source: doc/generic_types/generic_types.tex @ 7aa78b4

aaron-thesisarm-ehcleanup-dtorsdeferred_resndemanglerjacob/cs343-translationjenkins-sandboxnew-astnew-ast-unique-exprnew-envno_listpersistent-indexerresolv-newwith_gc
Last change on this file since 7aa78b4 was 7aa78b4, checked in by Aaron Moss <a3moss@…>, 5 years ago

Merge branch 'master' of plg.uwaterloo.ca:software/cfa/cfa-cc

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27\newcommand*{\eg}{%
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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
53\newcommand{\CCeleven}{\rm C\kern-.1em\hbox{+\kern-.25em+}11\xspace} % C++11 symbolic name
54\newcommand{\CCfourteen}{\rm C\kern-.1em\hbox{+\kern-.25em+}14\xspace} % C++14 symbolic name
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58\newcommand{\CS}{C\raisebox{-0.7ex}{\Large$^\sharp$}\xspace}
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
74tabsize=4,                                                                                              % 4 space tabbing
75xleftmargin=\parindentlnth,                                                             % indent code to paragraph indentation
76%mathescape=true,                                                                               % LaTeX math escape in CFA code $...$
77escapechar=\$,                                                                                  % LaTeX escape in CFA code
78keepspaces=true,                                                                                %
79showstringspaces=false,                                                                 % do not show spaces with cup
80showlines=true,                                                                                 % show blank lines at end of code
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83% replace/adjust listing characters that look bad in sanserif
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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}{@{}r|c|c|c|c|c|c|c@{}}
167                & 2017  & 2012  & 2007  & 2002  & 1997  & 1992  & 1987          \\
168\hline
169Java    & 1             & 1             & 1             & 1             & 12    & -             & -                     \\
170\hline
171\Textbf{C}      & \Textbf{2}& \Textbf{2}& \Textbf{2}& \Textbf{2}& \Textbf{1}& \Textbf{1}& \Textbf{1}    \\
172\hline
173\CC             & 3             & 3             & 3             & 3             & 2             & 2             & 4                     \\
174\end{tabular}
175\end{center}
176\lstMakeShortInline@%
177Love it or hate it, C is extremely popular, highly used, and one of the few systems languages.
178In many cases, \CC is often used solely as a better C.
179Nonetheless, C, first standardized over thirty years ago, lacks many features that make programming in more modern languages safer and more productive.
180
181\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.
182The four key design goals for \CFA~\citep{Bilson03} are:
183(1) The behaviour of standard C code must remain the same when translated by a \CFA compiler as when translated by a C compiler;
184(2) Standard C code must be as fast and as small when translated by a \CFA compiler as when translated by a C compiler;
185(3) \CFA code must be at least as portable as standard C code;
186(4) Extensions introduced by \CFA must be translated in the most efficient way possible.
187These 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.
188\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.
189
190\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).
191Ultimately, a compiler is necessary for advanced features and optimal performance.
192
193This 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.
194Specifically, 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.
195The new constructs are empirically compared with both standard C and \CC; the results show the new design is comparable in performance.
196
197
198\subsection{Polymorphic Functions}
199\label{sec:poly-fns}
200
201\CFA's polymorphism was originally formalized by \citet{Ditchfield92}, and first implemented by \citet{Bilson03}.
202The 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):
203\begin{lstlisting}
204`forall( otype T )` T identity( T val ) { return val; }
205int forty_two = identity( 42 );                         $\C{// T is bound to int, forty\_two == 42}$
206\end{lstlisting}
207The @identity@ function above can be applied to any complete \emph{object type} (or @otype@).
208The 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.
209The \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.
210If this extra information is not needed, \eg for a pointer, the type parameter can be declared as a \emph{data type} (or @dtype@).
211
212In \CFA, the polymorphism runtime-cost is spread over each polymorphic call, due to passing more arguments to polymorphic functions;
213the experiments in Section~\ref{sec:eval} show this overhead is similar to \CC virtual-function calls.
214A design advantage is that, unlike \CC template-functions, \CFA polymorphic-functions are compatible with C \emph{separate compilation}, preventing compilation and code bloat.
215
216Since 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.
217For example, the function @twice@ can be defined using the \CFA syntax for operator overloading:
218\newpage
219\begin{lstlisting}
220forall( otype T `| { T ?+?(T, T); }` ) T twice( T x ) { return x + x; } $\C{// ? denotes operands}$
221int val = twice( twice( 3.7 ) );
222\end{lstlisting}
223which works for any type @T@ with a matching addition operator.
224The 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@.
225There 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.
226The first approach has a late conversion from @double@ to @int@ on the final assignment, while the second has an eager conversion to @int@.
227\CFA minimizes the number of conversions and their potential to lose information, so it selects the first approach, which corresponds with C-programmer intuition.
228
229Crucial to the design of a new programming language are the libraries to access thousands of external software features.
230Like \CC, \CFA inherits a massive compatible library-base, where other programming languages must rewrite or provide fragile inter-language communication with C.
231A simple example is leveraging the existing type-unsafe (@void *@) C @bsearch@ to binary search a sorted floating-point array:
232\begin{lstlisting}
233void * bsearch( const void * key, const void * base, size_t nmemb, size_t size,
234                                int (* compar)( const void *, const void * ));
235int comp( const void * t1, const void * t2 ) { return *(double *)t1 < *(double *)t2 ? -1 :
236                                *(double *)t2 < *(double *)t1 ? 1 : 0; }
237double vals[10] = { /* 10 floating-point values */ };
238double key = 5.0;
239double * val = (double *)bsearch( &key, vals, 10, sizeof(vals[0]), comp );      $\C{// search sorted array}$
240\end{lstlisting}
241which can be augmented simply with a generalized, type-safe, \CFA-overloaded wrappers:
242\begin{lstlisting}
243forall( otype T | { int ?<?( T, T ); } ) T * bsearch( T key, const T * arr, size_t size ) {
244        int comp( const void * t1, const void * t2 ) { /* as above with double changed to T */ }
245        return (T *)bsearch( &key, arr, size, sizeof(T), comp ); }
246forall( otype T | { int ?<?( T, T ); } ) unsigned int bsearch( T key, const T * arr, size_t size ) {
247        T * result = bsearch( key, arr, size ); $\C{// call first version}$
248        return result ? result - arr : size; }  $\C{// pointer subtraction includes sizeof(T)}$
249double * val = bsearch( 5.0, vals, 10 );        $\C{// selection based on return type}$
250int posn = bsearch( 5.0, vals, 10 );
251\end{lstlisting}
252The nested function @comp@ provides the hidden interface from typed \CFA to untyped (@void *@) C, plus the cast of the result.
253Providing a hidden @comp@ function in \CC is awkward as lambdas do not use C calling-conventions and template declarations cannot appear at block scope.
254As well, an alternate kind of return is made available: position versus pointer to found element.
255\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@.
256
257\CFA has replacement libraries condensing hundreds of existing C functions into tens of \CFA overloaded functions, all without rewriting the actual computations.
258For example, it is possible to write a type-safe \CFA wrapper @malloc@ based on the C @malloc@:
259\begin{lstlisting}
260forall( dtype T | sized(T) ) T * malloc( void ) { return (T *)malloc( sizeof(T) ); }
261int * ip = malloc();                                            $\C{// select type and size from left-hand side}$
262double * dp = malloc();
263struct S {...} * sp = malloc();
264\end{lstlisting}
265where the return type supplies the type/size of the allocation, which is impossible in most type systems.
266
267Call-site inferencing and nested functions provide a localized form of inheritance.
268For example, the \CFA @qsort@ only sorts in ascending order using @<@.
