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Changeset 06cf47f for doc/generic_types

Timestamp:

Apr 2, 2017, 10:09:56 AM (8 years ago)

Author:

Peter A. Buhr <pabuhr@…>

Branches:

ADT, aaron-thesis, arm-eh, ast-experimental, cleanup-dtors, deferred_resn, demangler, enum, forall-pointer-decay, jacob/cs343-translation, jenkins-sandbox, master, new-ast, new-ast-unique-expr, new-env, no_list, persistent-indexer, pthread-emulation, qualifiedEnum, resolv-new, with_gc

Children:

Parents:

Message:

changes to OOPSLA paper

Location:

doc/generic_types

Files:

: 2 edited

acmart.cls (modified) (2 diffs)
generic_types.tex (modified) (33 diffs)

Legend:

: Unmodified
: Added
: Removed

doc/generic_types/acmart.cls

-                      r707446a
+                      r06cf47f
 \fi
 \if@ACM@screen
   \hypersetup{colorlinks,
     linkcolor=ACMRed,
     citecolor=ACMPurple,
     urlcolor=ACMDarkBlue,
     filecolor=ACMDarkBlue}
+%  \hypersetup{colorlinks,
+%    linkcolor=ACMRed,
+%    citecolor=ACMPurple,
+%    urlcolor=ACMDarkBlue,
+%    filecolor=ACMDarkBlue}
 \else
   \hypersetup{hidelinks}
 …
       \newlength\ACM@linecount@bxht\setlength{\ACM@linecount@bxht}{-\baselineskip}
       \@tempcnta\@ne\relax
+      \loop{\color{ACMRed}\scriptsize\the\@tempcnta}\\
+%      \loop{\color{ACMRed}\scriptsize\the\@tempcnta}\\
+      \loop{\scriptsize\the\@tempcnta}\\
       \advance\@tempcnta by \@ne
       \addtolength{\ACM@linecount@bxht}{\baselineskip}

