source: doc/generic_types/generic_types.tex @ b31fbf2

aaron-thesisarm-ehcleanup-dtorsdeferred_resndemanglerjacob/cs343-translationjenkins-sandboxnew-astnew-ast-unique-exprnew-envno_listpersistent-indexerresolv-newwith_gc
Last change on this file since b31fbf2 was b31fbf2, checked in by Aaron Moss <a3moss@…>, 4 years ago

Tidy up extra rules in TIOBE table

  • Property mode set to 100644
File size: 83.3 KB
Line 
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[usenames]{color}
9
10\makeatletter
11% parindent is relative, i.e., toggled on/off in environments like itemize, so store the value for
12% use rather than use \parident directly.
13\newlength{\parindentlnth}
14\setlength{\parindentlnth}{\parindent}
15
16\newlength{\gcolumnposn}                                % temporary hack because lstlisting does handle tabs correctly
17\newlength{\columnposn}
18\setlength{\gcolumnposn}{2.75in}
19\setlength{\columnposn}{\gcolumnposn}
20\newcommand{\C}[2][\@empty]{\ifx#1\@empty\else\global\setlength{\columnposn}{#1}\global\columnposn=\columnposn\fi\hfill\makebox[\textwidth-\columnposn][l]{\lst@commentstyle{#2}}}
21\newcommand{\CRT}{\global\columnposn=\gcolumnposn}
22
23\newcommand{\TODO}[1]{\textbf{TODO}: {\itshape #1}} % TODO included
24%\newcommand{\TODO}[1]{} % TODO elided
25% Latin abbreviation
26\newcommand{\abbrevFont}{\textit}       % set empty for no italics
27\newcommand*{\eg}{%
28        \@ifnextchar{,}{\abbrevFont{e}.\abbrevFont{g}.}%
29                {\@ifnextchar{:}{\abbrevFont{e}.\abbrevFont{g}.}%
30                        {\abbrevFont{e}.\abbrevFont{g}.,\xspace}}%
31}%
32\newcommand*{\ie}{%
33        \@ifnextchar{,}{\abbrevFont{i}.\abbrevFont{e}.}%
34                {\@ifnextchar{:}{\abbrevFont{i}.\abbrevFont{e}.}%
35                        {\abbrevFont{i}.\abbrevFont{e}.,\xspace}}%
36}%
37\newcommand*{\etc}{%
38        \@ifnextchar{.}{\abbrevFont{etc}}%
39        {\abbrevFont{etc}.\xspace}%
40}%
41\newcommand{\etal}{%
42        \@ifnextchar{.}{\abbrevFont{et~al}}%
43                {\abbrevFont{et al}.\xspace}%
44}%
45% \newcommand{\eg}{\textit{e}.\textit{g}.,\xspace}
46% \newcommand{\ie}{\textit{i}.\textit{e}.,\xspace}
47% \newcommand{\etc}{\textit{etc}.,\xspace}
48\makeatother
49
50% Useful macros
51\newcommand{\CFA}{C$\mathbf\forall$\xspace} % Cforall symbolic name
52\newcommand{\CC}{\rm C\kern-.1em\hbox{+\kern-.25em+}\xspace} % C++ symbolic name
53\newcommand{\CCeleven}{\rm C\kern-.1em\hbox{+\kern-.25em+}11\xspace} % C++11 symbolic name
54\newcommand{\CCfourteen}{\rm C\kern-.1em\hbox{+\kern-.25em+}14\xspace} % C++14 symbolic name
55\newcommand{\CCseventeen}{\rm C\kern-.1em\hbox{+\kern-.25em+}17\xspace} % C++17 symbolic name
56\newcommand{\CCtwenty}{\rm C\kern-.1em\hbox{+\kern-.25em+}20\xspace} % C++20 symbolic name
57\newcommand{\CCV}{\rm C\kern-.1em\hbox{+\kern-.25em+}obj\xspace} % C++ virtual symbolic name
58\newcommand{\CS}{C\raisebox{-0.7ex}{\Large$^\sharp$}\xspace}
59\newcommand{\Textbf}[1]{{\color{red}\textbf{#1}}}
60
61% CFA programming language, based on ANSI C (with some gcc additions)
62\lstdefinelanguage{CFA}[ANSI]{C}{
63        morekeywords={_Alignas,_Alignof,__alignof,__alignof__,asm,__asm,__asm__,_At,_Atomic,__attribute,__attribute__,auto,
64                _Bool,catch,catchResume,choose,_Complex,__complex,__complex__,__const,__const__,disable,dtype,enable,__extension__,
65                fallthrough,fallthru,finally,forall,ftype,_Generic,_Imaginary,inline,__label__,lvalue,_Noreturn,one_t,otype,restrict,_Static_assert,
66                _Thread_local,throw,throwResume,trait,try,ttype,typeof,__typeof,__typeof__,zero_t},
67}%
68
69\lstset{
70language=CFA,
71columns=fullflexible,
72basicstyle=\linespread{0.9}\sf,                                                 % reduce line spacing and use sanserif font
73stringstyle=\tt,                                                                                % use typewriter font
74tabsize=4,                                                                                              % 4 space tabbing
75xleftmargin=\parindentlnth,                                                             % indent code to paragraph indentation
76%mathescape=true,                                                                               % LaTeX math escape in CFA code $...$
77escapechar=\$,                                                                                  % LaTeX escape in CFA code
78keepspaces=true,                                                                                %
79showstringspaces=false,                                                                 % do not show spaces with cup
80showlines=true,                                                                                 % show blank lines at end of code
81aboveskip=4pt,                                                                                  % spacing above/below code block
82belowskip=3pt,
83% replace/adjust listing characters that look bad in sanserif
84literate={-}{\raisebox{-0.15ex}{\texttt{-}}}1 {^}{\raisebox{0.6ex}{$\scriptscriptstyle\land\,$}}1
85        {~}{\raisebox{0.3ex}{$\scriptstyle\sim\,$}}1%{_}{\makebox[1.2ex][c]{\rule{1ex}{0.1ex}}}1 % {`}{\ttfamily\upshape\hspace*{-0.1ex}`}1
86        {<-}{$\leftarrow$}2 {=>}{$\Rightarrow$}2,
87moredelim=**[is][\color{red}]{`}{`},
88}% lstset
89
90% inline code @...@
91\lstMakeShortInline@%
92
93% ACM Information
94\citestyle{acmauthoryear}
95
96\acmJournal{PACMPL}
97
98\title{Generic and Tuple Types with Efficient Dynamic Layout in \CFA}
99
100\author{Aaron Moss}
101\email{a3moss@uwaterloo.ca}
102\author{Robert Schluntz}
103\email{rschlunt@uwaterloo.ca}
104\author{Peter Buhr}
105\email{pabuhr@uwaterloo.ca}
106\affiliation{%
107        \institution{University of Waterloo}
108        \department{David R. Cheriton School of Computer Science}
109        \streetaddress{Davis Centre, University of Waterloo}
110        \city{Waterloo}
111        \state{ON}
112        \postcode{N2L 3G1}
113        \country{Canada}
114}
115
116\terms{generic, tuple, variadic, types}
117\keywords{generic types, tuple types, variadic types, polymorphic functions, C, Cforall}
118
119\begin{CCSXML}
120<ccs2012>
121<concept>
122<concept_id>10011007.10011006.10011008.10011024.10011025</concept_id>
123<concept_desc>Software and its engineering~Polymorphism</concept_desc>
124<concept_significance>500</concept_significance>
125</concept>
126<concept>
127<concept_id>10011007.10011006.10011008.10011024.10011028</concept_id>
128<concept_desc>Software and its engineering~Data types and structures</concept_desc>
129<concept_significance>500</concept_significance>
130</concept>
131<concept>
132<concept_id>10011007.10011006.10011041.10011047</concept_id>
133<concept_desc>Software and its engineering~Source code generation</concept_desc>
134<concept_significance>300</concept_significance>
135</concept>
136</ccs2012>
137\end{CCSXML}
138
139\ccsdesc[500]{Software and its engineering~Polymorphism}
140\ccsdesc[500]{Software and its engineering~Data types and structures}
141\ccsdesc[300]{Software and its engineering~Source code generation}
142
143\begin{abstract}
144The C programming language is a foundational technology for modern computing with millions of lines of code implementing everything from commercial operating-systems to hobby projects.
145This installation base and the programmers producing it represent a massive software-engineering investment spanning decades and likely to continue for decades more.
146Nonetheless, C, first standardized over thirty years ago, lacks many features that make programming in more modern languages safer and more productive.
147The goal of the \CFA project is to create an extension of C that provides modern safety and productivity features while still ensuring strong backwards compatibility with C and its programmers.
148Prior projects have attempted similar goals but failed to honour C programming-style; for instance, adding object-oriented or functional programming with garbage collection is a non-starter for many C developers.
149Specifically, \CFA is designed to have an orthogonal feature-set based closely on the C programming paradigm, so that \CFA features can be added \emph{incrementally} to existing C code-bases, and C programmers can learn \CFA extensions on an as-needed basis, preserving investment in existing code and engineers.