269However, it is trivial to locally change this behaviour:
270\begin{lstlisting}
271forall( otype T | { int ?<?( T, T ); } ) void qsort( const T * arr, size_t size ) { /* use C qsort */ }
272{       int ?<?( double x, double y ) { return x `>` y; }       $\C{// locally override behaviour}$
273        qsort( vals, size );                                    $\C{// descending sort}$
274}
275\end{lstlisting}
276Within the block, the nested version of @<@ performs @>@ and this local version overrides the built-in @<@ so it is passed to @qsort@.
277Hence, programmers can easily form local environments, adding and modifying appropriate functions, to maximize reuse of other existing functions and types.
278
279Finally, \CFA allows variable overloading:
280%\lstDeleteShortInline@%
281%\par\smallskip
282%\begin{tabular}{@{}l@{\hspace{1.5\parindent}}||@{\hspace{1.5\parindent}}l@{}}
283\begin{lstlisting}
284short int MAX = ...;
285int MAX = ...;
286double MAX = ...;
287short int s = MAX;  $\C{// select correct MAX}$
288int i = MAX;
289double d = MAX;
290\end{lstlisting}
291%\end{lstlisting}
292%&
293%\begin{lstlisting}
294%\end{tabular}
295%\smallskip\par\noindent
296%\lstMakeShortInline@%
297Here, the single name @MAX@ replaces all the C type-specific names: @SHRT_MAX@, @INT_MAX@, @DBL_MAX@.
298As 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.
299In addition, several operations are defined in terms values @0@ and @1@, \eg:
300\begin{lstlisting}
301int x;
302if (x) x++                                                                      $\C{// if (x != 0) x += 1;}$
303\end{lstlisting}
304Every 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.
305Due 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.
306The 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.
307
308
309\subsection{Traits}
310
311\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:
312\begin{lstlisting}
313trait summable( otype T ) {
314        void ?{}( T *, zero_t );                                $\C{// constructor from 0 literal}$
315        T ?+?( T, T );                                                  $\C{// assortment of additions}$
316        T ?+=?( T *, T );
317        T ++?( T * );
318        T ?++( T * ); };
319forall( otype T `| summable( T )` ) T sum( T a[$\,$], size_t size ) {  // use trait
320        `T` total = { `0` };                                    $\C{// instantiate T from 0 by calling its constructor}$
321        for ( unsigned int i = 0; i < size; i += 1 ) total `+=` a[i]; $\C{// select appropriate +}$
322        return total; }
323\end{lstlisting}
324
325In 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:
326\begin{lstlisting}
327trait otype( dtype T | sized(T) ) {  // sized is a pseudo-trait for types with known size and alignment
328        void ?{}( T * );                                                $\C{// default constructor}$
329        void ?{}( T *, T );                                             $\C{// copy constructor}$
330        void ?=?( T *, T );                                             $\C{// assignment operator}$
331        void ^?{}( T * ); };                                    $\C{// destructor}$
332\end{lstlisting}
333Given 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.
334
335In 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.
336Hence, trait names play no part in type equivalence;
337the names are simply macros for a list of polymorphic assertions, which are expanded at usage sites.
338Nevertheless, trait names form a logical subtype-hierarchy with @dtype@ at the top, where traits often contain overlapping assertions, \eg operator @+@.
339Traits are used like interfaces in Java or abstract base-classes in \CC, but without the nominal inheritance-relationships.
340Instead, 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.
341Hence, 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.
342(Nominal inheritance can be approximated with traits using marker variables or functions, as is done in Go.)
343
344% Nominal inheritance can be simulated with traits using marker variables or functions:
345% \begin{lstlisting}
346% trait nominal(otype T) {
347%     T is_nominal;
348% };
349% int is_nominal;                                                               $\C{// int now satisfies the nominal trait}$
350% \end{lstlisting}
351%
352% 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:
353% \begin{lstlisting}
354% trait pointer_like(otype Ptr, otype El) {
355%     lvalue El *?(Ptr);                                                $\C{// Ptr can be dereferenced into a modifiable value of type El}$
356% }
357% struct list {
358%     int value;
359%     list * next;                                                              $\C{// may omit "struct" on type names as in \CC}$
360% };
361% typedef list * list_iterator;
362%
363% lvalue int *?( list_iterator it ) { return it->value; }
364% \end{lstlisting}
365% 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@).
366% 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.
367
368
369\section{Generic Types}
370
371One of the known shortcomings of standard C is that it does not provide reusable type-safe abstractions for generic data structures and algorithms.
372Broadly speaking, there are three approaches to implement abstract data-structures in C.
373One approach is to write bespoke data structures for each context in which they are needed.
374While 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.
375A 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.
376However, 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.
377A 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.
378Furthermore, writing and using preprocessor macros can be unnatural and inflexible.
379
380\CC, Java, and other languages use \emph{generic types} to produce type-safe abstract data-types.
381\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.
382However, for known concrete parameters, the generic-type definition can be inlined, like \CC templates.
383
384A 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:
385\begin{lstlisting}
386forall( otype R, otype S ) struct pair {
387        R first;
388        S second;
389};
390forall( otype T ) T value( pair( const char *, T ) p ) { return p.second; }
391forall( dtype F, otype T ) T value_p( pair( F *, T * ) p ) { return * p.second; }
392pair( const char *, int ) p = { "magic", 42 };
393int magic = value( p );
394pair( void *, int * ) q = { 0, &p.second };
395magic = value_p( q );
396double d = 1.0;
397pair( double *, double * ) r = { &d, &d };
398d = value_p( r );
399\end{lstlisting}
400
401\CFA classifies generic types as either \emph{concrete} or \emph{dynamic}.
402Concrete types have a fixed memory layout regardless of type parameters, while dynamic types vary in memory layout depending on their type parameters.
403A type may have polymorphic parameters but still be concrete, called \emph{dtype-static}.
404Polymorphic 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.
405
406\CFA generic types also allow checked argument-constraints.
407For example, the following declaration of a sorted set-type ensures the set key supports equality and relational comparison:
408\begin{lstlisting}
409forall( otype Key | { _Bool ?==?(Key, Key); _Bool ?<?(Key, Key); } ) struct sorted_set;
410\end{lstlisting}
411
412
413\subsection{Concrete Generic-Types}
414
415The \CFA translator template-expands concrete generic-types into new structure types, affording maximal inlining.
416To 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.
417For 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.
418For example, the concrete instantiation for @pair( const char *, int )@ is:
419\begin{lstlisting}
420struct _pair_conc1 {
421        const char * first;
422        int second;
423};
424\end{lstlisting}
425
426A concrete generic-type with dtype-static parameters is also expanded to a structure type, but this type is used for all matching instantiations.
427In 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:
428\begin{lstlisting}
429struct _pair_conc0 {
430        void * first;
431        void * second;
432};
433\end{lstlisting}
434
435
436\subsection{Dynamic Generic-Types}
437
438Though \CFA implements concrete generic-types efficiently, it also has a fully general system for dynamic generic types.
439As 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.
440Dynamic generic-types also have an \emph{offset array} containing structure-member offsets.
441A dynamic generic-union needs no such offset array, as all members are at offset 0, but size and alignment are still necessary.
442Access 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.
443
444The offset arrays are statically generated where possible.
445If 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;
446if 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.
447As 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 )@.
448The offset array @_offsetof_pair@ is generated at the call site as @size_t _offsetof_pair[] = { offsetof(_pair_conc1, first), offsetof(_pair_conc1, second) }@.
449
450In some cases the offset arrays cannot be statically generated.
451For 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.
452\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.
453The \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.
454These 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).
455Results of these layout functions are cached so that they are only computed once per type per function. %, as in the example below for @pair@.
