source: doc/generic_types/generic_types.tex @ c13b2b8

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Last change on this file since c13b2b8 was c13b2b8, checked in by Peter A. Buhr <pabuhr@…>, 4 years ago

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48\makeatother
49
50% Useful macros
51\newcommand{\CFA}{C$\mathbf\forall$\xspace} % Cforall symbolic name
52\newcommand{\CC}{\rm C\kern-.1em\hbox{+\kern-.25em+}\xspace} % C++ symbolic name
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59\newcommand{\Textbf}[1]{{\color{red}\textbf{#1}}}
60
61% CFA programming language, based on ANSI C (with some gcc additions)
62\lstdefinelanguage{CFA}[ANSI]{C}{
63        morekeywords={_Alignas,_Alignof,__alignof,__alignof__,asm,__asm,__asm__,_At,_Atomic,__attribute,__attribute__,auto,
64                _Bool,catch,catchResume,choose,_Complex,__complex,__complex__,__const,__const__,disable,dtype,enable,__extension__,
65                fallthrough,fallthru,finally,forall,ftype,_Generic,_Imaginary,inline,__label__,lvalue,_Noreturn,one_t,otype,restrict,_Static_assert,
66                _Thread_local,throw,throwResume,trait,try,ttype,typeof,__typeof,__typeof__,zero_t},
67}%
68
69\lstset{
70language=CFA,
71columns=fullflexible,
72basicstyle=\linespread{0.9}\sf,                                                 % reduce line spacing and use sanserif font
73stringstyle=\tt,                                                                                % use typewriter font
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76%mathescape=true,                                                                               % LaTeX math escape in CFA code $...$
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86        {<-}{$\leftarrow$}2 {=>}{$\Rightarrow$}2,
87moredelim=**[is][\color{red}]{`}{`},
88}% lstset
89
90% inline code @...@
91\lstMakeShortInline@%
92
93% ACM Information
94\citestyle{acmauthoryear}
95
96\acmJournal{PACMPL}
97
98\title{Generic and Tuple Types with Efficient Dynamic Layout in \CFA}
99
100\author{Aaron Moss}
101\email{a3moss@uwaterloo.ca}
102\author{Robert Schluntz}
103\email{rschlunt@uwaterloo.ca}
104\author{Peter Buhr}
105\email{pabuhr@uwaterloo.ca}
106\affiliation{%
107        \institution{University of Waterloo}
108        \department{David R. Cheriton School of Computer Science}
109        \streetaddress{Davis Centre, University of Waterloo}
110        \city{Waterloo}
111        \state{ON}
112        \postcode{N2L 3G1}
113        \country{Canada}
114}
115
116\terms{generic, tuple, variadic, types}
117\keywords{generic types, tuple types, variadic types, polymorphic functions, C, Cforall}
118
119\begin{CCSXML}
120<ccs2012>
121<concept>
122<concept_id>10011007.10011006.10011008.10011024.10011025</concept_id>
123<concept_desc>Software and its engineering~Polymorphism</concept_desc>
124<concept_significance>500</concept_significance>
125</concept>
126<concept>
127<concept_id>10011007.10011006.10011008.10011024.10011028</concept_id>
128<concept_desc>Software and its engineering~Data types and structures</concept_desc>
129<concept_significance>500</concept_significance>
130</concept>
131<concept>
132<concept_id>10011007.10011006.10011041.10011047</concept_id>
133<concept_desc>Software and its engineering~Source code generation</concept_desc>
134<concept_significance>300</concept_significance>
135</concept>
136</ccs2012>
137\end{CCSXML}
138
139\ccsdesc[500]{Software and its engineering~Polymorphism}
140\ccsdesc[500]{Software and its engineering~Data types and structures}
141\ccsdesc[300]{Software and its engineering~Source code generation}
142
143\begin{abstract}
144The 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.
145This installation base and the programmers producing it represent a massive software-engineering investment spanning decades and likely to continue for decades more.
146Nonetheless, C, first standardized over thirty years ago, lacks many features that make programming in more modern languages safer and more productive.
147The 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.
148Prior 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.
149Specifically, \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.
150This 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.
151\end{abstract}
152
153\begin{document}
154\maketitle
155
156
157\section{Introduction and Background}
158
159The 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.
160This installation base and the programmers producing it represent a massive software-engineering investment spanning decades and likely to continue for decades more.
161The \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.
162The top 3 rankings over the past 30 years are:
163\lstDeleteShortInline@%
164\begin{center}
165\setlength{\tabcolsep}{10pt}
166\begin{tabular}{@{}rccccccc@{}}
167                & 2017  & 2012  & 2007  & 2002  & 1997  & 1992  & 1987          \\ \hline
168Java    & 1             & 1             & 1             & 1             & 12    & -             & -                     \\
169\Textbf{C}      & \Textbf{2}& \Textbf{2}& \Textbf{2}& \Textbf{2}& \Textbf{1}& \Textbf{1}& \Textbf{1}    \\
170\CC             & 3             & 3             & 3             & 3             & 2             & 2             & 4                     \\
171\end{tabular}
172\end{center}
173\lstMakeShortInline@%
174Love it or hate it, C is extremely popular, highly used, and one of the few systems languages.
175In many cases, \CC is often used solely as a better C.
176Nonetheless, C, first standardized over thirty years ago, lacks many features that make programming in more modern languages safer and more productive.
177
178\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.
179The four key design goals for \CFA~\citep{Bilson03} are:
180(1) The behaviour of standard C code must remain the same when translated by a \CFA compiler as when translated by a C compiler;
181(2) Standard C code must be as fast and as small when translated by a \CFA compiler as when translated by a C compiler;
182(3) \CFA code must be at least as portable as standard C code;
183(4) Extensions introduced by \CFA must be translated in the most efficient way possible.
184These 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.
185\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.
186
187\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).
188Ultimately, a compiler is necessary for advanced features and optimal performance.
189
190This 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.
191Specifically, 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.
192The new constructs are empirically compared with both standard C and \CC; the results show the new design is comparable in performance.
193
194
195\subsection{Polymorphic Functions}
196\label{sec:poly-fns}
197
198\CFA's polymorphism was originally formalized by \citet{Ditchfield92}, and first implemented by \citet{Bilson03}.
199The 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):
200\begin{lstlisting}
201`forall( otype T )` T identity( T val ) { return val; }
202int forty_two = identity( 42 );                         $\C{// T is bound to int, forty\_two == 42}$
203\end{lstlisting}
204The @identity@ function above can be applied to any complete \emph{object type} (or @otype@).
205The 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.
206The \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.
207If this extra information is not needed, \eg for a pointer, the type parameter can be declared as a \emph{data type} (or @dtype@).
208
209In \CFA, the polymorphism runtime-cost is spread over each polymorphic call, due to passing more arguments to polymorphic functions;
210the experiments in Section~\ref{sec:eval} show this overhead is similar to \CC virtual-function calls.
211A design advantage is that, unlike \CC template-functions, \CFA polymorphic-functions are compatible with C \emph{separate compilation}, preventing compilation and code bloat.
212
213Since 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.
214For example, the function @twice@ can be defined using the \CFA syntax for operator overloading:
215\begin{lstlisting}
216forall( otype T `| { T ?+?(T, T); }` ) T twice( T x ) { return x + x; } $\C{// ? denotes operands}$
217int val = twice( twice( 3.7 ) );
218\end{lstlisting}
219which works for any type @T@ with a matching addition operator.
220The 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@.
221There 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.
222The first approach has a late conversion from @double@ to @int@ on the final assignment, while the second has an eager conversion to @int@.
223\CFA minimizes the number of conversions and their potential to lose information, so it selects the first approach, which corresponds with C-programmer intuition.
224
225Crucial to the design of a new programming language are the libraries to access thousands of external software features.
226Like \CC, \CFA inherits a massive compatible library-base, where other programming languages must rewrite or provide fragile inter-language communication with C.