150This paper describes two \CFA extensions, generic and tuple types, details how their design avoids shortcomings of similar features in C and other C-like languages, and presents experimental results validating the design.
151\end{abstract}
152
153\begin{document}
154\maketitle
155
156
157\section{Introduction and Background}
158
159The C programming language is a foundational technology for modern computing with millions of lines of code implementing everything from commercial operating-systems to hobby projects.
160This installation base and the programmers producing it represent a massive software-engineering investment spanning decades and likely to continue for decades more.
161The \citet{TIOBE} ranks the top 5 most popular programming languages as: Java 16\%, \Textbf{C 7\%}, \Textbf{\CC 5\%}, \CS 4\%, Python 4\% = 36\%, where the next 50 languages are less than 3\% each with a long tail.
162The top 3 rankings over the past 30 years are:
163\lstDeleteShortInline@%
164\begin{center}
165\setlength{\tabcolsep}{10pt}
166\begin{tabular}{@{}rccccccc@{}}
167                & 2017  & 2012  & 2007  & 2002  & 1997  & 1992  & 1987          \\ \hline
168Java    & 1             & 1             & 1             & 1             & 12    & -             & -                     \\
169\Textbf{C}      & \Textbf{2}& \Textbf{2}& \Textbf{2}& \Textbf{2}& \Textbf{1}& \Textbf{1}& \Textbf{1}    \\
170\CC             & 3             & 3             & 3             & 3             & 2             & 2             & 4                     \\
171\end{tabular}
172\end{center}
173\lstMakeShortInline@%
174Love it or hate it, C is extremely popular, highly used, and one of the few systems languages.
175In many cases, \CC is often used solely as a better C.
176Nonetheless, C, first standardized over thirty years ago, lacks many features that make programming in more modern languages safer and more productive.
177
178\CFA (pronounced ``C-for-all'', and written \CFA or Cforall) is an evolutionary extension of the C programming language that aims to add modern language features to C while maintaining both source compatibility with C and a familiar programming model for programmers.
179The four key design goals for \CFA~\citep{Bilson03} are:
180(1) The behaviour of standard C code must remain the same when translated by a \CFA compiler as when translated by a C compiler;
181(2) Standard C code must be as fast and as small when translated by a \CFA compiler as when translated by a C compiler;
182(3) \CFA code must be at least as portable as standard C code;
183(4) Extensions introduced by \CFA must be translated in the most efficient way possible.
184These goals ensure existing C code-bases can be converted to \CFA incrementally with minimal effort, and C programmers can productively generate \CFA code without training beyond the features being used.
185\CC is used similarly, but has the disadvantages of multiple legacy design-choices that cannot be updated and active divergence of the language model from C, requiring significant effort and training to incrementally add \CC to a C-based project.
186
187\CFA is currently implemented as a source-to-source translator from \CFA to the GCC-dialect of C~\citep{GCCExtensions}, allowing it to leverage the portability and code optimizations provided by GCC, meeting goals (1)-(3).
188Ultimately, a compiler is necessary for advanced features and optimal performance.
189
190This paper identifies shortcomings in existing approaches to generic and variadic data types in C-like languages and presents a design for generic and variadic types avoiding those shortcomings.
191Specifically, the solution is both reusable and type-checked, as well as conforming to the design goals of \CFA with ergonomic use of existing C abstractions.
192The new constructs are empirically compared with both standard C and \CC; the results show the new design is comparable in performance.
193
194
195\subsection{Polymorphic Functions}
196\label{sec:poly-fns}
197
198\CFA's polymorphism was originally formalized by \citet{Ditchfield92}, and first implemented by \citet{Bilson03}.
199The signature feature of \CFA is parametric-polymorphic functions~\citep{forceone:impl,Cormack90,Duggan96} with functions generalized using a @forall@ clause (giving the language its name):
200\begin{lstlisting}
201`forall( otype T )` T identity( T val ) { return val; }
202int forty_two = identity( 42 );                         $\C{// T is bound to int, forty\_two == 42}$
203\end{lstlisting}
204The @identity@ function above can be applied to any complete \emph{object type} (or @otype@).
205The type variable @T@ is transformed into a set of additional implicit parameters encoding sufficient information about @T@ to create and return a variable of that type.
206The \CFA implementation passes the size and alignment of the type represented by an @otype@ parameter, as well as an assignment operator, constructor, copy constructor and destructor.
207If this extra information is not needed, \eg for a pointer, the type parameter can be declared as a \emph{data type} (or @dtype@).
208
209In \CFA, the polymorphism runtime-cost is spread over each polymorphic call, due to passing more arguments to polymorphic functions;
210the experiments in Section~\ref{sec:eval} show this overhead is similar to \CC virtual-function calls.
211A design advantage is that, unlike \CC template-functions, \CFA polymorphic-functions are compatible with C \emph{separate compilation}, preventing compilation and code bloat.
212
213Since bare polymorphic-types provide a restricted set of available operations, \CFA provides a \emph{type assertion}~\cite[pp.~37-44]{Alphard} mechanism to provide further type information, where type assertions may be variable or function declarations that depend on a polymorphic type-variable.
214For example, the function @twice@ can be defined using the \CFA syntax for operator overloading:
215\newpage
216\begin{lstlisting}
217forall( otype T `| { T ?+?(T, T); }` ) T twice( T x ) { return x + x; } $\C{// ? denotes operands}$
218int val = twice( twice( 3.7 ) );
219\end{lstlisting}
220which works for any type @T@ with a matching addition operator.
221The 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@.
222There 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.
223The first approach has a late conversion from @double@ to @int@ on the final assignment, while the second has an eager conversion to @int@.
224\CFA minimizes the number of conversions and their potential to lose information, so it selects the first approach, which corresponds with C-programmer intuition.
225
226Crucial to the design of a new programming language are the libraries to access thousands of external software features.
227Like \CC, \CFA inherits a massive compatible library-base, where other programming languages must rewrite or provide fragile inter-language communication with C.
228A simple example is leveraging the existing type-unsafe (@void *@) C @bsearch@ to binary search a sorted floating-point array:
229\begin{lstlisting}
230void * bsearch( const void * key, const void * base, size_t nmemb, size_t size,
231                                int (* compar)( const void *, const void * ));
232int comp( const void * t1, const void * t2 ) { return *(double *)t1 < *(double *)t2 ? -1 :
233                                *(double *)t2 < *(double *)t1 ? 1 : 0; }
234double vals[10] = { /* 10 floating-point values */ };
235double key = 5.0;
236double * val = (double *)bsearch( &key, vals, 10, sizeof(vals[0]), comp );      $\C{// search sorted array}$
237\end{lstlisting}
238which can be augmented simply with a generalized, type-safe, \CFA-overloaded wrappers:
239\begin{lstlisting}
240forall( otype T | { int ?<?( T, T ); } ) T * bsearch( T key, const T * arr, size_t size ) {
241        int comp( const void * t1, const void * t2 ) { /* as above with double changed to T */ }
242        return (T *)bsearch( &key, arr, size, sizeof(T), comp ); }
243forall( otype T | { int ?<?( T, T ); } ) unsigned int bsearch( T key, const T * arr, size_t size ) {
244        T * result = bsearch( key, arr, size ); $\C{// call first version}$
245        return result ? result - arr : size; }  $\C{// pointer subtraction includes sizeof(T)}$
246double * val = bsearch( 5.0, vals, 10 );        $\C{// selection based on return type}$
247int posn = bsearch( 5.0, vals, 10 );
248\end{lstlisting}
249The nested function @comp@ provides the hidden interface from typed \CFA to untyped (@void *@) C, plus the cast of the result.
250Providing a hidden @comp@ function in \CC is awkward as lambdas do not use C calling-conventions and template declarations cannot appear at block scope.
251As well, an alternate kind of return is made available: position versus pointer to found element.
252\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@.
253
254\CFA has replacement libraries condensing hundreds of existing C functions into tens of \CFA overloaded functions, all without rewriting the actual computations.
255For example, it is possible to write a type-safe \CFA wrapper @malloc@ based on the C @malloc@:
256\begin{lstlisting}
257forall( dtype T | sized(T) ) T * malloc( void ) { return (T *)malloc( sizeof(T) ); }
258int * ip = malloc();                                            $\C{// select type and size from left-hand side}$
259double * dp = malloc();
260struct S {...} * sp = malloc();
261\end{lstlisting}
262where the return type supplies the type/size of the allocation, which is impossible in most type systems.
263
264Call-site inferencing and nested functions provide a localized form of inheritance.
265For example, the \CFA @qsort@ only sorts in ascending order using @<@.
266However, it is trivial to locally change this behaviour:
267\begin{lstlisting}
268forall( otype T | { int ?<?( T, T ); } ) void qsort( const T * arr, size_t size ) { /* use C qsort */ }
269{       int ?<?( double x, double y ) { return x `>` y; }       $\C{// locally override behaviour}$
270        qsort( vals, size );                                    $\C{// descending sort}$
271}
272\end{lstlisting}
273Within the block, the nested version of @<@ performs @>@ and this local version overrides the built-in @<@ so it is passed to @qsort@.