doc/generic_types/generic_types.tex

-                      r707446a
+                      r06cf47f
 % take off review (for line numbers) and anonymous (for anonymization) on submission
 % \documentclass[format=acmlarge, anonymous, review]{acmart}
+\documentclass[format=acmlarge, review]{acmart}
+\usepackage{listings}   % For code listings
+\documentclass[format=acmlarge,review]{acmart}
+\usepackage{xspace,calc,comment}
+\usepackage{upquote}                                                                    % switch curled `'" to straight
+\usepackage{listings}                                                                   % format program code
+\makeatletter
+% parindent is relative, i.e., toggled on/off in environments like itemize, so store the value for
+% use rather than use \parident directly.
+\newlength{\parindentlnth}
+\setlength{\parindentlnth}{\parindent}
+\newlength{\gcolumnposn}                                % temporary hack because lstlisting does handle tabs correctly
+\newlength{\columnposn}
+\setlength{\gcolumnposn}{2.75in}
+\setlength{\columnposn}{\gcolumnposn}
+\newcommand{\C}[2][\@empty]{\ifx#1\@empty\else\global\setlength{\columnposn}{#1}\global\columnposn=\columnposn\fi\hfill\makebox[\textwidth-\columnposn][l]{\lst@commentstyle{#2}}}
+\newcommand{\CRT}{\global\columnposn=\gcolumnposn}
+\makeatother
 % Useful macros
 \newcommand{\CFA}{C$\mathbf\forall$} % Cforall symbolic name
 \newcommand{\CC}{\rm C\kern-.1em\hbox{+\kern-.25em+}} % C++ symbolic name
 \newcommand{\CCeleven}{\rm C\kern-.1em\hbox{+\kern-.25em+}11} % C++11 symbolic name
 \newcommand{\CCfourteen}{\rm C\kern-.1em\hbox{+\kern-.25em+}14} % C++14 symbolic name
 \newcommand{\CCseventeen}{\rm C\kern-.1em\hbox{+\kern-.25em+}17} % C++17 symbolic name
 \newcommand{\CCtwenty}{\rm C\kern-.1em\hbox{+\kern-.25em+}20} % C++20 symbolic name
+\newcommand{\CFA}{C$\mathbf\forall$\xspace} % Cforall symbolic name
+\newcommand{\CC}{\rm C\kern-.1em\hbox{+\kern-.25em+}\xspace} % C++ symbolic name
+\newcommand{\CCeleven}{\rm C\kern-.1em\hbox{+\kern-.25em+}11\xspace} % C++11 symbolic name
+\newcommand{\CCfourteen}{\rm C\kern-.1em\hbox{+\kern-.25em+}14\xspace} % C++14 symbolic name
+\newcommand{\CCseventeen}{\rm C\kern-.1em\hbox{+\kern-.25em+}17\xspace} % C++17 symbolic name
+\newcommand{\CCtwenty}{\rm C\kern-.1em\hbox{+\kern-.25em+}20\xspace} % C++20 symbolic name
 \newcommand{\TODO}{\textbf{TODO}}
 \newcommand{\eg}{\textit{e}.\textit{g}.}
 \newcommand{\ie}{\textit{i}.\textit{e}.}
 \newcommand{\etc}{\textit{etc}.}
+\newcommand{\eg}{\textit{e}.\textit{g}.,\xspace}
+\newcommand{\ie}{\textit{i}.\textit{e}.,\xspace}
+\newcommand{\etc}{\textit{etc}.,\xspace}
 % CFA programming language, based on ANSI C (with some gcc additions)
 \lstdefinelanguage{CFA}[ANSI]{C}{
         morekeywords={_Alignas,_Alignof,__alignof,__alignof__,asm,__asm,__asm__,_At,_Atomic,__attribute,__attribute__,auto,
                 _Bool,bool,catch,catchResume,choose,_Complex,__complex,__complex__,__const,__const__,disable,dtype,enable,__extension__,
                 fallthrough,fallthru,finally,forall,ftype,_Generic,_Imaginary,inline,__label__,lvalue,_Noreturn,one_t,otype,restrict,size_t,sized,_Static_assert,
+                _Bool,catch,catchResume,choose,_Complex,__complex,__complex__,__const,__const__,disable,dtype,enable,__extension__,
+                fallthrough,fallthru,finally,forall,ftype,_Generic,_Imaginary,inline,__label__,lvalue,_Noreturn,one_t,otype,restrict,_Static_assert,
                 _Thread_local,throw,throwResume,trait,try,ttype,typeof,__typeof,__typeof__,zero_t},
 }%
 …
 tabsize=4,                                                                                              % 4 space tabbing
 xleftmargin=\parindent,                                                                 % indent code to paragraph indentation
+% extendedchars=true,                                                                   % allow ASCII characters in the range 128-255
+% escapechar=§,                                                                                 % LaTeX escape in CFA code §...§ (section symbol), emacs: C-q M-'
+mathescape=true,                                                                                % LaTeX math escape in CFA code $...$
+keepspaces=true,                                                                                %
+%mathescape=true,                                                                               % LaTeX math escape in CFA code $...$
+escapechar=\$,                                                                                  % LaTeX escape in CFA code
+%keepspaces=true,                                                                               %
 showstringspaces=false,                                                                 % do not show spaces with cup
 showlines=true,                                                                                 % show blank lines at end of code
 …
 % replace/adjust listing characters that look bad in sanserif
 literate={-}{\raisebox{-0.15ex}{\texttt{-}}}1 {^}{\raisebox{0.6ex}{$\scriptscriptstyle\land\,$}}1
+        {~}{\raisebox{0.3ex}{$\scriptstyle\sim\,$}}1 {_}{\makebox[1.2ex][c]{\rule{1ex}{0.1ex}}}1 {`}{\ttfamily\upshape\hspace*{-0.1ex}`}1
+        {<-}{$\leftarrow$}2 {=>}{$\Rightarrow$}2 {->}{$\rightarrow$}2,
+% moredelim=**[is][\color{red}]{®}{®},                                  % red highlighting ®...® (registered trademark symbol) emacs: C-q M-.
+% moredelim=**[is][\color{blue}]{ß}{ß},                                 % blue highlighting ß...ß (sharp s symbol) emacs: C-q M-_
+% moredelim=**[is][\color{OliveGreen}]{¢}{¢},                   % green highlighting ¢...¢ (cent symbol) emacs: C-q M-"
+% moredelim=[is][\lstset{keywords={}}]{¶}{¶},                   % keyword escape ¶...¶ (pilcrow symbol) emacs: C-q M-^
+        {~}{\raisebox{0.3ex}{$\scriptstyle\sim\,$}}1 {_}{\makebox[1.2ex][c]{\rule{1ex}{0.1ex}}}1 % {`}{\ttfamily\upshape\hspace*{-0.1ex}`}1
+        {<-}{$\leftarrow$}2 {=>}{$\Rightarrow$}2,
+moredelim=**[is][\color{red}]{`}{`},
 }% lstset
 …
 \acmJournal{PACMPL}
 \title{Generic and Tuple Types with Efficient Dynamic Layout in \CFA{}}
+\title{Generic and Tuple Types with Efficient Dynamic Layout in \CFA}
 \author{Aaron Moss}
+\email{a3moss@uwaterloo.ca}
+\author{Robert Schluntz}
+\email{rschlunt@uwaterloo.ca}
+\author{Peter Buhr}
+\email{pabuhr@uwaterloo.ca}
 \affiliation{%
         \institution{University of Waterloo}
 …
         \country{Canada}
+}
-\email{a3moss@uwaterloo.ca}
-\author{Robert Schluntz}
-\affiliation{%
-        \institution{University of Waterloo}
-        \department{David R. Cheriton School of Computer Science}
-        \streetaddress{Davis Centre, University of Waterloo}
-        \city{Waterloo}
-        \state{ON}
-        \postcode{N2L 3G1}
-        \country{Canada}
+}
-\email{rschlunt@uwaterloo.ca}
-\author{Peter Buhr}
-\affiliation{%
-        \institution{University of Waterloo}
-        \department{David R. Cheriton School of Computer Science}
-        \streetaddress{Davis Centre, University of Waterloo}
-        \city{Waterloo}
-        \state{ON}
-        \postcode{N2L 3G1}
-        \country{Canada}
+}
-\email{pabuhr@uwaterloo.ca}
 \terms{generic, tuple, types}
 …
 \begin{abstract}
 The 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. This installed base of code and the programmers who produced it represent a massive software engineering investment spanning decades. Nonetheless, C, first standardized over thirty years ago, lacks many features that make programming in more modern languages safer and more productive. The 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. Particularly, \CFA{} is designed to have an orthogonal feature set based closely on the C programming paradigm, so that \CFA{} features can be added incrementally to existing C code-bases, and C programmers can learn \CFA{} extensions on an as-needed basis, preserving investment in existing engineers and code. This paper describes how generic and tuple types are implemented in \CFA{} in accordance with these principles.
