source: doc/papers/general/Paper.tex @ 604e76d

aaron-thesisarm-ehcleanup-dtorsdeferred_resndemanglerjacob/cs343-translationjenkins-sandboxnew-astnew-ast-unique-exprnew-envno_listpersistent-indexerresolv-newwith_gc
Last change on this file since 604e76d was 604e76d, checked in by Peter A. Buhr <pabuhr@…>, 4 years ago

initial setup for general and concurrency papers

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2
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80% CFA programming language, based on ANSI C (with some gcc additions)
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88\lstset{
89language=CFA,
90columns=fullflexible,
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109% inline code @...@
110\lstMakeShortInline@%
111
112\title{Generic and Tuple Types with Efficient Dynamic Layout in \protect\CFA}
113
114\author{Aaron Moss, Robert Schluntz, Peter Buhr}
115% \email{a3moss@uwaterloo.ca}
116% \email{rschlunt@uwaterloo.ca}
117% \email{pabuhr@uwaterloo.ca}
118% \affiliation{%
119%       \institution{University of Waterloo}
120%       \department{David R. Cheriton School of Computer Science}
121%       \streetaddress{Davis Centre, University of Waterloo}
122%       \city{Waterloo}
123%       \state{ON}
124%       \postcode{N2L 3G1}
125%       \country{Canada}
126% }
127
128%\terms{generic, tuple, variadic, types}
129%\keywords{generic types, tuple types, variadic types, polymorphic functions, C, Cforall}
130
131\begin{document}
132\maketitle
133
134
135\begin{abstract}
136The 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.
137This installation base and the programmers producing it represent a massive software-engineering investment spanning decades and likely to continue for decades more.
138Nonetheless, C, first standardized over thirty years ago, lacks many features that make programming in more modern languages safer and more productive.
139The 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.
140Prior 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.
141Specifically, \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.
142This 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.
143\end{abstract}
144
145
146\section{Introduction and Background}
147
148The 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.
149This installation base and the programmers producing it represent a massive software-engineering investment spanning decades and likely to continue for decades more.
150The \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.
151The top 3 rankings over the past 30 years are:
152\lstDeleteShortInline@%
153\begin{center}
154\setlength{\tabcolsep}{10pt}
155\begin{tabular}{@{}rccccccc@{}}
156                & 2017  & 2012  & 2007  & 2002  & 1997  & 1992  & 1987          \\ \hline
157Java    & 1             & 1             & 1             & 1             & 12    & -             & -                     \\
158\Textbf{C}      & \Textbf{2}& \Textbf{2}& \Textbf{2}& \Textbf{2}& \Textbf{1}& \Textbf{1}& \Textbf{1}    \\
159\CC             & 3             & 3             & 3             & 3             & 2             & 2             & 4                     \\
160\end{tabular}
161\end{center}
162\lstMakeShortInline@%
163Love it or hate it, C is extremely popular, highly used, and one of the few systems languages.
164In many cases, \CC is often used solely as a better C.
165Nonetheless, C, first standardized over thirty years ago, lacks many features that make programming in more modern languages safer and more productive.
166
167\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.
168The four key design goals for \CFA~\cite{Bilson03} are:
169(1) The behaviour of standard C code must remain the same when translated by a \CFA compiler as when translated by a C compiler;
170(2) Standard C code must be as fast and as small when translated by a \CFA compiler as when translated by a C compiler;
171(3) \CFA code must be at least as portable as standard C code;
172(4) Extensions introduced by \CFA must be translated in the most efficient way possible.
173These 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.
174\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.
175
176\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).
177Ultimately, a compiler is necessary for advanced features and optimal performance.
178
179This 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.
180Specifically, 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.
181The new constructs are empirically compared with both standard C and \CC; the results show the new design is comparable in performance.
182
183
184\subsection{Polymorphic Functions}
185\label{sec:poly-fns}
186
187\CFA{}\hspace{1pt}'s polymorphism was originally formalized by \cite{Ditchfield92}, and first implemented by \cite{Bilson03}.
188The 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):
189\begin{lstlisting}
190`forall( otype T )` T identity( T val ) { return val; }
191int forty_two = identity( 42 );                         $\C{// T is bound to int, forty\_two == 42}$
192\end{lstlisting}
193The @identity@ function above can be applied to any complete \emph{object type} (or @otype@).
194The 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.
195The \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.
196If this extra information is not needed, \eg for a pointer, the type parameter can be declared as a \emph{data type} (or @dtype@).
197
198In \CFA, the polymorphism runtime-cost is spread over each polymorphic call, due to passing more arguments to polymorphic functions;
199the experiments in Section~\ref{sec:eval} show this overhead is similar to \CC virtual-function calls.
200A design advantage is that, unlike \CC template-functions, \CFA polymorphic-functions are compatible with C \emph{separate compilation}, preventing compilation and code bloat.
201
202Since 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.
203For example, the function @twice@ can be defined using the \CFA syntax for operator overloading:
204\begin{lstlisting}
205forall( otype T `| { T ?+?(T, T); }` ) T twice( T x ) { return x + x; } $\C{// ? denotes operands}$
206int val = twice( twice( 3.7 ) );
207\end{lstlisting}
208which works for any type @T@ with a matching addition operator.
209The 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@.
210There 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.
211The first approach has a late conversion from @double@ to @int@ on the final assignment, while the second has an eager conversion to @int@.
212\CFA minimizes the number of conversions and their potential to lose information, so it selects the first approach, which corresponds with C-programmer intuition.
213
214Crucial to the design of a new programming language are the libraries to access thousands of external software features.
215Like \CC, \CFA inherits a massive compatible library-base, where other programming languages must rewrite or provide fragile inter-language communication with C.
216A simple example is leveraging the existing type-unsafe (@void *@) C @bsearch@ to binary search a sorted floating-point array:
217\begin{lstlisting}
218void * bsearch( const void * key, const void * base, size_t nmemb, size_t size,
219                                int (* compar)( const void *, const void * ));
220int comp( const void * t1, const void * t2 ) { return *(double *)t1 < *(double *)t2 ? -1 :
221                                *(double *)t2 < *(double *)t1 ? 1 : 0; }
222double key = 5.0, vals[10] = { /* 10 sorted floating-point values */ };
223double * val = (double *)bsearch( &key, vals, 10, sizeof(vals[0]), comp );      $\C{// search sorted array}$
224\end{lstlisting}
225which can be augmented simply with a generalized, type-safe, \CFA-overloaded wrappers:
226\begin{lstlisting}
227forall( otype T | { int ?<?( T, T ); } ) T * bsearch( T key, const T * arr, size_t size ) {
228        int comp( const void * t1, const void * t2 ) { /* as above with double changed to T */ }
229        return (T *)bsearch( &key, arr, size, sizeof(T), comp ); }
230forall( otype T | { int ?<?( T, T ); } ) unsigned int bsearch( T key, const T * arr, size_t size ) {
231        T * result = bsearch( key, arr, size ); $\C{// call first version}$
232        return result ? result - arr : size; }  $\C{// pointer subtraction includes sizeof(T)}$
233double * val = bsearch( 5.0, vals, 10 );        $\C{// selection based on return type}$
234int posn = bsearch( 5.0, vals, 10 );
235\end{lstlisting}
236The nested function @comp@ provides the hidden interface from typed \CFA to untyped (@void *@) C, plus the cast of the result.