456Layout functions also allow generic types to be used in a function definition without reflecting them in the function signature.
457For 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.
458This function could acquire the layout for @set(T)@ by calling its layout function with the layout of @T@ implicitly passed into the function.
459
460Whether a type is concrete, dtype-static, or dynamic is decided solely on the type parameters and @forall@ clause on a declaration.
461This 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.
462If 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.
463
464
465\subsection{Applications}
466\label{sec:generic-apps}
467
468The reuse of dtype-static structure instantiations enables useful programming patterns at zero runtime cost.
469The 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@:
470\begin{lstlisting}
471forall(dtype T) int lexcmp( pair( T *, T * ) * a, pair( T *, T * ) * b, int (* cmp)( T *, T * ) ) {
472        return cmp( a->first, b->first ) ? : cmp( a->second, b->second );
473}
474\end{lstlisting}
475%       int c = cmp( a->first, b->first );
476%       if ( c == 0 ) c = cmp( a->second, b->second );
477%       return c;
478Since @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.
479
480Another useful pattern enabled by reused dtype-static type instantiations is zero-cost \emph{tag-structures}.
481Sometimes information is only used for type-checking and can be omitted at runtime, \eg:
482\begin{lstlisting}
483forall(dtype Unit) struct scalar { unsigned long value; };
484struct metres {};
485struct litres {};
486
487forall(dtype U) scalar(U) ?+?( scalar(U) a, scalar(U) b ) {
488        return (scalar(U)){ a.value + b.value };
489}
490scalar(metres) half_marathon = { 21093 };
491scalar(litres) swimming_pool = { 2500000 };
492scalar(metres) marathon = half_marathon + half_marathon;
493scalar(litres) two_pools = swimming_pool + swimming_pool;
494marathon + swimming_pool;                                       $\C{// compilation ERROR}$
495\end{lstlisting}
496@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 @?+?@.
497These implementations may even be separately compiled, unlike \CC template functions.
498However, the \CFA type-checker ensures matching types are used by all calls to @?+?@, preventing nonsensical computations like adding a length to a volume.
499
500
501\section{Tuples}
502\label{sec:tuples}
503
504In many languages, functions can return at most one value;
505however, many operations have multiple outcomes, some exceptional.
506Consider C's @div@ and @remquo@ functions, which return the quotient and remainder for a division of integer and floating-point values, respectively.
507\begin{lstlisting}
508typedef struct { int quo, rem; } div_t;         $\C{// from include stdlib.h}$
509div_t div( int num, int den );
510double remquo( double num, double den, int * quo );
511div_t qr = div( 13, 5 );                                        $\C{// return quotient/remainder aggregate}$
512int q;
513double r = remquo( 13.5, 5.2, &q );                     $\C{// return remainder, alias quotient}$
514\end{lstlisting}
515@div@ aggregates the quotient/remainder in a structure, while @remquo@ aliases a parameter to an argument.
516Both approaches are awkward.
517Alternatively, a programming language can directly support returning multiple values, \eg in \CFA:
518\begin{lstlisting}
519[ int, int ] div( int num, int den );           $\C{// return two integers}$
520[ double, double ] div( double num, double den ); $\C{// return two doubles}$
521int q, r;                                                                       $\C{// overloaded variable names}$
522double q, r;
523[ q, r ] = div( 13, 5 );                                        $\C{// select appropriate div and q, r}$
524[ q, r ] = div( 13.5, 5.2 );                            $\C{// assign into tuple}$
525\end{lstlisting}
526Clearly, this approach is straightforward to understand and use;
527therefore, why do few programming languages support this obvious feature or provide it awkwardly?
528The answer is that there are complex consequences that cascade through multiple aspects of the language, especially the type-system.
529This section show these consequences and how \CFA handles them.
530
531
532\subsection{Tuple Expressions}
533
534The addition of multiple-return-value functions (MRVF) are useless without a syntax for accepting multiple values at the call-site.
535The simplest mechanism for capturing the return values is variable assignment, allowing the values to be retrieved directly.
536As 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}.
537
538However, 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:
539\begin{lstlisting}
540printf( "%d %d\n", div( 13, 5 ) );                      $\C{// return values seperated into arguments}$
541\end{lstlisting}
542Here, the values returned by @div@ are composed with the call to @printf@ by flattening the tuple into separate arguments.
543However, the \CFA type-system must support significantly more complex composition:
544\begin{lstlisting}
545[ int, int ] foo$\(_1\)$( int );
546[ double ] foo$\(_2\)$( int );
547void bar( int, double, double );
548bar( foo( 3 ), foo( 3 ) );
549\end{lstlisting}
550The type-resolver only has the tuple return-types to resolve the call to @bar@ as the @foo@ parameters are identical, which involves unifying the possible @foo@ functions with @bar@'s parameter list.
551No combination of @foo@s are an exact match with @bar@'s parameters, so the resolver applies C conversions.
552The minimal cost is @bar( foo@$_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.
553
554
555\subsection{Tuple Variables}
556
557An important observation from function composition is that new variable names are not required to initialize parameters from an MRVF.
558\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:
559\begin{lstlisting}
560[ int, int ] qr = div( 13, 5 );                         $\C{// tuple-variable declaration and initialization}$
561[ double, double ] qr = div( 13.5, 5.2 );
562\end{lstlisting}
563where the tuple variable-name serves the same purpose as the parameter name(s).
564Tuple variables can be composed of any types, except for array types, since array sizes are generally unknown.
565
566One way to access the tuple-variable components is with assignment or composition:
567\begin{lstlisting}
568[ q, r ] = qr;                                                          $\C{// access tuple-variable components}$
569printf( "%d %d\n", qr );
570\end{lstlisting}
571\CFA also supports \emph{tuple indexing} to access single components of a tuple expression:
572\begin{lstlisting}
573[int, int] * p = &qr;                                           $\C{// tuple pointer}$
574int rem = qr.1;                                                         $\C{// access remainder}$
575int quo = div( 13, 5 ).0;                                       $\C{// access quotient}$
576p->0 = 5;                                                                       $\C{// change quotient}$
577bar( qr.1, qr );                                                        $\C{// pass remainder and quotient/remainder}$
578rem = [42, div( 13, 5 )].0.1;                           $\C{// access 2nd component of 1st component of tuple expression}$
579\end{lstlisting}
580
581
582\subsection{Flattening and Restructuring}
583
584In function call contexts, tuples support implicit flattening and restructuring conversions.
585Tuple flattening recursively expands a tuple into the list of its basic components.
586Tuple structuring packages a list of expressions into a value of tuple type, \eg:
587%\lstDeleteShortInline@%
588%\par\smallskip
589%\begin{tabular}{@{}l@{\hspace{1.5\parindent}}||@{\hspace{1.5\parindent}}l@{}}
590\begin{lstlisting}
591int f( int, int );
592int g( [int, int] );
593int h( int, [int, int] );
594[int, int] x;
595int y;
596f( x );                 $\C{// flatten}$
597g( y, 10 );             $\C{// structure}$
598h( x, y );              $\C{// flatten and structure}$
599\end{lstlisting}
600%\end{lstlisting}
601%&
602%\begin{lstlisting}
603%\end{tabular}
604%\smallskip\par\noindent
605%\lstMakeShortInline@%
606In the call to @f@, @x@ is implicitly flattened so the components of @x@ are passed as the two arguments.
607In 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@.
608Finally, 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]@.
609The 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.
610
611
612\subsection{Tuple Assignment}
613
614An assignment where the left side is a tuple type is called \emph{tuple assignment}.
615There 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.