+The 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. This installation base and the programmers producing it represent a massive software-engineering investment spanning decades and likely to continue for decades more. Nonetheless, C, first standardized over thirty years ago, lacks many features that make programming in more modern languages safer and more productive. The 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. Prior projects have attempted similar goals~\cite{C++,Grossman06} but failed to honour C programming-style, e.g., adding object-oriented, functional programming with garbage collection is a non-starter for many C developers. Specifically, \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. This paper describes only two \CFA extensions, generic and tuple types, and how they are implemented in accordance with these principles.
 \end{abstract}
 \begin{document}
 \maketitle
 \section{Introduction \& Background}
 \CFA{}\footnote{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 mental model for programmers. Four key design goals were set out in the original design of \CFA{} \citep{Bilson03}:
+\CFA\footnote{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. Four key design goals were set out in the original design of \CFA~\citep{Bilson03}:
 \begin{enumerate}
 \item The behaviour of standard C code must remain the same when translated by a \CFA{} compiler as when translated by a C compiler.
 \item Standard C code must be as fast and as small when translated by a \CFA{} compiler as when translated by a C compiler.
 \item \CFA{} code must be at least as portable as standard C code.
 \item Extensions introduced by \CFA{} must be translated in the most efficient way possible.
+\item The behaviour of standard C code must remain the same when translated by a \CFA compiler as when translated by a C compiler.
+\item Standard C code must be as fast and as small when translated by a \CFA compiler as when translated by a C compiler.
+\item \CFA code must be at least as portable as standard C code.
+\item Extensions introduced by \CFA must be translated in the most efficient way possible.
 \end{enumerate}
+The purpose of these goals is to ensure that existing C code-bases can be converted to \CFA{} incrementally and with minimal effort, and that programmers who already know C can productively produce \CFA{} code without training in \CFA{} beyond the extension features they wish to employ. In its current implementation, \CFA{} is compiled by translating it to GCC-dialect C, allowing it to leverage the portability and code optimizations provided by GCC, meeting goals (1)-(3).
+\CFA{} has been previously extended with polymorphic functions and name overloading (including operator overloading) \citep{Bilson03}, and deterministically-executed constructors and destructors \citep{Schluntz17}. This paper describes how generic and tuple types are designed and implemented in \CFA{} in accordance with both the backward compatibility goals and existing features described above.
+The purpose of these goals is to ensure that existing C code-bases can be converted to \CFA incrementally and with minimal effort, and that programmers who know C can productively generate \CFA code without training beyond the features they wish to employ. In its current implementation, \CFA is compiled by translating it to the GCC-dialect of C, allowing it to leverage the portability and code optimizations provided by GCC, meeting goals (1)-(3).
+\CFA has been previously extended with polymorphic functions and name overloading (including operator overloading)~\citep{Bilson03}, and deterministically-executed constructors and destructors~\citep{Schluntz17}. This paper describes how generic and tuple types are designed and implemented in \CFA in accordance with both the backward compatibility goals and existing features described above.
 \subsection{Polymorphic Functions}
 \label{sec:poly-fns}
+\CFA{}'s polymorphism was originally formalized by \citet{Ditchfield92}, and first implemented by \citet{Bilson03}. The signature feature of \CFA{} is parametric-polymorphic functions; such functions are written using a @forall@ clause (which gives the language its name):
+\begin{lstlisting}
+forall(otype T)
+T identity(T x) { return x; }
+int forty_two = identity(42); // T is bound to int, forty_two == 42
+\end{lstlisting}
+The @identity@ function above can be applied to any complete object type (or ``@otype@''). The type variable @T@ is transformed into a set of additional implicit parameters to @identity@, that encode sufficient information about @T@ to create and return a variable of that type. The \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. If this extra information is not needed, the type parameter can be declared as @dtype T@, where @dtype@ is short for ``data type''.
+Here, the runtime cost of polymorphism is spread over each polymorphic call, due to passing more arguments to polymorphic functions; preliminary experiments have shown this overhead to be similar to \CC{} virtual function calls. An advantage of this design is that, unlike \CC{} template functions, \CFA{} @forall@ functions are compatible with separate compilation.
+Since bare polymorphic types do not provide a great range of available operations, \CFA{} provides a \emph{type assertion} mechanism to provide further information about a type:
+\begin{lstlisting}
+forall(otype T | { T twice(T); })
+T four_times(T x) { return twice( twice(x) ); }
+double twice(double d) { return d * 2.0; } // (1)
+double magic = four_times(10.5); // T is bound to double, uses (1) to satisfy type assertion
+\end{lstlisting}
+These type assertions may be either variable or function declarations that depend on a polymorphic type variable. @four_times@ can only be called with an argument for which there exists a function named @twice@ that can take that argument and return another value of the same type; a pointer to the appropriate @twice@ function is passed as an additional implicit parameter to the call of @four_times@.
+Monomorphic specializations of polymorphic functions can themselves be used to satisfy type assertions. For instance, @twice@ could have been defined using the \CFA{} syntax for operator overloading as:
+\begin{lstlisting}
+forall(otype S | { S ?+?(S, S); })
+S twice(S x) { return x + x; }  // (2)
+\end{lstlisting}
+This version of @twice@ works for any type @S@ that has an addition operator defined for it, and it could have been used to satisfy the type assertion on @four_times@.
+The translator accomplishes this polymorphism by creating a wrapper function calling @twice // (2)@ with @S@ bound to @double@, then providing this wrapper function to @four_times@\footnote{\lstinline@twice // (2)@ could also have had a type parameter named \lstinline@T@; \CFA{} specifies renaming of the type parameters, which would avoid the name conflict with the type variable \lstinline@T@ of \lstinline@four_times@.}.
+\CFA's polymorphism was originally formalized by~\citet{Ditchfield92}, and first implemented by~\citet{Bilson03}. The signature feature of \CFA is parametric-polymorphic functions; such functions are written using a @forall@ clause (which gives the language its name):
+\begin{lstlisting}
+`forall( otype T )` T identity( T val ) { return val; }
+int forty_two = identity( 42 );                         $\C{// T is bound to int, forty\_two == 42}$
+\end{lstlisting}
+The @identity@ function above can be applied to any complete object-type (or ``@otype@''). The type variable @T@ is transformed into a set of additional implicit parameters to @identity@ that encode sufficient information about @T@ to create and return a variable of that type. The \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. If this extra information is not needed, e.g., for a pointer, the type parameter can be declared as @dtype T@, where @dtype@ is short for ``data type''.
+Here, the runtime cost of polymorphism is spread over each polymorphic call, due to passing more arguments to polymorphic functions; preliminary experiments have shown this overhead to be similar to \CC virtual function calls. An advantage of this design is that, unlike \CC template functions, \CFA @forall@ functions are compatible with C separate compilation.
+Since bare polymorphic-types provide only a narrow set of available operations, \CFA provides a \emph{type assertion} mechanism to provide further type information, where type assertions may be variable or function declarations that depend on a polymorphic type variable. For instance, @twice@ can be defined using the \CFA syntax for operator overloading:
