source: doc/generic_types/generic_types.tex @ 07846d8

aaron-thesisarm-ehcleanup-dtorsdeferred_resndemanglerjacob/cs343-translationjenkins-sandboxnew-astnew-ast-unique-exprnew-envno_listpersistent-indexerresolv-newwith_gc
Last change on this file since 07846d8 was 07846d8, checked in by Peter A. Buhr <pabuhr@…>, 4 years ago

make inverted A in CFA name better

  • Property mode set to 100644
File size: 80.9 KB
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1% take off review (for line numbers) and anonymous (for anonymization) on submission
2\documentclass[format=acmlarge,anonymous,review]{acmart}
3% \documentclass[format=acmlarge,review]{acmart}
4
5\usepackage{xspace,calc,comment}
6\usepackage{upquote}                                                                    % switch curled `'" to straight
7\usepackage{listings}                                                                   % format program code
8\usepackage{rotating}
9\usepackage[usenames]{color}
10
11\makeatletter
12% Default underscore is too low and wide. Cannot use lstlisting "literate" as replacing underscore
13% removes it as a variable-name character so keyworks in variables are highlighted
14\DeclareTextCommandDefault{\textunderscore}{\leavevmode\makebox[1.2ex][c]{\rule{1ex}{0.1ex}}}
15
16% parindent is relative, i.e., toggled on/off in environments like itemize, so store the value for
17% use rather than use \parident directly.
18\newlength{\parindentlnth}
19\setlength{\parindentlnth}{\parindent}
20
21\newlength{\gcolumnposn}                                % temporary hack because lstlisting does not handle tabs correctly
22\newlength{\columnposn}
23\setlength{\gcolumnposn}{2.75in}
24\setlength{\columnposn}{\gcolumnposn}
25\newcommand{\C}[2][\@empty]{\ifx#1\@empty\else\global\setlength{\columnposn}{#1}\global\columnposn=\columnposn\fi\hfill\makebox[\textwidth-\columnposn][l]{\lst@commentstyle{#2}}}
26\newcommand{\CRT}{\global\columnposn=\gcolumnposn}
27
28% Latin abbreviation
29\newcommand{\abbrevFont}{\textit}       % set empty for no italics
30\newcommand*{\eg}{%
31        \@ifnextchar{,}{\abbrevFont{e}.\abbrevFont{g}.}%
32                {\@ifnextchar{:}{\abbrevFont{e}.\abbrevFont{g}.}%
33                        {\abbrevFont{e}.\abbrevFont{g}.,\xspace}}%
34}%
35\newcommand*{\ie}{%
36        \@ifnextchar{,}{\abbrevFont{i}.\abbrevFont{e}.}%
37                {\@ifnextchar{:}{\abbrevFont{i}.\abbrevFont{e}.}%
38                        {\abbrevFont{i}.\abbrevFont{e}.,\xspace}}%
39}%
40\newcommand*{\etc}{%
41        \@ifnextchar{.}{\abbrevFont{etc}}%
42        {\abbrevFont{etc}.\xspace}%
43}%
44\newcommand{\etal}{%
45        \@ifnextchar{.}{\abbrevFont{et~al}}%
46                {\abbrevFont{et al}.\xspace}%
47}%
48\makeatother
49
50% Useful macros
51\newcommand{\CFA}{C\raisebox{\depth}{\rotatebox{180}{\textsf{A}}}\hspace{-1pt}\xspace} % Cforall symbolic name
52%\newcommand{\CFA}{C$\mathbf\forall$\xspace} % Cforall symbolic name
53\newcommand{\CC}{\rm C\kern-.1em\hbox{+\kern-.25em+}\xspace} % C++ symbolic name
54\newcommand{\CCeleven}{\rm C\kern-.1em\hbox{+\kern-.25em+}11\xspace} % C++11 symbolic name
55\newcommand{\CCfourteen}{\rm C\kern-.1em\hbox{+\kern-.25em+}14\xspace} % C++14 symbolic name
56\newcommand{\CCseventeen}{\rm C\kern-.1em\hbox{+\kern-.25em+}17\xspace} % C++17 symbolic name
57\newcommand{\CCtwenty}{\rm C\kern-.1em\hbox{+\kern-.25em+}20\xspace} % C++20 symbolic name
58\newcommand{\CCV}{\rm C\kern-.1em\hbox{+\kern-.25em+}obj\xspace} % C++ virtual symbolic name
59\newcommand{\Csharp}{C\raisebox{-0.7ex}{\Large$^\sharp$}\xspace} % C# symbolic name
60\newcommand{\Textbf}[1]{{\color{red}\textbf{#1}}}
61\newcommand{\TODO}[1]{\textbf{TODO}: {\itshape #1}} % TODO included
62%\newcommand{\TODO}[1]{} % TODO elided
63
64% CFA programming language, based on ANSI C (with some gcc additions)
65\lstdefinelanguage{CFA}[ANSI]{C}{
66        morekeywords={_Alignas,_Alignof,__alignof,__alignof__,asm,__asm,__asm__,_At,_Atomic,__attribute,__attribute__,auto,
67                _Bool,catch,catchResume,choose,_Complex,__complex,__complex__,__const,__const__,disable,dtype,enable,__extension__,
68                fallthrough,fallthru,finally,forall,ftype,_Generic,_Imaginary,inline,__label__,lvalue,_Noreturn,one_t,otype,restrict,_Static_assert,
69                _Thread_local,throw,throwResume,trait,try,ttype,typeof,__typeof,__typeof__,zero_t},
70}%
71
72\lstset{
73language=CFA,
74columns=fullflexible,
75basicstyle=\linespread{0.9}\sf,                                                 % reduce line spacing and use sanserif font
76stringstyle=\tt,                                                                                % use typewriter font
77tabsize=4,                                                                                              % 4 space tabbing
78xleftmargin=\parindentlnth,                                                             % indent code to paragraph indentation
79%mathescape=true,                                                                               % LaTeX math escape in CFA code $...$
80escapechar=\$,                                                                                  % LaTeX escape in CFA code
81keepspaces=true,                                                                                %
82showstringspaces=false,                                                                 % do not show spaces with cup
83showlines=true,                                                                                 % show blank lines at end of code
84aboveskip=4pt,                                                                                  % spacing above/below code block
85belowskip=3pt,
86% replace/adjust listing characters that look bad in sanserif
87literate={-}{\makebox[1.4ex][c]{\raisebox{0.5ex}{\rule{1.2ex}{0.06ex}}}}1 {^}{\raisebox{0.6ex}{$\scriptscriptstyle\land\,$}}1
88        {~}{\raisebox{0.3ex}{$\scriptstyle\sim\,$}}1 % {`}{\ttfamily\upshape\hspace*{-0.1ex}`}1
89        {<-}{$\leftarrow$}2 {=>}{$\Rightarrow$}2 {->}{\makebox[1.4ex][c]{\raisebox{0.5ex}{\rule{1.2ex}{0.06ex}}}\kern-0.3ex\textgreater}2,
90moredelim=**[is][\color{red}]{`}{`},
91}% lstset
92
93% inline code @...@
94\lstMakeShortInline@%
95
96% ACM Information
97\citestyle{acmauthoryear}
98
99\acmJournal{PACMPL}
100
101\title{Generic and Tuple Types with Efficient Dynamic Layout in \protect\CFA}
102
103\author{Aaron Moss}
104\email{a3moss@uwaterloo.ca}
105\author{Robert Schluntz}
106\email{rschlunt@uwaterloo.ca}
107\author{Peter Buhr}
108\email{pabuhr@uwaterloo.ca}
109\affiliation{%
110        \institution{University of Waterloo}
111        \department{David R. Cheriton School of Computer Science}
112        \streetaddress{Davis Centre, University of Waterloo}
113        \city{Waterloo}
114        \state{ON}
115        \postcode{N2L 3G1}
116        \country{Canada}
117}
118
119\terms{generic, tuple, variadic, types}
120\keywords{generic types, tuple types, variadic types, polymorphic functions, C, Cforall}
121
122\begin{CCSXML}
123<ccs2012>
124<concept>
125<concept_id>10011007.10011006.10011008.10011024.10011025</concept_id>
126<concept_desc>Software and its engineering~Polymorphism</concept_desc>
127<concept_significance>500</concept_significance>
128</concept>
129<concept>
130<concept_id>10011007.10011006.10011008.10011024.10011028</concept_id>
131<concept_desc>Software and its engineering~Data types and structures</concept_desc>
132<concept_significance>500</concept_significance>
133</concept>
134<concept>
135<concept_id>10011007.10011006.10011041.10011047</concept_id>
136<concept_desc>Software and its engineering~Source code generation</concept_desc>
137<concept_significance>300</concept_significance>
138</concept>
139</ccs2012>
140\end{CCSXML}
141
142\ccsdesc[500]{Software and its engineering~Polymorphism}
143\ccsdesc[500]{Software and its engineering~Data types and structures}
144\ccsdesc[300]{Software and its engineering~Source code generation}
145
146\begin{abstract}
147The 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.