616%\lstDeleteShortInline@%
617%\par\smallskip
618%\begin{tabular}{@{}l@{\hspace{1.5\parindent}}||@{\hspace{1.5\parindent}}l@{}}
619\begin{lstlisting}
620int x = 10;
621double y = 3.5;
622[int, double] z;
623z = [x, y];             $\C{// multiple assignment}$
624[x, y] = z;             $\C{// multiple assignment}$
625z = 10;                 $\C{// mass assignment}$
626[y, x] = 3.14$\C{// mass assignment}$
627\end{lstlisting}
628%\end{lstlisting}
629%&
630%\begin{lstlisting}
631%\end{tabular}
632%\smallskip\par\noindent
633%\lstMakeShortInline@%
634Both kinds of tuple assignment have parallel semantics, so that each value on the left and right side is evaluated before any assignments occur.
635As a result, it is possible to swap the values in two variables without explicitly creating any temporary variables or calling a function, \eg, @[x, y] = [y, x]@.
636This semantics means mass assignment differs from C cascading assignment (\eg @a = b = c@) in that conversions are applied in each individual assignment, which prevents data loss from the chain of conversions that can happen during a cascading assignment.
637For example, @[y, x] = 3.14@ performs the assignments @y = 3.14@ and @x = 3.14@, yielding @y == 3.14@ and @x == 3@;
638whereas C cascading assignment @y = x = 3.14@ performs the assignments @x = 3.14@ and @y = x@, yielding @3@ in @y@ and @x@.
639Finally, tuple assignment is an expression where the result type is the type of the left-hand side of the assignment, just like all other assignment expressions in C.
640This example shows mass, multiple, and cascading assignment used in one expression:
641\begin{lstlisting}
642void f( [int, int] );
643f( [x, y] = z = 1.5 );                                          $\C{// assignments in parameter list}$
644\end{lstlisting}
645
646
647\subsection{Member Access}
648
649It is also possible to access multiple fields from a single expression using a \emph{member-access}.
650The result is a single tuple-valued expression whose type is the tuple of the types of the members, \eg:
651\begin{lstlisting}
652struct S { int x; double y; char * z; } s;
653s.[x, y, z] = 0;
654\end{lstlisting}
655Here, the mass assignment sets all members of @s@ to zero.
656Since tuple-index expressions are a form of member-access expression, it is possible to use tuple-index expressions in conjunction with member tuple expressions to manually restructure a tuple (\eg rearrange, drop, and duplicate components).
657%\lstDeleteShortInline@%
658%\par\smallskip
659%\begin{tabular}{@{}l@{\hspace{1.5\parindent}}||@{\hspace{1.5\parindent}}l@{}}
660\begin{lstlisting}
661[int, int, long, double] x;
662void f( double, long );
663x.[0, 1] = x.[1, 0];    $\C{// rearrange: [x.0, x.1] = [x.1, x.0]}$
664f( x.[0, 3] );            $\C{// drop: f(x.0, x.3)}$
665[int, int, int] y = x.[2, 0, 2]; $\C{// duplicate: [y.0, y.1, y.2] = [x.2, x.0.x.2]}$
666\end{lstlisting}
667%\end{lstlisting}
668%&
669%\begin{lstlisting}
670%\end{tabular}
671%\smallskip\par\noindent
672%\lstMakeShortInline@%
673It is also possible for a member access to contain other member accesses, \eg:
674\begin{lstlisting}
675struct A { double i; int j; };
676struct B { int * k; short l; };
677struct C { int x; A y; B z; } v;
678v.[x, y.[i, j], z.k];                                           $\C{// [v.x, [v.y.i, v.y.j], v.z.k]}$
679\end{lstlisting}
680
681
682\begin{comment}
683\subsection{Casting}
684
685In C, the cast operator is used to explicitly convert between types.
686In \CFA, the cast operator has a secondary use as type ascription.
687That 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:
688\begin{lstlisting}
689int f();     // (1)
690double f()// (2)
691
692f();       // ambiguous - (1),(2) both equally viable
693(int)f()// choose (2)
694\end{lstlisting}
695
696Since casting is a fundamental operation in \CFA, casts should be given a meaningful interpretation in the context of tuples.
697Taking a look at standard C provides some guidance with respect to the way casts should work with tuples:
698\begin{lstlisting}
699int f();
700void g();
701
702(void)f()// (1)
703(int)g()// (2)
704\end{lstlisting}
705In C, (1) is a valid cast, which calls @f@ and discards its result.
706On the other hand, (2) is invalid, because @g@ does not produce a result, so requesting an @int@ to materialize from nothing is nonsensical.
707Generalizing 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.
708
709Formally, 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 $T_i$.
710Excess 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.
711This approach follows naturally from the way that a cast to @void@ works in C.
712
713For example, in
714\begin{lstlisting}
715[int, int, int] f();
716[int, [int, int], int] g();
717
718([int, double])f();           $\C{// (1)}$
719([int, int, int])g();         $\C{// (2)}$
720([void, [int, int]])g();      $\C{// (3)}$
721([int, int, int, int])g();    $\C{// (4)}$
722([int, [int, int, int]])g()$\C{// (5)}$
723\end{lstlisting}
724
725(1) discards the last element of the return value and converts the second element to @double@.
726Since @int@ is effectively a 1-element tuple, (2) discards the second component of the second element of the return value of @g@.
727If @g@ is free of side effects, this expression is equivalent to @[(int)(g().0), (int)(g().1.0), (int)(g().2)]@.
728Since @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)]@).
729
730Note 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.}.
731As such, (4) is invalid because the cast target type contains 4 components, while the source type contains only 3.
732Similarly, (5) is invalid because the cast @([int, int, int])(g().1)@ is invalid.
733That is, it is invalid to cast @[int, int]@ to @[int, int, int]@.
734\end{comment}
735
736
737\subsection{Polymorphism}
738
739Tuples also integrate with \CFA polymorphism as a kind of generic type.
740Due 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:
741\begin{lstlisting}
742forall(otype T, dtype U) void f( T x, U * y );
743f( [5, "hello"] );
744\end{lstlisting}
745where @[5, "hello"]@ is flattened, giving argument list @5, "hello"@, and @T@ binds to @int@ and @U@ binds to @const char@.
746Tuples, however, may contain polymorphic components.
747For example, a plus operator can be written to add two triples together.
748\begin{lstlisting}
749forall(otype T | { T ?+?( T, T ); }) [T, T, T] ?+?( [T, T, T] x, [T, T, T] y ) {
750        return [x.0 + y.0, x.1 + y.1, x.2 + y.2];
751}
752[int, int, int] x;
753int i1, i2, i3;
754[i1, i2, i3] = x + ([10, 20, 30]);
755\end{lstlisting}
756
757Flattening and restructuring conversions are also applied to tuple types in polymorphic type assertions.
758\begin{lstlisting}
759int f( [int, double], double );
760forall(otype T, otype U | { T f( T, U, U ); }) void g( T, U );
761g( 5, 10.21 );
762\end{lstlisting}
763Hence, function parameter and return lists are flattened for the purposes of type unification allowing the example to pass expression resolution.
764This relaxation is possible by extending the thunk scheme described by \citet{Bilson03}.
765Whenever 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:
766\begin{lstlisting}
767int _thunk( int _p0, double _p1, double _p2 ) { return f( [_p0, _p1], _p2 ); }
768\end{lstlisting}
769so the thunk provides flattening and structuring conversions to inferred functions, improving the compatibility of tuples and polymorphism.
770These thunks take advantage of GCC C nested-functions to produce closures that have the usual function pointer signature.
771
772
773\subsection{Variadic Tuples}
774\label{sec:variadic-tuples}
775
776To define variadic functions, \CFA adds a new kind of type parameter, @ttype@ (tuple type).
