml} and~\cite{Scala}, which decompose tuples using pattern matching.
1102
1103
1104\section{Conclusion \& Future Work}
1105
1106The 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.
1107While 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.
1108The purpose of this paper is to introduce \CFA, and showcase two language features that illustrate the \CFA type-system and approaches taken to achieve the goal of evolutionary C extension.
1109The contributions are a powerful type-system using parametric polymorphism and overloading, generic types, and tuples, which all have complex interactions.
1110The work is a challenging design, engineering, and implementation exercise.
1111On the surface, the project may appear as a rehash of similar mechanisms in \CC.
1112However, 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.
1113All of these new features are being used by the \CFA development-team to build the \CFA runtime-system.
1114Finally, we demonstrate that \CFA performance for some idiomatic cases is better than C and close to \CC, showing the design is practically applicable.
1115
1116There is ongoing work on a wide range of \CFA feature extensions, including reference types, exceptions, concurrent primitives and modules.
1117(While all examples in the paper compile and run, a public beta-release of \CFA will take another 8--12 months to finalize these addition extensions.)
1118In addition, there are interesting future directions for the polymorphism design.
1119Notably, \CC template functions trade compile time and code bloat for optimal runtime of individual instantiations of polymorphic functions.
1120\CFA polymorphic functions, by contrast, uses a dynamic virtual dispatch.
1121The 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.
1122Two 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.
1123These approaches are not mutually exclusive and allow performance optimizations to be applied only when necessary, without suffering global code-bloat.
1124In general, we believe separate compilation, producing smaller code, works well with loaded hardware-caches, which may offset the benefit of larger inlined-code.
1125
1126
1127\begin{acks}
1128The authors would like to recognize the design assistance of Glen Ditchfield, Richard Bilson, and Thierry Delisle on the features described in this paper. They also thank Magnus Madsen and three anonymous reviewers for valuable editorial feedback.
1129
1130This work is supported in part by a corporate partnership with \grantsponsor{Huawei}{Huawei Ltd.}{http://www.huawei.com}\ and 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.
1131\end{acks}
1132
1133
1134\bibliographystyle{ACM-Reference-Format}
1135\bibliography{cfa}
1136
1137
1138\appendix
1139
1140\section{Benchmark Interfaces}
1141\label{sec:BenchmarkInterfaces}
1142
1143\lstset{basicstyle=\linespread{0.9}\sf\small}
1144
1145\CFA
1146\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1147forall(otype T) struct stack_node;
1148forall(otype T) struct stack { stack_node(T) * head; };
1149forall(otype T) void ?{}(stack(T) * s);
1150forall(otype T) void ?{}(stack(T) * s, stack(T) t);
1151forall(otype T) stack(T) ?=?(stack(T) * s, stack(T) t);
1152forall(otype T) void ^?{}(stack(T) * s);
1153forall(otype T) _Bool empty(const stack(T) * s);
1154forall(otype T) void push(stack(T) * s, T value);
1155forall(otype T) T pop(stack(T) * s);
1156forall(otype T) void clear(stack(T) * s);
1157
1158void print( FILE * out, const char * x );
1159void print( FILE * out, _Bool x );
1160void print( FILE * out, char x );
1161void print( FILE * out, int x );
1162forall(otype T, ttype Params | { void print( FILE *, T ); void print( FILE *, Params ); })
1163        void print( FILE * out, T arg, Params rest );
1164forall(otype R, otype S | { void print( FILE *, R ); void print( FILE *, S ); })
1165        void print( FILE * out, pair(R, S) x );
1166\end{lstlisting}
1167
1168\medskip\noindent
1169\CC
1170\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1171std::pair
1172std::forward_list wrapped in std::stack interface
1173
1174template<typename T> void print(ostream& out, const T& x) { out << x; }
1175template<> void print<bool>(ostream& out, const bool& x) { out << (x ? "true" : "false"); }
1176template<> void print<char>(ostream& out, const char& x ) { out << "'" << x << "'"; }
1177template<typename R, typename S> ostream& operator<< (ostream& out, const pair<R, S>& x) {
1178        out << "["; print(out, x.first); out << ", "; print(out, x.second); return out << "]"; }
1179template<typename T, typename... Args> void print(ostream& out, const T& arg, const Args&... rest) {
1180        out << arg;     print(out, rest...); }
1181\end{lstlisting}
1182
1183\medskip\noindent
1184C
1185\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1186struct pair { void * first, second; };
1187struct pair * new_pair( void * first, void * second );
1188struct pair * copy_pair( const struct pair * src,
1189        void * (*copy_first)( const void * ), void * (*copy_second)( const void * ) );
1190void free_pair( struct pair * p, void (*free_first)( void * ), void (*free_second)( void * ) );
1191int cmp_pair( const struct pair * a, const struct pair * b,
1192        int (*cmp_first)( const void *, const void * ), int (*cmp_second)( const void *, const void * ) );
1193
1194struct stack_node;
1195struct stack { struct stack_node * head; };
1196struct stack new_stack();
1197void copy_stack( struct stack * dst, const struct stack * src, void * (*copy)( const void * ) );
1198void clear_stack( struct stack * s, void (*free_el)( void * ) );
1199_Bool stack_empty( const struct stack * s );
1200void push_stack( struct stack * s, void * value );
1201void * pop_stack( struct stack * s );
1202
1203void print_string( FILE * out, const char * x );
1204void print_bool( FILE * out, _Bool x );
1205void print_char( FILE * out, char x );
1206void print_int( FILE * out, int x );
1207void print( FILE * out, const char * fmt, ... );
1208\end{lstlisting}
1209
1210
1211\begin{comment}
1212Throughout, @/***/@ designates a counted redundant type annotation.