148This installation base and the programmers producing it represent a massive software-engineering investment spanning decades and likely to continue for decades more.
149Nonetheless, C, first standardized over thirty years ago, lacks many features that make programming in more modern languages safer and more productive.
150The 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.
151Prior 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.
152Specifically, \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.
153This 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.
154\end{abstract}
155
156\begin{document}
157\maketitle
158
159
160\section{Introduction and Background}
161
162The 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.
163This installation base and the programmers producing it represent a massive software-engineering investment spanning decades and likely to continue for decades more.
164The \citet{TIOBE} ranks the top 5 most popular programming languages as: Java 16\%, \Textbf{C 7\%}, \Textbf{\CC 5\%}, \Csharp 4\%, Python 4\% = 36\%, where the next 50 languages are less than 3\% each with a long tail.
165The top 3 rankings over the past 30 years are:
166\lstDeleteShortInline@%
167\begin{center}
168\setlength{\tabcolsep}{10pt}
169\begin{tabular}{@{}rccccccc@{}}
170                & 2017  & 2012  & 2007  & 2002  & 1997  & 1992  & 1987          \\ \hline
171Java    & 1             & 1             & 1             & 1             & 12    & -             & -                     \\
172\Textbf{C}      & \Textbf{2}& \Textbf{2}& \Textbf{2}& \Textbf{2}& \Textbf{1}& \Textbf{1}& \Textbf{1}    \\
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{}\hspace{1pt}'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\begin{lstlisting}
219forall( otype T `| { T ?+?(T, T); }` ) T twice( T x ) { return x + x; } $\C{// ? denotes operands}$
220int val = twice( twice( 3.7 ) );
221\end{lstlisting}
222which works for any type @T@ with a matching addition operator.
223The polymorphism is achieved by creating a wrapper function for calling @+@ with @T@ bound to @double@, then passing this function to the first call of @twice@.
224There is now the option of using the same @twice@ and converting the result to @int@ on assignment, or creating another @twice@ with type parameter @T@ bound to @int@ because \CFA uses the return type~\cite{Cormack81,Baker82,Ada}, in its type analysis.
225The first approach has a late conversion from @double@ to @int@ on the final assignment, while the second has an eager conversion to @int@.
226\CFA minimizes the number of conversions and their potential to lose information, so it selects the first approach, which corresponds with C-programmer intuition.
227
228Crucial to the design of a new programming language are the libraries to access thousands of external software features.
229Like \CC, \CFA inherits a massive compatible library-base, where other programming languages must rewrite or provide fragile inter-language communication with C.
230A simple example is leveraging the existing type-unsafe (@void *@) C @bsearch@ to binary search a sorted floating-point array:
231\begin{lstlisting}
232void * bsearch( const void * key, const void * base, size_t nmemb, size_t size,
233                                int (* compar)( const void *, const void * ));
234int comp( const void * t1, const void * t2 ) { return *(double *)t1 < *(double *)t2 ? -1 :
235                                *(double *)t2 < *(double *)t1 ? 1 : 0; }
236double key = 5.0, vals[10] = { /* 10 sorted floating-point values */ };
237double * val = (double *)bsearch( &key, vals, 10, sizeof(vals[0]), comp );      $\C{// search sorted array}$
238\end{lstlisting}
239which can be augmented simply with a generalized, type-safe, \CFA-overloaded wrappers:
240\begin{lstlisting}
241forall( otype T | { int ?<?( T, T ); } ) T * bsearch( T key, const T * arr, size_t size ) {
242        int comp( const void * t1, const void * t2 ) { /* as above with double changed to T */ }
243        return (T *)bsearch( &key, arr, size, sizeof(T), comp ); }
244forall( otype T | { int ?<?( T, T ); } ) unsigned int bsearch( T key, const T * arr, size_t size ) {
245        T * result = bsearch( key, arr, size ); $\C{// call first version}$
246        return result ? result - arr : size; }  $\C{// pointer subtraction includes sizeof(T)}$
247double * val = bsearch( 5.0, vals, 10 );        $\C{// selection based on return type}$
248int posn = bsearch( 5.0, vals, 10 );
249\end{lstlisting}
250The nested function @comp@ provides the hidden interface from typed \CFA to untyped (@void *@) C, plus the cast of the result.
251Providing a hidden @comp@ function in \CC is awkward as lambdas do not use C calling-conventions and template declarations cannot appear at block scope.
252As well, an alternate kind of return is made available: position versus pointer to found element.
253\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@.
254
255\CFA has replacement libraries condensing hundreds of existing C functions into tens of \CFA overloaded functions, all without rewriting the actual computations.
256For example, it is possible to write a type-safe \CFA wrapper @malloc@ based on the C @malloc@:
257\begin{lstlisting}
258forall( dtype T | sized(T) ) T * malloc( void ) { return (T *)malloc( sizeof(T) ); }
259int * ip = malloc();                                            $\C{// select type and size from left-hand side}$
260double * dp = malloc();
261struct S {...} * sp = malloc();
262\end{lstlisting}
263where the return type supplies the type/size of the allocation, which is impossible in most type systems.
264
265Call-site inferencing and nested functions provide a localized form of inheritance.
266For example, the \CFA @qsort@ only sorts in ascending order using @<@.
267However, it is trivial to locally change this behaviour:
268\begin{lstlisting}
269forall( otype T | { int ?<?( T, T ); } ) void qsort( const T * arr, size_t size ) { /* use C qsort */ }
270{       int ?<?( double x, double y ) { return x `>` y; }       $\C{// locally override behaviour}$
271        qsort( vals, size );                                    $\C{// descending sort}$
272}
273\end{lstlisting}
274Within the block, the nested version of @<@ performs @>@ and this local version overrides the built-in @<@ so it is passed to @qsort@.
275Hence, programmers can easily form local environments, adding and modifying appropriate functions, to maximize reuse of other existing functions and types.
276
277Finally, \CFA allows variable overloading:
278\begin{lstlisting}
279short int MAX = ...;   int MAX = ...;  double MAX = ...;
280short int s = MAX;    int i = MAX;    double d = MAX;   $\C{// select correct MAX}$
281\end{lstlisting}
282Here, the single name @MAX@ replaces all the C type-specific names: @SHRT_MAX@, @INT_MAX@, @DBL_MAX@.
283As 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.
284In addition, several operations are defined in terms values @0@ and @1@, \eg:
285\begin{lstlisting}
286int x;
287if (x) x++                                                                      $\C{// if (x != 0) x += 1;}$
288\end{lstlisting}
289Every @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.
290Due 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.
291The 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.
292
293
294\subsection{Traits}
295
296\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:
297\begin{lstlisting}
298trait summable( otype T ) {
299        void ?{}( T *, zero_t );                                $\C{// constructor from 0 literal}$
300        T ?+?( T, T );                                                  $\C{// assortment of additions}$
301        T ?+=?( T *, T );
302        T ++?( T * );
303        T ?++( T * ); };
304forall( otype T `| summable( T )` ) T sum( T a[$\,$], size_t size ) {  // use trait
305        `T` total = { `0` };                                    $\C{// instantiate T from 0 by calling its constructor}$
306        for ( unsigned int i = 0; i < size; i += 1 ) total `+=` a[i]; $\C{// select appropriate +}$
307        return total; }
308\end{lstlisting}
309
310In 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:
311\begin{lstlisting}
312trait otype( dtype T | sized(T) ) {  // sized is a pseudo-trait for types with known size and alignment
313        void ?{}( T * );                                                $\C{// default constructor}$
314        void ?{}( T *, T );                                             $\C{// copy constructor}$
315        void ?=?( T *, T );                                             $\C{// assignment operator}$
316        void ^?{}( T * ); };                                    $\C{// destructor}$
317\end{lstlisting}
318Given 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.