274Hence, programmers can easily form local environments, adding and modifying appropriate functions, to maximize reuse of other existing functions and types.
275
276Finally, \CFA allows variable overloading:
277%\lstDeleteShortInline@%
278%\par\smallskip
279%\begin{tabular}{@{}l@{\hspace{1.5\parindent}}||@{\hspace{1.5\parindent}}l@{}}
280\begin{lstlisting}
281short int MAX = ...;
282int MAX = ...;
283double MAX = ...;
284short int s = MAX;  $\C{// select correct MAX}$
285int i = MAX;
286double d = MAX;
287\end{lstlisting}
288%\end{lstlisting}
289%&
290%\begin{lstlisting}
291%\end{tabular}
292%\smallskip\par\noindent
293%\lstMakeShortInline@%
294Here, the single name @MAX@ replaces all the C type-specific names: @SHRT_MAX@, @INT_MAX@, @DBL_MAX@.
295As 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.
296In addition, several operations are defined in terms values @0@ and @1@, \eg:
297\begin{lstlisting}
298int x;
299if (x) x++                                                                      $\C{// if (x != 0) x += 1;}$
300\end{lstlisting}
301Every 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.
302Due 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.
303The 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.
304
305
306\subsection{Traits}
307
308\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:
309\begin{lstlisting}
310trait summable( otype T ) {
311        void ?{}( T *, zero_t );                                $\C{// constructor from 0 literal}$
312        T ?+?( T, T );                                                  $\C{// assortment of additions}$
313        T ?+=?( T *, T );
314        T ++?( T * );
315        T ?++( T * ); };
316forall( otype T `| summable( T )` ) T sum( T a[$\,$], size_t size ) {  // use trait
317        `T` total = { `0` };                                    $\C{// instantiate T from 0 by calling its constructor}$
318        for ( unsigned int i = 0; i < size; i += 1 ) total `+=` a[i]; $\C{// select appropriate +}$
319        return total; }
320\end{lstlisting}
321
322In 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:
323\begin{lstlisting}
324trait otype( dtype T | sized(T) ) {  // sized is a pseudo-trait for types with known size and alignment
325        void ?{}( T * );                                                $\C{// default constructor}$
326        void ?{}( T *, T );                                             $\C{// copy constructor}$
327        void ?=?( T *, T );                                             $\C{// assignment operator}$
328        void ^?{}( T * ); };                                    $\C{// destructor}$
329\end{lstlisting}
330Given 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.
331
332In 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.
333Hence, trait names play no part in type equivalence;
334the names are simply macros for a list of polymorphic assertions, which are expanded at usage sites.
335Nevertheless, trait names form a logical subtype-hierarchy with @dtype@ at the top, where traits often contain overlapping assertions, \eg operator @+@.
336Traits are used like interfaces in Java or abstract base-classes in \CC, but without the nominal inheritance-relationships.
337Instead, 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.
338Hence, 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.
339(Nominal inheritance can be approximated with traits using marker variables or functions, as is done in Go.)
340
341% Nominal inheritance can be simulated with traits using marker variables or functions:
342% \begin{lstlisting}
343% trait nominal(otype T) {
344%     T is_nominal;
345% };
346% int is_nominal;                                                               $\C{// int now satisfies the nominal trait}$
347% \end{lstlisting}
348%
349% 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:
350% \begin{lstlisting}
351% trait pointer_like(otype Ptr, otype El) {
352%     lvalue El *?(Ptr);                                                $\C{// Ptr can be dereferenced into a modifiable value of type El}$
353% }
354% struct list {
355%     int value;
356%     list * next;                                                              $\C{// may omit "struct" on type names as in \CC}$
357% };
358% typedef list * list_iterator;
359%
360% lvalue int *?( list_iterator it ) { return it->value; }
361% \end{lstlisting}
362% 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@).
363% 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.
364
365
366\section{Generic Types}
367
368One of the known shortcomings of standard C is that it does not provide reusable type-safe abstractions for generic data structures and algorithms.
369Broadly speaking, there are three approaches to implement abstract data-structures in C.
370One approach is to write bespoke data structures for each context in which they are needed.
371While 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.
372A 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.
373However, 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.
374A 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.
375Furthermore, writing and using preprocessor macros can be unnatural and inflexible.
376
377\CC, Java, and other languages use \emph{generic types} to produce type-safe abstract data-types.
378\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.
379However, for known concrete parameters, the generic-type definition can be inlined, like \CC templates.
380
381A 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:
382\begin{lstlisting}
383forall( otype R, otype S ) struct pair {
384        R first;
385        S second;
386};
387forall( otype T ) T value( pair( const char *, T ) p ) { return p.second; }
388forall( dtype F, otype T ) T value_p( pair( F *, T * ) p ) { return * p.second; }
389pair( const char *, int ) p = { "magic", 42 };
390int magic = value( p );
391pair( void *, int * ) q = { 0, &p.second };
392magic = value_p( q );
393double d = 1.0;
394pair( double *, double * ) r = { &d, &d };
395d = value_p( r );
396\end{lstlisting}
397
398\CFA classifies generic types as either \emph{concrete} or \emph{dynamic}.
399Concrete types have a fixed memory layout regardless of type parameters, while dynamic types vary in memory layout depending on their type parameters.
400A type may have polymorphic parameters but still be concrete, called \emph{dtype-static}.
401Polymorphic 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.
402
403\CFA generic types also allow checked argument-constraints.
404For example, the following declaration of a sorted set-type ensures the set key supports equality and relational comparison:
405\begin{lstlisting}
406forall( otype Key | { _Bool ?==?(Key, Key); _Bool ?<?(Key, Key); } ) struct sorted_set;
407\end{lstlisting}
408
409
410\subsection{Concrete Generic-Types}
411
412The \CFA translator template-expands concrete generic-types into new structure types, affording maximal inlining.
413To 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.
414For example, a function declaration that accepts or returns a concrete generic-type produces a declaration for the instantiated struct in the same scope, which all callers may reuse.
415For example, the concrete instantiation for @pair( const char *, int )@ is:
416\begin{lstlisting}
417struct _pair_conc1 {
418        const char * first;
419        int second;
420};
421\end{lstlisting}
422
423A concrete generic-type with dtype-static parameters is also expanded to a structure type, but this type is used for all matching instantiations.
424In 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:
425\begin{lstlisting}
426struct _pair_conc0 {
427        void * first;
428        void * second;
429};
430\end{lstlisting}
431
432
433\subsection{Dynamic Generic-Types}
434
435Though \CFA implements concrete generic-types efficiently, it also has a fully general system for dynamic generic types.
436As 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.
437Dynamic generic-types also have an \emph{offset array} containing structure-member offsets.
438A dynamic generic-union needs no such offset array, as all members are at offset 0, but size and alignment are still necessary.
439Access 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.
440
441The offset arrays are statically generated where possible.
442If 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;
443if 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.
444As 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 )@.
445The offset array @_offsetof_pair@ is generated at the call site as @size_t _offsetof_pair[] = { offsetof(_pair_conc1, first), offsetof(_pair_conc1, second) }@.
446
447In some cases the offset arrays cannot be statically generated.
448For 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.
449\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.
450The \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.
451These 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).
452Results of these layout functions are cached so that they are only computed once per type per function. %, as in the example below for @pair@.
453Layout functions also allow generic types to be used in a function definition without reflecting them in the function signature.
454For 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.
455This function could acquire the layout for @set(T)@ by calling its layout function with the layout of @T@ implicitly passed into the function.
456
457Whether a type is concrete, dtype-static, or dynamic is decided solely on the type parameters and @forall@ clause on a declaration.
458This 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.
459If 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.
460
461
462\subsection{Applications}
463\label{sec:generic-apps}
464
465The reuse of dtype-static structure instantiations enables useful programming patterns at zero runtime cost.
466The 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@:
467\begin{lstlisting}
468forall(dtype T) int lexcmp( pair( T *, T * ) * a, pair( T *, T * ) * b, int (* cmp)( T *, T * ) ) {
469        return cmp( a->first, b->first ) ? : cmp( a->second, b->second );
470}
471\end{lstlisting}
472%       int c = cmp( a->first, b->first );
473%       if ( c == 0 ) c = cmp( a->second, b->second );
474%       return c;
475Since @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.
476
477Another useful pattern enabled by reused dtype-static type instantiations is zero-cost \emph{tag-structures}.
478Sometimes information is only used for type-checking and can be omitted at runtime, \eg:
479\begin{lstlisting}
480forall(dtype Unit) struct scalar { unsigned long value; };
481struct metres {};
482struct litres {};
483
484forall(dtype U) scalar(U) ?+?( scalar(U) a, scalar(U) b ) {
485        return (scalar(U)){ a.value + b.value };
486}
487scalar(metres) half_marathon = { 21093 };
488scalar(litres) swimming_pool = { 2500000 };
489scalar(metres) marathon = half_marathon + half_marathon;
490scalar(litres) two_pools = swimming_pool + swimming_pool;
491marathon + swimming_pool;                                       $\C{// compilation ERROR}$
492\end{lstlisting}
493@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 @?+?@.