237Providing a hidden @comp@ function in \CC is awkward as lambdas do not use C calling-conventions and template declarations cannot appear at block scope.
238As well, an alternate kind of return is made available: position versus pointer to found element.
239\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@.
240
241\CFA has replacement libraries condensing hundreds of existing C functions into tens of \CFA overloaded functions, all without rewriting the actual computations.
242For example, it is possible to write a type-safe \CFA wrapper @malloc@ based on the C @malloc@:
243\begin{lstlisting}
244forall( dtype T | sized(T) ) T * malloc( void ) { return (T *)malloc( sizeof(T) ); }
245int * ip = malloc();                                            $\C{// select type and size from left-hand side}$
246double * dp = malloc();
247struct S {...} * sp = malloc();
248\end{lstlisting}
249where the return type supplies the type/size of the allocation, which is impossible in most type systems.
250
251Call-site inferencing and nested functions provide a localized form of inheritance.
252For example, the \CFA @qsort@ only sorts in ascending order using @<@.
253However, it is trivial to locally change this behaviour:
254\begin{lstlisting}
255forall( otype T | { int ?<?( T, T ); } ) void qsort( const T * arr, size_t size ) { /* use C qsort */ }
256{       int ?<?( double x, double y ) { return x `>` y; }       $\C{// locally override behaviour}$
257        qsort( vals, size );                                    $\C{// descending sort}$
258}
259\end{lstlisting}
260Within the block, the nested version of @<@ performs @>@ and this local version overrides the built-in @<@ so it is passed to @qsort@.
261Hence, programmers can easily form local environments, adding and modifying appropriate functions, to maximize reuse of other existing functions and types.
262
263Finally, \CFA allows variable overloading:
264\begin{lstlisting}
265short int MAX = ...;   int MAX = ...;  double MAX = ...;
266short int s = MAX;    int i = MAX;    double d = MAX;   $\C{// select correct MAX}$
267\end{lstlisting}
268Here, the single name @MAX@ replaces all the C type-specific names: @SHRT_MAX@, @INT_MAX@, @DBL_MAX@.
269As 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.
270In addition, several operations are defined in terms values @0@ and @1@, \eg:
271\begin{lstlisting}
272int x;
273if (x) x++                                                                      $\C{// if (x != 0) x += 1;}$
274\end{lstlisting}
275Every @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.
276Due 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.
277The 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.
278
279
280\subsection{Traits}
281
282\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:
283\begin{lstlisting}
284trait summable( otype T ) {
285        void ?{}( T *, zero_t );                                $\C{// constructor from 0 literal}$
286        T ?+?( T, T );                                                  $\C{// assortment of additions}$
287        T ?+=?( T *, T );
288        T ++?( T * );
289        T ?++( T * ); };
290forall( otype T `| summable( T )` ) T sum( T a[$\,$], size_t size ) {  // use trait
291        `T` total = { `0` };                                    $\C{// instantiate T from 0 by calling its constructor}$
292        for ( unsigned int i = 0; i < size; i += 1 ) total `+=` a[i]; $\C{// select appropriate +}$
293        return total; }
294\end{lstlisting}
295
296In 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:
297\begin{lstlisting}
298trait otype( dtype T | sized(T) ) {  // sized is a pseudo-trait for types with known size and alignment
299        void ?{}( T * );                                                $\C{// default constructor}$
300        void ?{}( T *, T );                                             $\C{// copy constructor}$
301        void ?=?( T *, T );                                             $\C{// assignment operator}$
302        void ^?{}( T * ); };                                    $\C{// destructor}$
303\end{lstlisting}
304Given 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.
305
306In 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.
307Hence, trait names play no part in type equivalence;
308the names are simply macros for a list of polymorphic assertions, which are expanded at usage sites.
309Nevertheless, trait names form a logical subtype-hierarchy with @dtype@ at the top, where traits often contain overlapping assertions, \eg operator @+@.
310Traits are used like interfaces in Java or abstract base-classes in \CC, but without the nominal inheritance-relationships.
311Instead, 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.
312Hence, 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.
313(Nominal inheritance can be approximated with traits using marker variables or functions, as is done in Go.)
314
315% Nominal inheritance can be simulated with traits using marker variables or functions:
316% \begin{lstlisting}
317% trait nominal(otype T) {
318%     T is_nominal;
319% };
320% int is_nominal;                                                               $\C{// int now satisfies the nominal trait}$
321% \end{lstlisting}
322%
323% 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:
324% \begin{lstlisting}
325% trait pointer_like(otype Ptr, otype El) {
326%     lvalue El *?(Ptr);                                                $\C{// Ptr can be dereferenced into a modifiable value of type El}$
327% }
328% struct list {
329%     int value;
330%     list * next;                                                              $\C{// may omit "struct" on type names as in \CC}$
331% };
332% typedef list * list_iterator;
333%
334% lvalue int *?( list_iterator it ) { return it->value; }
335% \end{lstlisting}
336% 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@).
337% 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.
338
339
340\section{Generic Types}
341
342One of the known shortcomings of standard C is that it does not provide reusable type-safe abstractions for generic data structures and algorithms.
343Broadly speaking, there are three approaches to implement abstract data-structures in C.
344One approach is to write bespoke data-structures for each context in which they are needed.
345While 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.
346A 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.
347However, 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.
348A 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.
349Furthermore, writing and using preprocessor macros can be unnatural and inflexible.
350
351\CC, Java, and other languages use \emph{generic types} to produce type-safe abstract data-types.
352\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.
353However, for known concrete parameters, the generic-type definition can be inlined, like \CC templates.
354
355A 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:
356\begin{lstlisting}
357forall( otype R, otype S ) struct pair {
358        R first;
359        S second;
360};
361forall( otype T ) T value( pair( const char *, T ) p ) { return p.second; }
362forall( dtype F, otype T ) T value_p( pair( F *, T * ) p ) { return * p.second; }
363pair( const char *, int ) p = { "magic", 42 };
364int magic = value( p );
365pair( void *, int * ) q = { 0, &p.second };
366magic = value_p( q );
367double d = 1.0;
368pair( double *, double * ) r = { &d, &d };
369d = value_p( r );
370\end{lstlisting}
371
372\CFA classifies generic types as either \emph{concrete} or \emph{dynamic}.
373Concrete types have a fixed memory layout regardless of type parameters, while dynamic types vary in memory layout depending on their type parameters.
374A type may have polymorphic parameters but still be concrete, called \emph{dtype-static}.
375Polymorphic 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.
376
377\CFA generic types also allow checked argument-constraints.
378For example, the following declaration of a sorted set-type ensures the set key supports equality and relational comparison:
379\begin{lstlisting}
380forall( otype Key | { _Bool ?==?(Key, Key); _Bool ?<?(Key, Key); } ) struct sorted_set;
381\end{lstlisting}
382
383
384\subsection{Concrete Generic-Types}
385
386The \CFA translator template-expands concrete generic-types into new structure types, affording maximal inlining.
387To 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.
388A 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.
389For example, the concrete instantiation for @pair( const char *, int )@ is:
390\begin{lstlisting}
391struct _pair_conc1 {
392        const char * first;
393        int second;
394};
395\end{lstlisting}
396
397A concrete generic-type with dtype-static parameters is also expanded to a structure type, but this type is used for all matching instantiations.