319
320In 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.
321Hence, trait names play no part in type equivalence;
322the names are simply macros for a list of polymorphic assertions, which are expanded at usage sites.
323Nevertheless, trait names form a logical subtype-hierarchy with @dtype@ at the top, where traits often contain overlapping assertions, \eg operator @+@.
324Traits are used like interfaces in Java or abstract base-classes in \CC, but without the nominal inheritance-relationships.
325Instead, 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.
326Hence, 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.
327(Nominal inheritance can be approximated with traits using marker variables or functions, as is done in Go.)
328
329% Nominal inheritance can be simulated with traits using marker variables or functions:
330% \begin{lstlisting}
331% trait nominal(otype T) {
332%     T is_nominal;
333% };
334% int is_nominal;                                                               $\C{// int now satisfies the nominal trait}$
335% \end{lstlisting}
336%
337% 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:
338% \begin{lstlisting}
339% trait pointer_like(otype Ptr, otype El) {
340%     lvalue El *?(Ptr);                                                $\C{// Ptr can be dereferenced into a modifiable value of type El}$
341% }
342% struct list {
343%     int value;
344%     list * next;                                                              $\C{// may omit "struct" on type names as in \CC}$
345% };
346% typedef list * list_iterator;
347%
348% lvalue int *?( list_iterator it ) { return it->value; }
349% \end{lstlisting}
350% 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@).
351% 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.
352
353
354\section{Generic Types}
355
356One of the known shortcomings of standard C is that it does not provide reusable type-safe abstractions for generic data structures and algorithms.
357Broadly speaking, there are three approaches to implement abstract data-structures in C.
358One approach is to write bespoke data-structures for each context in which they are needed.
359While 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.
360A 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.
361However, 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.
362A 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.
363Furthermore, writing and using preprocessor macros can be unnatural and inflexible.
364
365\CC, Java, and other languages use \emph{generic types} to produce type-safe abstract data-types.
366\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.
367However, for known concrete parameters, the generic-type definition can be inlined, like \CC templates.
368
369A 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:
370\begin{lstlisting}
371forall( otype R, otype S ) struct pair {
372        R first;
373        S second;
374};
375forall( otype T ) T value( pair( const char *, T ) p ) { return p.second; }
376forall( dtype F, otype T ) T value_p( pair( F *, T * ) p ) { return * p.second; }
377pair( const char *, int ) p = { "magic", 42 };
378int magic = value( p );
379pair( void *, int * ) q = { 0, &p.second };
380magic = value_p( q );
381double d = 1.0;
382pair( double *, double * ) r = { &d, &d };
383d = value_p( r );
384\end{lstlisting}
385
386\CFA classifies generic types as either \emph{concrete} or \emph{dynamic}.
387Concrete types have a fixed memory layout regardless of type parameters, while dynamic types vary in memory layout depending on their type parameters.
388A type may have polymorphic parameters but still be concrete, called \emph{dtype-static}.
389Polymorphic 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.
390
391\CFA generic types also allow checked argument-constraints.
392For example, the following declaration of a sorted set-type ensures the set key supports equality and relational comparison:
393\begin{lstlisting}
394forall( otype Key | { _Bool ?==?(Key, Key); _Bool ?<?(Key, Key); } ) struct sorted_set;
395\end{lstlisting}
396
397
398\subsection{Concrete Generic-Types}
399
400The \CFA translator template-expands concrete generic-types into new structure types, affording maximal inlining.
401To 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.
402A function declaration that accepts or returns a concrete generic-type produces a declaration for the instantiated structure in the same scope, which all callers may reuse.
403For example, the concrete instantiation for @pair( const char *, int )@ is:
404\begin{lstlisting}
405struct _pair_conc1 {
406        const char * first;
407        int second;
408};
409\end{lstlisting}
410
411A concrete generic-type with dtype-static parameters is also expanded to a structure type, but this type is used for all matching instantiations.
412In 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:
413\begin{lstlisting}
414struct _pair_conc0 {
415        void * first;
416        void * second;
417};
418\end{lstlisting}
419
420
421\subsection{Dynamic Generic-Types}
422
423Though \CFA implements concrete generic-types efficiently, it also has a fully general system for dynamic generic types.
424As 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.
425Dynamic generic-types also have an \emph{offset array} containing structure-member offsets.
426A dynamic generic-union needs no such offset array, as all members are at offset 0, but size and alignment are still necessary.
427Access 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.
428
429The offset arrays are statically generated where possible.
430If 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;
431if 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.
432As 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 )@.
433The offset array @_offsetof_pair@ is generated at the call site as @size_t _offsetof_pair[] = { offsetof(_pair_conc1, first), offsetof(_pair_conc1, second) }@.
434
435In some cases the offset arrays cannot be statically generated.
436For 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.
437\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.
438The \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.
439These 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).
440Results of these layout functions are cached so that they are only computed once per type per function. %, as in the example below for @pair@.
441Layout functions also allow generic types to be used in a function definition without reflecting them in the function signature.
442For 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.
443This function could acquire the layout for @set(T)@ by calling its layout function with the layout of @T@ implicitly passed into the function.
444
445Whether a type is concrete, dtype-static, or dynamic is decided solely on the type parameters and @forall@ clause on a declaration.
446This 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.
447If 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.
448
449
450\subsection{Applications}
451\label{sec:generic-apps}
452
453The reuse of dtype-static structure instantiations enables useful programming patterns at zero runtime cost.
454The 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@:
455\begin{lstlisting}
456forall(dtype T) int lexcmp( pair( T *, T * ) * a, pair( T *, T * ) * b, int (* cmp)( T *, T * ) ) {
457        return cmp( a->first, b->first ) ? : cmp( a->second, b->second );
458}
459\end{lstlisting}
460Since @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.
461
462Another useful pattern enabled by reused dtype-static type instantiations is zero-cost \emph{tag-structures}.
463Sometimes information is only used for type-checking and can be omitted at runtime, \eg:
464\begin{lstlisting}
465forall(dtype Unit) struct scalar { unsigned long value; };
466struct metres {};
467struct litres {};
468
469forall(dtype U) scalar(U) ?+?( scalar(U) a, scalar(U) b ) {
470        return (scalar(U)){ a.value + b.value };
471}
472scalar(metres) half_marathon = { 21093 };
473scalar(litres) swimming_pool = { 2500000 };
474scalar(metres) marathon = half_marathon + half_marathon;
475scalar(litres) two_pools = swimming_pool + swimming_pool;
476marathon + swimming_pool;                                       $\C{// compilation ERROR}$
477\end{lstlisting}
478@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 @?+?@.
479These implementations may even be separately compiled, unlike \CC template functions.
480However, the \CFA type-checker ensures matching types are used by all calls to @?+?@, preventing nonsensical computations like adding a length to a volume.
481
482
483\section{Tuples}
484\label{sec:tuples}
485
486In many languages, functions can return at most one value;
487however, many operations have multiple outcomes, some exceptional.
488Consider C's @div@ and @remquo@ functions, which return the quotient and remainder for a division of integer and floating-point values, respectively.
489\begin{lstlisting}
490typedef struct { int quo, rem; } div_t;         $\C{// from include stdlib.h}$
491div_t div( int num, int den );
492double remquo( double num, double den, int * quo );
493div_t qr = div( 13, 5 );                                        $\C{// return quotient/remainder aggregate}$
494int q;
495double r = remquo( 13.5, 5.2, &q );                     $\C{// return remainder, alias quotient}$
496\end{lstlisting}
497@div@ aggregates the quotient/remainder in a structure, while @remquo@ aliases a parameter to an argument.