777Matching against a @ttype@ parameter consumes all remaining argument components and packages them into a tuple, binding to the resulting tuple of types.
778In 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.
779As such, @ttype@ variables are also called \emph{argument packs}.
780
781Like variadic templates, the main way to manipulate @ttype@ polymorphic functions is via recursion.
782Since nothing is known about a parameter pack by default, assertion parameters are key to doing anything meaningful.
783Unlike variadic templates, @ttype@ polymorphic functions can be separately compiled.
784For example, a generalized @sum@ function written using @ttype@:
785\begin{lstlisting}
786int sum$\(_0\)$() { return 0; }
787forall(ttype Params | { int sum( Params ); } ) int sum$\(_1\)$( int x, Params rest ) {
788        return x + sum( rest );
789}
790sum( 10, 20, 30 );
791\end{lstlisting}
792Since @sum@\(_0\) does not accept any arguments, it is not a valid candidate function for the call @sum(10, 20, 30)@.
793In 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]@.
794The process continues, @Params@ is bound to @[]@, requiring an assertion @int sum()@, which matches @sum@\(_0\) and terminates the recursion.
795Effectively, 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))@.
796
797It is reasonable to take the @sum@ function a step further to enforce a minimum number of arguments:
798\begin{lstlisting}
799int sum( int x, int y ) { return x + y; }
800forall(ttype Params | { int sum( int, Params ); } ) int sum( int x, int y, Params rest ) {
801        return sum( x + y, rest );
802}
803\end{lstlisting}
804One more step permits the summation of any summable type with all arguments of the same type:
805\begin{lstlisting}
806trait summable(otype T) {
807        T ?+?( T, T );
808};
809forall(otype R | summable( R ) ) R sum( R x, R y ) {
810        return x + y;
811}
812forall(otype R, ttype Params | summable(R) | { R sum(R, Params); } ) R sum(R x, R y, Params rest) {
813        return sum( x + y, rest );
814}
815\end{lstlisting}
816Unlike C variadic functions, it is unnecessary to hard code the number and expected types.
817Furthermore, this code is extendable so any user-defined type with a @?+?@ operator.
818Summing arbitrary heterogeneous lists is possible with similar code by adding the appropriate type variables and addition operators.
819
820It is also possible to write a type-safe variadic print function to replace @printf@:
821\begin{lstlisting}
822struct S { int x, y; };
823forall(otype T, ttype Params | { void print(T); void print(Params); }) void print(T arg, Params rest) {
824        print(arg);  print(rest);
825}
826void print( char * x ) { printf( "%s", x ); }
827void print( int x ) { printf( "%d", x ); }
828void print( S s ) { print( "{ ", s.x, ",", s.y, " }" ); }
829print( "s = ", (S){ 1, 2 }, "\n" );
830\end{lstlisting}
831This example showcases a variadic-template-like decomposition of the provided argument list.
832The individual @print@ functions allow printing a single element of a type.
833The polymorphic @print@ allows printing any list of types, as long as each individual type has a @print@ function.
834The individual print functions can be used to build up more complicated @print@ functions, such as for @S@, which is something that cannot be done with @printf@ in C.
835
836Finally, it is possible to use @ttype@ polymorphism to provide arbitrary argument forwarding functions.
837For example, it is possible to write @new@ as a library function:
838\begin{lstlisting}
839forall( otype R, otype S ) void ?{}( pair(R, S) *, R, S );
840forall( dtype T, ttype Params | sized(T) | { void ?{}( T *, Params ); } ) T * new( Params p ) {
841        return ((T *)malloc()){ p };                    $\C{// construct into result of malloc}$
842}
843pair( int, char ) * x = new( 42, '!' );
844\end{lstlisting}
845The @new@ function provides the combination of type-safe @malloc@ with a \CFA constructor call, making it impossible to forget constructing dynamically allocated objects.
846This function provides the type-safety of @new@ in \CC, without the need to specify the allocated type again, thanks to return-type inference.
847
848
849\subsection{Implementation}
850
851Tuples are implemented in the \CFA translator via a transformation into generic types.
852For each $N$, the first time an $N$-tuple is seen in a scope a generic type with $N$ type parameters is generated, \eg:
853\begin{lstlisting}
854[int, int] f() {
855        [double, double] x;
856        [int, double, int] y;
857}
858\end{lstlisting}
859is transformed into:
860\begin{lstlisting}
861forall(dtype T0, dtype T1 | sized(T0) | sized(T1)) struct _tuple2 {
862        T0 field_0;                     $\C{// generated before the first 2-tuple}$
863        T1 field_1;
864};
865_tuple2(int, int) f() {
866        _tuple2(double, double) x;
867        forall(dtype T0, dtype T1, dtype T2 | sized(T0) | sized(T1) | sized(T2)) struct _tuple3 {
868                T0 field_0;             $\C{// generated before the first 3-tuple}$
869                T1 field_1;
870                T2 field_2;
871        };
872        _tuple3(int, double, int) y;
873}
874\end{lstlisting}
875Tuple expressions are then simply converted directly into compound literals, \eg @[5, 'x', 1.24]@ becomes @(_tuple3(int, char, double)){ 5, 'x', 1.24 }@.
876
877\begin{comment}
878Since tuples are essentially structures, tuple indexing expressions are just field accesses:
879\begin{lstlisting}
880void f(int, [double, char]);
881[int, double] x;
882
883x.0+x.1;
884printf("%d %g\n", x);
885f(x, 'z');
886\end{lstlisting}
887Is transformed into:
888\begin{lstlisting}
889void f(int, _tuple2(double, char));
890_tuple2(int, double) x;
891
892x.field_0+x.field_1;
893printf("%d %g\n", x.field_0, x.field_1);
894f(x.field_0, (_tuple2){ x.field_1, 'z' });
895\end{lstlisting}
896Note that due to flattening, @x@ used in the argument position is converted into the list of its fields.
897In the call to @f@, the second and third argument components are structured into a tuple argument.
898Similarly, tuple member expressions are recursively expanded into a list of member access expressions.
899
900Expressions that may contain side effects are made into \emph{unique expressions} before being expanded by the flattening conversion.
901Each unique expression is assigned an identifier and is guaranteed to be executed exactly once:
902\begin{lstlisting}
903void g(int, double);
904[int, double] h();
905g(h());
906\end{lstlisting}
907Internally, this expression is converted to two variables and an expression:
908\begin{lstlisting}
909void g(int, double);
910[int, double] h();
911
912_Bool _unq0_finished_ = 0;
913[int, double] _unq0;
914g(
915        (_unq0_finished_ ? _unq0 : (_unq0 = f(), _unq0_finished_ = 1, _unq0)).0,
916        (_unq0_finished_ ? _unq0 : (_unq0 = f(), _unq0_finished_ = 1, _unq0)).1,
917);
918\end{lstlisting}
919Since argument evaluation order is not specified by the C programming language, this scheme is built to work regardless of evaluation order.
920The first time a unique expression is executed, the actual expression is evaluated and the accompanying boolean is set to true.
921Every subsequent evaluation of the unique expression then results in an access to the stored result of the actual expression.
922Tuple member expressions also take advantage of unique expressions in the case of possible impurity.
923
924Currently, the \CFA translator has a very broad, imprecise definition of impurity, where any function call is assumed to be impure.
925This 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.
926
927The various kinds of tuple assignment, constructors, and destructors generate GNU C statement expressions.
928A 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.
929The 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.
930However, 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.
931\end{comment}
932
933
934\section{Evaluation}
935\label{sec:eval}
936
937Though \CFA provides significant added functionality over C, these features have a low runtime penalty.
938In fact, \CFA's features for generic programming can enable faster runtime execution than idiomatic @void *@-based C code.