398In 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:
399\begin{lstlisting}
400struct _pair_conc0 {
401        void * first;
402        void * second;
403};
404\end{lstlisting}
405
406
407\subsection{Dynamic Generic-Types}
408
409Though \CFA implements concrete generic-types efficiently, it also has a fully general system for dynamic generic types.
410As 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.
411Dynamic generic-types also have an \emph{offset array} containing structure-member offsets.
412A dynamic generic-union needs no such offset array, as all members are at offset 0, but size and alignment are still necessary.
413Access 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.
414
415The offset arrays are statically generated where possible.
416If 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;
417if 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.
418As 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 )@.
419The offset array @_offsetof_pair@ is generated at the call site as @size_t _offsetof_pair[] = { offsetof(_pair_conc1, first), offsetof(_pair_conc1, second) }@.
420
421In some cases the offset arrays cannot be statically generated.
422For 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.
423\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.
424The \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.
425These 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).
426Results of these layout functions are cached so that they are only computed once per type per function. %, as in the example below for @pair@.
427Layout functions also allow generic types to be used in a function definition without reflecting them in the function signature.
428For 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.
429This function could acquire the layout for @set(T)@ by calling its layout function with the layout of @T@ implicitly passed into the function.
430
431Whether a type is concrete, dtype-static, or dynamic is decided solely on the @forall@'s type parameters.
432This 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.
433If 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.
434
435
436\subsection{Applications}
437\label{sec:generic-apps}
438
439The reuse of dtype-static structure instantiations enables useful programming patterns at zero runtime cost.
440The 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@:
441\begin{lstlisting}
442forall(dtype T) int lexcmp( pair( T *, T * ) * a, pair( T *, T * ) * b, int (* cmp)( T *, T * ) ) {
443        return cmp( a->first, b->first ) ? : cmp( a->second, b->second );
444}
445\end{lstlisting}
446Since @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.
447
448Another useful pattern enabled by reused dtype-static type instantiations is zero-cost \emph{tag-structures}.
449Sometimes information is only used for type-checking and can be omitted at runtime, \eg:
450\begin{lstlisting}
451forall(dtype Unit) struct scalar { unsigned long value; };
452struct metres {};
453struct litres {};
454
455forall(dtype U) scalar(U) ?+?( scalar(U) a, scalar(U) b ) {
456        return (scalar(U)){ a.value + b.value };
457}
458scalar(metres) half_marathon = { 21093 };
459scalar(litres) swimming_pool = { 2500000 };
460scalar(metres) marathon = half_marathon + half_marathon;
461scalar(litres) two_pools = swimming_pool + swimming_pool;
462marathon + swimming_pool;                                       $\C{// compilation ERROR}$
463\end{lstlisting}
464@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 @?+?@.
465These implementations may even be separately compiled, unlike \CC template functions.
466However, the \CFA type-checker ensures matching types are used by all calls to @?+?@, preventing nonsensical computations like adding a length to a volume.
467
468
469\section{Tuples}
470\label{sec:tuples}
471
472In many languages, functions can return at most one value;
473however, many operations have multiple outcomes, some exceptional.
474Consider C's @div@ and @remquo@ functions, which return the quotient and remainder for a division of integer and floating-point values, respectively.
475\begin{lstlisting}
476typedef struct { int quo, rem; } div_t;         $\C{// from include stdlib.h}$
477div_t div( int num, int den );
478double remquo( double num, double den, int * quo );
479div_t qr = div( 13, 5 );                                        $\C{// return quotient/remainder aggregate}$
480int q;
481double r = remquo( 13.5, 5.2, &q );                     $\C{// return remainder, alias quotient}$
482\end{lstlisting}
483@div@ aggregates the quotient/remainder in a structure, while @remquo@ aliases a parameter to an argument.
484Both approaches are awkward.
485Alternatively, a programming language can directly support returning multiple values, \eg in \CFA:
486\begin{lstlisting}
487[ int, int ] div( int num, int den );           $\C{// return two integers}$
488[ double, double ] div( double num, double den ); $\C{// return two doubles}$
489int q, r;                                                                       $\C{// overloaded variable names}$
490double q, r;
491[ q, r ] = div( 13, 5 );                                        $\C{// select appropriate div and q, r}$
492[ q, r ] = div( 13.5, 5.2 );                            $\C{// assign into tuple}$
493\end{lstlisting}
494Clearly, this approach is straightforward to understand and use;
495therefore, why do few programming languages support this obvious feature or provide it awkwardly?
496The answer is that there are complex consequences that cascade through multiple aspects of the language, especially the type-system.
497This section show these consequences and how \CFA handles them.
498
499
500\subsection{Tuple Expressions}
501
502The addition of multiple-return-value functions (MRVF) are useless without a syntax for accepting multiple values at the call-site.
503The simplest mechanism for capturing the return values is variable assignment, allowing the values to be retrieved directly.
504As 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}.
505
506However, 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:
507\begin{lstlisting}
508printf( "%d %d\n", div( 13, 5 ) );                      $\C{// return values seperated into arguments}$
509\end{lstlisting}
510Here, the values returned by @div@ are composed with the call to @printf@ by flattening the tuple into separate arguments.
511However, the \CFA type-system must support significantly more complex composition:
512\begin{lstlisting}
513[ int, int ] foo$\(_1\)$( int );                        $\C{// overloaded foo functions}$
514[ double ] foo$\(_2\)$( int );
515void bar( int, double, double );
516bar( foo( 3 ), foo( 3 ) );
517\end{lstlisting}
518The type-resolver only has the tuple return-types to resolve the call to @bar@ as the @foo@ parameters are identical, which involves unifying the possible @foo@ functions with @bar@'s parameter list.
519No combination of @foo@s are an exact match with @bar@'s parameters, so the resolver applies C conversions.
520The minimal cost is @bar( foo@$_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.
521
522
523\subsection{Tuple Variables}
524
525An important observation from function composition is that new variable names are not required to initialize parameters from an MRVF.
526\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:
527\begin{lstlisting}
528[ int, int ] qr = div( 13, 5 );                         $\C{// tuple-variable declaration and initialization}$
529[ double, double ] qr = div( 13.5, 5.2 );
530\end{lstlisting}
531where the tuple variable-name serves the same purpose as the parameter name(s).
532Tuple variables can be composed of any types, except for array types, since array sizes are generally unknown in C.
533
534One way to access the tuple-variable components is with assignment or composition:
535\begin{lstlisting}
536[ q, r ] = qr;                                                          $\C{// access tuple-variable components}$
537printf( "%d %d\n", qr );
538\end{lstlisting}
539\CFA also supports \emph{tuple indexing} to access single components of a tuple expression:
540\begin{lstlisting}
541[int, int] * p = &qr;                                           $\C{// tuple pointer}$
542int rem = qr`.1`;                                                       $\C{// access remainder}$
543int quo = div( 13, 5 )`.0`;                                     $\C{// access quotient}$
544p`->0` = 5;                                                                     $\C{// change quotient}$
545bar( qr`.1`, qr );                                                      $\C{// pass remainder and quotient/remainder}$
546rem = [42, div( 13, 5 )]`.0.1`;                         $\C{// access 2nd component of 1st component of tuple expression}$
547\end{lstlisting}
548
549
550\subsection{Flattening and Restructuring}
551
552In function call contexts, tuples support implicit flattening and restructuring conversions.