494These implementations may even be separately compiled, unlike \CC template functions.
495However, the \CFA type-checker ensures matching types are used by all calls to @?+?@, preventing nonsensical computations like adding a length to a volume.
496
497
498\section{Tuples}
499\label{sec:tuples}
500
501In many languages, functions can return at most one value;
502however, many operations have multiple outcomes, some exceptional.
503Consider C's @div@ and @remquo@ functions, which return the quotient and remainder for a division of integer and floating-point values, respectively.
504\begin{lstlisting}
505typedef struct { int quo, rem; } div_t;         $\C{// from include stdlib.h}$
506div_t div( int num, int den );
507double remquo( double num, double den, int * quo );
508div_t qr = div( 13, 5 );                                        $\C{// return quotient/remainder aggregate}$
509int q;
510double r = remquo( 13.5, 5.2, &q );                     $\C{// return remainder, alias quotient}$
511\end{lstlisting}
512@div@ aggregates the quotient/remainder in a structure, while @remquo@ aliases a parameter to an argument.
513Both approaches are awkward.
514Alternatively, a programming language can directly support returning multiple values, \eg in \CFA:
515\begin{lstlisting}
516[ int, int ] div( int num, int den );           $\C{// return two integers}$
517[ double, double ] div( double num, double den ); $\C{// return two doubles}$
518int q, r;                                                                       $\C{// overloaded variable names}$
519double q, r;
520[ q, r ] = div( 13, 5 );                                        $\C{// select appropriate div and q, r}$
521[ q, r ] = div( 13.5, 5.2 );                            $\C{// assign into tuple}$
522\end{lstlisting}
523Clearly, this approach is straightforward to understand and use;
524therefore, why do few programming languages support this obvious feature or provide it awkwardly?
525The answer is that there are complex consequences that cascade through multiple aspects of the language, especially the type-system.
526This section show these consequences and how \CFA handles them.
527
528
529\subsection{Tuple Expressions}
530
531The addition of multiple-return-value functions (MRVF) are useless without a syntax for accepting multiple values at the call-site.
532The simplest mechanism for capturing the return values is variable assignment, allowing the values to be retrieved directly.
533As 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}.
534
535However, 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:
536\begin{lstlisting}
537printf( "%d %d\n", div( 13, 5 ) );                      $\C{// return values seperated into arguments}$
538\end{lstlisting}
539Here, the values returned by @div@ are composed with the call to @printf@ by flattening the tuple into separate arguments.
540However, the \CFA type-system must support significantly more complex composition:
541\begin{lstlisting}
542[ int, int ] foo$\(_1\)$( int );
543[ double ] foo$\(_2\)$( int );
544void bar( int, double, double );
545bar( foo( 3 ), foo( 3 ) );
546\end{lstlisting}
547The type-resolver only has the tuple return-types to resolve the call to @bar@ as the @foo@ parameters are identical, which involves unifying the possible @foo@ functions with @bar@'s parameter list.
548No combination of @foo@s are an exact match with @bar@'s parameters, so the resolver applies C conversions.
549The minimal cost is @bar( foo@$_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.
550
551
552\subsection{Tuple Variables}
553
554An important observation from function composition is that new variable names are not required to initialize parameters from an MRVF.
555\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:
556\begin{lstlisting}
557[ int, int ] qr = div( 13, 5 );                         $\C{// tuple-variable declaration and initialization}$
558[ double, double ] qr = div( 13.5, 5.2 );
559\end{lstlisting}
560where the tuple variable-name serves the same purpose as the parameter name(s).
561Tuple variables can be composed of any types, except for array types, since array sizes are generally unknown.
562
563One way to access the tuple-variable components is with assignment or composition:
564\begin{lstlisting}
565[ q, r ] = qr;                                                          $\C{// access tuple-variable components}$
566printf( "%d %d\n", qr );
567\end{lstlisting}
568\CFA also supports \emph{tuple indexing} to access single components of a tuple expression:
569\begin{lstlisting}
570[int, int] * p = &qr;                                           $\C{// tuple pointer}$
571int rem = qr.1;                                                         $\C{// access remainder}$
572int quo = div( 13, 5 ).0;                                       $\C{// access quotient}$
573p->0 = 5;                                                                       $\C{// change quotient}$
574bar( qr.1, qr );                                                        $\C{// pass remainder and quotient/remainder}$
575rem = [42, div( 13, 5 )].0.1;                           $\C{// access 2nd component of 1st component of tuple expression}$
576\end{lstlisting}
577
578
579\subsection{Flattening and Restructuring}
580
581In function call contexts, tuples support implicit flattening and restructuring conversions.
582Tuple flattening recursively expands a tuple into the list of its basic components.
583Tuple structuring packages a list of expressions into a value of tuple type, \eg:
584%\lstDeleteShortInline@%
585%\par\smallskip
586%\begin{tabular}{@{}l@{\hspace{1.5\parindent}}||@{\hspace{1.5\parindent}}l@{}}
587\begin{lstlisting}
588int f( int, int );
589int g( [int, int] );
590int h( int, [int, int] );
591[int, int] x;
592int y;
593f( x );                 $\C{// flatten}$
594g( y, 10 );             $\C{// structure}$
595h( x, y );              $\C{// flatten and structure}$
596\end{lstlisting}
597%\end{lstlisting}
598%&
599%\begin{lstlisting}
600%\end{tabular}
601%\smallskip\par\noindent
602%\lstMakeShortInline@%
603In the call to @f@, @x@ is implicitly flattened so the components of @x@ are passed as the two arguments.
604In 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@.
605Finally, 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]@.
606The 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.
607
608
609\subsection{Tuple Assignment}
610
611An assignment where the left side is a tuple type is called \emph{tuple assignment}.
612There 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.
613%\lstDeleteShortInline@%
614%\par\smallskip
615%\begin{tabular}{@{}l@{\hspace{1.5\parindent}}||@{\hspace{1.5\parindent}}l@{}}
616\begin{lstlisting}
617int x = 10;
618double y = 3.5;
619[int, double] z;
620z = [x, y];             $\C{// multiple assignment}$
621[x, y] = z;             $\C{// multiple assignment}$
622z = 10;                 $\C{// mass assignment}$
623[y, x] = 3.14$\C{// mass assignment}$
624\end{lstlisting}
625%\end{lstlisting}
626%&
627%\begin{lstlisting}
628%\end{tabular}
629%\smallskip\par\noindent
630%\lstMakeShortInline@%
631Both kinds of tuple assignment have parallel semantics, so that each value on the left and right side is evaluated before any assignments occur.
632As 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]@.
633This 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.
634For example, @[y, x] = 3.14@ performs the assignments @y = 3.14@ and @x = 3.14@, yielding @y == 3.14@ and @x == 3@;
635whereas C cascading assignment @y = x = 3.14@ performs the assignments @x = 3.14@ and @y = x@, yielding @3@ in @y@ and @x@.
636Finally, 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.
637This example shows mass, multiple, and cascading assignment used in one expression:
638\begin{lstlisting}
639void f( [int, int] );
640f( [x, y] = z = 1.5 );                                          $\C{// assignments in parameter list}$
641\end{lstlisting}
642
643
644\subsection{Member Access}
645
646It is also possible to access multiple fields from a single expression using a \emph{member-access}.
647The result is a single tuple-valued expression whose type is the tuple of the types of the members, \eg:
648\begin{lstlisting}
649struct S { int x; double y; char * z; } s;
650s.[x, y, z] = 0;
651\end{lstlisting}
652Here, the mass assignment sets all members of @s@ to zero.
653Since 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).
654%\lstDeleteShortInline@%
655%\par\smallskip
656%\begin{tabular}{@{}l@{\hspace{1.5\parindent}}||@{\hspace{1.5\parindent}}l@{}}
657\begin{lstlisting}
658[int, int, long, double] x;
659void f( double, long );
660x.[0, 1] = x.[1, 0];    $\C{// rearrange: [x.0, x.1] = [x.1, x.0]}$
661f( x.[0, 3] );            $\C{// drop: f(x.0, x.3)}$
662[int, int, int] y = x.[2, 0, 2]; $\C{// duplicate: [y.0, y.1, y.2] = [x.2, x.0.x.2]}$
663\end{lstlisting}
664%\end{lstlisting}
665%&
666%\begin{lstlisting}
667%\end{tabular}
668%\smallskip\par\noindent
669%\lstMakeShortInline@%
670It is also possible for a member access to contain other member accesses, \eg:
671\begin{lstlisting}
672struct A { double i; int j; };
673struct B { int * k; short l; };
674struct C { int x; A y; B z; } v;
675v.[x, y.[i, j], z.k];                                           $\C{// [v.x, [v.y.i, v.y.j], v.z.k]}$
676\end{lstlisting}
677
678
679\begin{comment}
680\subsection{Casting}
681
682In C, the cast operator is used to explicitly convert between types.