227A simple example is leveraging the existing type-unsafe (@void *@) C @bsearch@ to binary search a sorted floating-point array:
228\begin{lstlisting}
229void * bsearch( const void * key, const void * base, size_t nmemb, size_t size,
230                                int (* compar)( const void *, const void * ));
231int comp( const void * t1, const void * t2 ) { return *(double *)t1 < *(double *)t2 ? -1 :
232                                *(double *)t2 < *(double *)t1 ? 1 : 0; }
233double key = 5.0, vals[10] = { /* 10 floating-point values */ };
234double * val = (double *)bsearch( &key, vals, 10, sizeof(vals[0]), comp );      $\C{// search sorted array}$
235\end{lstlisting}
236which can be augmented simply with a generalized, type-safe, \CFA-overloaded wrappers:
237\begin{lstlisting}
238forall( otype T | { int ?<?( T, T ); } ) T * bsearch( T key, const T * arr, size_t size ) {
239        int comp( const void * t1, const void * t2 ) { /* as above with double changed to T */ }
240        return (T *)bsearch( &key, arr, size, sizeof(T), comp ); }
241forall( otype T | { int ?<?( T, T ); } ) unsigned int bsearch( T key, const T * arr, size_t size ) {
242        T * result = bsearch( key, arr, size ); $\C{// call first version}$
243        return result ? result - arr : size; }  $\C{// pointer subtraction includes sizeof(T)}$
244double * val = bsearch( 5.0, vals, 10 );        $\C{// selection based on return type}$
245int posn = bsearch( 5.0, vals, 10 );
246\end{lstlisting}
247The nested function @comp@ provides the hidden interface from typed \CFA to untyped (@void *@) C, plus the cast of the result.
248Providing a hidden @comp@ function in \CC is awkward as lambdas do not use C calling-conventions and template declarations cannot appear at block scope.
249As well, an alternate kind of return is made available: position versus pointer to found element.
250\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@.
251
252\CFA has replacement libraries condensing hundreds of existing C functions into tens of \CFA overloaded functions, all without rewriting the actual computations.
253For example, it is possible to write a type-safe \CFA wrapper @malloc@ based on the C @malloc@:
254\begin{lstlisting}
255forall( dtype T | sized(T) ) T * malloc( void ) { return (T *)malloc( sizeof(T) ); }
256int * ip = malloc();                                            $\C{// select type and size from left-hand side}$
257double * dp = malloc();
258struct S {...} * sp = malloc();
259\end{lstlisting}
260where the return type supplies the type/size of the allocation, which is impossible in most type systems.
261
262Call-site inferencing and nested functions provide a localized form of inheritance.
263For example, the \CFA @qsort@ only sorts in ascending order using @<@.
264However, it is trivial to locally change this behaviour:
265\begin{lstlisting}
266forall( otype T | { int ?<?( T, T ); } ) void qsort( const T * arr, size_t size ) { /* use C qsort */ }
267{       int ?<?( double x, double y ) { return x `>` y; }       $\C{// locally override behaviour}$
268        qsort( vals, size );                                    $\C{// descending sort}$
269}
270\end{lstlisting}
271Within the block, the nested version of @<@ performs @>@ and this local version overrides the built-in @<@ so it is passed to @qsort@.
272Hence, programmers can easily form local environments, adding and modifying appropriate functions, to maximize reuse of other existing functions and types.
273
274Finally, \CFA allows variable overloading:
275%\lstDeleteShortInline@%
276%\par\smallskip
277%\begin{tabular}{@{}l@{\hspace{1.5\parindent}}||@{\hspace{1.5\parindent}}l@{}}
278\begin{lstlisting}
279short int MAX = ...;   int MAX = ...;  double MAX = ...;
280short int s = MAX;    int i = MAX;    double d = MAX;   $\C{// select correct MAX}$
281\end{lstlisting}
282%\end{lstlisting}
283%&
284%\begin{lstlisting}
285%\end{tabular}
286%\smallskip\par\noindent
287%\lstMakeShortInline@%
288Here, the single name @MAX@ replaces all the C type-specific names: @SHRT_MAX@, @INT_MAX@, @DBL_MAX@.
289As 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.
290In addition, several operations are defined in terms values @0@ and @1@, \eg:
291\begin{lstlisting}
292int x;
293if (x) x++                                                                      $\C{// if (x != 0) x += 1;}$
294\end{lstlisting}
295Every 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.
296Due 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.
297The 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.
298
299
300\subsection{Traits}
301
302\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:
303\begin{lstlisting}
304trait summable( otype T ) {
305        void ?{}( T *, zero_t );                                $\C{// constructor from 0 literal}$
306        T ?+?( T, T );                                                  $\C{// assortment of additions}$
307        T ?+=?( T *, T );
308        T ++?( T * );
309        T ?++( T * ); };
310forall( otype T `| summable( T )` ) T sum( T a[$\,$], size_t size ) {  // use trait
311        `T` total = { `0` };                                    $\C{// instantiate T from 0 by calling its constructor}$
312        for ( unsigned int i = 0; i < size; i += 1 ) total `+=` a[i]; $\C{// select appropriate +}$
313        return total; }
314\end{lstlisting}
315
316In 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:
317\begin{lstlisting}
318trait otype( dtype T | sized(T) ) {  // sized is a pseudo-trait for types with known size and alignment
319        void ?{}( T * );                                                $\C{// default constructor}$
320        void ?{}( T *, T );                                             $\C{// copy constructor}$
321        void ?=?( T *, T );                                             $\C{// assignment operator}$
322        void ^?{}( T * ); };                                    $\C{// destructor}$
323\end{lstlisting}
324Given 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.
325
326In 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.
327Hence, trait names play no part in type equivalence;
328the names are simply macros for a list of polymorphic assertions, which are expanded at usage sites.
329Nevertheless, trait names form a logical subtype-hierarchy with @dtype@ at the top, where traits often contain overlapping assertions, \eg operator @+@.
330Traits are used like interfaces in Java or abstract base-classes in \CC, but without the nominal inheritance-relationships.
331Instead, 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.
332Hence, 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.
333(Nominal inheritance can be approximated with traits using marker variables or functions, as is done in Go.)
334
335% Nominal inheritance can be simulated with traits using marker variables or functions:
336% \begin{lstlisting}
337% trait nominal(otype T) {
338%     T is_nominal;
339% };
340% int is_nominal;                                                               $\C{// int now satisfies the nominal trait}$
341% \end{lstlisting}
342%
343% 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:
344% \begin{lstlisting}
345% trait pointer_like(otype Ptr, otype El) {
346%     lvalue El *?(Ptr);                                                $\C{// Ptr can be dereferenced into a modifiable value of type El}$
347% }
348% struct list {
349%     int value;
350%     list * next;                                                              $\C{// may omit "struct" on type names as in \CC}$
351% };
352% typedef list * list_iterator;
353%
354% lvalue int *?( list_iterator it ) { return it->value; }
355% \end{lstlisting}
356% 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@).
357% 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.
358
359
360\section{Generic Types}
361
362One of the known shortcomings of standard C is that it does not provide reusable type-safe abstractions for generic data structures and algorithms.
363Broadly speaking, there are three approaches to implement abstract data-structures in C.
364One approach is to write bespoke data structures for each context in which they are needed.
365While 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.
366A 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.
367However, 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.
368A 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.
369Furthermore, writing and using preprocessor macros can be unnatural and inflexible.
370
371\CC, Java, and other languages use \emph{generic types} to produce type-safe abstract data-types.
372\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.
373However, for known concrete parameters, the generic-type definition can be inlined, like \CC templates.
374
375A 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:
376\begin{lstlisting}
377forall( otype R, otype S ) struct pair {
378        R first;
379        S second;
380};
381forall( otype T ) T value( pair( const char *, T ) p ) { return p.second; }
382forall( dtype F, otype T ) T value_p( pair( F *, T * ) p ) { return * p.second; }
383pair( const char *, int ) p = { "magic", 42 };
384int magic = value( p );
385pair( void *, int * ) q = { 0, &p.second };
386magic = value_p( q );
387double d = 1.0;
388pair( double *, double * ) r = { &d, &d };
389d = value_p( r );
390\end{lstlisting}
391
392\CFA classifies generic types as either \emph{concrete} or \emph{dynamic}.