939This 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}).
940Since 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.
941A more illustrative benchmark measures the costs of idiomatic usage of each language's features.
942Figure~\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}.
943The benchmark test is similar for C and \CC.
944The 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.
945
946\begin{figure}
947\begin{lstlisting}[xleftmargin=3\parindentlnth,aboveskip=0pt,belowskip=0pt]
948int main( int argc, char * argv[] ) {
949        FILE * out = fopen( "cfa-out.txt", "w" );
950        int maxi = 0, vali = 42;
951        stack(int) si, ti;
952
953        REPEAT_TIMED( "push_int", N, push( &si, vali ); )
954        TIMED( "copy_int", ti = si; )
955        TIMED( "clear_int", clear( &si ); )
956        REPEAT_TIMED( "pop_int", N,
957                int xi = pop( &ti ); if ( xi > maxi ) { maxi = xi; } )
958        REPEAT_TIMED( "print_int", N/2, print( out, vali, ":", vali, "\n" ); )
959
960        pair(_Bool, char) maxp = { (_Bool)0, '\0' }, valp = { (_Bool)1, 'a' };
961        stack(pair(_Bool, char)) sp, tp;
962
963        REPEAT_TIMED( "push_pair", N, push( &sp, valp ); )
964        TIMED( "copy_pair", tp = sp; )
965        TIMED( "clear_pair", clear( &sp ); )
966        REPEAT_TIMED( "pop_pair", N,
967                pair(_Bool, char) xp = pop( &tp ); if ( xp > maxp ) { maxp = xp; } )
968        REPEAT_TIMED( "print_pair", N/2, print( out, valp, ":", valp, "\n" ); )
969        fclose(out);
970}
971\end{lstlisting}
972\caption{\CFA Benchmark Test}
973\label{fig:BenchmarkTest}
974\end{figure}
975
976The 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.
977The \CCV variant illustrates an alternative object-oriented idiom where all objects inherit from a base @object@ class, mimicking a Java-like interface;
978hence runtime checks are necessary to safely down-cast objects.
979The 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.
980For 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.
981Note, the C benchmark uses unchecked casts as there is no runtime mechanism to perform such checks, while \CFA and \CC provide type-safety statically.
982
983Figure~\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.
984The graph plots the median of 5 consecutive runs of each program, with an initial warm-up run omitted.
985All code is compiled at \texttt{-O2} by GCC or G++ 6.2.0, with all \CC code compiled as \CCfourteen.
986The 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.
987
988\begin{figure}
989\centering
990\input{timing}
991\caption{Benchmark Timing Results (smaller is better)}
992\label{fig:eval}
993\end{figure}
994
995\begin{table}
996\caption{Properties of benchmark code}
997\label{tab:eval}
998\newcommand{\CT}[1]{\multicolumn{1}{c}{#1}}
999\begin{tabular}{rrrrr}
1000                                                                        & \CT{C}        & \CT{\CFA}     & \CT{\CC}      & \CT{\CCV}             \\ \hline
1001maximum memory usage (MB)                       & 10001         & 2502          & 2503          & 11253                 \\
1002source code size (lines)                        & 247           & 222           & 165           & 339                   \\
1003redundant type annotations (lines)      & 39            & 2                     & 2                     & 15                    \\
1004binary size (KB)                                        & 14            & 229           & 18            & 38                    \\
1005\end{tabular}
1006\end{table}
1007
1008The 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;
1009this inefficiency is exacerbated by the second level of generic types in the pair-based benchmarks.
1010By 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.
1011\CCV is slower than C largely due to the cost of runtime type-checking of down-casts (implemented with @dynamic_cast@);
1012There are two outliers in the graph for \CFA: all prints and pop of @pair@.
1013Both 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.
1014A compiler designed for \CFA could easily perform these optimizations.
1015Finally, the binary size for \CFA is larger because of static linking with the \CFA libraries.
1016
1017\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.
1018On 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.
1019\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;
1020with their omission the \CCV line count is similar to C.
1021We 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.
1022
1023Raw line-count, however, is a fairly rough measure of code complexity;
1024another important factor is how much type information the programmer must manually specify, especially where that information is not checked by the compiler.
1025Such 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@).
1026To 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.
1027The \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.
1028The 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).
1029These uses are similar to the @new@ expressions in \CC, though the \CFA compiler's type resolver should shortly render even these type casts superfluous.
1030
1031
1032\section{Related Work}
1033
1034
1035\subsection{Polymorphism}
1036
1037\CC is the most similar language to \CFA;
1038both are extensions to C with source and runtime backwards compatibility.
1039The fundamental difference is in their engineering approach to C compatibility and programmer expectation.
1040While \CC provides good backwards compatibility with C, it has a steep learning curve for many of its extensions.
1041For example, polymorphism is provided via three disjoint mechanisms: overloading, inheritance, and templates.
1042The 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.
1043In 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.
1044The key mechanism to support separate compilation is \CFA's \emph{explicit} use of assumed properties for a type.
1045Until \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;
1046furthermore, \CC concepts are restricted to template polymorphism.
1047
1048Cyclone~\citep{Grossman06} also provides capabilities for polymorphic functions and existential types, similar to \CFA's @forall@ functions and generic types.
1049Cyclone 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.
1050Furthermore, 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@.
1051In \CFA terms, all Cyclone polymorphism must be dtype-static.
1052While 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.
1053
1054\citet{obj-c-book} is an industrially successful extension to C.
1055However, Objective-C is a radical departure from C, using an object-oriented model with message-passing.
1056Objective-C did not support type-checked generics until recently~\citet{xcode7}, historically using less-efficient and more error-prone runtime checking of object types.
1057The~\citet{GObject} framework also adds object-oriented programming with runtime type-checking and reference-counting garbage-collection to C;
1058these features are more intrusive additions than those provided by \CFA, in addition to the runtime overhead of reference-counting.
1059\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.
1060Java~\citep{Java8} included generic types in Java~5;
1061Java's generic types are type-checked at compilation and type-erased at runtime, similar to \CFA's.
1062However, in Java, each object carries its own table of method pointers, while \CFA passes the method pointers separately to maintain a C-compatible layout.
1063Java is also a garbage-collected, object-oriented language, with the associated resource usage and C-interoperability burdens.
1064
1065D~\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.
1066However, 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.
1067D and Go are garbage-collected languages, imposing the associated runtime overhead.
1068The necessity of accounting for data transfer between managed runtimes and the unmanaged C runtime complicates foreign-function interfaces to C.
1069Furthermore, 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.
1070D 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.
1071Rust also possesses much more powerful abstraction capabilities for writing generic code than Go.
1072On 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.
1073\CFA, with its more modest safety features, allows direct ports of C code while maintaining the idiomatic style of the original source.
1074
1075
1076\subsection{Tuples/Variadics}
1077
1078Many programming languages have some form of tuple construct and/or variadic functions, \eg SETL, C, KW-C, \CC, D, Go, Java, ML, and Scala.
1079SETL~\cite{SETL} is a high-level mathematical programming language, with tuples being one of the primary data types.
1080Tuples in SETL allow subscripting, dynamic expansion, and multiple assignment.
1081C 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.
1082KW-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.
1083The main contributions of that work were adding MRVF, tuple mass and multiple assignment, and record-field access.
1084\CCeleven introduced @std::tuple@ as a library variadic template structure.
1085Tuples are a generalization of @std::pair@, in that they allow for arbitrary length, fixed-size aggregation of heterogeneous values.
1086Operations include @std::get<N>@ to extract vales, @std::tie@ to create a tuple of references used for assignment, and lexicographic comparisons.