498Both approaches are awkward.
499Alternatively, a programming language can directly support returning multiple values, \eg in \CFA:
500\begin{lstlisting}
501[ int, int ] div( int num, int den );           $\C{// return two integers}$
502[ double, double ] div( double num, double den ); $\C{// return two doubles}$
503int q, r;                                                                       $\C{// overloaded variable names}$
504double q, r;
505[ q, r ] = div( 13, 5 );                                        $\C{// select appropriate div and q, r}$
506[ q, r ] = div( 13.5, 5.2 );                            $\C{// assign into tuple}$
507\end{lstlisting}
508Clearly, this approach is straightforward to understand and use;
509therefore, why do few programming languages support this obvious feature or provide it awkwardly?
510The answer is that there are complex consequences that cascade through multiple aspects of the language, especially the type-system.
511This section show these consequences and how \CFA handles them.
512
513
514\subsection{Tuple Expressions}
515
516The addition of multiple-return-value functions (MRVF) are useless without a syntax for accepting multiple values at the call-site.
517The simplest mechanism for capturing the return values is variable assignment, allowing the values to be retrieved directly.
518As 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}.
519
520However, 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:
521\begin{lstlisting}
522printf( "%d %d\n", div( 13, 5 ) );                      $\C{// return values seperated into arguments}$
523\end{lstlisting}
524Here, the values returned by @div@ are composed with the call to @printf@ by flattening the tuple into separate arguments.
525However, the \CFA type-system must support significantly more complex composition:
526\begin{lstlisting}
527[ int, int ] foo$\(_1\)$( int );                        $\C{// overloaded foo functions}$
528[ double ] foo$\(_2\)$( int );
529void bar( int, double, double );
530bar( foo( 3 ), foo( 3 ) );
531\end{lstlisting}
532The type-resolver only has the tuple return-types to resolve the call to @bar@ as the @foo@ parameters are identical, which involves unifying the possible @foo@ functions with @bar@'s parameter list.
533No combination of @foo@s are an exact match with @bar@'s parameters, so the resolver applies C conversions.
534The minimal cost is @bar( foo@$_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.
535
536
537\subsection{Tuple Variables}
538
539An important observation from function composition is that new variable names are not required to initialize parameters from an MRVF.
540\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:
541\begin{lstlisting}
542[ int, int ] qr = div( 13, 5 );                         $\C{// tuple-variable declaration and initialization}$
543[ double, double ] qr = div( 13.5, 5.2 );
544\end{lstlisting}
545where the tuple variable-name serves the same purpose as the parameter name(s).
546Tuple variables can be composed of any types, except for array types, since array sizes are generally unknown in C.
547
548One way to access the tuple-variable components is with assignment or composition:
549\begin{lstlisting}
550[ q, r ] = qr;                                                          $\C{// access tuple-variable components}$
551printf( "%d %d\n", qr );
552\end{lstlisting}
553\CFA also supports \emph{tuple indexing} to access single components of a tuple expression:
554\begin{lstlisting}
555[int, int] * p = &qr;                                           $\C{// tuple pointer}$
556int rem = qr`.1`;                                                       $\C{// access remainder}$
557int quo = div( 13, 5 )`.0`;                                     $\C{// access quotient}$
558p`->0` = 5;                                                                     $\C{// change quotient}$
559bar( qr`.1`, qr );                                                      $\C{// pass remainder and quotient/remainder}$
560rem = [42, div( 13, 5 )]`.0.1`;                         $\C{// access 2nd component of 1st component of tuple expression}$
561\end{lstlisting}
562
563
564\subsection{Flattening and Restructuring}
565
566In function call contexts, tuples support implicit flattening and restructuring conversions.
567Tuple flattening recursively expands a tuple into the list of its basic components.
568Tuple structuring packages a list of expressions into a value of tuple type, \eg:
569%\lstDeleteShortInline@%
570%\par\smallskip
571%\begin{tabular}{@{}l@{\hspace{1.5\parindent}}||@{\hspace{1.5\parindent}}l@{}}
572\begin{lstlisting}
573int f( int, int );
574int g( [int, int] );
575int h( int, [int, int] );
576[int, int] x;
577int y;
578f( x );                 $\C{// flatten}$
579g( y, 10 );             $\C{// structure}$
580h( x, y );              $\C{// flatten and structure}$
581\end{lstlisting}
582%\end{lstlisting}
583%&
584%\begin{lstlisting}
585%\end{tabular}
586%\smallskip\par\noindent
587%\lstMakeShortInline@%
588In the call to @f@, @x@ is implicitly flattened so the components of @x@ are passed as the two arguments.
589In 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@.
590Finally, 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]@.
591The 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.
592
593
594\subsection{Tuple Assignment}
595
596An assignment where the left side is a tuple type is called \emph{tuple assignment}.
597There 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.
598%\lstDeleteShortInline@%
599%\par\smallskip
600%\begin{tabular}{@{}l@{\hspace{1.5\parindent}}||@{\hspace{1.5\parindent}}l@{}}
601\begin{lstlisting}
602int x = 10;
603double y = 3.5;
604[int, double] z;
605z = [x, y];                                                                     $\C{// multiple assignment}$
606[x, y] = z;                                                                     $\C{// multiple assignment}$
607z = 10;                                                                         $\C{// mass assignment}$
608[y, x] = 3.14;                                                          $\C{// mass assignment}$
609\end{lstlisting}
610%\end{lstlisting}
611%&
612%\begin{lstlisting}
613%\end{tabular}
614%\smallskip\par\noindent
615%\lstMakeShortInline@%
616Both kinds of tuple assignment have parallel semantics, so that each value on the left and right side is evaluated before any assignments occur.
617As 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]@.
618This 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.
619For example, @[y, x] = 3.14@ performs the assignments @y = 3.14@ and @x = 3.14@, yielding @y == 3.14@ and @x == 3@;
620whereas, C cascading assignment @y = x = 3.14@ performs the assignments @x = 3.14@ and @y = x@, yielding @3@ in @y@ and @x@.
621Finally, 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.
622This example shows mass, multiple, and cascading assignment used in one expression:
623\begin{lstlisting}
624void f( [int, int] );
625f( [x, y] = z = 1.5 );                                          $\C{// assignments in parameter list}$
626\end{lstlisting}
627
628
629\subsection{Member Access}
630
631It is also possible to access multiple fields from a single expression using a \emph{member-access}.
632The result is a single tuple-valued expression whose type is the tuple of the types of the members, \eg:
633\begin{lstlisting}
634struct S { int x; double y; char * z; } s;
635s.[x, y, z] = 0;
636\end{lstlisting}
637Here, the mass assignment sets all members of @s@ to zero.
638Since 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).
639%\lstDeleteShortInline@%
640%\par\smallskip
641%\begin{tabular}{@{}l@{\hspace{1.5\parindent}}||@{\hspace{1.5\parindent}}l@{}}
642\begin{lstlisting}
643[int, int, long, double] x;
644void f( double, long );
645x.[0, 1] = x.[1, 0];                                            $\C{// rearrange: [x.0, x.1] = [x.1, x.0]}$
646f( x.[0, 3] );                                                          $\C{// drop: f(x.0, x.3)}$
647[int, int, int] y = x.[2, 0, 2];                        $\C{// duplicate: [y.0, y.1, y.2] = [x.2, x.0.x.2]}$
648\end{lstlisting}
649%\end{lstlisting}
650%&
651%\begin{lstlisting}
652%\end{tabular}
653%\smallskip\par\noindent
654%\lstMakeShortInline@%
655It is also possible for a member access to contain other member accesses, \eg:
656\begin{lstlisting}
657struct A { double i; int j; };
658struct B { int * k; short l; };
659struct C { int x; A y; B z; } v;
660v.[x, y.[i, j], z.k];                                           $\C{// [v.x, [v.y.i, v.y.j], v.z.k]}$
661\end{lstlisting}
662
663
664\begin{comment}
665\subsection{Casting}
666
667In C, the cast operator is used to explicitly convert between types.
668In \CFA, the cast operator has a secondary use as type ascription.