393Concrete types have a fixed memory layout regardless of type parameters, while dynamic types vary in memory layout depending on their type parameters.
394A type may have polymorphic parameters but still be concrete, called \emph{dtype-static}.
395Polymorphic 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.
396
397\CFA generic types also allow checked argument-constraints.
398For example, the following declaration of a sorted set-type ensures the set key supports equality and relational comparison:
399\begin{lstlisting}
400forall( otype Key | { _Bool ?==?(Key, Key); _Bool ?<?(Key, Key); } ) struct sorted_set;
401\end{lstlisting}
402
403
404\subsection{Concrete Generic-Types}
405
406The \CFA translator template-expands concrete generic-types into new structure types, affording maximal inlining.
407To 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.
408For 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.
409For example, the concrete instantiation for @pair( const char *, int )@ is:
410\begin{lstlisting}
411struct _pair_conc1 {
412        const char * first;
413        int second;
414};
415\end{lstlisting}
416
417A concrete generic-type with dtype-static parameters is also expanded to a structure type, but this type is used for all matching instantiations.
418In 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:
419\begin{lstlisting}
420struct _pair_conc0 {
421        void * first;
422        void * second;
423};
424\end{lstlisting}
425
426
427\subsection{Dynamic Generic-Types}
428
429Though \CFA implements concrete generic-types efficiently, it also has a fully general system for dynamic generic types.
430As 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.
431Dynamic generic-types also have an \emph{offset array} containing structure-member offsets.
432A dynamic generic-union needs no such offset array, as all members are at offset 0, but size and alignment are still necessary.
433Access 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.
434
435The offset arrays are statically generated where possible.
436If 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;
437if 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.
438As 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 )@.
439The offset array @_offsetof_pair@ is generated at the call site as @size_t _offsetof_pair[] = { offsetof(_pair_conc1, first), offsetof(_pair_conc1, second) }@.
440
441In some cases the offset arrays cannot be statically generated.
442For 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.
443\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.
444The \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.
445These 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).
446Results of these layout functions are cached so that they are only computed once per type per function. %, as in the example below for @pair@.
447Layout functions also allow generic types to be used in a function definition without reflecting them in the function signature.
448For 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.
449This function could acquire the layout for @set(T)@ by calling its layout function with the layout of @T@ implicitly passed into the function.
450
451Whether a type is concrete, dtype-static, or dynamic is decided solely on the type parameters and @forall@ clause on a declaration.
452This 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.
453If 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.
454
455
456\subsection{Applications}
457\label{sec:generic-apps}
458
459The reuse of dtype-static structure instantiations enables useful programming patterns at zero runtime cost.
460The 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@:
461\begin{lstlisting}
462forall(dtype T) int lexcmp( pair( T *, T * ) * a, pair( T *, T * ) * b, int (* cmp)( T *, T * ) ) {
463        return cmp( a->first, b->first ) ? : cmp( a->second, b->second );
464}
465\end{lstlisting}
466%       int c = cmp( a->first, b->first );
467%       if ( c == 0 ) c = cmp( a->second, b->second );
468%       return c;
469Since @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.
470
471Another useful pattern enabled by reused dtype-static type instantiations is zero-cost \emph{tag-structures}.
472Sometimes information is only used for type-checking and can be omitted at runtime, \eg:
473\begin{lstlisting}
474forall(dtype Unit) struct scalar { unsigned long value; };
475struct metres {};
476struct litres {};
477
478forall(dtype U) scalar(U) ?+?( scalar(U) a, scalar(U) b ) {
479        return (scalar(U)){ a.value + b.value };
480}
481scalar(metres) half_marathon = { 21093 };
482scalar(litres) swimming_pool = { 2500000 };
483scalar(metres) marathon = half_marathon + half_marathon;
484scalar(litres) two_pools = swimming_pool + swimming_pool;
485marathon + swimming_pool;                                       $\C{// compilation ERROR}$
486\end{lstlisting}
487@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 @?+?@.
488These implementations may even be separately compiled, unlike \CC template functions.
489However, the \CFA type-checker ensures matching types are used by all calls to @?+?@, preventing nonsensical computations like adding a length to a volume.
490
491
492\section{Tuples}
493\label{sec:tuples}
494
495In many languages, functions can return at most one value;
496however, many operations have multiple outcomes, some exceptional.
497Consider C's @div@ and @remquo@ functions, which return the quotient and remainder for a division of integer and floating-point values, respectively.
498\begin{lstlisting}
499typedef struct { int quo, rem; } div_t;         $\C{// from include stdlib.h}$
500div_t div( int num, int den );
501double remquo( double num, double den, int * quo );
502div_t qr = div( 13, 5 );                                        $\C{// return quotient/remainder aggregate}$
503int q;
504double r = remquo( 13.5, 5.2, &q );                     $\C{// return remainder, alias quotient}$
505\end{lstlisting}
506@div@ aggregates the quotient/remainder in a structure, while @remquo@ aliases a parameter to an argument.
507Both approaches are awkward.
508Alternatively, a programming language can directly support returning multiple values, \eg in \CFA:
509\begin{lstlisting}
510[ int, int ] div( int num, int den );           $\C{// return two integers}$
511[ double, double ] div( double num, double den ); $\C{// return two doubles}$
512int q, r;                                                                       $\C{// overloaded variable names}$
513double q, r;
514[ q, r ] = div( 13, 5 );                                        $\C{// select appropriate div and q, r}$
515[ q, r ] = div( 13.5, 5.2 );                            $\C{// assign into tuple}$
516\end{lstlisting}
517Clearly, this approach is straightforward to understand and use;
518therefore, why do few programming languages support this obvious feature or provide it awkwardly?
519The answer is that there are complex consequences that cascade through multiple aspects of the language, especially the type-system.
520This section show these consequences and how \CFA handles them.
521
522
523\subsection{Tuple Expressions}
524
525The addition of multiple-return-value functions (MRVF) are useless without a syntax for accepting multiple values at the call-site.
526The simplest mechanism for capturing the return values is variable assignment, allowing the values to be retrieved directly.
527As 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}.
528
529However, 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:
530\begin{lstlisting}
531printf( "%d %d\n", div( 13, 5 ) );                      $\C{// return values seperated into arguments}$
532\end{lstlisting}
533Here, the values returned by @div@ are composed with the call to @printf@ by flattening the tuple into separate arguments.
534However, the \CFA type-system must support significantly more complex composition:
535\begin{lstlisting}
536[ int, int ] foo$\(_1\)$( int );
537[ double ] foo$\(_2\)$( int );
538void bar( int, double, double );
539bar( foo( 3 ), foo( 3 ) );
540\end{lstlisting}
541The type-resolver only has the tuple return-types to resolve the call to @bar@ as the @foo@ parameters are identical, which involves unifying the possible @foo@ functions with @bar@'s parameter list.
542No combination of @foo@s are an exact match with @bar@'s parameters, so the resolver applies C conversions.
543The minimal cost is @bar( foo@$_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.
544
545
546\subsection{Tuple Variables}
547
548An important observation from function composition is that new variable names are not required to initialize parameters from an MRVF.
549\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:
550\begin{lstlisting}
551[ int, int ] qr = div( 13, 5 );                         $\C{// tuple-variable declaration and initialization}$
552[ double, double ] qr = div( 13.5, 5.2 );
553\end{lstlisting}
554where the tuple variable-name serves the same purpose as the parameter name(s).
555Tuple variables can be composed of any types, except for array types, since array sizes are generally unknown.