1213
1214\subsubsection{bench.h}
1215(\texttt{bench.hpp} is similar.)
1216
1217\lstinputlisting{evaluation/bench.h}
1218
1219\subsection{C}
1220
1221\subsubsection{c-stack.h} ~
1222
1223\lstinputlisting{evaluation/c-stack.h}
1224
1225\subsubsection{c-stack.c} ~
1226
1227\lstinputlisting{evaluation/c-stack.c}
1228
1229\subsubsection{c-pair.h} ~
1230
1231\lstinputlisting{evaluation/c-pair.h}
1232
1233\subsubsection{c-pair.c} ~
1234
1235\lstinputlisting{evaluation/c-pair.c}
1236
1237\subsubsection{c-print.h} ~
1238
1239\lstinputlisting{evaluation/c-print.h}
1240
1241\subsubsection{c-print.c} ~
1242
1243\lstinputlisting{evaluation/c-print.c}
1244
1245\subsubsection{c-bench.c} ~
1246
1247\lstinputlisting{evaluation/c-bench.c}
1248
1249\subsection{\CFA}
1250
1251\subsubsection{cfa-stack.h} ~
1252
1253\lstinputlisting{evaluation/cfa-stack.h}
1254
1255\subsubsection{cfa-stack.c} ~
1256
1257\lstinputlisting{evaluation/cfa-stack.c}
1258
1259\subsubsection{cfa-print.h} ~
1260
1261\lstinputlisting{evaluation/cfa-print.h}
1262
1263\subsubsection{cfa-print.c} ~
1264
1265\lstinputlisting{evaluation/cfa-print.c}
1266
1267\subsubsection{cfa-bench.c} ~
1268
1269\lstinputlisting{evaluation/cfa-bench.c}
1270
1271\subsection{\CC}
1272
1273\subsubsection{cpp-stack.hpp} ~
1274
1275\lstinputlisting[language=c++]{evaluation/cpp-stack.hpp}
1276
1277\subsubsection{cpp-print.hpp} ~
1278
1279\lstinputlisting[language=c++]{evaluation/cpp-print.hpp}
1280
1281\subsubsection{cpp-bench.cpp} ~
1282
1283\lstinputlisting[language=c++]{evaluation/cpp-bench.cpp}
1284
1285\subsection{\CCV}
1286
1287\subsubsection{object.hpp} ~
1288
1289\lstinputlisting[language=c++]{evaluation/object.hpp}
1290
1291\subsubsection{cpp-vstack.hpp} ~
1292
1293\lstinputlisting[language=c++]{evaluation/cpp-vstack.hpp}
1294
1295\subsubsection{cpp-vstack.cpp} ~
1296
1297\lstinputlisting[language=c++]{evaluation/cpp-vstack.cpp}
1298
1299\subsubsection{cpp-vprint.hpp} ~
1300
1301\lstinputlisting[language=c++]{evaluation/cpp-vprint.hpp}
1302
1303\subsubsection{cpp-vbench.cpp} ~
1304
1305\lstinputlisting[language=c++]{evaluation/cpp-vbench.cpp}
1306\end{comment}
1307
1308\end{document}
1309
1310% Local Variables: %
1311% tab-width: 4 %
1312% compile-command: "make" %
1313% End: %
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