+\begin{lstlisting}
+forall( otype T | { T `?`+`?`(T, T); } )        $\C{// ? denotes operands}$
+  T twice( T x ) { return x + x; }                      $\C{// (2)}$
+int val = twice( twice( 3.7 ) );
+\end{lstlisting}
+which works for any type @T@ with an addition operator defined. The translator accomplishes this polymorphism by creating a wrapper function for calling @+@ with @T@ bound to @double@, then providing this function to the first call of @twice@. It then has the option of using the same @twice@ again 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 in its type analysis. The first approach has a late conversion from integer to floating-point on the final assignment, while the second has an eager conversion to integer. \CFA minimize the number of conversions and their potential to lose information, so it selects the first approach.
+Monomorphic specializations of polymorphic functions can satisfy polymorphic type-assertions.
+% \begin{lstlisting}
+% forall(otype T `| { T twice(T); }`)           $\C{// type assertion}$
+% T four_times(T x) { return twice( twice(x) ); }
+% double twice(double d) { return d * 2.0; }    $\C{// (1)}$
+% double magic = four_times(10.5);                      $\C{// T bound to double, uses (1) to satisfy type assertion}$
+% \end{lstlisting}
+\begin{lstlisting}
+forall( otype T `| { int ?<?( T, T ); }` )      $\C{// type assertion}$
+  void qsort( const T * arr, size_t dimension );
+forall( otype T `| { int ?<?( T, T ); }` )      $\C{// type assertion}$
+  T * bsearch( T key, const T * arr, size_t dimension );
+double vals[10] = { /* 10 floating-point values */ };
+qsort( vals, 10 );                                                      $\C{// sort array}$
+double * val = bsearch( 5.0, vals, 10 );        $\C{// binary search sorted array for key}$
+\end{lstlisting}
+@qsort@ and @bsearch@ can only be called with arguments for which there exists a function named @<@ taking two arguments of the same type and returning an @int@ value.
+Here, the build-in monomorphic specialization of @<@ for type @double@ is passed as an additional implicit parameter to the calls of @qsort@ and @bsearch@.
+Crucial to the design of a new programming language are the libraries to access thousands of external features.
+\CFA inherits a massive compatible library-base, where other programming languages have to rewrite or provide fragile inter-language communication with C.
+A simple example is leveraging the existing type-unsafe C @bsearch@:
+\begin{lstlisting}
+void * bsearch( const void * key, const void * base, size_t nmemb, size_t size,
+                     int (* compar)(const void *, const void *));
+int comp( const void * t1, const void * t2 ) { return *(double *)t1 < *(double *)t2 ? -1 :
+                                         *(double *)t2 < *(double *)t1 ? 1 : 0; }
+double key = ...;
+double *v = (double *)bsearch( &key, vals, size, sizeof( vals[0] ), comp );
+\end{lstlisting}
+but providing a type-safe \CFA overloaded wrapper.
+\begin{lstlisting}
+forall( otype T | { int ?<?( T, T ); } )
+  T * bsearch( T key, const T * arr, size_t dimension ) {
+        int comp( const void * t1, const void * t2 ) { /* as above with double changed to T */ }
+        return (T *)bsearch( &key, arr, dimension, sizeof(T), comp );
+}
+forall( otype T | { int ?<?( T, T ); } )
+  unsigned int bsearch( T key, const T * arr, size_t dimension ) {
+        T *result = bsearch( key, arr, dimension );     $\C{// call first version}$
+        return result ? result - arr : dimension;       $\C{// pointer subtraction includes sizeof(T)}$
+}
+double * val = bsearch( 5.0, vals, 10 );                $\C{// selection based on return type}$
+int posn = bsearch( 5.0, vals, 10 );
+\end{lstlisting}
+The nested routine @comp@ provides the hidden interface from typed \CFA to untyped (@void *@) C, plus the cast of the result.
+As well, an alternate kind of return is made available, position versus pointer to found element.
+\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@.
+Call-site inferencing and nested functions provide a localized form of inhertance. For example, @qsort@ only sorts in asending order using @<@. However, it is trivial to locally change this behaviour:
+\begin{lstlisting}
+{
+        int ?<?( double x, double y ) { return x `>` y; }       $\C{// override behaviour}$
+        qsort( vals, size );                                    $\C{// descending sort}$
+}
+\end{lstlisting}
+Within the block, the nested version of @<@ performs @>@ and this local version overrides the built-in @<@ so it is passed to @qsort@.
+Hence, programmers can easily form new local environments to maximize reuse of existing functions and types.
+Finally, variables can also be overloaded:
+\begin{lstlisting}
+short int MAX = ...;
+int MAX = ...;
+double MAX = ...;
+\end{lstlisting}
+\begin{lstlisting}
+short int s = MAX;  // select correct MAX
+int i = MAX;
+double d = MAX;
+\end{lstlisting}
 \subsection{Traits}
+\CFA{} provides \emph{traits} as a means to name a group of type assertions, as in the example below:
+\begin{lstlisting}
+trait has_magnitude(otype T) {
+    bool ?<?(T, T);  // comparison operator for T
+    T -?(T);  // negation operator for T
+    void ?{}(T*, zero_t);  // constructor from 0 literal
+\CFA provides \emph{traits} to name a group of type assertions:
+% \begin{lstlisting}
+% trait has_magnitude(otype T) {
+%     _Bool ?<?(T, T);                                          $\C{// comparison operator for T}$
+%     T -?(T);                                                          $\C{// negation operator for T}$
+%     void ?{}(T*, zero_t);                                     $\C{// constructor from 0 literal}$
+% };
+% forall(otype M | has_magnitude(M))
+% M abs( M m ) {
+%     M zero = { 0 };                                                   $\C{// uses zero\_t constructor from trait}$
+%     return m < zero ? -m : m;
+% }
+% forall(otype M | has_magnitude(M))
+% M max_magnitude( M a, M b ) {
+%     return abs(a) < abs(b) ? b : a;
+% }
+% \end{lstlisting}
+\begin{lstlisting}
+trait sumable( otype T ) {
+        const T 0;                                                              $\C{// variable zero}$
+        T ?+?( T, T );                                                  $\C{// assortment of additions}$
+        T ?+=?( T *, T );
+        T ++?( T * );
+        T ?++( T * );
 };
+forall(otype M | has_magnitude(M))
+M abs( M m ) {
+    M zero = { 0 };  // uses zero_t constructor from trait
+    return m < zero ? -m : m;
+}
+forall(otype M | has_magnitude(M))
+M max_magnitude( M a, M b ) {
+    return abs(a) < abs(b) ? b : a;
+}
+\end{lstlisting}
+This capability allows specifying the same set of assertions in multiple locations, without the repetition and likelihood of mistakes that come with manually writing them out for each function declaration.
+@otype@ is essentially syntactic sugar for the following trait:
+\begin{lstlisting}
+trait otype(dtype T | sized(T)) {
+        // sized is a compiler-provided pseudo-trait for types with known size & alignment
+        void ?{}(T*);  // default constructor
+        void ?{}(T*, T);  // copy constructor
+        void ?=?(T*, T);  // assignment operator
+        void ^?{}(T*);  // destructor
+forall( otype T | sumable( T ) )
+  T sum( T a[$\,$], size_t dimension ) {
+        T total = 0;                                                    $\C{// instantiate T, select 0}$
+        for ( unsigned int i = 0; i < dimension; i += 1 )
+                total += a[i];                                          $\C{// select appropriate +}$
+        return total;
+}
+\end{lstlisting}
+The trait name allows specifying the same set of assertions in multiple locations, preventing repetition mistakes at each function declaration.
+In fact, the set of operators is incomplete, \eg no assignment, but @otype@ is syntactic sugar for the following implicit trait:
+\begin{lstlisting}
+trait otype( dtype T | sized(T) ) {
+        // sized is a compiler-provided pseudo-trait for types with known size and alignment}
+        void ?{}( T * );                                                $\C{// default constructor}$