683In \CFA, the cast operator has a secondary use as type ascription.
684That 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:
685\begin{lstlisting}
686int f();     // (1)
687double f()// (2)
688
689f();       // ambiguous - (1),(2) both equally viable
690(int)f()// choose (2)
691\end{lstlisting}
692
693Since casting is a fundamental operation in \CFA, casts should be given a meaningful interpretation in the context of tuples.
694Taking a look at standard C provides some guidance with respect to the way casts should work with tuples:
695\begin{lstlisting}
696int f();
697void g();
698
699(void)f()// (1)
700(int)g()// (2)
701\end{lstlisting}
702In C, (1) is a valid cast, which calls @f@ and discards its result.
703On the other hand, (2) is invalid, because @g@ does not produce a result, so requesting an @int@ to materialize from nothing is nonsensical.
704Generalizing 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.
705
706Formally, 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 $T_i$.
707Excess 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.
708This approach follows naturally from the way that a cast to @void@ works in C.
709
710For example, in
711\begin{lstlisting}
712[int, int, int] f();
713[int, [int, int], int] g();
714
715([int, double])f();           $\C{// (1)}$
716([int, int, int])g();         $\C{// (2)}$
717([void, [int, int]])g();      $\C{// (3)}$
718([int, int, int, int])g();    $\C{// (4)}$
719([int, [int, int, int]])g()$\C{// (5)}$
720\end{lstlisting}
721
722(1) discards the last element of the return value and converts the second element to @double@.
723Since @int@ is effectively a 1-element tuple, (2) discards the second component of the second element of the return value of @g@.
724If @g@ is free of side effects, this expression is equivalent to @[(int)(g().0), (int)(g().1.0), (int)(g().2)]@.
725Since @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)]@).
726
727Note 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.}.
728As such, (4) is invalid because the cast target type contains 4 components, while the source type contains only 3.
729Similarly, (5) is invalid because the cast @([int, int, int])(g().1)@ is invalid.
730That is, it is invalid to cast @[int, int]@ to @[int, int, int]@.
731\end{comment}
732
733
734\subsection{Polymorphism}
735
736Tuples also integrate with \CFA polymorphism as a kind of generic type.
737Due 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:
738\begin{lstlisting}
739forall(otype T, dtype U) void f( T x, U * y );
740f( [5, "hello"] );
741\end{lstlisting}
742where @[5, "hello"]@ is flattened, giving argument list @5, "hello"@, and @T@ binds to @int@ and @U@ binds to @const char@.
743Tuples, however, may contain polymorphic components.
744For example, a plus operator can be written to add two triples together.
745\begin{lstlisting}
746forall(otype T | { T ?+?( T, T ); }) [T, T, T] ?+?( [T, T, T] x, [T, T, T] y ) {
747        return [x.0 + y.0, x.1 + y.1, x.2 + y.2];
748}
749[int, int, int] x;
750int i1, i2, i3;
751[i1, i2, i3] = x + ([10, 20, 30]);
752\end{lstlisting}
753
754Flattening and restructuring conversions are also applied to tuple types in polymorphic type assertions.
755\begin{lstlisting}
756int f( [int, double], double );
757forall(otype T, otype U | { T f( T, U, U ); }) void g( T, U );
758g( 5, 10.21 );
759\end{lstlisting}
760Hence, function parameter and return lists are flattened for the purposes of type unification allowing the example to pass expression resolution.
761This relaxation is possible by extending the thunk scheme described by \citet{Bilson03}.
762Whenever 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:
763\begin{lstlisting}
764int _thunk( int _p0, double _p1, double _p2 ) { return f( [_p0, _p1], _p2 ); }
765\end{lstlisting}
766so the thunk provides flattening and structuring conversions to inferred functions, improving the compatibility of tuples and polymorphism.
767These thunks take advantage of GCC C nested-functions to produce closures that have the usual function pointer signature.
768
769
770\subsection{Variadic Tuples}
771\label{sec:variadic-tuples}
772
773To define variadic functions, \CFA adds a new kind of type parameter, @ttype@ (tuple type).
774Matching against a @ttype@ parameter consumes all remaining argument components and packages them into a tuple, binding to the resulting tuple of types.
775In 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.
776As such, @ttype@ variables are also called \emph{argument packs}.
777
778Like variadic templates, the main way to manipulate @ttype@ polymorphic functions is via recursion.
779Since nothing is known about a parameter pack by default, assertion parameters are key to doing anything meaningful.
780Unlike variadic templates, @ttype@ polymorphic functions can be separately compiled.
781For example, a generalized @sum@ function written using @ttype@:
782\begin{lstlisting}
783int sum$\(_0\)$() { return 0; }
784forall(ttype Params | { int sum( Params ); } ) int sum$\(_1\)$( int x, Params rest ) {
785        return x + sum( rest );
786}
787sum( 10, 20, 30 );
788\end{lstlisting}
789Since @sum@\(_0\) does not accept any arguments, it is not a valid candidate function for the call @sum(10, 20, 30)@.
790In 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]@.
791The process continues, @Params@ is bound to @[]@, requiring an assertion @int sum()@, which matches @sum@\(_0\) and terminates the recursion.
792Effectively, 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))@.
793
794It is reasonable to take the @sum@ function a step further to enforce a minimum number of arguments:
795\begin{lstlisting}
796int sum( int x, int y ) { return x + y; }
797forall(ttype Params | { int sum( int, Params ); } ) int sum( int x, int y, Params rest ) {
798        return sum( x + y, rest );
799}
800\end{lstlisting}
801One more step permits the summation of any summable type with all arguments of the same type:
802\begin{lstlisting}
803trait summable(otype T) {
804        T ?+?( T, T );
805};
806forall(otype R | summable( R ) ) R sum( R x, R y ) {
807        return x + y;
808}
809forall(otype R, ttype Params | summable(R) | { R sum(R, Params); } ) R sum(R x, R y, Params rest) {
810        return sum( x + y, rest );
811}
812\end{lstlisting}
813Unlike C variadic functions, it is unnecessary to hard code the number and expected types.
814Furthermore, this code is extendable so any user-defined type with a @?+?@ operator.
815Summing arbitrary heterogeneous lists is possible with similar code by adding the appropriate type variables and addition operators.
816
817It is also possible to write a type-safe variadic print function to replace @printf@:
818\begin{lstlisting}
819struct S { int x, y; };
820forall(otype T, ttype Params | { void print(T); void print(Params); }) void print(T arg, Params rest) {
821        print(arg);  print(rest);
822}
823void print( char * x ) { printf( "%s", x ); }
824void print( int x ) { printf( "%d", x ); }
825void print( S s ) { print( "{ ", s.x, ",", s.y, " }" ); }
826print( "s = ", (S){ 1, 2 }, "\n" );
827\end{lstlisting}
828This example showcases a variadic-template-like decomposition of the provided argument list.
829The individual @print@ functions allow printing a single element of a type.
830The polymorphic @print@ allows printing any list of types, as long as each individual type has a @print@ function.
831The individual print functions can be used to build up more complicated @print@ functions, such as for @S@, which is something that cannot be done with @printf@ in C.
832
833Finally, it is possible to use @ttype@ polymorphism to provide arbitrary argument forwarding functions.
834For example, it is possible to write @new@ as a library function:
835\begin{lstlisting}
836forall( otype R, otype S ) void ?{}( pair(R, S) *, R, S );
837forall( dtype T, ttype Params | sized(T) | { void ?{}( T *, Params ); } ) T * new( Params p ) {
838        return ((T *)malloc()){ p };                    $\C{// construct into result of malloc}$
839}
840pair( int, char ) * x = new( 42, '!' );
841\end{lstlisting}
842The @new@ function provides the combination of type-safe @malloc@ with a \CFA constructor call, making it impossible to forget constructing dynamically allocated objects.
843This function provides the type-safety of @new@ in \CC, without the need to specify the allocated type again, thanks to return-type inference.
844
845
846\subsection{Implementation}
847
848Tuples are implemented in the \CFA translator via a transformation into generic types.
849For each $N$, the first time an $N$-tuple is seen in a scope a generic type with $N$ type parameters is generated, \eg:
850\begin{lstlisting}
851[int, int] f() {
852        [double, double] x;
853        [int, double, int] y;
854}
855\end{lstlisting}
856is transformed into:
857\begin{lstlisting}
858forall(dtype T0, dtype T1 | sized(T0) | sized(T1)) struct _tuple2 {
859        T0 field_0;                     $\C{// generated before the first 2-tuple}$
860        T1 field_1;
861};
862_tuple2(int, int) f() {
863        _tuple2(double, double) x;
864        forall(dtype T0, dtype T1, dtype T2 | sized(T0) | sized(T1) | sized(T2)) struct _tuple3 {
865                T0 field_0;             $\C{// generated before the first 3-tuple}$
866                T1 field_1;
867                T2 field_2;
868        };
869        _tuple3(int, double, int) y;
870}
871\end{lstlisting}
872Tuple expressions are then simply converted directly into compound literals, \eg @[5, 'x', 1.24]@ becomes @(_tuple3(int, char, double)){ 5, 'x', 1.24 }@.