553Tuple flattening recursively expands a tuple into the list of its basic components.
554Tuple structuring packages a list of expressions into a value of tuple type, \eg:
555%\lstDeleteShortInline@%
556%\par\smallskip
557%\begin{tabular}{@{}l@{\hspace{1.5\parindent}}||@{\hspace{1.5\parindent}}l@{}}
558\begin{lstlisting}
559int f( int, int );
560int g( [int, int] );
561int h( int, [int, int] );
562[int, int] x;
563int y;
564f( x );                 $\C{// flatten}$
565g( y, 10 );             $\C{// structure}$
566h( x, y );              $\C{// flatten and structure}$
567\end{lstlisting}
568%\end{lstlisting}
569%&
570%\begin{lstlisting}
571%\end{tabular}
572%\smallskip\par\noindent
573%\lstMakeShortInline@%
574In the call to @f@, @x@ is implicitly flattened so the components of @x@ are passed as the two arguments.
575In 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@.
576Finally, 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]@.
577The 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.
578
579
580\subsection{Tuple Assignment}
581
582An assignment where the left side is a tuple type is called \emph{tuple assignment}.
583There 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.
584%\lstDeleteShortInline@%
585%\par\smallskip
586%\begin{tabular}{@{}l@{\hspace{1.5\parindent}}||@{\hspace{1.5\parindent}}l@{}}
587\begin{lstlisting}
588int x = 10;
589double y = 3.5;
590[int, double] z;
591z = [x, y];                                                                     $\C{// multiple assignment}$
592[x, y] = z;                                                                     $\C{// multiple assignment}$
593z = 10;                                                                         $\C{// mass assignment}$
594[y, x] = 3.14;                                                          $\C{// mass assignment}$
595\end{lstlisting}
596%\end{lstlisting}
597%&
598%\begin{lstlisting}
599%\end{tabular}
600%\smallskip\par\noindent
601%\lstMakeShortInline@%
602Both kinds of tuple assignment have parallel semantics, so that each value on the left and right side is evaluated before any assignments occur.
603As 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]@.
604This 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.
605For example, @[y, x] = 3.14@ performs the assignments @y = 3.14@ and @x = 3.14@, yielding @y == 3.14@ and @x == 3@;
606whereas, C cascading assignment @y = x = 3.14@ performs the assignments @x = 3.14@ and @y = x@, yielding @3@ in @y@ and @x@.
607Finally, 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.
608This example shows mass, multiple, and cascading assignment used in one expression:
609\begin{lstlisting}
610void f( [int, int] );
611f( [x, y] = z = 1.5 );                                          $\C{// assignments in parameter list}$
612\end{lstlisting}
613
614
615\subsection{Member Access}
616
617It is also possible to access multiple fields from a single expression using a \emph{member-access}.
618The result is a single tuple-valued expression whose type is the tuple of the types of the members, \eg:
619\begin{lstlisting}
620struct S { int x; double y; char * z; } s;
621s.[x, y, z] = 0;
622\end{lstlisting}
623Here, the mass assignment sets all members of @s@ to zero.
624Since 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).
625%\lstDeleteShortInline@%
626%\par\smallskip
627%\begin{tabular}{@{}l@{\hspace{1.5\parindent}}||@{\hspace{1.5\parindent}}l@{}}
628\begin{lstlisting}
629[int, int, long, double] x;
630void f( double, long );
631x.[0, 1] = x.[1, 0];                                            $\C{// rearrange: [x.0, x.1] = [x.1, x.0]}$
632f( x.[0, 3] );                                                          $\C{// drop: f(x.0, x.3)}$
633[int, int, int] y = x.[2, 0, 2];                        $\C{// duplicate: [y.0, y.1, y.2] = [x.2, x.0.x.2]}$
634\end{lstlisting}
635%\end{lstlisting}
636%&
637%\begin{lstlisting}
638%\end{tabular}
639%\smallskip\par\noindent
640%\lstMakeShortInline@%
641It is also possible for a member access to contain other member accesses, \eg:
642\begin{lstlisting}
643struct A { double i; int j; };
644struct B { int * k; short l; };
645struct C { int x; A y; B z; } v;
646v.[x, y.[i, j], z.k];                                           $\C{// [v.x, [v.y.i, v.y.j], v.z.k]}$
647\end{lstlisting}
648
649
650\begin{comment}
651\subsection{Casting}
652
653In C, the cast operator is used to explicitly convert between types.
654In \CFA, the cast operator has a secondary use as type ascription.
655That 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:
656\begin{lstlisting}
657int f();     // (1)
658double f()// (2)
659
660f();       // ambiguous - (1),(2) both equally viable
661(int)f()// choose (2)
662\end{lstlisting}
663
664Since casting is a fundamental operation in \CFA, casts should be given a meaningful interpretation in the context of tuples.
665Taking a look at standard C provides some guidance with respect to the way casts should work with tuples:
666\begin{lstlisting}
667int f();
668void g();
669
670(void)f()// (1)
671(int)g()// (2)
672\end{lstlisting}
673In C, (1) is a valid cast, which calls @f@ and discards its result.
674On the other hand, (2) is invalid, because @g@ does not produce a result, so requesting an @int@ to materialize from nothing is nonsensical.
675Generalizing 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.
676
677Formally, 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 $T_i$.
678Excess 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.
679This approach follows naturally from the way that a cast to @void@ works in C.
680
681For example, in
682\begin{lstlisting}
683[int, int, int] f();
684[int, [int, int], int] g();
685
686([int, double])f();           $\C{// (1)}$
687([int, int, int])g();         $\C{// (2)}$
688([void, [int, int]])g();      $\C{// (3)}$
689([int, int, int, int])g();    $\C{// (4)}$
690([int, [int, int, int]])g()$\C{// (5)}$
691\end{lstlisting}
692
693(1) discards the last element of the return value and converts the second element to @double@.
694Since @int@ is effectively a 1-element tuple, (2) discards the second component of the second element of the return value of @g@.
695If @g@ is free of side effects, this expression is equivalent to @[(int)(g().0), (int)(g().1.0), (int)(g().2)]@.
696Since @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)]@).
697
698Note 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.}.
699As such, (4) is invalid because the cast target type contains 4 components, while the source type contains only 3.
700Similarly, (5) is invalid because the cast @([int, int, int])(g().1)@ is invalid.
701That is, it is invalid to cast @[int, int]@ to @[int, int, int]@.
702\end{comment}
703
704
705\subsection{Polymorphism}
706
707Tuples also integrate with \CFA polymorphism as a kind of generic type.
708Due 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:
709\begin{lstlisting}
710forall(otype T, dtype U) void f( T x, U * y );
711f( [5, "hello"] );
712\end{lstlisting}
713where @[5, "hello"]@ is flattened, giving argument list @5, "hello"@, and @T@ binds to @int@ and @U@ binds to @const char@.
714Tuples, however, may contain polymorphic components.
715For example, a plus operator can be written to add two triples together.