+        void ?{}( T *, T );                                             $\C{// copy constructor}$
+        void ?=?( T *, T );                                             $\C{// assignment operator}$
+        void ^?{}( T * );                                               $\C{// destructor}$
 };
 \end{lstlisting}
 Given the information provided for an @otype@, variables of polymorphic type can be treated as if they were a complete struct type -- they can be stack-allocated using the @alloca@ compiler builtin, default or copy-initialized, assigned, and deleted. As an example, the @abs@ function above produces generated code something like the following (simplified for clarity and brevity):
+Given the information provided for an @otype@, variables of polymorphic type can be treated as if they were a complete struct type -- they can be stack-allocated using the @alloca@ compiler builtin, default or copy-initialized, assigned, and deleted. As an example, the @sum@ function produces generated code something like the following (simplified for clarity and brevity):
 \begin{lstlisting}
 void abs( size_t _sizeof_M, size_t _alignof_M,
                 void (*_ctor_M)(void*), void (*_copy_M)(void*, void*),
                 void (*_assign_M)(void*, void*), void (*_dtor_M)(void*),
                 bool (*_lt_M)(void*, void*), void (*_neg_M)(void*, void*),
+                _Bool (*_lt_M)(void*, void*), void (*_neg_M)(void*, void*),
         void (*_ctor_M_zero)(void*, int),
                 void* m, void* _rtn ) {  // polymorphic parameter and return passed as void*
         // M zero = { 0 };
         void* zero = alloca(_sizeof_M);  // stack allocate zero temporary
         _ctor_M_zero(zero, 0);  // initialize using zero_t constructor
         // return m < zero ? -m : m;
+                void* m, void* _rtn ) {                         $\C{// polymorphic parameter and return passed as void*}$
+                                                                                        $\C{// M zero = { 0 };}$
+        void* zero = alloca(_sizeof_M);                 $\C{// stack allocate zero temporary}$
+        _ctor_M_zero(zero, 0);                                  $\C{// initialize using zero\_t constructor}$
+                                                                                        $\C{// return m < zero ? -m : m;}$
         void *_tmp = alloca(_sizeof_M);
         _copy_M( _rtn,  // copy-initialize return value
                 _lt_M( m, zero ) ?  // check condition
                  (_neg_M(m, _tmp), _tmp) :  // negate m
+        _copy_M( _rtn,                                                  $\C{// copy-initialize return value}$
+                _lt_M( m, zero ) ?                                      $\C{// check condition}$
+                 (_neg_M(m, _tmp), _tmp) :                      $\C{// negate m}$
                  m);
         _dtor_M(_tmp); _dtor_M(zero);  // destroy temporaries
+}
 \end{lstlisting}
 Semantically, traits are simply a named lists of type assertions, but they may be used for many of the same purposes that interfaces in Java or abstract base classes in \CC{} are used for. Unlike Java interfaces or \CC{} base classes, \CFA{} types do not explicitly state any inheritance relationship to traits they satisfy; this can be considered a form of structural inheritance, similar to implementation of an interface in Go, as opposed to the nominal inheritance model of Java and \CC{}. Nominal inheritance can be simulated with traits using marker variables or functions:
+        _dtor_M(_tmp); _dtor_M(zero);                   $\C{// destroy temporaries}$
+}
+\end{lstlisting}
+Semantically, traits are simply a named lists of type assertions, but they may be used for many of the same purposes that interfaces in Java or abstract base classes in \CC are used for. Unlike Java interfaces or \CC base classes, \CFA types do not explicitly state any inheritance relationship to traits they satisfy; this can be considered a form of structural inheritance, similar to implementation of an interface in Go, as opposed to the nominal inheritance model of Java and \CC. Nominal inheritance can be simulated with traits using marker variables or functions:
 \begin{lstlisting}
 trait nominal(otype T) {
 …
 };
 int is_nominal;  // int now satisfies the nominal trait
+int is_nominal;                                                         $\C{// int now satisfies the nominal trait}$
 \end{lstlisting}
 …
 \begin{lstlisting}
 trait pointer_like(otype Ptr, otype El) {
     lvalue El *?(Ptr); // Ptr can be dereferenced into a modifiable value of type El
+    lvalue El *?(Ptr);                                          $\C{// Ptr can be dereferenced into a modifiable value of type El}$
+}
 struct list {
     int value;
     list *next;  // may omit "struct" on type names
+    list *next;                                                         $\C{// may omit "struct" on type names}$
 };
 …
 \end{lstlisting}
 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@).
+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@).
 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.
 …
 One of the known shortcomings of standard C is that it does not provide reusable type-safe abstractions for generic data structures and algorithms. Broadly speaking, there are three approaches to create data structures in C. One approach is to write bespoke data structures for each context in which they are needed. While 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. A second approach is to use @void*@-based polymorphism. This approach is taken by the C standard library functions @qsort@ and @bsearch@, and does allow the use of common code for common functionality. However, basing all polymorphism on @void*@ eliminates the type-checker's ability to ensure that argument types are properly matched, often requires a number of extra function parameters, and also adds pointer indirection and dynamic allocation to algorithms and data structures that would not otherwise require them. A third approach to generic code is to use pre-processor macros to generate it -- this approach does allow the generated code to be both generic and type-checked, though any errors produced may be difficult to interpret. Furthermore, writing and invoking C code as preprocessor macros is unnatural and somewhat inflexible.
 Other C-like languages such as \CC{} and Java use \emph{generic types} to produce type-safe abstract data types. The authors have chosen to implement generic types as well, with some care taken that the generic types design for \CFA{} integrates efficiently and naturally with the existing polymorphic functions in \CFA{} while retaining backwards compatibility with C; maintaining separate compilation is a particularly important constraint on the design. However, where the concrete parameters of the generic type are known, there is not extra overhead for the use of a generic type.
+Other C-like languages such as \CC and Java use \emph{generic types} to produce type-safe abstract data types. The authors have chosen to implement generic types as well, with some care taken that the generic types design for \CFA integrates efficiently and naturally with the existing polymorphic functions in \CFA while retaining backwards compatibility with C; maintaining separate compilation is a particularly important constraint on the design. However, where the concrete parameters of the generic type are known, there is not extra overhead for the use of a generic type.
 A 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:
 …
 \end{lstlisting}
 \CFA{} classifies generic types as either \emph{concrete} or \emph{dynamic}. Dynamic generic types vary in their in-memory layout depending on their type parameters, while concrete generic types have a fixed memory layout regardless of type parameters. A type may have polymorphic parameters but still be concrete; in \CFA{} such types are called \emph{dtype-static}. Polymorphic pointers are an example of dtype-static types -- @forall(dtype T) T*@ is a polymorphic type, but for any @T@ chosen, @T*@ has exactly the same in-memory representation as a @void*@, and can therefore be represented by a @void*@ in code generation.