873
874\begin{comment}
875Since tuples are essentially structures, tuple indexing expressions are just field accesses:
876\begin{lstlisting}
877void f(int, [double, char]);
878[int, double] x;
879
880x.0+x.1;
881printf("%d %g\n", x);
882f(x, 'z');
883\end{lstlisting}
884Is transformed into:
885\begin{lstlisting}
886void f(int, _tuple2(double, char));
887_tuple2(int, double) x;
888
889x.field_0+x.field_1;
890printf("%d %g\n", x.field_0, x.field_1);
891f(x.field_0, (_tuple2){ x.field_1, 'z' });
892\end{lstlisting}
893Note that due to flattening, @x@ used in the argument position is converted into the list of its fields.
894In the call to @f@, the second and third argument components are structured into a tuple argument.
895Similarly, tuple member expressions are recursively expanded into a list of member access expressions.
896
897Expressions that may contain side effects are made into \emph{unique expressions} before being expanded by the flattening conversion.
898Each unique expression is assigned an identifier and is guaranteed to be executed exactly once:
899\begin{lstlisting}
900void g(int, double);
901[int, double] h();
902g(h());
903\end{lstlisting}
904Internally, this expression is converted to two variables and an expression:
905\begin{lstlisting}
906void g(int, double);
907[int, double] h();
908
909_Bool _unq0_finished_ = 0;
910[int, double] _unq0;
911g(
912        (_unq0_finished_ ? _unq0 : (_unq0 = f(), _unq0_finished_ = 1, _unq0)).0,
913        (_unq0_finished_ ? _unq0 : (_unq0 = f(), _unq0_finished_ = 1, _unq0)).1,
914);
915\end{lstlisting}
916Since argument evaluation order is not specified by the C programming language, this scheme is built to work regardless of evaluation order.
917The first time a unique expression is executed, the actual expression is evaluated and the accompanying boolean is set to true.
918Every subsequent evaluation of the unique expression then results in an access to the stored result of the actual expression.
919Tuple member expressions also take advantage of unique expressions in the case of possible impurity.
920
921Currently, the \CFA translator has a very broad, imprecise definition of impurity, where any function call is assumed to be impure.
922This 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.
923
924The various kinds of tuple assignment, constructors, and destructors generate GNU C statement expressions.
925A 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.
926The 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.
927However, 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.
928\end{comment}
929
930
931\section{Evaluation}
932\label{sec:eval}
933
934Though \CFA provides significant added functionality over C, these features have a low runtime penalty.
935In fact, \CFA's features for generic programming can enable faster runtime execution than idiomatic @void *@-based C code.
936This 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}).
937Since 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.
938A more illustrative benchmark measures the costs of idiomatic usage of each language's features.
939Figure~\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}.
940The benchmark test is similar for C and \CC.
941The 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.
942
943\begin{figure}
944\begin{lstlisting}[xleftmargin=3\parindentlnth,aboveskip=0pt,belowskip=0pt]
945int main( int argc, char * argv[] ) {
946        FILE * out = fopen( "cfa-out.txt", "w" );
947        int maxi = 0, vali = 42;
948        stack(int) si, ti;
949
950        REPEAT_TIMED( "push_int", N, push( &si, vali ); )
951        TIMED( "copy_int", ti = si; )
952        TIMED( "clear_int", clear( &si ); )
953        REPEAT_TIMED( "pop_int", N,
954                int xi = pop( &ti ); if ( xi > maxi ) { maxi = xi; } )
955        REPEAT_TIMED( "print_int", N/2, print( out, vali, ":", vali, "\n" ); )
956
957        pair(_Bool, char) maxp = { (_Bool)0, '\0' }, valp = { (_Bool)1, 'a' };
958        stack(pair(_Bool, char)) sp, tp;
959
960        REPEAT_TIMED( "push_pair", N, push( &sp, valp ); )
961        TIMED( "copy_pair", tp = sp; )
962        TIMED( "clear_pair", clear( &sp ); )
963        REPEAT_TIMED( "pop_pair", N,
964                pair(_Bool, char) xp = pop( &tp ); if ( xp > maxp ) { maxp = xp; } )
965        REPEAT_TIMED( "print_pair", N/2, print( out, valp, ":", valp, "\n" ); )
966        fclose(out);
967}
968\end{lstlisting}
969\caption{\CFA Benchmark Test}
970\label{fig:BenchmarkTest}
971\end{figure}
972
973The 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.
974The \CCV variant illustrates an alternative object-oriented idiom where all objects inherit from a base @object@ class, mimicking a Java-like interface;
975hence runtime checks are necessary to safely down-cast objects.
976The 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.
977For 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.
978Note, the C benchmark uses unchecked casts as there is no runtime mechanism to perform such checks, while \CFA and \CC provide type-safety statically.
979
980Figure~\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.
981The graph plots the median of 5 consecutive runs of each program, with an initial warm-up run omitted.
982All code is compiled at \texttt{-O2} by GCC or G++ 6.2.0, with all \CC code compiled as \CCfourteen.
983The 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.
984
985\begin{figure}
986\centering
987\input{timing}
988\caption{Benchmark Timing Results (smaller is better)}
989\label{fig:eval}
990\end{figure}
991
992\begin{table}
993\caption{Properties of benchmark code}
994\label{tab:eval}
995\newcommand{\CT}[1]{\multicolumn{1}{c}{#1}}
996\begin{tabular}{rrrrr}
997                                                                        & \CT{C}        & \CT{\CFA}     & \CT{\CC}      & \CT{\CCV}             \\ \hline
998maximum memory usage (MB)                       & 10001         & 2502          & 2503          & 11253                 \\
999source code size (lines)                        & 247           & 222           & 165           & 339                   \\
1000redundant type annotations (lines)      & 39            & 2                     & 2                     & 15                    \\
1001binary size (KB)                                        & 14            & 229           & 18            & 38                    \\
1002\end{tabular}
1003\end{table}
1004
1005The 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;
1006this inefficiency is exacerbated by the second level of generic types in the pair-based benchmarks.
1007By 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.
1008\CCV is slower than C largely due to the cost of runtime type-checking of down-casts (implemented with @dynamic_cast@);
1009There are two outliers in the graph for \CFA: all prints and pop of @pair@.
1010Both 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.
1011A compiler designed for \CFA could easily perform these optimizations.
1012Finally, the binary size for \CFA is larger because of static linking with the \CFA libraries.
1013
1014\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.
1015On 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.
1016\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;
1017with their omission the \CCV line count is similar to C.
1018We 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.
1019
1020Raw line-count, however, is a fairly rough measure of code complexity;
1021another important factor is how much type information the programmer must manually specify, especially where that information is not checked by the compiler.
1022Such 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@).
1023To 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.
1024The \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.
1025The 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).
1026These uses are similar to the @new@ expressions in \CC, though the \CFA compiler's type resolver should shortly render even these type casts superfluous.
1027
1028
1029\section{Related Work}
1030
1031
1032\subsection{Polymorphism}
1033
1034\CC is the most similar language to \CFA;
1035both are extensions to C with source and runtime backwards compatibility.
1036The fundamental difference is in their engineering approach to C compatibility and programmer expectation.
1037While \CC provides good backwards compatibility with C, it has a steep learning curve for many of its extensions.
1038For example, polymorphism is provided via three disjoint mechanisms: overloading, inheritance, and templates.
1039The overloading is restricted because resolution does not using the return type, inheritance requires learning object-oriented programming and coping with a restricted nominal-inheritance hierarchy, templates cannot be separately compiled resulting in compilation/code bloat and poor error messages, and determining how these mechanisms interact and which to use is confusing.
1040In 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.
1041The key mechanism to support separate compilation is \CFA's \emph{explicit} use of assumed properties for a type.
1042Until \CC~\citep{C++Concepts} are standardized (anticipated for \CCtwenty), \CC provides no way to specify the requirements of a generic function in code beyond compilation errors during template expansion;
1043furthermore, \CC concepts are restricted to template polymorphism.
1044
1045Cyclone~\citep{Grossman06} also provides capabilities for polymorphic functions and existential types, similar to \CFA's @forall@ functions and generic types.
1046Cyclone 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.
1047Furthermore, 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@.
1048In \CFA terms, all Cyclone polymorphism must be dtype-static.
1049While 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.
1050
1051\citet{obj-c-book} is an industrially successful extension to C.
1052However, Objective-C is a radical departure from C, using an object-oriented model with message-passing.
1053Objective-C did not support type-checked generics until recently~\citet{xcode7}, historically using less-efficient and more error-prone runtime checking of object types.
1054The~\citet{GObject} framework also adds object-oriented programming with runtime type-checking and reference-counting garbage-collection to C;
1055these features are more intrusive additions than those provided by \CFA, in addition to the runtime overhead of reference-counting.