716\begin{lstlisting}
717forall(otype T | { T ?+?( T, T ); }) [T, T, T] ?+?( [T, T, T] x, [T, T, T] y ) {
718        return [x.0 + y.0, x.1 + y.1, x.2 + y.2];
719}
720[int, int, int] x;
721int i1, i2, i3;
722[i1, i2, i3] = x + ([10, 20, 30]);
723\end{lstlisting}
724
725Flattening and restructuring conversions are also applied to tuple types in polymorphic type assertions.
726\begin{lstlisting}
727int f( [int, double], double );
728forall(otype T, otype U | { T f( T, U, U ); }) void g( T, U );
729g( 5, 10.21 );
730\end{lstlisting}
731Hence, function parameter and return lists are flattened for the purposes of type unification allowing the example to pass expression resolution.
732This relaxation is possible by extending the thunk scheme described by~\cite{Bilson03}.
733Whenever 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:
734\begin{lstlisting}
735int _thunk( int _p0, double _p1, double _p2 ) { return f( [_p0, _p1], _p2 ); }
736\end{lstlisting}
737so the thunk provides flattening and structuring conversions to inferred functions, improving the compatibility of tuples and polymorphism.
738These thunks take advantage of GCC C nested-functions to produce closures that have the usual function-pointer signature.
739
740
741\subsection{Variadic Tuples}
742\label{sec:variadic-tuples}
743
744To define variadic functions, \CFA adds a new kind of type parameter, @ttype@ (tuple type).
745Matching against a @ttype@ parameter consumes all remaining argument components and packages them into a tuple, binding to the resulting tuple of types.
746In 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.
747As such, @ttype@ variables are also called \emph{argument packs}.
748
749Like variadic templates, the main way to manipulate @ttype@ polymorphic functions is via recursion.
750Since nothing is known about a parameter pack by default, assertion parameters are key to doing anything meaningful.
751Unlike variadic templates, @ttype@ polymorphic functions can be separately compiled.
752For example, a generalized @sum@ function written using @ttype@:
753\begin{lstlisting}
754int sum$\(_0\)$() { return 0; }
755forall(ttype Params | { int sum( Params ); } ) int sum$\(_1\)$( int x, Params rest ) {
756        return x + sum( rest );
757}
758sum( 10, 20, 30 );
759\end{lstlisting}
760Since @sum@\(_0\) does not accept any arguments, it is not a valid candidate function for the call @sum(10, 20, 30)@.
761In 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]@.
762The process continues unitl @Params@ is bound to @[]@, requiring an assertion @int sum()@, which matches @sum@\(_0\) and terminates the recursion.
763Effectively, 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))@.
764
765It is reasonable to take the @sum@ function a step further to enforce a minimum number of arguments:
766\begin{lstlisting}
767int sum( int x, int y ) { return x + y; }
768forall(ttype Params | { int sum( int, Params ); } ) int sum( int x, int y, Params rest ) {
769        return sum( x + y, rest );
770}
771\end{lstlisting}
772One more step permits the summation of any summable type with all arguments of the same type:
773\begin{lstlisting}
774trait summable(otype T) {
775        T ?+?( T, T );
776};
777forall(otype R | summable( R ) ) R sum( R x, R y ) {
778        return x + y;
779}
780forall(otype R, ttype Params | summable(R) | { R sum(R, Params); } ) R sum(R x, R y, Params rest) {
781        return sum( x + y, rest );
782}
783\end{lstlisting}
784Unlike C variadic functions, it is unnecessary to hard code the number and expected types.
785Furthermore, this code is extendable for any user-defined type with a @?+?@ operator.
786Summing arbitrary heterogeneous lists is possible with similar code by adding the appropriate type variables and addition operators.
787
788It is also possible to write a type-safe variadic print function to replace @printf@:
789\begin{lstlisting}
790struct S { int x, y; };
791forall(otype T, ttype Params | { void print(T); void print(Params); }) void print(T arg, Params rest) {
792        print(arg);  print(rest);
793}
794void print( char * x ) { printf( "%s", x ); }
795void print( int x ) { printf( "%d", x ); }
796void print( S s ) { print( "{ ", s.x, ",", s.y, " }" ); }
797print( "s = ", (S){ 1, 2 }, "\n" );
798\end{lstlisting}
799This example showcases a variadic-template-like decomposition of the provided argument list.
800The individual @print@ functions allow printing a single element of a type.
801The polymorphic @print@ allows printing any list of types, where as each individual type has a @print@ function.
802The individual print functions can be used to build up more complicated @print@ functions, such as @S@, which cannot be done with @printf@ in C.
803
804Finally, it is possible to use @ttype@ polymorphism to provide arbitrary argument forwarding functions.
805For example, it is possible to write @new@ as a library function:
806\begin{lstlisting}
807forall( otype R, otype S ) void ?{}( pair(R, S) *, R, S );
808forall( dtype T, ttype Params | sized(T) | { void ?{}( T *, Params ); } ) T * new( Params p ) {
809        return ((T *)malloc()){ p };                    $\C{// construct into result of malloc}$
810}
811pair( int, char ) * x = new( 42, '!' );
812\end{lstlisting}
813The @new@ function provides the combination of type-safe @malloc@ with a \CFA constructor call, making it impossible to forget constructing dynamically allocated objects.
814This function provides the type-safety of @new@ in \CC, without the need to specify the allocated type again, thanks to return-type inference.
815
816
817\subsection{Implementation}
818
819Tuples are implemented in the \CFA translator via a transformation into \emph{generic types}.
820For each $N$, the first time an $N$-tuple is seen in a scope a generic type with $N$ type parameters is generated, \eg:
821\begin{lstlisting}
822[int, int] f() {
823        [double, double] x;
824        [int, double, int] y;
825}
826\end{lstlisting}
827is transformed into:
828\begin{lstlisting}
829forall(dtype T0, dtype T1 | sized(T0) | sized(T1)) struct _tuple2 {
830        T0 field_0;                                                             $\C{// generated before the first 2-tuple}$
831        T1 field_1;
832};
833_tuple2(int, int) f() {
834        _tuple2(double, double) x;
835        forall(dtype T0, dtype T1, dtype T2 | sized(T0) | sized(T1) | sized(T2)) struct _tuple3 {
836                T0 field_0;                                                     $\C{// generated before the first 3-tuple}$
837                T1 field_1;
838                T2 field_2;
839        };
840        _tuple3(int, double, int) y;
841}
842\end{lstlisting}
843\begin{sloppypar}
844Tuple expressions are then simply converted directly into compound literals, \eg @[5, 'x', 1.24]@ becomes @(_tuple3(int, char, double)){ 5, 'x', 1.24 }@.
845\end{sloppypar}
846
847\begin{comment}
848Since tuples are essentially structures, tuple indexing expressions are just field accesses:
849\begin{lstlisting}
850void f(int, [double, char]);
851[int, double] x;
852
853x.0+x.1;
854printf("%d %g\n", x);
855f(x, 'z');
856\end{lstlisting}
857Is transformed into:
858\begin{lstlisting}
859void f(int, _tuple2(double, char));
860_tuple2(int, double) x;
861
862x.field_0+x.field_1;
863printf("%d %g\n", x.field_0, x.field_1);
864f(x.field_0, (_tuple2){ x.field_1, 'z' });
865\end{lstlisting}
866Note that due to flattening, @x@ used in the argument position is converted into the list of its fields.