 \CFA{} generic types may also specify constraints on their argument type to be checked by the compiler. For example, consider the following declaration of a sorted set type, which ensures that the set key supports comparison and tests for equality:
 \begin{lstlisting}
 forall(otype Key | { bool ?==?(Key, Key); bool ?<?(Key, Key); })
+\CFA classifies generic types as either \emph{concrete} or \emph{dynamic}. Dynamic generic types vary in their in-memory layout depending on their type parameters, while concrete generic types have a fixed memory layout regardless of type parameters. A type may have polymorphic parameters but still be concrete; in \CFA such types are called \emph{dtype-static}. Polymorphic pointers are an example of dtype-static types -- @forall(dtype T) T*@ is a polymorphic type, but for any @T@ chosen, @T*@ has exactly the same in-memory representation as a @void*@, and can therefore be represented by a @void*@ in code generation.
+\CFA generic types may also specify constraints on their argument type to be checked by the compiler. For example, consider the following declaration of a sorted set type, which ensures that the set key supports comparison and tests for equality:
+\begin{lstlisting}
+forall(otype Key | { _Bool ?==?(Key, Key); _Bool ?<?(Key, Key); })
 struct sorted_set;
 \end{lstlisting}
 …
 \subsection{Concrete Generic Types}
 The \CFA{} translator instantiates concrete generic types by template-expanding them to fresh struct types; concrete generic types can therefore be used with zero runtime overhead. To enable inter-operation among equivalent instantiations of a generic type, the translator saves the set of instantiations currently in scope and reuses the generated struct declarations where appropriate. For 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 that can see that declaration may reuse. As an example of the expansion, the concrete instantiation for @pair(const char*, int)@ looks like this:
+The \CFA translator instantiates concrete generic types by template-expanding them to fresh struct types; concrete generic types can therefore be used with zero runtime overhead. To enable inter-operation among equivalent instantiations of a generic type, the translator saves the set of instantiations currently in scope and reuses the generated struct declarations where appropriate. For 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 that can see that declaration may reuse. As an example of the expansion, the concrete instantiation for @pair(const char*, int)@ looks like this:
 \begin{lstlisting}
 struct _pair_conc1 {
 …
 \subsection{Dynamic Generic Types}
 Though \CFA{} implements concrete generic types efficiently, it also has a fully general system for computing with dynamic generic types. As 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. Dynamic generic structs have the same size and alignment parameter, and also an \emph{offset array} which contains the offsets of each member of the struct\footnote{Dynamic generic unions need no such offset array, as all members are at offset 0; the size and alignment parameters are still provided for dynamic unions, however.}. Access to members\footnote{The \lstinline@offsetof@ macro is implemented similarly.} of a dynamic generic struct is provided by adding the corresponding member of the offset array to the struct pointer at runtime, essentially moving a compile-time offset calculation to runtime where necessary.
+Though \CFA implements concrete generic types efficiently, it also has a fully general system for computing with dynamic generic types. As 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. Dynamic generic structs have the same size and alignment parameter, and also an \emph{offset array} which contains the offsets of each member of the struct\footnote{Dynamic generic unions need no such offset array, as all members are at offset 0; the size and alignment parameters are still provided for dynamic unions, however.}. Access to members\footnote{The \lstinline@offsetof@ macro is implemented similarly.} of a dynamic generic struct is provided by adding the corresponding member of the offset array to the struct pointer at runtime, essentially moving a compile-time offset calculation to runtime where necessary.
 These offset arrays are statically generated where possible. If a dynamic generic type is declared to be passed or returned by value from a polymorphic function, the translator can safely assume that the generic type is complete (that is, has a known layout) at any call-site, and the offset array is passed from the caller; if 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. As 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 in to @value@ for @pair(const char*, T)@. The offset array @_offsetof_pair@ is generated at the call site as @size_t _offsetof_pair[] = { offsetof(_pair_conc1, first), offsetof(_pair_conc1, second) };@.
 In some cases the offset arrays cannot be statically generated. For instance, modularity is generally provided in C by including an opaque forward-declaration of a struct and associated accessor and mutator routines in a header file, with the actual implementations in a separately-compiled \texttt{.c} file. \CFA{} supports this pattern for generic types, and in this instance the caller does not know the actual layout or size of the dynamic generic type, and only holds it by pointer. The \CFA{} translator automatically generates \emph{layout functions} for cases where the size, alignment, and offset array of a generic struct cannot be passed in to a function from that function's caller. These 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 struct (un-@sized@ parameters are forbidden from the language from being used in a context that affects layout). Results of these layout functions are cached so that they are only computed once per type per function.%, as in the example below for @pair@.
+In some cases the offset arrays cannot be statically generated. For instance, modularity is generally provided in C by including an opaque forward-declaration of a struct and associated accessor and mutator routines in a header file, with the actual implementations in a separately-compiled \texttt{.c} file. \CFA supports this pattern for generic types, and in this instance the caller does not know the actual layout or size of the dynamic generic type, and only holds it by pointer. The \CFA translator automatically generates \emph{layout functions} for cases where the size, alignment, and offset array of a generic struct cannot be passed in to a function from that function's caller. These 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 struct (un-@sized@ parameters are forbidden from the language from being used in a context that affects layout). Results of these layout functions are cached so that they are only computed once per type per function.%, as in the example below for @pair@.
 % \begin{lstlisting}
 % static inline void _layoutof_pair(size_t* _szeof_pair, size_t* _alignof_pair, size_t* _offsetof_pair,
 …
 Layout functions also allow generic types to be used in a function definition without reflecting them in the function signature. For 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. This function could acquire the layout for @set(T)@ by calling its layout function with the layout of @T@ implicitly passed into the function.
 Whether a type is concrete, dtype-static, or dynamic is decided based solely on the type parameters and @forall@ clause on the struct declaration. This design allows opaque forward declarations of generic types like @forall(otype T) struct Box;@ -- like in C, all uses of @Box(T)@ can be in a separately compiled translation unit, and callers from other translation units know the proper calling conventions to use. If the definition of a struct type was included in the decision of 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.
+Whether a type is concrete, dtype-static, or dynamic is decided based solely on the type parameters and @forall@ clause on the struct declaration. This design allows opaque forward declarations of generic types like @forall(otype T) struct Box;@ -- like in C, all uses of @Box(T)@ can be in a separately compiled translation unit, and callers from other translation units know the proper calling conventions to use. If the definition of a struct type was included in the decision of 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.