556
557One way to access the tuple-variable components is with assignment or composition:
558\begin{lstlisting}
559[ q, r ] = qr;                                                          $\C{// access tuple-variable components}$
560printf( "%d %d\n", qr );
561\end{lstlisting}
562\CFA also supports \emph{tuple indexing} to access single components of a tuple expression:
563\begin{lstlisting}
564[int, int] * p = &qr;                                           $\C{// tuple pointer}$
565int rem = qr.1;                                                         $\C{// access remainder}$
566int quo = div( 13, 5 ).0;                                       $\C{// access quotient}$
567p->0 = 5;                                                                       $\C{// change quotient}$
568bar( qr.1, qr );                                                        $\C{// pass remainder and quotient/remainder}$
569rem = [42, div( 13, 5 )].0.1;                           $\C{// access 2nd component of 1st component of tuple expression}$
570\end{lstlisting}
571
572
573\subsection{Flattening and Restructuring}
574
575In function call contexts, tuples support implicit flattening and restructuring conversions.
576Tuple flattening recursively expands a tuple into the list of its basic components.
577Tuple structuring packages a list of expressions into a value of tuple type, \eg:
578%\lstDeleteShortInline@%
579%\par\smallskip
580%\begin{tabular}{@{}l@{\hspace{1.5\parindent}}||@{\hspace{1.5\parindent}}l@{}}
581\begin{lstlisting}
582int f( int, int );
583int g( [int, int] );
584int h( int, [int, int] );
585[int, int] x;
586int y;
587f( x );                 $\C{// flatten}$
588g( y, 10 );             $\C{// structure}$
589h( x, y );              $\C{// flatten and structure}$
590\end{lstlisting}
591%\end{lstlisting}
592%&
593%\begin{lstlisting}
594%\end{tabular}
595%\smallskip\par\noindent
596%\lstMakeShortInline@%
597In the call to @f@, @x@ is implicitly flattened so the components of @x@ are passed as the two arguments.
598In 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@.
599Finally, 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]@.
600The 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.
601
602
603\subsection{Tuple Assignment}
604
605An assignment where the left side is a tuple type is called \emph{tuple assignment}.
606There 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.
607%\lstDeleteShortInline@%
608%\par\smallskip
609%\begin{tabular}{@{}l@{\hspace{1.5\parindent}}||@{\hspace{1.5\parindent}}l@{}}
610\begin{lstlisting}
611int x = 10;
612double y = 3.5;
613[int, double] z;
614z = [x, y];             $\C{// multiple assignment}$
615[x, y] = z;             $\C{// multiple assignment}$
616z = 10;                 $\C{// mass assignment}$
617[y, x] = 3.14$\C{// mass assignment}$
618\end{lstlisting}
619%\end{lstlisting}
620%&
621%\begin{lstlisting}
622%\end{tabular}
623%\smallskip\par\noindent
624%\lstMakeShortInline@%
625Both kinds of tuple assignment have parallel semantics, so that each value on the left and right side is evaluated before any assignments occur.
626As 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]@.
627This 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.
628For example, @[y, x] = 3.14@ performs the assignments @y = 3.14@ and @x = 3.14@, yielding @y == 3.14@ and @x == 3@;
629whereas C cascading assignment @y = x = 3.14@ performs the assignments @x = 3.14@ and @y = x@, yielding @3@ in @y@ and @x@.
630Finally, 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.
631This example shows mass, multiple, and cascading assignment used in one expression:
632\begin{lstlisting}
633void f( [int, int] );
634f( [x, y] = z = 1.5 );                                          $\C{// assignments in parameter list}$
635\end{lstlisting}
636
637
638\subsection{Member Access}
639
640It is also possible to access multiple fields from a single expression using a \emph{member-access}.
641The result is a single tuple-valued expression whose type is the tuple of the types of the members, \eg:
642\begin{lstlisting}
643struct S { int x; double y; char * z; } s;
644s.[x, y, z] = 0;
645\end{lstlisting}
646Here, the mass assignment sets all members of @s@ to zero.
647Since 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).
648%\lstDeleteShortInline@%
649%\par\smallskip
650%\begin{tabular}{@{}l@{\hspace{1.5\parindent}}||@{\hspace{1.5\parindent}}l@{}}
651\begin{lstlisting}
652[int, int, long, double] x;
653void f( double, long );
654x.[0, 1] = x.[1, 0];    $\C{// rearrange: [x.0, x.1] = [x.1, x.0]}$
655f( x.[0, 3] );            $\C{// drop: f(x.0, x.3)}$
656[int, int, int] y = x.[2, 0, 2]; $\C{// duplicate: [y.0, y.1, y.2] = [x.2, x.0.x.2]}$
657\end{lstlisting}
658%\end{lstlisting}
659%&
660%\begin{lstlisting}
661%\end{tabular}
662%\smallskip\par\noindent
663%\lstMakeShortInline@%
664It is also possible for a member access to contain other member accesses, \eg:
665\begin{lstlisting}
666struct A { double i; int j; };
667struct B { int * k; short l; };
668struct C { int x; A y; B z; } v;
669v.[x, y.[i, j], z.k];                                           $\C{// [v.x, [v.y.i, v.y.j], v.z.k]}$
670\end{lstlisting}
671
672
673\begin{comment}
674\subsection{Casting}
675
676In C, the cast operator is used to explicitly convert between types.
677In \CFA, the cast operator has a secondary use as type ascription.
678That 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:
679\begin{lstlisting}
680int f();     // (1)
681double f()// (2)
682
683f();       // ambiguous - (1),(2) both equally viable
684(int)f()// choose (2)
685\end{lstlisting}
686
687Since casting is a fundamental operation in \CFA, casts should be given a meaningful interpretation in the context of tuples.
688Taking a look at standard C provides some guidance with respect to the way casts should work with tuples:
689\begin{lstlisting}
690int f();
691void g();
692
693(void)f()// (1)
694(int)g()// (2)
695\end{lstlisting}
696In C, (1) is a valid cast, which calls @f@ and discards its result.
697On the other hand, (2) is invalid, because @g@ does not produce a result, so requesting an @int@ to materialize from nothing is nonsensical.
698Generalizing 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.
699
700Formally, 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 $T_i$.
701Excess 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.
702This approach follows naturally from the way that a cast to @void@ works in C.
703
704For example, in
705\begin{lstlisting}
706[int, int, int] f();
707[int, [int, int], int] g();
708
709([int, double])f();           $\C{// (1)}$
710([int, int, int])g();         $\C{// (2)}$
711([void, [int, int]])g();      $\C{// (3)}$
712([int, int, int, int])g();    $\C{// (4)}$
713([int, [int, int, int]])g()$\C{// (5)}$
714\end{lstlisting}
715
716(1) discards the last element of the return value and converts the second element to @double@.
717Since @int@ is effectively a 1-element tuple, (2) discards the second component of the second element of the return value of @g@.
718If @g@ is free of side effects, this expression is equivalent to @[(int)(g().0), (int)(g().1.0), (int)(g().2)]@.
719Since @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)]@).
720
721Note 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.}.
722As such, (4) is invalid because the cast target type contains 4 components, while the source type contains only 3.
723Similarly, (5) is invalid because the cast @([int, int, int])(g().1)@ is invalid.
724That is, it is invalid to cast @[int, int]@ to @[int, int, int]@.
725\end{comment}
726
727
728\subsection{Polymorphism}
729
730Tuples also integrate with \CFA polymorphism as a kind of generic type.
731Due 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:
732\begin{lstlisting}
733forall(otype T, dtype U) void f( T x, U * y );
734f( [5, "hello"] );
735\end{lstlisting}
736where @[5, "hello"]@ is flattened, giving argument list @5, "hello"@, and @T@ binds to @int@ and @U@ binds to @const char@.
737Tuples, however, may contain polymorphic components.
738For example, a plus operator can be written to add two triples together.
739\begin{lstlisting}
740forall(otype T | { T ?+?( T, T ); }) [T, T, T] ?+?( [T, T, T] x, [T, T, T] y ) {
741        return [x.0 + y.0, x.1 + y.1, x.2 + y.2];
742}
743[int, int, int] x;
744int i1, i2, i3;
745[i1, i2, i3] = x + ([10, 20, 30]);
746\end{lstlisting}
747
748Flattening and restructuring conversions are also applied to tuple types in polymorphic type assertions.