1087\CCseventeen proposes \emph{structured bindings}~\cite{Sutter15} to eliminate pre-declaring variables and use of @std::tie@ for binding the results.
1088This 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.
1089Furthermore, structured bindings are not a full replacement for @std::tie@, as it always declares new variables.
1090Like \CC, D provides tuples through a library variadic-template structure.
1091Go does not have tuples but supports MRVF.
1092Java'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.
1093Tuples are a fundamental abstraction in most functional programming languages, such as Standard ML~\cite{sml} and~\cite{Scala}, which decompose tuples using pattern matching.
1094
1095
1096\section{Conclusion and Future Work}
1097
1098The 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.
1099While 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.
1100The 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.
1101The contributions are a powerful type-system using parametric polymorphism and overloading, generic types, and tuples, which all have complex interactions.
1102The work is a challenging design, engineering, and implementation exercise.
1103On the surface, the project may appear as a rehash of similar mechanisms in \CC.
1104However, 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.
1105All of these new features are being used by the \CFA development-team to build the \CFA runtime-system.
1106Finally, we demonstrate that \CFA performance for some idiomatic cases is better than C and close to \CC, showing the design is practically applicable.
1107
1108There is ongoing work on a wide range of \CFA feature extensions, including reference types, exceptions, concurrent primitives and modules.
1109(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.)
1110In addition, there are interesting future directions for the polymorphism design.
1111Notably, \CC template functions trade compile time and code bloat for optimal runtime of individual instantiations of polymorphic functions.
1112\CFA polymorphic functions, by contrast, uses a dynamic virtual dispatch.
1113The 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.
1114Two 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.
1115These approaches are not mutually exclusive and allow performance optimizations to be applied only when necessary, without suffering global code-bloat.
1116In general, we believe separate compilation, producing smaller code, works well with loaded hardware-caches, which may offset the benefit of larger inlined-code.
1117
1118
1119\begin{acks}
1120The 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.
1121
1122This 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.
1123\end{acks}
1124
1125
1126\bibliographystyle{ACM-Reference-Format}
1127\bibliography{cfa}
1128
1129
1130\appendix
1131
1132\section{Benchmark Stack Implementation}
1133\label{sec:BenchmarkStackImplementation}
1134
1135\lstset{basicstyle=\linespread{0.9}\sf\small}
1136
1137\begin{comment}
1138\CFA
1139\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1140forall(otype T) struct stack_node;
1141forall(otype T) struct stack { stack_node(T) * head; };
1142forall(otype T) void ?{}(stack(T) * s);
1143forall(otype T) void ?{}(stack(T) * s, stack(T) t);
1144forall(otype T) stack(T) ?=?(stack(T) * s, stack(T) t);
1145forall(otype T) void ^?{}(stack(T) * s);
1146forall(otype T) _Bool empty(const stack(T) * s);
1147forall(otype T) void push(stack(T) * s, T value);
1148forall(otype T) T pop(stack(T) * s);
1149forall(otype T) void clear(stack(T) * s);
1150
1151void print( FILE * out, const char * x );
1152void print( FILE * out, _Bool x );
1153void print( FILE * out, char x );
1154void print( FILE * out, int x );
1155forall(otype T, ttype Params | { void print( FILE *, T ); void print( FILE *, Params ); })
1156        void print( FILE * out, T arg, Params rest );
1157forall(otype R, otype S | { void print( FILE *, R ); void print( FILE *, S ); })
1158        void print( FILE * out, pair(R, S) x );
1159\end{lstlisting}
1160
1161\medskip\noindent
1162\CC
1163\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1164std::pair
1165std::forward_list wrapped in std::stack interface
1166
1167template<typename T> void print(ostream & out, const T & x) { out << x; }
1168template<> void print<bool>(ostream & out, const bool & x) { out << (x ? "true" : "false"); }
1169template<> void print<char>(ostream & out, const char & x ) { out << "'" << x << "'"; }
1170template<typename R, typename S> ostream & operator<< (ostream & out, const pair<R, S>& x) {
1171        out << "["; print(out, x.first); out << ", "; print(out, x.second); return out << "]"; }
1172template<typename T, typename... Args> void print(ostream & out, const T & arg, const Args &... rest) {
1173        out << arg;     print(out, rest...); }
1174\end{lstlisting}
1175
1176\medskip\noindent
1177C
1178\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1179struct pair { void * first, second; };
1180struct pair * new_pair( void * first, void * second );
1181struct pair * copy_pair( const struct pair * src,
1182        void * (*copy_first)( const void * ), void * (*copy_second)( const void * ) );
1183void free_pair( struct pair * p, void (*free_first)( void * ), void (*free_second)( void * ) );
1184int cmp_pair( const struct pair * a, const struct pair * b,
1185        int (*cmp_first)( const void *, const void * ), int (*cmp_second)( const void *, const void * ) );
1186
1187struct stack_node;
1188struct stack { struct stack_node * head; };
1189struct stack new_stack();
1190void copy_stack( struct stack * dst, const struct stack * src, void * (*copy)( const void * ) );
1191void clear_stack( struct stack * s, void (*free_el)( void * ) );
1192_Bool stack_empty( const struct stack * s );
1193void push_stack( struct stack * s, void * value );
1194void * pop_stack( struct stack * s );
1195
1196void print_string( FILE * out, const char * x );
1197void print_bool( FILE * out, _Bool x );
1198void print_char( FILE * out, char x );
1199void print_int( FILE * out, int x );
1200void print( FILE * out, const char * fmt, ... );
1201\end{lstlisting}
1202\end{comment}
1203
1204Throughout, @/***/@ designates a counted redundant type annotation.