867In the call to @f@, the second and third argument components are structured into a tuple argument.
868Similarly, tuple member expressions are recursively expanded into a list of member access expressions.
869
870Expressions that may contain side effects are made into \emph{unique expressions} before being expanded by the flattening conversion.
871Each unique expression is assigned an identifier and is guaranteed to be executed exactly once:
872\begin{lstlisting}
873void g(int, double);
874[int, double] h();
875g(h());
876\end{lstlisting}
877Internally, this expression is converted to two variables and an expression:
878\begin{lstlisting}
879void g(int, double);
880[int, double] h();
881
882_Bool _unq0_finished_ = 0;
883[int, double] _unq0;
884g(
885        (_unq0_finished_ ? _unq0 : (_unq0 = f(), _unq0_finished_ = 1, _unq0)).0,
886        (_unq0_finished_ ? _unq0 : (_unq0 = f(), _unq0_finished_ = 1, _unq0)).1,
887);
888\end{lstlisting}
889Since argument evaluation order is not specified by the C programming language, this scheme is built to work regardless of evaluation order.
890The first time a unique expression is executed, the actual expression is evaluated and the accompanying boolean is set to true.
891Every subsequent evaluation of the unique expression then results in an access to the stored result of the actual expression.
892Tuple member expressions also take advantage of unique expressions in the case of possible impurity.
893
894Currently, the \CFA translator has a very broad, imprecise definition of impurity, where any function call is assumed to be impure.
895This 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.
896
897The various kinds of tuple assignment, constructors, and destructors generate GNU C statement expressions.
898A 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.
899The 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.
900However, 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.
901\end{comment}
902
903
904\section{Evaluation}
905\label{sec:eval}
906
907Though \CFA provides significant added functionality over C, these features have a low runtime penalty.
908In fact, \CFA's features for generic programming can enable faster runtime execution than idiomatic @void *@-based C code.
909This 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}).
910Since 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.
911A more illustrative benchmark measures the costs of idiomatic usage of each language's features.
912Figure~\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}.
913The benchmark test is similar for C and \CC.
914The 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.
915
916\begin{figure}
917\begin{lstlisting}[xleftmargin=3\parindentlnth,aboveskip=0pt,belowskip=0pt]
918int main( int argc, char * argv[] ) {
919        FILE * out = fopen( "cfa-out.txt", "w" );
920        int maxi = 0, vali = 42;
921        stack(int) si, ti;
922
923        REPEAT_TIMED( "push_int", N, push( &si, vali ); )
924        TIMED( "copy_int", ti = si; )
925        TIMED( "clear_int", clear( &si ); )
926        REPEAT_TIMED( "pop_int", N,
927                int xi = pop( &ti ); if ( xi > maxi ) { maxi = xi; } )
928        REPEAT_TIMED( "print_int", N/2, print( out, vali, ":", vali, "\n" ); )
929
930        pair(_Bool, char) maxp = { (_Bool)0, '\0' }, valp = { (_Bool)1, 'a' };
931        stack(pair(_Bool, char)) sp, tp;
932
933        REPEAT_TIMED( "push_pair", N, push( &sp, valp ); )
934        TIMED( "copy_pair", tp = sp; )
935        TIMED( "clear_pair", clear( &sp ); )
936        REPEAT_TIMED( "pop_pair", N,
937                pair(_Bool, char) xp = pop( &tp ); if ( xp > maxp ) { maxp = xp; } )
938        REPEAT_TIMED( "print_pair", N/2, print( out, valp, ":", valp, "\n" ); )
939        fclose(out);
940}
941\end{lstlisting}
942\caption{\protect\CFA Benchmark Test}
943\label{fig:BenchmarkTest}
944\end{figure}
945
946The 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.
947The \CCV variant illustrates an alternative object-oriented idiom where all objects inherit from a base @object@ class, mimicking a Java-like interface;
948hence runtime checks are necessary to safely down-cast objects.
949The 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.
950For 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.
951Note, the C benchmark uses unchecked casts as there is no runtime mechanism to perform such checks, while \CFA and \CC provide type-safety statically.
952
953Figure~\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.
954The graph plots the median of 5 consecutive runs of each program, with an initial warm-up run omitted.
955All code is compiled at \texttt{-O2} by GCC or G++ 6.2.0, with all \CC code compiled as \CCfourteen.
956The 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.
957
958\begin{figure}
959\centering
960\input{timing}
961\caption{Benchmark Timing Results (smaller is better)}
962\label{fig:eval}
963\end{figure}
964
965\begin{table}
966\caption{Properties of benchmark code}
967\label{tab:eval}
968\newcommand{\CT}[1]{\multicolumn{1}{c}{#1}}
969\begin{tabular}{rrrrr}
970                                                                        & \CT{C}        & \CT{\CFA}     & \CT{\CC}      & \CT{\CCV}             \\ \hline
971maximum memory usage (MB)                       & 10001         & 2502          & 2503          & 11253                 \\
972source code size (lines)                        & 247           & 222           & 165           & 339                   \\
973redundant type annotations (lines)      & 39            & 2                     & 2                     & 15                    \\
974binary size (KB)                                        & 14            & 229           & 18            & 38                    \\
975\end{tabular}
976\end{table}
977
978The 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;
979this inefficiency is exacerbated by the second level of generic types in the pair-based benchmarks.
980By 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.
981\CCV is slower than C largely due to the cost of runtime type-checking of down-casts (implemented with @dynamic_cast@);
982There are two outliers in the graph for \CFA: all prints and pop of @pair@.
983Both 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.
984A compiler designed for \CFA could easily perform these optimizations.
985Finally, the binary size for \CFA is larger because of static linking with the \CFA libraries.
986
987\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.
988On 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.
989\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;
990with their omission, the \CCV line count is similar to C.
991We 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.
992
993Raw line-count, however, is a fairly rough measure of code complexity;
994another important factor is how much type information the programmer must manually specify, especially where that information is not checked by the compiler.
995Such 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@).
996To 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.
997The \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.
998The 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).
999These uses are similar to the @new@ expressions in \CC, though the \CFA compiler's type resolver should shortly render even these type casts superfluous.
1000
1001
1002\section{Related Work}
1003
1004
1005\subsection{Polymorphism}
1006
1007\CC is the most similar language to \CFA;
1008both are extensions to C with source and runtime backwards compatibility.
1009The fundamental difference is in their engineering approach to C compatibility and programmer expectation.
1010While \CC provides good backwards compatibility with C, it has a steep learning curve for many of its extensions.
1011For example, polymorphism is provided via three disjoint mechanisms: overloading, inheritance, and templates.
1012The 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.
1013In 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.
1014The key mechanism to support separate compilation is \CFA's \emph{explicit} use of assumed properties for a type.
1015Until \CC~\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;
1016furthermore, \CC concepts are restricted to template polymorphism.
1017
1018Cyclone~\cite{Grossman06} also provides capabilities for polymorphic functions and existential types, similar to \CFA's @forall@ functions and generic types.
1019Cyclone 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.
1020Furthermore, 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@.
1021In \CFA terms, all Cyclone polymorphism must be dtype-static.
1022While 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.
1023\cite{Smith98} present Polymorphic C, an ML dialect with polymorphic functions and 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.