749\begin{lstlisting}
750int f( [int, double], double );
751forall(otype T, otype U | { T f( T, U, U ); }) void g( T, U );
752g( 5, 10.21 );
753\end{lstlisting}
754Hence, function parameter and return lists are flattened for the purposes of type unification allowing the example to pass expression resolution.
755This relaxation is possible by extending the thunk scheme described by \citet{Bilson03}.
756Whenever 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:
757\begin{lstlisting}
758int _thunk( int _p0, double _p1, double _p2 ) { return f( [_p0, _p1], _p2 ); }
759\end{lstlisting}
760so the thunk provides flattening and structuring conversions to inferred functions, improving the compatibility of tuples and polymorphism.
761These thunks take advantage of GCC C nested-functions to produce closures that have the usual function pointer signature.
762
763
764\subsection{Variadic Tuples}
765\label{sec:variadic-tuples}
766
767To define variadic functions, \CFA adds a new kind of type parameter, @ttype@ (tuple type).
768Matching against a @ttype@ parameter consumes all remaining argument components and packages them into a tuple, binding to the resulting tuple of types.
769In 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.
770As such, @ttype@ variables are also called \emph{argument packs}.
771
772Like variadic templates, the main way to manipulate @ttype@ polymorphic functions is via recursion.
773Since nothing is known about a parameter pack by default, assertion parameters are key to doing anything meaningful.
774Unlike variadic templates, @ttype@ polymorphic functions can be separately compiled.
775For example, a generalized @sum@ function written using @ttype@:
776\begin{lstlisting}
777int sum$\(_0\)$() { return 0; }
778forall(ttype Params | { int sum( Params ); } ) int sum$\(_1\)$( int x, Params rest ) {
779        return x + sum( rest );
780}
781sum( 10, 20, 30 );
782\end{lstlisting}
783Since @sum@\(_0\) does not accept any arguments, it is not a valid candidate function for the call @sum(10, 20, 30)@.
784In 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]@.
785The process continues, @Params@ is bound to @[]@, requiring an assertion @int sum()@, which matches @sum@\(_0\) and terminates the recursion.
786Effectively, 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))@.
787
788It is reasonable to take the @sum@ function a step further to enforce a minimum number of arguments:
789\begin{lstlisting}
790int sum( int x, int y ) { return x + y; }
791forall(ttype Params | { int sum( int, Params ); } ) int sum( int x, int y, Params rest ) {
792        return sum( x + y, rest );
793}
794\end{lstlisting}
795One more step permits the summation of any summable type with all arguments of the same type:
796\begin{lstlisting}
797trait summable(otype T) {
798        T ?+?( T, T );
799};
800forall(otype R | summable( R ) ) R sum( R x, R y ) {
801        return x + y;
802}
803forall(otype R, ttype Params | summable(R) | { R sum(R, Params); } ) R sum(R x, R y, Params rest) {
804        return sum( x + y, rest );
805}
806\end{lstlisting}
807Unlike C variadic functions, it is unnecessary to hard code the number and expected types.
808Furthermore, this code is extendable so any user-defined type with a @?+?@ operator.
809Summing arbitrary heterogeneous lists is possible with similar code by adding the appropriate type variables and addition operators.
810
811It is also possible to write a type-safe variadic print function to replace @printf@:
812\begin{lstlisting}
813struct S { int x, y; };
814forall(otype T, ttype Params | { void print(T); void print(Params); }) void print(T arg, Params rest) {
815        print(arg);  print(rest);
816}
817void print( char * x ) { printf( "%s", x ); }
818void print( int x ) { printf( "%d", x ); }
819void print( S s ) { print( "{ ", s.x, ",", s.y, " }" ); }
820print( "s = ", (S){ 1, 2 }, "\n" );
821\end{lstlisting}
822This example showcases a variadic-template-like decomposition of the provided argument list.
823The individual @print@ functions allow printing a single element of a type.
824The polymorphic @print@ allows printing any list of types, where as each individual type has a @print@ function.
825The individual print functions can be used to build up more complicated @print@ functions, such as @S@, which cannot be done with @printf@ in C.
826
827Finally, it is possible to use @ttype@ polymorphism to provide arbitrary argument forwarding functions.
828For example, it is possible to write @new@ as a library function:
829\begin{lstlisting}
830forall( otype R, otype S ) void ?{}( pair(R, S) *, R, S );
831forall( dtype T, ttype Params | sized(T) | { void ?{}( T *, Params ); } ) T * new( Params p ) {
832        return ((T *)malloc()){ p };                    $\C{// construct into result of malloc}$
833}
834pair( int, char ) * x = new( 42, '!' );
835\end{lstlisting}
836The @new@ function provides the combination of type-safe @malloc@ with a \CFA constructor call, making it impossible to forget constructing dynamically allocated objects.
837This function provides the type-safety of @new@ in \CC, without the need to specify the allocated type again, thanks to return-type inference.
838
839
840\subsection{Implementation}
841
842Tuples are implemented in the \CFA translator via a transformation into generic types.
843For each $N$, the first time an $N$-tuple is seen in a scope a generic type with $N$ type parameters is generated, \eg:
844\begin{lstlisting}
845[int, int] f() {
846        [double, double] x;
847        [int, double, int] y;
848}
849\end{lstlisting}
850is transformed into:
851\begin{lstlisting}
852forall(dtype T0, dtype T1 | sized(T0) | sized(T1)) struct _tuple2 {
853        T0 field_0;                     $\C{// generated before the first 2-tuple}$
854        T1 field_1;
855};
856_tuple2(int, int) f() {
857        _tuple2(double, double) x;
858        forall(dtype T0, dtype T1, dtype T2 | sized(T0) | sized(T1) | sized(T2)) struct _tuple3 {
859                T0 field_0;             $\C{// generated before the first 3-tuple}$
860                T1 field_1;
861                T2 field_2;
862        };
863        _tuple3(int, double, int) y;
864}
865\end{lstlisting}
866Tuple expressions are then simply converted directly into compound literals, \eg @[5, 'x', 1.24]@ becomes @(_tuple3(int, char, double)){ 5, 'x', 1.24 }@.
867
868\begin{comment}
869Since tuples are essentially structures, tuple indexing expressions are just field accesses:
870\begin{lstlisting}
871void f(int, [double, char]);
872[int, double] x;
873
874x.0+x.1;
875printf("%d %g\n", x);
876f(x, 'z');
877\end{lstlisting}
878Is transformed into:
879\begin{lstlisting}
880void f(int, _tuple2(double, char));
881_tuple2(int, double) x;
882
883x.field_0+x.field_1;
884printf("%d %g\n", x.field_0, x.field_1);
885f(x.field_0, (_tuple2){ x.field_1, 'z' });
886\end{lstlisting}
887Note that due to flattening, @x@ used in the argument position is converted into the list of its fields.
888In the call to @f@, the second and third argument components are structured into a tuple argument.
889Similarly, tuple member expressions are recursively expanded into a list of member access expressions.
890
891Expressions that may contain side effects are made into \emph{unique expressions} before being expanded by the flattening conversion.
892Each unique expression is assigned an identifier and is guaranteed to be executed exactly once:
893\begin{lstlisting}
894void g(int, double);
895[int, double] h();
896g(h());
897\end{lstlisting}
898Internally, this expression is converted to two variables and an expression:
899\begin{lstlisting}
900void g(int, double);
901[int, double] h();
902
903_Bool _unq0_finished_ = 0;
904[int, double] _unq0;
905g(
906        (_unq0_finished_ ? _unq0 : (_unq0 = f(), _unq0_finished_ = 1, _unq0)).0,
907        (_unq0_finished_ ? _unq0 : (_unq0 = f(), _unq0_finished_ = 1, _unq0)).1,
908);
909\end{lstlisting}
910Since argument evaluation order is not specified by the C programming language, this scheme is built to work regardless of evaluation order.