669That 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:
670\begin{lstlisting}
671int f();     // (1)
672double f()// (2)
673
674f();       // ambiguous - (1),(2) both equally viable
675(int)f()// choose (2)
676\end{lstlisting}
677
678Since casting is a fundamental operation in \CFA, casts should be given a meaningful interpretation in the context of tuples.
679Taking a look at standard C provides some guidance with respect to the way casts should work with tuples:
680\begin{lstlisting}
681int f();
682void g();
683
684(void)f()// (1)
685(int)g()// (2)
686\end{lstlisting}
687In C, (1) is a valid cast, which calls @f@ and discards its result.
688On the other hand, (2) is invalid, because @g@ does not produce a result, so requesting an @int@ to materialize from nothing is nonsensical.
689Generalizing 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.
690
691Formally, 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 $T_i$.
692Excess 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.
693This approach follows naturally from the way that a cast to @void@ works in C.
694
695For example, in
696\begin{lstlisting}
697[int, int, int] f();
698[int, [int, int], int] g();
699
700([int, double])f();           $\C{// (1)}$
701([int, int, int])g();         $\C{// (2)}$
702([void, [int, int]])g();      $\C{// (3)}$
703([int, int, int, int])g();    $\C{// (4)}$
704([int, [int, int, int]])g()$\C{// (5)}$
705\end{lstlisting}
706
707(1) discards the last element of the return value and converts the second element to @double@.
708Since @int@ is effectively a 1-element tuple, (2) discards the second component of the second element of the return value of @g@.
709If @g@ is free of side effects, this expression is equivalent to @[(int)(g().0), (int)(g().1.0), (int)(g().2)]@.
710Since @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)]@).
711
712Note 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.}.
713As such, (4) is invalid because the cast target type contains 4 components, while the source type contains only 3.
714Similarly, (5) is invalid because the cast @([int, int, int])(g().1)@ is invalid.
715That is, it is invalid to cast @[int, int]@ to @[int, int, int]@.
716\end{comment}
717
718
719\subsection{Polymorphism}
720
721Tuples also integrate with \CFA polymorphism as a kind of generic type.
722Due 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:
723\begin{lstlisting}
724forall(otype T, dtype U) void f( T x, U * y );
725f( [5, "hello"] );
726\end{lstlisting}
727where @[5, "hello"]@ is flattened, giving argument list @5, "hello"@, and @T@ binds to @int@ and @U@ binds to @const char@.
728Tuples, however, may contain polymorphic components.
729For example, a plus operator can be written to add two triples together.
730\begin{lstlisting}
731forall(otype T | { T ?+?( T, T ); }) [T, T, T] ?+?( [T, T, T] x, [T, T, T] y ) {
732        return [x.0 + y.0, x.1 + y.1, x.2 + y.2];
733}
734[int, int, int] x;
735int i1, i2, i3;
736[i1, i2, i3] = x + ([10, 20, 30]);
737\end{lstlisting}
738
739Flattening and restructuring conversions are also applied to tuple types in polymorphic type assertions.
740\begin{lstlisting}
741int f( [int, double], double );
742forall(otype T, otype U | { T f( T, U, U ); }) void g( T, U );
743g( 5, 10.21 );
744\end{lstlisting}
745Hence, function parameter and return lists are flattened for the purposes of type unification allowing the example to pass expression resolution.
746This relaxation is possible by extending the thunk scheme described by~\citet{Bilson03}.
747Whenever 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:
748\begin{lstlisting}
749int _thunk( int _p0, double _p1, double _p2 ) { return f( [_p0, _p1], _p2 ); }
750\end{lstlisting}
751so the thunk provides flattening and structuring conversions to inferred functions, improving the compatibility of tuples and polymorphism.
752These thunks take advantage of GCC C nested-functions to produce closures that have the usual function-pointer signature.
753
754
755\subsection{Variadic Tuples}
756\label{sec:variadic-tuples}
757
758To define variadic functions, \CFA adds a new kind of type parameter, @ttype@ (tuple type).
759Matching against a @ttype@ parameter consumes all remaining argument components and packages them into a tuple, binding to the resulting tuple of types.
760In 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.
761As such, @ttype@ variables are also called \emph{argument packs}.
762
763Like variadic templates, the main way to manipulate @ttype@ polymorphic functions is via recursion.
764Since nothing is known about a parameter pack by default, assertion parameters are key to doing anything meaningful.
765Unlike variadic templates, @ttype@ polymorphic functions can be separately compiled.
766For example, a generalized @sum@ function written using @ttype@:
767\begin{lstlisting}
768int sum$\(_0\)$() { return 0; }
769forall(ttype Params | { int sum( Params ); } ) int sum$\(_1\)$( int x, Params rest ) {
770        return x + sum( rest );
771}
772sum( 10, 20, 30 );
773\end{lstlisting}
774Since @sum@\(_0\) does not accept any arguments, it is not a valid candidate function for the call @sum(10, 20, 30)@.
775In 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]@.
776The process continues unitl @Params@ is bound to @[]@, requiring an assertion @int sum()@, which matches @sum@\(_0\) and terminates the recursion.
777Effectively, 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))@.
778
779It is reasonable to take the @sum@ function a step further to enforce a minimum number of arguments:
780\begin{lstlisting}
781int sum( int x, int y ) { return x + y; }
782forall(ttype Params | { int sum( int, Params ); } ) int sum( int x, int y, Params rest ) {
783        return sum( x + y, rest );
784}
785\end{lstlisting}
786One more step permits the summation of any summable type with all arguments of the same type:
787\begin{lstlisting}
788trait summable(otype T) {
789        T ?+?( T, T );
790};
791forall(otype R | summable( R ) ) R sum( R x, R y ) {
792        return x + y;
793}
794forall(otype R, ttype Params | summable(R) | { R sum(R, Params); } ) R sum(R x, R y, Params rest) {
795        return sum( x + y, rest );
796}
797\end{lstlisting}
798Unlike C variadic functions, it is unnecessary to hard code the number and expected types.
799Furthermore, this code is extendable for any user-defined type with a @?+?@ operator.
800Summing arbitrary heterogeneous lists is possible with similar code by adding the appropriate type variables and addition operators.
801
802It is also possible to write a type-safe variadic print function to replace @printf@:
803\begin{lstlisting}
804struct S { int x, y; };
805forall(otype T, ttype Params | { void print(T); void print(Params); }) void print(T arg, Params rest) {
806        print(arg);  print(rest);
807}
808void print( char * x ) { printf( "%s", x ); }
809void print( int x ) { printf( "%d", x ); }
810void print( S s ) { print( "{ ", s.x, ",", s.y, " }" ); }
811print( "s = ", (S){ 1, 2 }, "\n" );
812\end{lstlisting}
813This example showcases a variadic-template-like decomposition of the provided argument list.
814The individual @print@ functions allow printing a single element of a type.
815The polymorphic @print@ allows printing any list of types, where as each individual type has a @print@ function.
816The individual print functions can be used to build up more complicated @print@ functions, such as @S@, which cannot be done with @printf@ in C.
817
818Finally, it is possible to use @ttype@ polymorphism to provide arbitrary argument forwarding functions.
819For example, it is possible to write @new@ as a library function:
820\begin{lstlisting}
821forall( otype R, otype S ) void ?{}( pair(R, S) *, R, S );
822forall( dtype T, ttype Params | sized(T) | { void ?{}( T *, Params ); } ) T * new( Params p ) {
823        return ((T *)malloc()){ p };                    $\C{// construct into result of malloc}$
824}
825pair( int, char ) * x = new( 42, '!' );
826\end{lstlisting}
827The @new@ function provides the combination of type-safe @malloc@ with a \CFA constructor call, making it impossible to forget constructing dynamically allocated objects.
828This function provides the type-safety of @new@ in \CC, without the need to specify the allocated type again, thanks to return-type inference.
829
830
831\subsection{Implementation}
832
833Tuples are implemented in the \CFA translator via a transformation into \emph{generic types}.