 \subsection{Applications}
 …
+}
 \end{lstlisting}
 Since @pair(T*, T*)@ is a concrete type, there are no added implicit parameters to @lexcmp@, so the code generated by \CFA{} is effectively identical to a version of this function written in standard C using @void*@, yet the \CFA{} version is type-checked to ensure that the fields of both pairs and the arguments to the comparison function match in type.
+Since @pair(T*, T*)@ is a concrete type, there are no added implicit parameters to @lexcmp@, so the code generated by \CFA is effectively identical to a version of this function written in standard C using @void*@, yet the \CFA version is type-checked to ensure that the fields of both pairs and the arguments to the comparison function match in type.
 Another useful pattern enabled by reused dtype-static type instantiations is zero-cost ``tag'' structs. Sometimes a particular bit of information is only useful for type-checking, and can be omitted at runtime. Tag structs can be used to provide this information to the compiler without further runtime overhead, as in the following example:
 …
 marathon + swimming_pool; // ERROR -- caught by compiler
 \end{lstlisting}
 @scalar@ is a dtype-static type, so all uses of it use a single struct definition, containing only a single @unsigned long@, and can share the same implementations of common routines like @?+?@ -- these implementations may even be separately compiled, unlike \CC{} template functions. However, the \CFA{} type-checker ensures that matching types are used by all calls to @?+?@, preventing nonsensical computations like adding the length of a marathon to the volume of an olympic pool.
+@scalar@ is a dtype-static type, so all uses of it use a single struct definition, containing only a single @unsigned long@, and can share the same implementations of common routines like @?+?@ -- these implementations may even be separately compiled, unlike \CC template functions. However, the \CFA type-checker ensures that matching types are used by all calls to @?+?@, preventing nonsensical computations like adding the length of a marathon to the volume of an olympic pool.
 \section{Tuples}
 \label{sec:tuples}
 The @pair(R, S)@ generic type used as an example in the previous section can be considered a special case of a more general \emph{tuple} data structure. The authors have implemented tuples in \CFA{}, with a design particularly motivated by two use cases: \emph{multiple-return-value functions} and \emph{variadic functions}.
+The @pair(R, S)@ generic type used as an example in the previous section can be considered a special case of a more general \emph{tuple} data structure. The authors have implemented tuples in \CFA, with a design particularly motivated by two use cases: \emph{multiple-return-value functions} and \emph{variadic functions}.
 In standard C, functions can return at most one value. This restriction results in code that emulates functions with multiple return values by \emph{aggregation} or by \emph{aliasing}. In the former situation, the function designer creates a record type that combines all of the return values into a single type. Unfortunately, the designer must come up with a name for the return type and for each of its fields. Unnecessary naming is a common programming language issue, introducing verbosity and a complication of the user's mental model. As such, this technique is effective when used sparingly, but can quickly get out of hand if many functions need to return different combinations of types. In the latter approach, the designer simulates multiple return values by passing the additional return values as pointer parameters. The pointer parameters are assigned inside of the routine body to emulate a return. Using this approach, the caller is directly responsible for allocating storage for the additional temporary return values. This responsibility complicates the call site with a sequence of variable declarations leading up to the call. Also, while a disciplined use of @const@ can give clues about whether a pointer parameter is going to be used as an out parameter, it is not immediately obvious from only the routine signature whether the callee expects such a parameter to be initialized before the call. Furthermore, while many C routines that accept pointers are designed so that it is safe to pass @NULL@ as a parameter, there are many C routines that are not null-safe. On a related note, C does not provide a standard mechanism to state that a parameter is going to be used as an additional return value, which makes the job of ensuring that a value is returned more difficult for the compiler.
 …
 \end{lstlisting}
 The @va_list@ type is a special C data type that abstracts variadic argument manipulation. The @va_start@ macro initializes a @va_list@, given the last named parameter. Each use of the @va_arg@ macro allows access to the next variadic argument, given a type. Since the function signature does not provide any information on what types can be passed to a variadic function, the compiler does not perform any error checks on a variadic call. As such, it is possible to pass any value to the @sum@ function, including pointers, floating-point numbers, and structures. In the case where the provided type is not compatible with the argument's actual type after default argument promotions, or if too many arguments are accessed, the behaviour is undefined \citep{C11}. Furthermore, there is no way to perform the necessary error checks in the @sum@ function at run-time, since type information is not carried into the function body. Since they rely on programmer convention rather than compile-time checks, variadic functions are inherently unsafe.
+The @va_list@ type is a special C data type that abstracts variadic argument manipulation. The @va_start@ macro initializes a @va_list@, given the last named parameter. Each use of the @va_arg@ macro allows access to the next variadic argument, given a type. Since the function signature does not provide any information on what types can be passed to a variadic function, the compiler does not perform any error checks on a variadic call. As such, it is possible to pass any value to the @sum@ function, including pointers, floating-point numbers, and structures. In the case where the provided type is not compatible with the argument's actual type after default argument promotions, or if too many arguments are accessed, the behaviour is undefined~\citep{C11}. Furthermore, there is no way to perform the necessary error checks in the @sum@ function at run-time, since type information is not carried into the function body. Since they rely on programmer convention rather than compile-time checks, variadic functions are inherently unsafe.
 In practice, compilers can provide warnings to help mitigate some of the problems. For example, GCC provides the @format@ attribute to specify that a function uses a format string, which allows the compiler to perform some checks related to the standard format specifiers. Unfortunately, this attribute does not permit extensions to the format string syntax, so a programmer cannot extend it to warn for mismatches with custom types.
 …
 \subsection{Tuple Expressions}
 The tuple extensions in \CFA{} can express multiple return values and variadic function parameters in an efficient and type-safe manner. \CFA{} introduces \emph{tuple expressions} and \emph{tuple types}. A tuple expression is an expression producing a fixed-size, ordered list of values of heterogeneous types. The type of a tuple expression is the tuple of the subexpression types, or a \emph{tuple type}. In \CFA{}, a tuple expression is denoted by a comma-separated list of expressions enclosed in square brackets. For example, the expression @[5, 'x', 10.5]@ has type @[int, char, double]@. The previous expression has three \emph{components}. Each component in a tuple expression can be any \CFA{} expression, including another tuple expression. The order of evaluation of the components in a tuple expression is unspecified, to allow a compiler the greatest flexibility for program optimization. It is, however, guaranteed that each component of a tuple expression is evaluated for side-effects, even if the result is not used. Multiple-return-value functions can equivalently be called \emph{tuple-returning functions}.