911The first time a unique expression is executed, the actual expression is evaluated and the accompanying boolean is set to true.
912Every subsequent evaluation of the unique expression then results in an access to the stored result of the actual expression.
913Tuple member expressions also take advantage of unique expressions in the case of possible impurity.
914
915Currently, the \CFA translator has a very broad, imprecise definition of impurity, where any function call is assumed to be impure.
916This 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.
917
918The various kinds of tuple assignment, constructors, and destructors generate GNU C statement expressions.
919A 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.
920The 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.
921However, 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.
922\end{comment}
923
924
925\section{Evaluation}
926\label{sec:eval}
927
928Though \CFA provides significant added functionality over C, these features have a low runtime penalty.
929In fact, \CFA's features for generic programming can enable faster runtime execution than idiomatic @void *@-based C code.
930This 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}).
931Since 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.
932A more illustrative benchmark measures the costs of idiomatic usage of each language's features.
933Figure~\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}.
934The benchmark test is similar for C and \CC.
935The 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.
936
937\begin{figure}
938\begin{lstlisting}[xleftmargin=3\parindentlnth,aboveskip=0pt,belowskip=0pt]
939int main( int argc, char * argv[] ) {
940        FILE * out = fopen( "cfa-out.txt", "w" );
941        int maxi = 0, vali = 42;
942        stack(int) si, ti;
943
944        REPEAT_TIMED( "push_int", N, push( &si, vali ); )
945        TIMED( "copy_int", ti = si; )
946        TIMED( "clear_int", clear( &si ); )
947        REPEAT_TIMED( "pop_int", N,
948                int xi = pop( &ti ); if ( xi > maxi ) { maxi = xi; } )
949        REPEAT_TIMED( "print_int", N/2, print( out, vali, ":", vali, "\n" ); )
950
951        pair(_Bool, char) maxp = { (_Bool)0, '\0' }, valp = { (_Bool)1, 'a' };
952        stack(pair(_Bool, char)) sp, tp;
953
954        REPEAT_TIMED( "push_pair", N, push( &sp, valp ); )
955        TIMED( "copy_pair", tp = sp; )
956        TIMED( "clear_pair", clear( &sp ); )
957        REPEAT_TIMED( "pop_pair", N,
958                pair(_Bool, char) xp = pop( &tp ); if ( xp > maxp ) { maxp = xp; } )
959        REPEAT_TIMED( "print_pair", N/2, print( out, valp, ":", valp, "\n" ); )
960        fclose(out);
961}
962\end{lstlisting}
963\caption{\CFA Benchmark Test}
964\label{fig:BenchmarkTest}
965\end{figure}
966
967The 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.
968The \CCV variant illustrates an alternative object-oriented idiom where all objects inherit from a base @object@ class, mimicking a Java-like interface;
969hence runtime checks are necessary to safely down-cast objects.
970The 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.
971For 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.
972Note, the C benchmark uses unchecked casts as there is no runtime mechanism to perform such checks, while \CFA and \CC provide type-safety statically.
973
974Figure~\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.
975The graph plots the median of 5 consecutive runs of each program, with an initial warm-up run omitted.
976All code is compiled at \texttt{-O2} by GCC or G++ 6.2.0, with all \CC code compiled as \CCfourteen.
977The 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.
978
979\begin{figure}
980\centering
981\input{timing}
982\caption{Benchmark Timing Results (smaller is better)}
983\label{fig:eval}
984\end{figure}
985
986\begin{table}
987\caption{Properties of benchmark code}
988\label{tab:eval}
989\newcommand{\CT}[1]{\multicolumn{1}{c}{#1}}
990\begin{tabular}{rrrrr}
991                                                                        & \CT{C}        & \CT{\CFA}     & \CT{\CC}      & \CT{\CCV}             \\ \hline
992maximum memory usage (MB)                       & 10001         & 2502          & 2503          & 11253                 \\
993source code size (lines)                        & 247           & 222           & 165           & 339                   \\
994redundant type annotations (lines)      & 39            & 2                     & 2                     & 15                    \\
995binary size (KB)                                        & 14            & 229           & 18            & 38                    \\
996\end{tabular}
997\end{table}
998
999The 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;
1000this inefficiency is exacerbated by the second level of generic types in the pair-based benchmarks.
1001By 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.
1002\CCV is slower than C largely due to the cost of runtime type-checking of down-casts (implemented with @dynamic_cast@);
1003There are two outliers in the graph for \CFA: all prints and pop of @pair@.
1004Both 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.
1005A compiler designed for \CFA could easily perform these optimizations.
1006Finally, the binary size for \CFA is larger because of static linking with the \CFA libraries.
1007
1008\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.
1009On 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.
1010\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;
1011with their omission the \CCV line count is similar to C.
1012We 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.
1013
1014Raw line-count, however, is a fairly rough measure of code complexity;
1015another important factor is how much type information the programmer must manually specify, especially where that information is not checked by the compiler.
1016Such 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@).
1017To 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.
1018The \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.
1019The 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).
1020These uses are similar to the @new@ expressions in \CC, though the \CFA compiler's type resolver should shortly render even these type casts superfluous.
1021
1022
1023\section{Related Work}
1024
1025
1026\subsection{Polymorphism}
1027
1028\CC is the most similar language to \CFA;
1029both are extensions to C with source and runtime backwards compatibility.
1030The fundamental difference is in their engineering approach to C compatibility and programmer expectation.
1031While \CC provides good backwards compatibility with C, it has a steep learning curve for many of its extensions.
1032For example, polymorphism is provided via three disjoint mechanisms: overloading, inheritance, and templates.
1033The 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.
1034In 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.
1035The key mechanism to support separate compilation is \CFA's \emph{explicit} use of assumed properties for a type.
1036Until \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;
1037furthermore, \CC concepts are restricted to template polymorphism.
1038
1039Cyclone~\citep{Grossman06} also provides capabilities for polymorphic functions and existential types, similar to \CFA's @forall@ functions and generic types.
1040Cyclone 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.
1041Furthermore, 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@.
1042In \CFA terms, all Cyclone polymorphism must be dtype-static.
1043While 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.
1044
1045\citet{obj-c-book} is an industrially successful extension to C.
1046However, Objective-C is a radical departure from C, using an object-oriented model with message-passing.
1047Objective-C did not support type-checked generics until recently~\citet{xcode7}, historically using less-efficient and more error-prone runtime checking of object types.
1048The~\citet{GObject} framework also adds object-oriented programming with runtime type-checking and reference-counting garbage-collection to C;
1049these features are more intrusive additions than those provided by \CFA, in addition to the runtime overhead of reference-counting.
1050\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.
1051Java~\citep{Java8} included generic types in Java~5;
1052Java's generic types are type-checked at compilation and type-erased at runtime, similar to \CFA's.
1053However, in Java, each object carries its own table of method pointers, while \CFA passes the method pointers separately to maintain a C-compatible layout.
1054Java is also a garbage-collected, object-oriented language, with the associated resource usage and C-interoperability burdens.
1055
1056D~\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.
1057However, 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.
1058D and Go are garbage-collected languages, imposing the associated runtime overhead.
1059The necessity of accounting for data transfer between managed runtimes and the unmanaged C runtime complicates foreign-function interfaces to C.
1060Furthermore, 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.
1061D 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.
1062Rust also possesses much more powerful abstraction capabilities for writing generic code than Go.
1063On 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.
1064\CFA, with its more modest safety features, allows direct ports of C code while maintaining the idiomatic style of the original source.
1065
1066
1067\subsection{Tuples/Variadics}
1068
1069Many programming languages have some form of tuple construct and/or variadic functions, \eg SETL, C, KW-C, \CC, D, Go, Java, ML, and Scala.
1070SETL~\cite{SETL} is a high-level mathematical programming language, with tuples being one of the primary data types.