834For each $N$, the first time an $N$-tuple is seen in a scope a generic type with $N$ type parameters is generated, \eg:
835\begin{lstlisting}
836[int, int] f() {
837        [double, double] x;
838        [int, double, int] y;
839}
840\end{lstlisting}
841is transformed into:
842\begin{lstlisting}
843forall(dtype T0, dtype T1 | sized(T0) | sized(T1)) struct _tuple2 {
844        T0 field_0;                                                             $\C{// generated before the first 2-tuple}$
845        T1 field_1;
846};
847_tuple2(int, int) f() {
848        _tuple2(double, double) x;
849        forall(dtype T0, dtype T1, dtype T2 | sized(T0) | sized(T1) | sized(T2)) struct _tuple3 {
850                T0 field_0;                                                     $\C{// generated before the first 3-tuple}$
851                T1 field_1;
852                T2 field_2;
853        };
854        _tuple3(int, double, int) y;
855}
856\end{lstlisting}
857Tuple expressions are then simply converted directly into compound literals, \eg @[5, 'x', 1.24]@ becomes @(_tuple3(int, char, double)){ 5, 'x', 1.24 }@.
858
859\begin{comment}
860Since tuples are essentially structures, tuple indexing expressions are just field accesses:
861\begin{lstlisting}
862void f(int, [double, char]);
863[int, double] x;
864
865x.0+x.1;
866printf("%d %g\n", x);
867f(x, 'z');
868\end{lstlisting}
869Is transformed into:
870\begin{lstlisting}
871void f(int, _tuple2(double, char));
872_tuple2(int, double) x;
873
874x.field_0+x.field_1;
875printf("%d %g\n", x.field_0, x.field_1);
876f(x.field_0, (_tuple2){ x.field_1, 'z' });
877\end{lstlisting}
878Note that due to flattening, @x@ used in the argument position is converted into the list of its fields.
879In the call to @f@, the second and third argument components are structured into a tuple argument.
880Similarly, tuple member expressions are recursively expanded into a list of member access expressions.
881
882Expressions that may contain side effects are made into \emph{unique expressions} before being expanded by the flattening conversion.
883Each unique expression is assigned an identifier and is guaranteed to be executed exactly once:
884\begin{lstlisting}
885void g(int, double);
886[int, double] h();
887g(h());
888\end{lstlisting}
889Internally, this expression is converted to two variables and an expression:
890\begin{lstlisting}
891void g(int, double);
892[int, double] h();
893
894_Bool _unq0_finished_ = 0;
895[int, double] _unq0;
896g(
897        (_unq0_finished_ ? _unq0 : (_unq0 = f(), _unq0_finished_ = 1, _unq0)).0,
898        (_unq0_finished_ ? _unq0 : (_unq0 = f(), _unq0_finished_ = 1, _unq0)).1,
899);
900\end{lstlisting}
901Since argument evaluation order is not specified by the C programming language, this scheme is built to work regardless of evaluation order.
902The first time a unique expression is executed, the actual expression is evaluated and the accompanying boolean is set to true.
903Every subsequent evaluation of the unique expression then results in an access to the stored result of the actual expression.
904Tuple member expressions also take advantage of unique expressions in the case of possible impurity.
905
906Currently, the \CFA translator has a very broad, imprecise definition of impurity, where any function call is assumed to be impure.
907This 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.
908
909The various kinds of tuple assignment, constructors, and destructors generate GNU C statement expressions.
910A 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.
911The 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.
912However, 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.
913\end{comment}
914
915
916\section{Evaluation}
917\label{sec:eval}
918
919Though \CFA provides significant added functionality over C, these features have a low runtime penalty.
920In fact, \CFA's features for generic programming can enable faster runtime execution than idiomatic @void *@-based C code.
921This 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}).
922Since 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.
923A more illustrative benchmark measures the costs of idiomatic usage of each language's features.
924Figure~\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}.
925The benchmark test is similar for C and \CC.
926The 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.
927
928\begin{figure}
929\begin{lstlisting}[xleftmargin=3\parindentlnth,aboveskip=0pt,belowskip=0pt]
930int main( int argc, char * argv[] ) {
931        FILE * out = fopen( "cfa-out.txt", "w" );
932        int maxi = 0, vali = 42;
933        stack(int) si, ti;
934
935        REPEAT_TIMED( "push_int", N, push( &si, vali ); )
936        TIMED( "copy_int", ti = si; )
937        TIMED( "clear_int", clear( &si ); )
938        REPEAT_TIMED( "pop_int", N,
939                int xi = pop( &ti ); if ( xi > maxi ) { maxi = xi; } )
940        REPEAT_TIMED( "print_int", N/2, print( out, vali, ":", vali, "\n" ); )
941
942        pair(_Bool, char) maxp = { (_Bool)0, '\0' }, valp = { (_Bool)1, 'a' };
943        stack(pair(_Bool, char)) sp, tp;
944
945        REPEAT_TIMED( "push_pair", N, push( &sp, valp ); )
946        TIMED( "copy_pair", tp = sp; )
947        TIMED( "clear_pair", clear( &sp ); )
948        REPEAT_TIMED( "pop_pair", N,
949                pair(_Bool, char) xp = pop( &tp ); if ( xp > maxp ) { maxp = xp; } )
950        REPEAT_TIMED( "print_pair", N/2, print( out, valp, ":", valp, "\n" ); )
951        fclose(out);
952}
953\end{lstlisting}
954\caption{\protect\CFA Benchmark Test}
955\label{fig:BenchmarkTest}
956\end{figure}
957
958The 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.
959The \CCV variant illustrates an alternative object-oriented idiom where all objects inherit from a base @object@ class, mimicking a Java-like interface;
960hence runtime checks are necessary to safely down-cast objects.
961The 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.
962For 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.
963Note, the C benchmark uses unchecked casts as there is no runtime mechanism to perform such checks, while \CFA and \CC provide type-safety statically.
964
965Figure~\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.
966The graph plots the median of 5 consecutive runs of each program, with an initial warm-up run omitted.
967All code is compiled at \texttt{-O2} by GCC or G++ 6.2.0, with all \CC code compiled as \CCfourteen.
968The 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.
969
970\begin{figure}
971\centering
972\input{timing}
973\caption{Benchmark Timing Results (smaller is better)}
974\label{fig:eval}
975\end{figure}
976
977\begin{table}
978\caption{Properties of benchmark code}
979\label{tab:eval}
980\newcommand{\CT}[1]{\multicolumn{1}{c}{#1}}
981\begin{tabular}{rrrrr}
982                                                                        & \CT{C}        & \CT{\CFA}     & \CT{\CC}      & \CT{\CCV}             \\ \hline
983maximum memory usage (MB)                       & 10001         & 2502          & 2503          & 11253                 \\
984source code size (lines)                        & 247           & 222           & 165           & 339                   \\
985redundant type annotations (lines)      & 39            & 2                     & 2                     & 15                    \\
986binary size (KB)                                        & 14            & 229           & 18            & 38                    \\
987\end{tabular}
988\end{table}
989
990The 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;
991this inefficiency is exacerbated by the second level of generic types in the pair-based benchmarks.
992By 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.
993\CCV is slower than C largely due to the cost of runtime type-checking of down-casts (implemented with @dynamic_cast@);
994There are two outliers in the graph for \CFA: all prints and pop of @pair@.
995Both 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.
996A compiler designed for \CFA could easily perform these optimizations.
997Finally, the binary size for \CFA is larger because of static linking with the \CFA libraries.
998
999\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.
1000On 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.
1001\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;
1002with their omission, the \CCV line count is similar to C.
1003We 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.
1004
1005Raw line-count, however, is a fairly rough measure of code complexity;
1006another important factor is how much type information the programmer must manually specify, especially where that information is not checked by the compiler.
1007Such 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@).
1008To 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.
1009The \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.
1010The 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).
1011These uses are similar to the @new@ expressions in \CC, though the \CFA compiler's type resolver should shortly render even these type casts superfluous.
1012
1013
1014\section{Related Work}
1015
1016
1017\subsection{Polymorphism}
1018
1019\CC is the most similar language to \CFA;
1020both are extensions to C with source and runtime backwards compatibility.
1021The fundamental difference is in their engineering approach to C compatibility and programmer expectation.
1022While \CC provides good backwards compatibility with C, it has a steep learning curve for many of its extensions.