1205
1206\medskip\noindent
1207\CFA
1208\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1209forall(otype T) struct stack_node {
1210        T value;
1211        stack_node(T) * next;
1212};
1213forall(otype T) void ?{}(stack(T) * s) { (&s->head){ 0 }; }
1214forall(otype T) void ?{}(stack(T) * s, stack(T) t) {
1215        stack_node(T) ** crnt = &s->head;
1216        for ( stack_node(T) * next = t.head; next; next = next->next ) {
1217                *crnt = ((stack_node(T) *)malloc()){ next->value }; /***/
1218                stack_node(T) * acrnt = *crnt;
1219                crnt = &acrnt->next;
1220        }
1221        *crnt = 0;
1222}
1223forall(otype T) stack(T) ?=?(stack(T) * s, stack(T) t) {
1224        if ( s->head == t.head ) return *s;
1225        clear(s);
1226        s{ t };
1227        return *s;
1228}
1229forall(otype T) void ^?{}(stack(T) * s) { clear(s); }
1230forall(otype T) _Bool empty(const stack(T) * s) { return s->head == 0; }
1231forall(otype T) void push(stack(T) * s, T value) {
1232        s->head = ((stack_node(T) *)malloc()){ value, s->head }; /***/
1233}
1234forall(otype T) T pop(stack(T) * s) {
1235        stack_node(T) * n = s->head;
1236        s->head = n->next;
1237        T x = n->value;
1238        ^n{};
1239        free(n);
1240        return x;
1241}
1242forall(otype T) void clear(stack(T) * s) {
1243        for ( stack_node(T) * next = s->head; next; ) {
1244                stack_node(T) * crnt = next;
1245                next = crnt->next;
1246                delete(crnt);
1247        }
1248        s->head = 0;
1249}
1250\end{lstlisting}
1251
1252\medskip\noindent
1253\CC
1254\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1255template<typename T> class stack {
1256        struct node {
1257                T value;
1258                node * next;
1259                node( const T & v, node * n = nullptr ) : value(v), next(n) {}
1260        };
1261        node * head;
1262        void copy(const stack<T>& o) {
1263                node ** crnt = &head;
1264                for ( node * next = o.head;; next; next = next->next ) {
1265                        *crnt = new node{ next->value }; /***/
1266                        crnt = &(*crnt)->next;
1267                }
1268                *crnt = nullptr;
1269        }
1270  public:
1271        stack() : head(nullptr) {}
1272        stack(const stack<T>& o) { copy(o); }
1273        stack(stack<T> && o) : head(o.head) { o.head = nullptr; }
1274        ~stack() { clear(); }
1275        stack & operator= (const stack<T>& o) {
1276                if ( this == &o ) return *this;
1277                clear();
1278                copy(o);
1279                return *this;
1280        }
1281        stack & operator= (stack<T> && o) {
1282                if ( this == &o ) return *this;
1283                head = o.head;
1284                o.head = nullptr;
1285                return *this;
1286        }
1287        bool empty() const { return head == nullptr; }
1288        void push(const T & value) { head = new node{ value, head };  /***/ }
1289        T pop() {
1290                node * n = head;
1291                head = n->next;
1292                T x = std::move(n->value);
1293                delete n;
1294                return x;
1295        }
1296        void clear() {
1297                for ( node * next = head; next; ) {
1298                        node * crnt = next;
1299                        next = crnt->next;
1300                        delete crnt;
1301                }
1302                head = nullptr;
1303        }
1304};
1305\end{lstlisting}
1306
1307\medskip\noindent
1308C
1309\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1310struct stack_node {
1311        void * value;
1312        struct stack_node * next;
1313};
1314struct stack new_stack() { return (struct stack){ NULL }; /***/ }
1315void copy_stack(struct stack * s, const struct stack * t, void * (*copy)(const void *)) {
1316        struct stack_node ** crnt = &s->head;
1317        for ( struct stack_node * next = t->head; next; next = next->next ) {
1318                *crnt = malloc(sizeof(struct stack_node)); /***/
1319                **crnt = (struct stack_node){ copy(next->value) }; /***/
1320                crnt = &(*crnt)->next;
1321        }
1322        *crnt = 0;
1323}
1324_Bool stack_empty(const struct stack * s) { return s->head == NULL; }
1325void push_stack(struct stack * s, void * value) {
1326        struct stack_node * n = malloc(sizeof(struct stack_node)); /***/
1327        *n = (struct stack_node){ value, s->head }; /***/
1328        s->head = n;
1329}
1330void * pop_stack(struct stack * s) {
1331        struct stack_node * n = s->head;
1332        s->head = n->next;
1333        void * x = n->value;
1334        free(n);
1335        return x;
1336}
1337void clear_stack(struct stack * s, void (*free_el)(void *)) {
1338        for ( struct stack_node * next = s->head; next; ) {
1339                struct stack_node * crnt = next;
1340                next = crnt->next;
1341                free_el(crnt->value);
1342                free(crnt);
1343        }
1344        s->head = NULL;
1345}
1346\end{lstlisting}
1347
1348\medskip\noindent
1349\CCV
1350\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1351stack::node::node( const object & v, node * n ) : value( v.new_copy() ), next( n ) {}
1352void stack::copy(const stack & o) {
1353        node ** crnt = &head;
1354        for ( node * next = o.head; next; next = next->next ) {
1355                *crnt = new node{ *next->value };
1356                crnt = &(*crnt)->next;
1357        }
1358        *crnt = nullptr;
1359}
1360stack::stack() : head(nullptr) {}
1361stack::stack(const stack & o) { copy(o); }
1362stack::stack(stack && o) : head(o.head) { o.head = nullptr; }
1363stack::~stack() { clear(); }
1364stack & stack::operator= (const stack & o) {
1365        if ( this == &o ) return *this;
1366        clear();
1367        copy(o);
1368        return *this;
1369}
1370stack & stack::operator= (stack && o) {
1371        if ( this == &o ) return *this;
1372        head = o.head;
1373        o.head = nullptr;
1374        return *this;
1375}
1376bool stack::empty() const { return head == nullptr; }
1377void stack::push(const object & value) { head = new node{ value, head }; /***/ }
1378ptr<object> stack::pop() {
1379        node * n = head;
1380        head = n->next;
1381        ptr<object> x = std::move(n->value);
1382        delete n;
1383        return x;
1384}
1385void stack::clear() {
1386        for ( node * next = head; next; ) {
1387                node * crnt = next;
1388                next = crnt->next;
1389                delete crnt;
1390        }
1391        head = nullptr;
1392}
1393\end{lstlisting}
1394
1395
1396\begin{comment}
1397
1398\subsubsection{bench.h}
1399(\texttt{bench.hpp} is similar.)
1400
1401\lstinputlisting{evaluation/bench.h}
1402
1403\subsection{C}
1404
1405\subsubsection{c-stack.h} ~
1406
1407\lstinputlisting{evaluation/c-stack.h}
1408
1409\subsubsection{c-stack.c} ~
1410
1411\lstinputlisting{evaluation/c-stack.c}
1412
1413\subsubsection{c-pair.h} ~
1414
1415\lstinputlisting{evaluation/c-pair.h}
1416
1417\subsubsection{c-pair.c} ~
1418
1419\lstinputlisting{evaluation/c-pair.c}
1420
1421\subsubsection{c-print.h} ~
1422
1423\lstinputlisting{evaluation/c-print.h}
1424
1425\subsubsection{c-print.c} ~
1426
1427\lstinputlisting{evaluation/c-print.c}
1428
1429\subsubsection{c-bench.c} ~
1430
1431\lstinputlisting{evaluation/c-bench.c}
1432
1433\subsection{\CFA}
1434
1435\subsubsection{cfa-stack.h} ~
1436
1437\lstinputlisting{evaluation/cfa-stack.h}
1438
1439\subsubsection{cfa-stack.c} ~
1440
1441\lstinputlisting{evaluation/cfa-stack.c}
1442
1443\subsubsection{cfa-print.h} ~
1444
1445\lstinputlisting{evaluation/cfa-print.h}
1446
1447\subsubsection{cfa-print.c} ~
1448
1449\lstinputlisting{evaluation/cfa-print.c}
1450
1451\subsubsection{cfa-bench.c} ~
1452
1453\lstinputlisting{evaluation/cfa-bench.c}
1454
1455\subsection{\CC}
1456
1457\subsubsection{cpp-stack.hpp} ~
1458
1459\lstinputlisting[language=c++]{evaluation/cpp-stack.hpp}
1460
1461\subsubsection{cpp-print.hpp} ~
1462
1463\lstinputlisting[language=c++]{evaluation/cpp-print.hpp}
1464
1465\subsubsection{cpp-bench.cpp} ~
1466
1467\lstinputlisting[language=c++]{evaluation/cpp-bench.cpp}
1468
1469\subsection{\CCV}
1470
1471\subsubsection{object.hpp} ~
1472
1473\lstinputlisting[language=c++]{evaluation/object.hpp}
1474
1475\subsubsection{cpp-vstack.hpp} ~
1476
1477\lstinputlisting[language=c++]{evaluation/cpp-vstack.hpp}
1478
1479\subsubsection{cpp-vstack.cpp} ~
1480
1481\lstinputlisting[language=c++]{evaluation/cpp-vstack.cpp}
1482
1483\subsubsection{cpp-vprint.hpp} ~
1484
1485\lstinputlisting[language=c++]{evaluation/cpp-vprint.hpp}
1486
1487\subsubsection{cpp-vbench.cpp} ~
1488
1489\lstinputlisting[language=c++]{evaluation/cpp-vbench.cpp}
1490\end{comment}
1491
1492\end{document}
1493
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1495% tab-width: 4 %
1496% compile-command: "make" %
1497% End: %
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