1071Tuples in SETL allow subscripting, dynamic expansion, and multiple assignment.
1072C 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.
1073KW-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.
1074The main contributions of that work were adding MRVF, tuple mass and multiple assignment, and record-field access.
1075\CCeleven introduced @std::tuple@ as a library variadic template structure.
1076Tuples are a generalization of @std::pair@, in that they allow for arbitrary length, fixed-size aggregation of heterogeneous values.
1077Operations include @std::get<N>@ to extract vales, @std::tie@ to create a tuple of references used for assignment, and lexicographic comparisons.
1078\CCseventeen proposes \emph{structured bindings}~\cite{Sutter15} to eliminate pre-declaring variables and use of @std::tie@ for binding the results.
1079This 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.
1080Furthermore, structured bindings are not a full replacement for @std::tie@, as it always declares new variables.
1081Like \CC, D provides tuples through a library variadic-template structure.
1082Go does not have tuples but supports MRVF.
1083Java'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.
1084Tuples are a fundamental abstraction in most functional programming languages, such as Standard ML~\cite{sml} and~\cite{Scala}, which decompose tuples using pattern matching.
1085
1086
1087\section{Conclusion and Future Work}
1088
1089The 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.
1090While 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.
1091The 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.
1092The contributions are a powerful type-system using parametric polymorphism and overloading, generic types, and tuples, which all have complex interactions.
1093The work is a challenging design, engineering, and implementation exercise.
1094On the surface, the project may appear as a rehash of similar mechanisms in \CC.
1095However, 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.
1096All of these new features are being used by the \CFA development-team to build the \CFA runtime-system.
1097Finally, we demonstrate that \CFA performance for some idiomatic cases is better than C and close to \CC, showing the design is practically applicable.
1098
1099There is ongoing work on a wide range of \CFA feature extensions, including reference types, exceptions, concurrent primitives and modules.
1100(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.)
1101In addition, there are interesting future directions for the polymorphism design.
1102Notably, \CC template functions trade compile time and code bloat for optimal runtime of individual instantiations of polymorphic functions.
1103\CFA polymorphic functions uses a dynamic virtual-dispatch.
1104The 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.
1105Two 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.
1106These approaches are not mutually exclusive and allow performance optimizations to be applied only when necessary, without suffering global code-bloat.
1107In general, we believe separate compilation, producing smaller code, works well with loaded hardware-caches, which may offset the benefit of larger inlined-code.
1108
1109
1110\begin{acks}
1111The 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.
1112
1113This 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.
1114\end{acks}
1115
1116
1117\bibliographystyle{ACM-Reference-Format}
1118\bibliography{cfa}
1119
1120
1121\appendix
1122
1123\section{Benchmark Stack Implementation}
1124\label{sec:BenchmarkStackImplementation}
1125
1126\lstset{basicstyle=\linespread{0.9}\sf\small}
1127
1128\begin{comment}
1129\CFA
1130\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1131forall(otype T) struct stack_node;
1132forall(otype T) struct stack { stack_node(T) * head; };
1133forall(otype T) void ?{}(stack(T) * s);
1134forall(otype T) void ?{}(stack(T) * s, stack(T) t);
1135forall(otype T) stack(T) ?=?(stack(T) * s, stack(T) t);
1136forall(otype T) void ^?{}(stack(T) * s);
1137forall(otype T) _Bool empty(const stack(T) * s);
1138forall(otype T) void push(stack(T) * s, T value);
1139forall(otype T) T pop(stack(T) * s);
1140forall(otype T) void clear(stack(T) * s);
1141
1142void print( FILE * out, const char * x );
1143void print( FILE * out, _Bool x );
1144void print( FILE * out, char x );
1145void print( FILE * out, int x );
1146forall(otype T, ttype Params | { void print( FILE *, T ); void print( FILE *, Params ); })
1147        void print( FILE * out, T arg, Params rest );
1148forall(otype R, otype S | { void print( FILE *, R ); void print( FILE *, S ); })
1149        void print( FILE * out, pair(R, S) x );
1150\end{lstlisting}
1151
1152\medskip\noindent
1153\CC
1154\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1155std::pair
1156std::forward_list wrapped in std::stack interface
1157
1158template<typename T> void print(ostream & out, const T & x) { out << x; }
1159template<> void print<bool>(ostream & out, const bool & x) { out << (x ? "true" : "false"); }
1160template<> void print<char>(ostream & out, const char & x ) { out << "'" << x << "'"; }
1161template<typename R, typename S> ostream & operator<< (ostream & out, const pair<R, S>& x) {
1162        out << "["; print(out, x.first); out << ", "; print(out, x.second); return out << "]"; }
1163template<typename T, typename... Args> void print(ostream & out, const T & arg, const Args &... rest) {
1164        out << arg;     print(out, rest...); }
1165\end{lstlisting}
1166
1167\medskip\noindent
1168C
1169\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1170struct pair { void * first, second; };
1171struct pair * new_pair( void * first, void * second );
1172struct pair * copy_pair( const struct pair * src,
1173        void * (*copy_first)( const void * ), void * (*copy_second)( const void * ) );
1174void free_pair( struct pair * p, void (*free_first)( void * ), void (*free_second)( void * ) );
1175int cmp_pair( const struct pair * a, const struct pair * b,
1176        int (*cmp_first)( const void *, const void * ), int (*cmp_second)( const void *, const void * ) );
1177
1178struct stack_node;
1179struct stack { struct stack_node * head; };
1180struct stack new_stack();
1181void copy_stack( struct stack * dst, const struct stack * src, void * (*copy)( const void * ) );
1182void clear_stack( struct stack * s, void (*free_el)( void * ) );
1183_Bool stack_empty( const struct stack * s );
1184void push_stack( struct stack * s, void * value );
1185void * pop_stack( struct stack * s );
1186
1187void print_string( FILE * out, const char * x );
1188void print_bool( FILE * out, _Bool x );
1189void print_char( FILE * out, char x );
1190void print_int( FILE * out, int x );
1191void print( FILE * out, const char * fmt, ... );
1192\end{lstlisting}
1193\end{comment}
1194
1195Throughout, @/***/@ designates a counted redundant type annotation.