1024
1025\cite{obj-c-book} is an industrially successful extension to C.
1026However, Objective-C is a radical departure from C, using an object-oriented model with message-passing.
1027Objective-C did not support type-checked generics until recently \cite{xcode7}, historically using less-efficient runtime checking of object types.
1028The~\cite{GObject} framework also adds object-oriented programming with runtime type-checking and reference-counting garbage-collection to C;
1029these features are more intrusive additions than those provided by \CFA, in addition to the runtime overhead of reference-counting.
1030\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.
1031Java~\cite{Java8} included generic types in Java~5, which are type-checked at compilation and type-erased at runtime, similar to \CFA's.
1032However, in Java, each object carries its own table of method pointers, while \CFA passes the method pointers separately to maintain a C-compatible layout.
1033Java is also a garbage-collected, object-oriented language, with the associated resource usage and C-interoperability burdens.
1034
1035D~\cite{D}, Go, and~\cite{Rust} are modern, compiled languages with abstraction features similar to \CFA traits, \emph{interfaces} in D and Go and \emph{traits} in Rust.
1036However, 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.
1037D and Go are garbage-collected languages, imposing the associated runtime overhead.
1038The necessity of accounting for data transfer between managed runtimes and the unmanaged C runtime complicates foreign-function interfaces to C.
1039Furthermore, 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.
1040D 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.
1041Rust also possesses much more powerful abstraction capabilities for writing generic code than Go.
1042On 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.
1043\CFA, with its more modest safety features, allows direct ports of C code while maintaining the idiomatic style of the original source.
1044
1045
1046\subsection{Tuples/Variadics}
1047
1048Many programming languages have some form of tuple construct and/or variadic functions, \eg SETL, C, KW-C, \CC, D, Go, Java, ML, and Scala.
1049SETL~\cite{SETL} is a high-level mathematical programming language, with tuples being one of the primary data types.
1050Tuples in SETL allow subscripting, dynamic expansion, and multiple assignment.
1051C 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.
1052KW-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.
1053The main contributions of that work were adding MRVF, tuple mass and multiple assignment, and record-field access.
1054\CCeleven introduced @std::tuple@ as a library variadic template structure.
1055Tuples are a generalization of @std::pair@, in that they allow for arbitrary length, fixed-size aggregation of heterogeneous values.
1056Operations include @std::get<N>@ to extract vales, @std::tie@ to create a tuple of references used for assignment, and lexicographic comparisons.
1057\CCseventeen proposes \emph{structured bindings}~\cite{Sutter15} to eliminate pre-declaring variables and use of @std::tie@ for binding the results.
1058This 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.
1059Furthermore, structured bindings are not a full replacement for @std::tie@, as it always declares new variables.
1060Like \CC, D provides tuples through a library variadic-template structure.
1061Go does not have tuples but supports MRVF.
1062Java'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.
1063Tuples are a fundamental abstraction in most functional programming languages, such as Standard ML~\cite{sml} and~\cite{Scala}, which decompose tuples using pattern matching.
1064
1065
1066\section{Conclusion and Future Work}
1067
1068The 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.
1069While 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.
1070The 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.
1071The contributions are a powerful type-system using parametric polymorphism and overloading, generic types, and tuples, which all have complex interactions.
1072The work is a challenging design, engineering, and implementation exercise.
1073On the surface, the project may appear as a rehash of similar mechanisms in \CC.
1074However, 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.
1075All of these new features are being used by the \CFA development-team to build the \CFA runtime-system.
1076Finally, we demonstrate that \CFA performance for some idiomatic cases is better than C and close to \CC, showing the design is practically applicable.
1077
1078There is ongoing work on a wide range of \CFA feature extensions, including reference types, arrays with size, exceptions, concurrent primitives and modules.
1079(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.)
1080In addition, there are interesting future directions for the polymorphism design.
1081Notably, \CC template functions trade compile time and code bloat for optimal runtime of individual instantiations of polymorphic functions.
1082\CFA polymorphic functions use dynamic virtual-dispatch;
1083the 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.
1084Two 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).
1085These approaches are not mutually exclusive and allow performance optimizations to be applied only when necessary, without suffering global code-bloat.
1086In general, we believe separate compilation, producing smaller code, works well with loaded hardware-caches, which may offset the benefit of larger inlined-code.
1087
1088
1089\section{Acknowledgments}
1090
1091The 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.
1092%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.
1093% 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.
1094
1095
1096\bibliographystyle{plain}
1097\bibliography{cfa}
1098
1099
1100\appendix
1101
1102\section{Benchmark Stack Implementation}
1103\label{sec:BenchmarkStackImplementation}
1104
1105\lstset{basicstyle=\linespread{0.9}\sf\small}
1106
1107Throughout, @/***/@ designates a counted redundant type annotation.
1108
1109\smallskip\noindent
1110\CFA
1111\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1112forall(otype T) struct stack_node {
1113        T value;
1114        stack_node(T) * next;
1115};
1116forall(otype T) void ?{}(stack(T) * s) { (&s->head){ 0 }; }
1117forall(otype T) void ?{}(stack(T) * s, stack(T) t) {
1118        stack_node(T) ** crnt = &s->head;
1119        for ( stack_node(T) * next = t.head; next; next = next->next ) {
1120                *crnt = ((stack_node(T) *)malloc()){ next->value }; /***/
1121                stack_node(T) * acrnt = *crnt;
1122                crnt = &acrnt->next;
1123        }
1124        *crnt = 0;
1125}
1126forall(otype T) stack(T) ?=?(stack(T) * s, stack(T) t) {
1127        if ( s->head == t.head ) return *s;
1128        clear(s);
1129        s{ t };
1130        return *s;
1131}
1132forall(otype T) void ^?{}(stack(T) * s) { clear(s); }
1133forall(otype T) _Bool empty(const stack(T) * s) { return s->head == 0; }
1134forall(otype T) void push(stack(T) * s, T value) {
1135        s->head = ((stack_node(T) *)malloc()){ value, s->head }; /***/
1136}
1137forall(otype T) T pop(stack(T) * s) {
1138        stack_node(T) * n = s->head;
1139        s->head = n->next;
1140        T x = n->value;
1141        ^n{};
1142        free(n);
1143        return x;
1144}
1145forall(otype T) void clear(stack(T) * s) {
1146        for ( stack_node(T) * next = s->head; next; ) {
1147                stack_node(T) * crnt = next;