1023For example, polymorphism is provided via three disjoint mechanisms: overloading, inheritance, and templates.
1024The overloading is restricted because resolution does not use the return type, inheritance requires learning object-oriented programming and coping with a restricted nominal-inheritance hierarchy, templates cannot be separately compiled resulting in compilation/code bloat and poor error messages, and determining how these mechanisms interact and which to use is confusing.
1025In 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.
1026The key mechanism to support separate compilation is \CFA's \emph{explicit} use of assumed properties for a type.
1027Until \CC~\citet{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;
1028furthermore, \CC concepts are restricted to template polymorphism.
1029
1030Cyclone~\citep{Grossman06} also provides capabilities for polymorphic functions and existential types, similar to \CFA's @forall@ functions and generic types.
1031Cyclone 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.
1032Furthermore, 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@.
1033In \CFA terms, all Cyclone polymorphism must be dtype-static.
1034While 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.
1035\citet{Smith98} present Polymorphic C, an ML dialect with polymorphic functions and C-like syntax and pointer types; it lacks many of C's features, however, most notably structure types, and so is not a practical C replacement.
1036
1037\citet{obj-c-book} is an industrially successful extension to C.
1038However, Objective-C is a radical departure from C, using an object-oriented model with message-passing.
1039Objective-C did not support type-checked generics until recently \citet{xcode7}, historically using less-efficient runtime checking of object types.
1040The~\citet{GObject} framework also adds object-oriented programming with runtime type-checking and reference-counting garbage-collection to C;
1041these features are more intrusive additions than those provided by \CFA, in addition to the runtime overhead of reference-counting.
1042\citet{Vala} compiles to GObject-based C, adding the burden of learning a separate language syntax to the aforementioned demerits of GObject as a modernization path for existing C code-bases.
1043Java~\citep{Java8} included generic types in Java~5, which are type-checked at compilation and type-erased at runtime, similar to \CFA's.
1044However, in Java, each object carries its own table of method pointers, while \CFA passes the method pointers separately to maintain a C-compatible layout.
1045Java is also a garbage-collected, object-oriented language, with the associated resource usage and C-interoperability burdens.
1046
1047D~\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.
1048However, 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.
1049D and Go are garbage-collected languages, imposing the associated runtime overhead.
1050The necessity of accounting for data transfer between managed runtimes and the unmanaged C runtime complicates foreign-function interfaces to C.
1051Furthermore, 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.
1052D 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.
1053Rust also possesses much more powerful abstraction capabilities for writing generic code than Go.
1054On 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.
1055\CFA, with its more modest safety features, allows direct ports of C code while maintaining the idiomatic style of the original source.
1056
1057
1058\subsection{Tuples/Variadics}
1059
1060Many programming languages have some form of tuple construct and/or variadic functions, \eg SETL, C, KW-C, \CC, D, Go, Java, ML, and Scala.
1061SETL~\cite{SETL} is a high-level mathematical programming language, with tuples being one of the primary data types.
1062Tuples in SETL allow subscripting, dynamic expansion, and multiple assignment.
1063C 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.
1064KW-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.
1065The main contributions of that work were adding MRVF, tuple mass and multiple assignment, and record-field access.
1066\CCeleven introduced @std::tuple@ as a library variadic template structure.
1067Tuples are a generalization of @std::pair@, in that they allow for arbitrary length, fixed-size aggregation of heterogeneous values.
1068Operations include @std::get<N>@ to extract vales, @std::tie@ to create a tuple of references used for assignment, and lexicographic comparisons.
1069\CCseventeen proposes \emph{structured bindings}~\cite{Sutter15} to eliminate pre-declaring variables and use of @std::tie@ for binding the results.
1070This 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.
1071Furthermore, structured bindings are not a full replacement for @std::tie@, as it always declares new variables.
1072Like \CC, D provides tuples through a library variadic-template structure.
1073Go does not have tuples but supports MRVF.
1074Java'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.
1075Tuples are a fundamental abstraction in most functional programming languages, such as Standard ML~\cite{sml} and~\cite{Scala}, which decompose tuples using pattern matching.
1076
1077
1078\section{Conclusion and Future Work}
1079
1080The 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.
1081While 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.
1082The 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.
1083The contributions are a powerful type-system using parametric polymorphism and overloading, generic types, and tuples, which all have complex interactions.
1084The work is a challenging design, engineering, and implementation exercise.
1085On the surface, the project may appear as a rehash of similar mechanisms in \CC.
1086However, 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.
1087All of these new features are being used by the \CFA development-team to build the \CFA runtime-system.
1088Finally, we demonstrate that \CFA performance for some idiomatic cases is better than C and close to \CC, showing the design is practically applicable.
1089
1090There is ongoing work on a wide range of \CFA feature extensions, including reference types, arrays with size, exceptions, concurrent primitives and modules.
1091(While all examples in the paper compile and run, a public beta-release of \CFA will take another 8--12 months to finalize these additional extensions.)
1092In addition, there are interesting future directions for the polymorphism design.
1093Notably, \CC template functions trade compile time and code bloat for optimal runtime of individual instantiations of polymorphic functions.
1094\CFA polymorphic functions use dynamic virtual-dispatch;
1095the 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.
1096Two promising approaches are an @inline@ annotation at polymorphic function call sites to create a template-specialization of the function (provided the code is visible) or placing an @inline@ annotation on polymorphic function-definitions to instantiate a specialized version for some set of types (\CC template specialization).
1097These approaches are not mutually exclusive and allow performance optimizations to be applied only when necessary, without suffering global code-bloat.
1098In general, we believe separate compilation, producing smaller code, works well with loaded hardware-caches, which may offset the benefit of larger inlined-code.
1099
1100
1101\begin{acks}
1102The authors would like to recognize the design assistance of Glen Ditchfield, Richard Bilson, and Thierry Delisle on the features described in this paper, and thank Magnus Madsen and the three anonymous reviewers for valuable feedback.
1103This work is supported in part by a corporate partnership with \grantsponsor{Huawei}{Huawei Ltd.}{http://www.huawei.com}, and Aaron Moss and Peter Buhr are funded by the \grantsponsor{Natural Sciences and Engineering Research Council} of Canada.
1104% 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.
1105\end{acks}
1106
1107
1108\bibliographystyle{ACM-Reference-Format}
1109\bibliography{cfa}
1110
1111
1112\appendix
1113
1114\section{Benchmark Stack Implementation}
1115\label{sec:BenchmarkStackImplementation}
1116
1117\lstset{basicstyle=\linespread{0.9}\sf\small}
1118
1119Throughout, @/***/@ designates a counted redundant type annotation.