1196
1197\medskip\noindent
1198\CFA
1199\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1200forall(otype T) struct stack_node {
1201        T value;
1202        stack_node(T) * next;
1203};
1204forall(otype T) void ?{}(stack(T) * s) { (&s->head){ 0 }; }
1205forall(otype T) void ?{}(stack(T) * s, stack(T) t) {
1206        stack_node(T) ** crnt = &s->head;
1207        for ( stack_node(T) * next = t.head; next; next = next->next ) {
1208                *crnt = ((stack_node(T) *)malloc()){ next->value }; /***/
1209                stack_node(T) * acrnt = *crnt;
1210                crnt = &acrnt->next;
1211        }
1212        *crnt = 0;
1213}
1214forall(otype T) stack(T) ?=?(stack(T) * s, stack(T) t) {
1215        if ( s->head == t.head ) return *s;
1216        clear(s);
1217        s{ t };
1218        return *s;
1219}
1220forall(otype T) void ^?{}(stack(T) * s) { clear(s); }
1221forall(otype T) _Bool empty(const stack(T) * s) { return s->head == 0; }
1222forall(otype T) void push(stack(T) * s, T value) {
1223        s->head = ((stack_node(T) *)malloc()){ value, s->head }; /***/
1224}
1225forall(otype T) T pop(stack(T) * s) {
1226        stack_node(T) * n = s->head;
1227        s->head = n->next;
1228        T x = n->value;
1229        ^n{};
1230        free(n);
1231        return x;
1232}
1233forall(otype T) void clear(stack(T) * s) {
1234        for ( stack_node(T) * next = s->head; next; ) {
1235                stack_node(T) * crnt = next;
1236                next = crnt->next;
1237                delete(crnt);
1238        }
1239        s->head = 0;
1240}
1241\end{lstlisting}
1242
1243\medskip\noindent
1244\CC
1245\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1246template<typename T> class stack {
1247        struct node {
1248                T value;
1249                node * next;
1250                node( const T & v, node * n = nullptr ) : value(v), next(n) {}
1251        };
1252        node * head;
1253        void copy(const stack<T>& o) {
1254                node ** crnt = &head;
1255                for ( node * next = o.head;; next; next = next->next ) {
1256                        *crnt = new node{ next->value }; /***/
1257                        crnt = &(*crnt)->next;
1258                }
1259                *crnt = nullptr;
1260        }
1261  public:
1262        stack() : head(nullptr) {}
1263        stack(const stack<T>& o) { copy(o); }
1264        stack(stack<T> && o) : head(o.head) { o.head = nullptr; }
1265        ~stack() { clear(); }
1266        stack & operator= (const stack<T>& o) {
1267                if ( this == &o ) return *this;
1268                clear();
1269                copy(o);
1270                return *this;
1271        }
1272        stack & operator= (stack<T> && o) {
1273                if ( this == &o ) return *this;
1274                head = o.head;
1275                o.head = nullptr;
1276                return *this;
1277        }
1278        bool empty() const { return head == nullptr; }
1279        void push(const T & value) { head = new node{ value, head };  /***/ }
1280        T pop() {
1281                node * n = head;
1282                head = n->next;
1283                T x = std::move(n->value);
1284                delete n;
1285                return x;
1286        }
1287        void clear() {
1288                for ( node * next = head; next; ) {
1289                        node * crnt = next;
1290                        next = crnt->next;
1291                        delete crnt;
1292                }
1293                head = nullptr;
1294        }
1295};
1296\end{lstlisting}
1297
1298\medskip\noindent
1299C
1300\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1301struct stack_node {
1302        void * value;
1303        struct stack_node * next;
1304};
1305struct stack new_stack() { return (struct stack){ NULL }; /***/ }
1306void copy_stack(struct stack * s, const struct stack * t, void * (*copy)(const void *)) {
1307        struct stack_node ** crnt = &s->head;
1308        for ( struct stack_node * next = t->head; next; next = next->next ) {
1309                *crnt = malloc(sizeof(struct stack_node)); /***/
1310                **crnt = (struct stack_node){ copy(next->value) }; /***/
1311                crnt = &(*crnt)->next;
1312        }
1313        *crnt = 0;
1314}
1315_Bool stack_empty(const struct stack * s) { return s->head == NULL; }
1316void push_stack(struct stack * s, void * value) {
1317        struct stack_node * n = malloc(sizeof(struct stack_node)); /***/
1318        *n = (struct stack_node){ value, s->head }; /***/
1319        s->head = n;
1320}
1321void * pop_stack(struct stack * s) {
1322        struct stack_node * n = s->head;
1323        s->head = n->next;
1324        void * x = n->value;
1325        free(n);
1326        return x;
1327}
1328void clear_stack(struct stack * s, void (*free_el)(void *)) {
1329        for ( struct stack_node * next = s->head; next; ) {
1330                struct stack_node * crnt = next;
1331                next = crnt->next;
1332                free_el(crnt->value);
1333                free(crnt);
1334        }
1335        s->head = NULL;
1336}
1337\end{lstlisting}
1338
1339\medskip\noindent
1340\CCV
1341\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1342stack::node::node( const object & v, node * n ) : value( v.new_copy() ), next( n ) {}
1343void stack::copy(const stack & o) {
1344        node ** crnt = &head;
1345        for ( node * next = o.head; next; next = next->next ) {
1346                *crnt = new node{ *next->value };
1347                crnt = &(*crnt)->next;
1348        }
1349        *crnt = nullptr;
1350}
1351stack::stack() : head(nullptr) {}
1352stack::stack(const stack & o) { copy(o); }
1353stack::stack(stack && o) : head(o.head) { o.head = nullptr; }
1354stack::~stack() { clear(); }
1355stack & stack::operator= (const stack & o) {
1356        if ( this == &o ) return *this;
1357        clear();
1358        copy(o);
1359        return *this;
1360}
1361stack & stack::operator= (stack && o) {
1362        if ( this == &o ) return *this;
1363        head = o.head;
1364        o.head = nullptr;
1365        return *this;
1366}
1367bool stack::empty() const { return head == nullptr; }
1368void stack::push(const object & value) { head = new node{ value, head }; /***/ }
1369ptr<object> stack::pop() {
1370        node * n = head;
1371        head = n->next;
1372        ptr<object> x = std::move(n->value);
1373        delete n;
1374        return x;
1375}
1376void stack::clear() {
1377        for ( node * next = head; next; ) {
1378                node * crnt = next;
1379                next = crnt->next;
1380                delete crnt;
1381        }
1382        head = nullptr;
1383}
1384\end{lstlisting}
1385
1386
1387\begin{comment}
1388
1389\subsubsection{bench.h}
1390(\texttt{bench.hpp} is similar.)
1391
1392\lstinputlisting{evaluation/bench.h}
1393
1394\subsection{C}
1395
1396\subsubsection{c-stack.h} ~
1397
1398\lstinputlisting{evaluation/c-stack.h}
1399
1400\subsubsection{c-stack.c} ~
1401
1402\lstinputlisting{evaluation/c-stack.c}
1403
1404\subsubsection{c-pair.h} ~
1405
1406\lstinputlisting{evaluation/c-pair.h}
1407
1408\subsubsection{c-pair.c} ~
1409
1410\lstinputlisting{evaluation/c-pair.c}
1411
1412\subsubsection{c-print.h} ~
1413
1414\lstinputlisting{evaluation/c-print.h}
1415
1416\subsubsection{c-print.c} ~
1417
1418\lstinputlisting{evaluation/c-print.c}
1419
1420\subsubsection{c-bench.c} ~
1421
1422\lstinputlisting{evaluation/c-bench.c}
1423
1424\subsection{\CFA}
1425
1426\subsubsection{cfa-stack.h} ~
1427
1428\lstinputlisting{evaluation/cfa-stack.h}
1429
1430\subsubsection{cfa-stack.c} ~
1431
1432\lstinputlisting{evaluation/cfa-stack.c}
1433
1434\subsubsection{cfa-print.h} ~
1435
1436\lstinputlisting{evaluation/cfa-print.h}
1437
1438\subsubsection{cfa-print.c} ~
1439
1440\lstinputlisting{evaluation/cfa-print.c}
1441
1442\subsubsection{cfa-bench.c} ~
1443
1444\lstinputlisting{evaluation/cfa-bench.c}
1445
1446\subsection{\CC}
1447
1448\subsubsection{cpp-stack.hpp} ~
1449
1450\lstinputlisting[language=c++]{evaluation/cpp-stack.hpp}
1451
1452\subsubsection{cpp-print.hpp} ~
1453
1454\lstinputlisting[language=c++]{evaluation/cpp-print.hpp}
1455
1456\subsubsection{cpp-bench.cpp} ~
1457
1458\lstinputlisting[language=c++]{evaluation/cpp-bench.cpp}
1459
1460\subsection{\CCV}
1461
1462\subsubsection{object.hpp} ~
1463
1464\lstinputlisting[language=c++]{evaluation/object.hpp}
1465
1466\subsubsection{cpp-vstack.hpp} ~
1467
1468\lstinputlisting[language=c++]{evaluation/cpp-vstack.hpp}
1469
1470\subsubsection{cpp-vstack.cpp} ~
1471
1472\lstinputlisting[language=c++]{evaluation/cpp-vstack.cpp}
1473
1474\subsubsection{cpp-vprint.hpp} ~
1475
1476\lstinputlisting[language=c++]{evaluation/cpp-vprint.hpp}
1477
1478\subsubsection{cpp-vbench.cpp} ~
1479
1480\lstinputlisting[language=c++]{evaluation/cpp-vbench.cpp}
1481\end{comment}
1482
1483\end{document}
1484
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1486% tab-width: 4 %
1487% compile-command: "make" %
1488% End: %
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