1148                next = crnt->next;
1149                delete(crnt);
1150        }
1151        s->head = 0;
1152}
1153\end{lstlisting}
1154
1155\medskip\noindent
1156\CC
1157\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1158template<typename T> class stack {
1159        struct node {
1160                T value;
1161                node * next;
1162                node( const T & v, node * n = nullptr ) : value(v), next(n) {}
1163        };
1164        node * head;
1165        void copy(const stack<T>& o) {
1166                node ** crnt = &head;
1167                for ( node * next = o.head;; next; next = next->next ) {
1168                        *crnt = new node{ next->value }; /***/
1169                        crnt = &(*crnt)->next;
1170                }
1171                *crnt = nullptr;
1172        }
1173  public:
1174        stack() : head(nullptr) {}
1175        stack(const stack<T>& o) { copy(o); }
1176        stack(stack<T> && o) : head(o.head) { o.head = nullptr; }
1177        ~stack() { clear(); }
1178        stack & operator= (const stack<T>& o) {
1179                if ( this == &o ) return *this;
1180                clear();
1181                copy(o);
1182                return *this;
1183        }
1184        stack & operator= (stack<T> && o) {
1185                if ( this == &o ) return *this;
1186                head = o.head;
1187                o.head = nullptr;
1188                return *this;
1189        }
1190        bool empty() const { return head == nullptr; }
1191        void push(const T & value) { head = new node{ value, head };  /***/ }
1192        T pop() {
1193                node * n = head;
1194                head = n->next;
1195                T x = std::move(n->value);
1196                delete n;
1197                return x;
1198        }
1199        void clear() {
1200                for ( node * next = head; next; ) {
1201                        node * crnt = next;
1202                        next = crnt->next;
1203                        delete crnt;
1204                }
1205                head = nullptr;
1206        }
1207};
1208\end{lstlisting}
1209
1210\medskip\noindent
1211C
1212\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1213struct stack_node {
1214        void * value;
1215        struct stack_node * next;
1216};
1217struct stack new_stack() { return (struct stack){ NULL }; /***/ }
1218void copy_stack(struct stack * s, const struct stack * t, void * (*copy)(const void *)) {
1219        struct stack_node ** crnt = &s->head;
1220        for ( struct stack_node * next = t->head; next; next = next->next ) {
1221                *crnt = malloc(sizeof(struct stack_node)); /***/
1222                **crnt = (struct stack_node){ copy(next->value) }; /***/
1223                crnt = &(*crnt)->next;
1224        }
1225        *crnt = 0;
1226}
1227_Bool stack_empty(const struct stack * s) { return s->head == NULL; }
1228void push_stack(struct stack * s, void * value) {
1229        struct stack_node * n = malloc(sizeof(struct stack_node)); /***/
1230        *n = (struct stack_node){ value, s->head }; /***/
1231        s->head = n;
1232}
1233void * pop_stack(struct stack * s) {
1234        struct stack_node * n = s->head;
1235        s->head = n->next;
1236        void * x = n->value;
1237        free(n);
1238        return x;
1239}
1240void clear_stack(struct stack * s, void (*free_el)(void *)) {
1241        for ( struct stack_node * next = s->head; next; ) {
1242                struct stack_node * crnt = next;
1243                next = crnt->next;
1244                free_el(crnt->value);
1245                free(crnt);
1246        }
1247        s->head = NULL;
1248}
1249\end{lstlisting}
1250
1251\medskip\noindent
1252\CCV
1253\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1254stack::node::node( const object & v, node * n ) : value( v.new_copy() ), next( n ) {}
1255void stack::copy(const stack & o) {
1256        node ** crnt = &head;
1257        for ( node * next = o.head; next; next = next->next ) {
1258                *crnt = new node{ *next->value };
1259                crnt = &(*crnt)->next;
1260        }
1261        *crnt = nullptr;
1262}
1263stack::stack() : head(nullptr) {}
1264stack::stack(const stack & o) { copy(o); }
1265stack::stack(stack && o) : head(o.head) { o.head = nullptr; }
1266stack::~stack() { clear(); }
1267stack & stack::operator= (const stack & o) {
1268        if ( this == &o ) return *this;
1269        clear();
1270        copy(o);
1271        return *this;
1272}
1273stack & stack::operator= (stack && o) {
1274        if ( this == &o ) return *this;
1275        head = o.head;
1276        o.head = nullptr;
1277        return *this;
1278}
1279bool stack::empty() const { return head == nullptr; }
1280void stack::push(const object & value) { head = new node{ value, head }; /***/ }
1281ptr<object> stack::pop() {
1282        node * n = head;
1283        head = n->next;
1284        ptr<object> x = std::move(n->value);
1285        delete n;
1286        return x;
1287}
1288void stack::clear() {
1289        for ( node * next = head; next; ) {
1290                node * crnt = next;
1291                next = crnt->next;
1292                delete crnt;
1293        }
1294        head = nullptr;
1295}
1296\end{lstlisting}
1297
1298
1299\begin{comment}
1300
1301\subsubsection{bench.h}
1302(\texttt{bench.hpp} is similar.)
1303
1304\lstinputlisting{evaluation/bench.h}
1305
1306\subsection{C}
1307
1308\subsubsection{c-stack.h} ~
1309
1310\lstinputlisting{evaluation/c-stack.h}
1311
1312\subsubsection{c-stack.c} ~
1313
1314\lstinputlisting{evaluation/c-stack.c}
1315
1316\subsubsection{c-pair.h} ~
1317
1318\lstinputlisting{evaluation/c-pair.h}
1319
1320\subsubsection{c-pair.c} ~
1321
1322\lstinputlisting{evaluation/c-pair.c}
1323
1324\subsubsection{c-print.h} ~
1325
1326\lstinputlisting{evaluation/c-print.h}
1327
1328\subsubsection{c-print.c} ~
1329
1330\lstinputlisting{evaluation/c-print.c}
1331
1332\subsubsection{c-bench.c} ~
1333
1334\lstinputlisting{evaluation/c-bench.c}
1335
1336\subsection{\CFA}
1337
1338\subsubsection{cfa-stack.h} ~
1339
1340\lstinputlisting{evaluation/cfa-stack.h}
1341
1342\subsubsection{cfa-stack.c} ~
1343
1344\lstinputlisting{evaluation/cfa-stack.c}
1345
1346\subsubsection{cfa-print.h} ~
1347
1348\lstinputlisting{evaluation/cfa-print.h}
1349
1350\subsubsection{cfa-print.c} ~
1351
1352\lstinputlisting{evaluation/cfa-print.c}
1353
1354\subsubsection{cfa-bench.c} ~
1355
1356\lstinputlisting{evaluation/cfa-bench.c}
1357
1358\subsection{\CC}
1359
1360\subsubsection{cpp-stack.hpp} ~
1361
1362\lstinputlisting[language=c++]{evaluation/cpp-stack.hpp}
1363
1364\subsubsection{cpp-print.hpp} ~
1365
1366\lstinputlisting[language=c++]{evaluation/cpp-print.hpp}
1367
1368\subsubsection{cpp-bench.cpp} ~
1369
1370\lstinputlisting[language=c++]{evaluation/cpp-bench.cpp}
1371
1372\subsection{\CCV}
1373
1374\subsubsection{object.hpp} ~
1375
1376\lstinputlisting[language=c++]{evaluation/object.hpp}
1377
1378\subsubsection{cpp-vstack.hpp} ~
1379
1380\lstinputlisting[language=c++]{evaluation/cpp-vstack.hpp}
1381
1382\subsubsection{cpp-vstack.cpp} ~
1383
1384\lstinputlisting[language=c++]{evaluation/cpp-vstack.cpp}
1385
1386\subsubsection{cpp-vprint.hpp} ~
1387
1388\lstinputlisting[language=c++]{evaluation/cpp-vprint.hpp}
1389
1390\subsubsection{cpp-vbench.cpp} ~
1391
1392\lstinputlisting[language=c++]{evaluation/cpp-vbench.cpp}
1393\end{comment}
1394
1395\end{document}
1396
1397% Local Variables: %
1398% tab-width: 4 %
1399% compile-command: "make" %
1400% End: %
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