1120
1121\smallskip\noindent
1122\CFA
1123\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1124forall(otype T) struct stack_node {
1125        T value;
1126        stack_node(T) * next;
1127};
1128forall(otype T) void ?{}(stack(T) * s) { (&s->head){ 0 }; }
1129forall(otype T) void ?{}(stack(T) * s, stack(T) t) {
1130        stack_node(T) ** crnt = &s->head;
1131        for ( stack_node(T) * next = t.head; next; next = next->next ) {
1132                *crnt = ((stack_node(T) *)malloc()){ next->value }; /***/
1133                stack_node(T) * acrnt = *crnt;
1134                crnt = &acrnt->next;
1135        }
1136        *crnt = 0;
1137}
1138forall(otype T) stack(T) ?=?(stack(T) * s, stack(T) t) {
1139        if ( s->head == t.head ) return *s;
1140        clear(s);
1141        s{ t };
1142        return *s;
1143}
1144forall(otype T) void ^?{}(stack(T) * s) { clear(s); }
1145forall(otype T) _Bool empty(const stack(T) * s) { return s->head == 0; }
1146forall(otype T) void push(stack(T) * s, T value) {
1147        s->head = ((stack_node(T) *)malloc()){ value, s->head }; /***/
1148}
1149forall(otype T) T pop(stack(T) * s) {
1150        stack_node(T) * n = s->head;
1151        s->head = n->next;
1152        T x = n->value;
1153        ^n{};
1154        free(n);
1155        return x;
1156}
1157forall(otype T) void clear(stack(T) * s) {
1158        for ( stack_node(T) * next = s->head; next; ) {
1159                stack_node(T) * crnt = next;
1160                next = crnt->next;
1161                delete(crnt);
1162        }
1163        s->head = 0;
1164}
1165\end{lstlisting}
1166
1167\medskip\noindent
1168\CC
1169\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1170template<typename T> class stack {
1171        struct node {
1172                T value;
1173                node * next;
1174                node( const T & v, node * n = nullptr ) : value(v), next(n) {}
1175        };
1176        node * head;
1177        void copy(const stack<T>& o) {
1178                node ** crnt = &head;
1179                for ( node * next = o.head;; next; next = next->next ) {
1180                        *crnt = new node{ next->value }; /***/
1181                        crnt = &(*crnt)->next;
1182                }
1183                *crnt = nullptr;
1184        }
1185  public:
1186        stack() : head(nullptr) {}
1187        stack(const stack<T>& o) { copy(o); }
1188        stack(stack<T> && o) : head(o.head) { o.head = nullptr; }
1189        ~stack() { clear(); }
1190        stack & operator= (const stack<T>& o) {
1191                if ( this == &o ) return *this;
1192                clear();
1193                copy(o);
1194                return *this;
1195        }
1196        stack & operator= (stack<T> && o) {
1197                if ( this == &o ) return *this;
1198                head = o.head;
1199                o.head = nullptr;
1200                return *this;
1201        }
1202        bool empty() const { return head == nullptr; }
1203        void push(const T & value) { head = new node{ value, head };  /***/ }
1204        T pop() {
1205                node * n = head;
1206                head = n->next;
1207                T x = std::move(n->value);
1208                delete n;
1209                return x;
1210        }
1211        void clear() {
1212                for ( node * next = head; next; ) {
1213                        node * crnt = next;
1214                        next = crnt->next;
1215                        delete crnt;
1216                }
1217                head = nullptr;
1218        }
1219};
1220\end{lstlisting}
1221
1222\medskip\noindent
1223C
1224\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1225struct stack_node {
1226        void * value;
1227        struct stack_node * next;
1228};
1229struct stack new_stack() { return (struct stack){ NULL }; /***/ }
1230void copy_stack(struct stack * s, const struct stack * t, void * (*copy)(const void *)) {
1231        struct stack_node ** crnt = &s->head;
1232        for ( struct stack_node * next = t->head; next; next = next->next ) {
1233                *crnt = malloc(sizeof(struct stack_node)); /***/
1234                **crnt = (struct stack_node){ copy(next->value) }; /***/
1235                crnt = &(*crnt)->next;
1236        }
1237        *crnt = 0;
1238}
1239_Bool stack_empty(const struct stack * s) { return s->head == NULL; }
1240void push_stack(struct stack * s, void * value) {
1241        struct stack_node * n = malloc(sizeof(struct stack_node)); /***/
1242        *n = (struct stack_node){ value, s->head }; /***/
1243        s->head = n;
1244}
1245void * pop_stack(struct stack * s) {
1246        struct stack_node * n = s->head;
1247        s->head = n->next;
1248        void * x = n->value;
1249        free(n);
1250        return x;
1251}
1252void clear_stack(struct stack * s, void (*free_el)(void *)) {
1253        for ( struct stack_node * next = s->head; next; ) {
1254                struct stack_node * crnt = next;
1255                next = crnt->next;
1256                free_el(crnt->value);
1257                free(crnt);
1258        }
1259        s->head = NULL;
1260}
1261\end{lstlisting}
1262
1263\medskip\noindent
1264\CCV
1265\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1266stack::node::node( const object & v, node * n ) : value( v.new_copy() ), next( n ) {}
1267void stack::copy(const stack & o) {
1268        node ** crnt = &head;
1269        for ( node * next = o.head; next; next = next->next ) {
1270                *crnt = new node{ *next->value };
1271                crnt = &(*crnt)->next;
1272        }
1273        *crnt = nullptr;
1274}
1275stack::stack() : head(nullptr) {}
1276stack::stack(const stack & o) { copy(o); }
1277stack::stack(stack && o) : head(o.head) { o.head = nullptr; }
1278stack::~stack() { clear(); }
1279stack & stack::operator= (const stack & o) {
1280        if ( this == &o ) return *this;
1281        clear();
1282        copy(o);
1283        return *this;
1284}
1285stack & stack::operator= (stack && o) {
1286        if ( this == &o ) return *this;
1287        head = o.head;
1288        o.head = nullptr;
1289        return *this;
1290}
1291bool stack::empty() const { return head == nullptr; }
1292void stack::push(const object & value) { head = new node{ value, head }; /***/ }
1293ptr<object> stack::pop() {
1294        node * n = head;
1295        head = n->next;
1296        ptr<object> x = std::move(n->value);
1297        delete n;
1298        return x;
1299}
1300void stack::clear() {
1301        for ( node * next = head; next; ) {
1302                node * crnt = next;
1303                next = crnt->next;
1304                delete crnt;
1305        }
1306        head = nullptr;
1307}
1308\end{lstlisting}
1309
1310
1311\begin{comment}
1312
1313\subsubsection{bench.h}
1314(\texttt{bench.hpp} is similar.)
1315
1316\lstinputlisting{evaluation/bench.h}
1317
1318\subsection{C}
1319
1320\subsubsection{c-stack.h} ~
1321
1322\lstinputlisting{evaluation/c-stack.h}
1323
1324\subsubsection{c-stack.c} ~
1325
1326\lstinputlisting{evaluation/c-stack.c}
1327
1328\subsubsection{c-pair.h} ~
1329
1330\lstinputlisting{evaluation/c-pair.h}
1331
1332\subsubsection{c-pair.c} ~
1333
1334\lstinputlisting{evaluation/c-pair.c}
1335
1336\subsubsection{c-print.h} ~
1337
1338\lstinputlisting{evaluation/c-print.h}
1339
1340\subsubsection{c-print.c} ~
1341
1342\lstinputlisting{evaluation/c-print.c}
1343
1344\subsubsection{c-bench.c} ~
1345
1346\lstinputlisting{evaluation/c-bench.c}
1347
1348\subsection{\CFA}
1349
1350\subsubsection{cfa-stack.h} ~
1351
1352\lstinputlisting{evaluation/cfa-stack.h}
1353
1354\subsubsection{cfa-stack.c} ~
1355
1356\lstinputlisting{evaluation/cfa-stack.c}
1357
1358\subsubsection{cfa-print.h} ~
1359
1360\lstinputlisting{evaluation/cfa-print.h}
1361
1362\subsubsection{cfa-print.c} ~
1363
1364\lstinputlisting{evaluation/cfa-print.c}
1365
1366\subsubsection{cfa-bench.c} ~
1367
1368\lstinputlisting{evaluation/cfa-bench.c}
1369
1370\subsection{\CC}
1371
1372\subsubsection{cpp-stack.hpp} ~
1373
1374\lstinputlisting[language=c++]{evaluation/cpp-stack.hpp}
1375
1376\subsubsection{cpp-print.hpp} ~
1377
1378\lstinputlisting[language=c++]{evaluation/cpp-print.hpp}
1379
1380\subsubsection{cpp-bench.cpp} ~
1381
1382\lstinputlisting[language=c++]{evaluation/cpp-bench.cpp}
1383
1384\subsection{\CCV}
1385
1386\subsubsection{object.hpp} ~
1387
1388\lstinputlisting[language=c++]{evaluation/object.hpp}
1389
1390\subsubsection{cpp-vstack.hpp} ~
1391
1392\lstinputlisting[language=c++]{evaluation/cpp-vstack.hpp}
1393
1394\subsubsection{cpp-vstack.cpp} ~
1395
1396\lstinputlisting[language=c++]{evaluation/cpp-vstack.cpp}
1397
1398\subsubsection{cpp-vprint.hpp} ~
1399
1400\lstinputlisting[language=c++]{evaluation/cpp-vprint.hpp}
1401
1402\subsubsection{cpp-vbench.cpp} ~
1403
1404\lstinputlisting[language=c++]{evaluation/cpp-vbench.cpp}
1405\end{comment}
1406
1407\end{document}
1408
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1410% tab-width: 4 %
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