1056\citet{Vala} compiles to GObject-based C, and so adds the burden of learning a separate language syntax to the aforementioned demerits of GObject as a modernization path for the existing C code-bases.
1057Java~\citep{Java8} included generic types in Java~5;
1058Java's generic types are type-checked at compilation and type-erased at runtime, similar to \CFA's.
1059However, in Java, each object carries its own table of method pointers, while \CFA passes the method pointers separately to maintain a C-compatible layout.
1060Java is also a garbage-collected, object-oriented language, with the associated resource usage and C-interoperability burdens.
1061
1062D~\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.
1063However, 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.
1064D and Go are garbage-collected languages, imposing the associated runtime overhead.
1065The necessity of accounting for data transfer between managed runtimes and the unmanaged C runtime complicates foreign-function interfaces to C.
1066Furthermore, 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.
1067D 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.
1068Rust also possesses much more powerful abstraction capabilities for writing generic code than Go.
1069On 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.
1070\CFA, with its more modest safety features, allows direct ports of C code while maintaining the idiomatic style of the original source.
1071
1072
1073\subsection{Tuples/Variadics}
1074
1075Many programming languages have some form of tuple construct and/or variadic functions, \eg SETL, C, KW-C, \CC, D, Go, Java, ML, and Scala.
1076SETL~\cite{SETL} is a high-level mathematical programming language, with tuples being one of the primary data types.
1077Tuples in SETL allow subscripting, dynamic expansion, and multiple assignment.
1078C 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.
1079KW-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.
1080The main contributions of that work were adding MRVF, tuple mass and multiple assignment, and record-field access.
1081\CCeleven introduced @std::tuple@ as a library variadic template structure.
1082Tuples are a generalization of @std::pair@, in that they allow for arbitrary length, fixed-size aggregation of heterogeneous values.
1083Operations include @std::get<N>@ to extract vales, @std::tie@ to create a tuple of references used for assignment, and lexicographic comparisons.
1084\CCseventeen proposes \emph{structured bindings}~\cite{Sutter15} to eliminate pre-declaring variables and use of @std::tie@ for binding the results.
1085This 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.
1086Furthermore, structured bindings are not a full replacement for @std::tie@, as it always declares new variables.
1087Like \CC, D provides tuples through a library variadic-template structure.
1088Go does not have tuples but supports MRVF.
1089Java'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.
1090Tuples are a fundamental abstraction in most functional programming languages, such as Standard ML~\cite{sml} and~\cite{Scala}, which decompose tuples using pattern matching.
1091
1092
1093\section{Conclusion and Future Work}
1094
1095The 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.
1096While 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.
1097The 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.
1098The contributions are a powerful type-system using parametric polymorphism and overloading, generic types, and tuples, which all have complex interactions.
1099The work is a challenging design, engineering, and implementation exercise.
1100On the surface, the project may appear as a rehash of similar mechanisms in \CC.
1101However, 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.
1102All of these new features are being used by the \CFA development-team to build the \CFA runtime-system.
1103Finally, we demonstrate that \CFA performance for some idiomatic cases is better than C and close to \CC, showing the design is practically applicable.
1104
1105There is ongoing work on a wide range of \CFA feature extensions, including reference types, exceptions, concurrent primitives and modules.
1106(While all examples in the paper compile and run, a public beta-release of \CFA will take another 8--12 months to finalize these addition extensions.)
1107In addition, there are interesting future directions for the polymorphism design.
1108Notably, \CC template functions trade compile time and code bloat for optimal runtime of individual instantiations of polymorphic functions.
1109\CFA polymorphic functions, by contrast, uses a dynamic virtual dispatch.
1110The 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.
1111Two 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.
1112These approaches are not mutually exclusive and allow performance optimizations to be applied only when necessary, without suffering global code-bloat.
1113In general, we believe separate compilation, producing smaller code, works well with loaded hardware-caches, which may offset the benefit of larger inlined-code.
1114
1115
1116\begin{acks}
1117The authors would like to recognize the design assistance of Glen Ditchfield, Richard Bilson, and Thierry Delisle on the features described in this paper. They also thank Magnus Madsen and three anonymous reviewers for valuable editorial feedback.
1118
1119This work is supported in part by a corporate partnership with \grantsponsor{Huawei}{Huawei Ltd.}{http://www.huawei.com}\ and the first author's \grantsponsor{NSERC-PGS}{NSERC PGS D}{http://www.nserc-crsng.gc.ca/Students-Etudiants/PG-CS/BellandPostgrad-BelletSuperieures_eng.asp} scholarship.
1120\end{acks}
1121
1122
1123\bibliographystyle{ACM-Reference-Format}
1124\bibliography{cfa}
1125
1126
1127\appendix
1128
1129\section{Benchmark Stack Implementation}
1130\label{sec:BenchmarkStackImplementation}
1131
1132\lstset{basicstyle=\linespread{0.9}\sf\small}
1133
1134\begin{comment}
1135\CFA
1136\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1137forall(otype T) struct stack_node;
1138forall(otype T) struct stack { stack_node(T) * head; };
1139forall(otype T) void ?{}(stack(T) * s);
1140forall(otype T) void ?{}(stack(T) * s, stack(T) t);
1141forall(otype T) stack(T) ?=?(stack(T) * s, stack(T) t);
1142forall(otype T) void ^?{}(stack(T) * s);
1143forall(otype T) _Bool empty(const stack(T) * s);
1144forall(otype T) void push(stack(T) * s, T value);
1145forall(otype T) T pop(stack(T) * s);
1146forall(otype T) void clear(stack(T) * s);
1147
1148void print( FILE * out, const char * x );
1149void print( FILE * out, _Bool x );
1150void print( FILE * out, char x );
1151void print( FILE * out, int x );
1152forall(otype T, ttype Params | { void print( FILE *, T ); void print( FILE *, Params ); })
1153        void print( FILE * out, T arg, Params rest );
1154forall(otype R, otype S | { void print( FILE *, R ); void print( FILE *, S ); })
1155        void print( FILE * out, pair(R, S) x );
1156\end{lstlisting}
1157
1158\medskip\noindent
1159\CC
1160\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1161std::pair
1162std::forward_list wrapped in std::stack interface
1163
1164template<typename T> void print(ostream & out, const T & x) { out << x; }
1165template<> void print<bool>(ostream & out, const bool & x) { out << (x ? "true" : "false"); }
1166template<> void print<char>(ostream & out, const char & x ) { out << "'" << x << "'"; }
1167template<typename R, typename S> ostream & operator<< (ostream & out, const pair<R, S>& x) {
1168        out << "["; print(out, x.first); out << ", "; print(out, x.second); return out << "]"; }
1169template<typename T, typename... Args> void print(ostream & out, const T & arg, const Args &... rest) {
1170        out << arg;     print(out, rest...); }
1171\end{lstlisting}
1172
1173\medskip\noindent
1174C
1175\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1176struct pair { void * first, second; };
1177struct pair * new_pair( void * first, void * second );
1178struct pair * copy_pair( const struct pair * src,
1179        void * (*copy_first)( const void * ), void * (*copy_second)( const void * ) );
1180void free_pair( struct pair * p, void (*free_first)( void * ), void (*free_second)( void * ) );
1181int cmp_pair( const struct pair * a, const struct pair * b,
1182        int (*cmp_first)( const void *, const void * ), int (*cmp_second)( const void *, const void * ) );
1183
1184struct stack_node;
1185struct stack { struct stack_node * head; };
1186struct stack new_stack();
1187void copy_stack( struct stack * dst, const struct stack * src, void * (*copy)( const void * ) );
1188void clear_stack( struct stack * s, void (*free_el)( void * ) );
1189_Bool stack_empty( const struct stack * s );
1190void push_stack( struct stack * s, void * value );
1191void * pop_stack( struct stack * s );
1192
1193void print_string( FILE * out, const char * x );
1194void print_bool( FILE * out, _Bool x );
1195void print_char( FILE * out, char x );
1196void print_int( FILE * out, int x );
1197void print( FILE * out, const char * fmt, ... );
1198\end{lstlisting}
1199\end{comment}
1200
1201Throughout, @/***/@ designates a counted redundant type annotation.
1202
1203\medskip\noindent
1204\CFA
1205\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1206forall(otype T) struct stack_node {
1207        T value;
1208        stack_node(T) * next;
1209};
1210forall(otype T) void ?{}(stack(T) * s) { (&s->head){ 0 }; }
1211forall(otype T) void ?{}(stack(T) * s, stack(T) t) {
1212        stack_node(T) ** crnt = &s->head;
1213        for ( stack_node(T) * next = t.head; next; next = next->next ) {
1214                *crnt = ((stack_node(T) *)malloc()){ next->value }; /***/
1215                stack_node(T) * acrnt = *crnt;
1216                crnt = &acrnt->next;
1217        }
1218        *crnt = 0;
1219}
1220forall(otype T) stack(T) ?=?(stack(T) * s, stack(T) t) {
1221        if ( s->head == t.head ) return *s;
1222        clear(s);
1223        s{ t };
1224        return *s;
1225}
1226forall(otype T) void ^?{}(stack(T) * s) { clear(s); }
1227forall(otype T) _Bool empty(const stack(T) * s) { return s->head == 0; }
1228forall(otype T) void push(stack(T) * s, T value) {
1229        s->head = ((stack_node(T) *)malloc()){ value, s->head }; /***/
1230}
1231forall(otype T) T pop(stack(T) * s) {
1232        stack_node(T) * n = s->head;
1233        s->head = n->next;
1234        T x = n->value;
1235        ^n{};
1236        free(n);
1237        return x;
1238}
1239forall(otype T) void clear(stack(T) * s) {
1240        for ( stack_node(T) * next = s->head; next; ) {
1241                stack_node(T) * crnt = next;
1242                next = crnt->next;
1243                delete(crnt);
1244        }
1245        s->head = 0;
1246}
1247\end{lstlisting}
1248
1249\medskip\noindent
1250\CC
1251\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1252template<typename T> class stack {
1253        struct node {
1254                T value;
1255                node * next;
1256                node( const T & v, node * n = nullptr ) : value(v), next(n) {}
1257        };
1258        node * head;
1259        void copy(const stack<T>& o) {
1260                node ** crnt = &head;
1261                for ( node * next = o.head;; next; next = next->next ) {
1262                        *crnt = new node{ next->value }; /***/
1263                        crnt = &(*crnt)->next;
1264                }
1265                *crnt = nullptr;
1266        }
1267  public:
1268        stack() : head(nullptr) {}
1269        stack(const stack<T>& o) { copy(o); }
1270        stack(stack<T> && o) : head(o.head) { o.head = nullptr; }
1271        ~stack() { clear(); }
1272        stack & operator= (const stack<T>& o) {
1273                if ( this == &o ) return *this;
1274                clear();
1275                copy(o);
1276                return *this;
1277        }
1278        stack & operator= (stack<T> && o) {
1279                if ( this == &o ) return *this;
1280                head = o.head;
1281                o.head = nullptr;
1282                return *this;
1283        }
1284        bool empty() const { return head == nullptr; }
1285        void push(const T & value) { head = new node{ value, head };  /***/ }
1286        T pop() {
1287                node * n = head;
1288                head = n->next;
1289                T x = std::move(n->value);
1290                delete n;
1291                return x;
1292        }
1293        void clear() {
1294                for ( node * next = head; next; ) {
1295                        node * crnt = next;
1296                        next = crnt->next;
1297                        delete crnt;
1298                }
1299                head = nullptr;
1300        }
1301};
1302\end{lstlisting}
1303
1304\medskip\noindent
1305C
1306\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1307struct stack_node {
1308        void * value;
1309        struct stack_node * next;
1310};
1311struct stack new_stack() { return (struct stack){ NULL }; /***/ }
1312void copy_stack(struct stack * s, const struct stack * t, void * (*copy)(const void *)) {
1313        struct stack_node ** crnt = &s->head;
1314        for ( struct stack_node * next = t->head; next; next = next->next ) {
1315                *crnt = malloc(sizeof(struct stack_node)); /***/
1316                **crnt = (struct stack_node){ copy(next->value) }; /***/
1317                crnt = &(*crnt)->next;
1318        }
1319        *crnt = 0;
1320}
1321_Bool stack_empty(const struct stack * s) { return s->head == NULL; }
1322void push_stack(struct stack * s, void * value) {
1323        struct stack_node * n = malloc(sizeof(struct stack_node)); /***/
1324        *n = (struct stack_node){ value, s->head }; /***/
1325        s->head = n;
1326}
1327void * pop_stack(struct stack * s) {
1328        struct stack_node * n = s->head;
1329        s->head = n->next;
1330        void * x = n->value;
1331        free(n);
1332        return x;
1333}
1334void clear_stack(struct stack * s, void (*free_el)(void *)) {
1335        for ( struct stack_node * next = s->head; next; ) {
1336                struct stack_node * crnt = next;
1337                next = crnt->next;
1338                free_el(crnt->value);
1339                free(crnt);
1340        }
1341        s->head = NULL;
1342}
1343\end{lstlisting}
1344
1345\medskip\noindent
1346\CCV
1347\begin{lstlisting}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
1348stack::node::node( const object & v, node * n ) : value( v.new_copy() ), next( n ) {}
1349void stack::copy(const stack & o) {
1350        node ** crnt = &head;
1351        for ( node * next = o.head; next; next = next->next ) {
1352                *crnt = new node{ *next->value };
1353                crnt = &(*crnt)->next;
1354        }
1355        *crnt = nullptr;
1356}
1357stack::stack() : head(nullptr) {}
1358stack::stack(const stack & o) { copy(o); }
1359stack::stack(stack && o) : head(o.head) { o.head = nullptr; }
1360stack::~stack() { clear(); }
1361stack & stack::operator= (const stack & o) {
1362        if ( this == &o ) return *this;
1363        clear();
1364        copy(o);
1365        return *this;
1366}
1367stack & stack::operator= (stack && o) {
1368        if ( this == &o ) return *this;
1369        head = o.head;
1370        o.head = nullptr;
1371        return *this;
1372}
1373bool stack::empty() const { return head == nullptr; }
1374void stack::push(const object & value) { head = new node{ value, head }; /***/ }
1375ptr<object> stack::pop() {
1376        node * n = head;
1377        head = n->next;
1378        ptr<object> x = std::move(n->value);
1379        delete n;
1380        return x;
1381}
1382void stack::clear() {
1383        for ( node * next = head; next; ) {
1384                node * crnt = next;
1385                next = crnt->next;
1386                delete crnt;
1387        }
1388        head = nullptr;
1389}
1390\end{lstlisting}
1391
1392
1393\begin{comment}
1394
1395\subsubsection{bench.h}
1396(\texttt{bench.hpp} is similar.)
1397
1398\lstinputlisting{evaluation/bench.h}
1399
1400\subsection{C}
1401
1402\subsubsection{c-stack.h} ~
1403
1404\lstinputlisting{evaluation/c-stack.h}
1405
1406\subsubsection{c-stack.c} ~
1407
1408\lstinputlisting{evaluation/c-stack.c}
1409
1410\subsubsection{c-pair.h} ~
1411
1412\lstinputlisting{evaluation/c-pair.h}
1413
1414\subsubsection{c-pair.c} ~
1415
1416\lstinputlisting{evaluation/c-pair.c}
1417
1418\subsubsection{c-print.h} ~
1419
1420\lstinputlisting{evaluation/c-print.h}
1421
1422\subsubsection{c-print.c} ~
1423
1424\lstinputlisting{evaluation/c-print.c}
1425
1426\subsubsection{c-bench.c} ~
1427
1428\lstinputlisting{evaluation/c-bench.c}
1429
1430\subsection{\CFA}
1431
1432\subsubsection{cfa-stack.h} ~
1433
1434\lstinputlisting{evaluation/cfa-stack.h}
1435
1436\subsubsection{cfa-stack.c} ~
1437
1438\lstinputlisting{evaluation/cfa-stack.c}
1439
1440\subsubsection{cfa-print.h} ~
1441
1442\lstinputlisting{evaluation/cfa-print.h}
1443
1444\subsubsection{cfa-print.c} ~
1445
1446\lstinputlisting{evaluation/cfa-print.c}
1447
1448\subsubsection{cfa-bench.c} ~
1449
1450\lstinputlisting{evaluation/cfa-bench.c}
1451
1452\subsection{\CC}
1453
1454\subsubsection{cpp-stack.hpp} ~
1455
1456\lstinputlisting[language=c++]{evaluation/cpp-stack.hpp}
1457
1458\subsubsection{cpp-print.hpp} ~
1459
1460\lstinputlisting[language=c++]{evaluation/cpp-print.hpp}
1461
1462\subsubsection{cpp-bench.cpp} ~
1463
1464\lstinputlisting[language=c++]{evaluation/cpp-bench.cpp}
1465
1466\subsection{\CCV}
1467
1468\subsubsection{object.hpp} ~
1469
1470\lstinputlisting[language=c++]{evaluation/object.hpp}
1471
1472\subsubsection{cpp-vstack.hpp} ~
1473
1474\lstinputlisting[language=c++]{evaluation/cpp-vstack.hpp}
1475
1476\subsubsection{cpp-vstack.cpp} ~
1477
1478\lstinputlisting[language=c++]{evaluation/cpp-vstack.cpp}
1479
1480\subsubsection{cpp-vprint.hpp} ~
1481
1482\lstinputlisting[language=c++]{evaluation/cpp-vprint.hpp}
1483
1484\subsubsection{cpp-vbench.cpp} ~
1485
1486\lstinputlisting[language=c++]{evaluation/cpp-vbench.cpp}
1487\end{comment}
1488
1489\end{document}
1490
1491% Local Variables: %
1492% tab-width: 4 %
1493% compile-command: "make" %
1494% End: %
Note: See TracBrowser for help on using the repository browser.