 \CFA{} allows declaration of \emph{tuple variables}, variables of tuple type. For example:
+The tuple extensions in \CFA can express multiple return values and variadic function parameters in an efficient and type-safe manner. \CFA introduces \emph{tuple expressions} and \emph{tuple types}. A tuple expression is an expression producing a fixed-size, ordered list of values of heterogeneous types. The type of a tuple expression is the tuple of the subexpression types, or a \emph{tuple type}. In \CFA, a tuple expression is denoted by a comma-separated list of expressions enclosed in square brackets. For example, the expression @[5, 'x', 10.5]@ has type @[int, char, double]@. The previous expression has three \emph{components}. Each component in a tuple expression can be any \CFA expression, including another tuple expression. The order of evaluation of the components in a tuple expression is unspecified, to allow a compiler the greatest flexibility for program optimization. It is, however, guaranteed that each component of a tuple expression is evaluated for side-effects, even if the result is not used. Multiple-return-value functions can equivalently be called \emph{tuple-returning functions}.
+\CFA allows declaration of \emph{tuple variables}, variables of tuple type. For example:
 \begin{lstlisting}
 [int, char] most_frequent(const char*);
 …
 h(x, y);   // flatten & structure
 \end{lstlisting}
 In \CFA{}, each of these calls is valid. In the call to @f@, @x@ is implicitly flattened so that the components of @x@ are passed as the two arguments to @f@. For the call to @g@, the values @y@ and @10@ are structured into a single argument of type @[int, int]@ to match the type of the parameter of @g@. Finally, in the call to @h@, @y@ 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]@. The flexible structure of tuples permits a simple and expressive function call syntax to work seamlessly with both single- and multiple-return-value functions, and with any number of arguments of arbitrarily complex structure.
 In {K-W C} \citep{Buhr94a,Till89}, a precursor to \CFA{}, there were 4 tuple coercions: opening, closing, flattening, and structuring. Opening coerces a tuple value into a tuple of values, while closing converts a tuple of values into a single tuple value. Flattening coerces a nested tuple into a flat tuple, \ie{} it takes a tuple with tuple components and expands it into a tuple with only non-tuple components. Structuring moves in the opposite direction, \ie{} it takes a flat tuple value and provides structure by introducing nested tuple components.
 In \CFA{}, the design has been simplified to require only the two conversions previously described, which trigger only in function call and return situations. Specifically, the expression resolution algorithm examines all of the possible alternatives for an expression to determine the best match. In resolving a function call expression, each combination of function value and list of argument alternatives is examined. Given a particular argument list and function value, the list of argument alternatives is flattened to produce a list of non-tuple valued expressions. Then the flattened list of expressions is compared with each value in the function's parameter list. If the parameter's type is not a tuple type, then the current argument value is unified with the parameter type, and on success the next argument and parameter are examined. If the parameter's type is a tuple type, then the structuring conversion takes effect, recursively applying the parameter matching algorithm using the tuple's component types as the parameter list types. Assuming a successful unification, eventually the algorithm gets to the end of the tuple type, which causes all of the matching expressions to be consumed and structured into a tuple expression. For example, in
+In \CFA, each of these calls is valid. In the call to @f@, @x@ is implicitly flattened so that the components of @x@ are passed as the two arguments to @f@. For the call to @g@, the values @y@ and @10@ are structured into a single argument of type @[int, int]@ to match the type of the parameter of @g@. Finally, in the call to @h@, @y@ 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]@. The flexible structure of tuples permits a simple and expressive function call syntax to work seamlessly with both single- and multiple-return-value functions, and with any number of arguments of arbitrarily complex structure.
+In {K-W C}~\citep{Buhr94a,Till89}, a precursor to \CFA, there were 4 tuple coercions: opening, closing, flattening, and structuring. Opening coerces a tuple value into a tuple of values, while closing converts a tuple of values into a single tuple value. Flattening coerces a nested tuple into a flat tuple, \ie it takes a tuple with tuple components and expands it into a tuple with only non-tuple components. Structuring moves in the opposite direction, \ie it takes a flat tuple value and provides structure by introducing nested tuple components.
+In \CFA, the design has been simplified to require only the two conversions previously described, which trigger only in function call and return situations. Specifically, the expression resolution algorithm examines all of the possible alternatives for an expression to determine the best match. In resolving a function call expression, each combination of function value and list of argument alternatives is examined. Given a particular argument list and function value, the list of argument alternatives is flattened to produce a list of non-tuple valued expressions. Then the flattened list of expressions is compared with each value in the function's parameter list. If the parameter's type is not a tuple type, then the current argument value is unified with the parameter type, and on success the next argument and parameter are examined. If the parameter's type is a tuple type, then the structuring conversion takes effect, recursively applying the parameter matching algorithm using the tuple's component types as the parameter list types. Assuming a successful unification, eventually the algorithm gets to the end of the tuple type, which causes all of the matching expressions to be consumed and structured into a tuple expression. For example, in
 \begin{lstlisting}
 int f(int, [double, int]);
 …
 double z = [x, f()].0.1;  // access second component of first component of tuple expression
 \end{lstlisting}
 As seen above, tuple-index expressions can occur on any tuple-typed expression, including tuple-returning functions, square-bracketed tuple expressions, and other tuple-index expressions, provided the retrieved component is also a tuple. This feature was proposed for {K-W C}, but never implemented \citep[p.~45]{Till89}.
+As seen above, tuple-index expressions can occur on any tuple-typed expression, including tuple-returning functions, square-bracketed tuple expressions, and other tuple-index expressions, provided the retrieved component is also a tuple. This feature was proposed for {K-W C}, but never implemented~\citep[p.~45]{Till89}.
 It is possible to access multiple fields from a single expression using a \emph{member-access tuple expression}. The result is a single tuple expression whose type is the tuple of the types of the members. For example,
 …
 Here, the type of @s.[x, y, z]@ is @[int, double, char *]@. A member tuple expression has the form @a.[x, y, z];@ where @a@ is an expression with type @T@, where @T@ supports member access expressions, and @x, y, z@ are all members of @T@ with types @T$_x$@, @T$_y$@, and @T$_z$@ respectively. Then the type of @a.[x, y, z]@ is @[T$_x$, T$_y$, T$_z$]@.
 Since 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 components, drop components, duplicate components, etc.):
+Since 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 components, drop components, duplicate components, etc.):
 \begin{lstlisting}
 [int, int, long, double] x;
 …
 That is, @?=?(&$L_i$, $R_i$)@ must be a well-typed expression. In the previous example, @[x, y] = z@, @z@ is flattened into @z.0, z.1@, and the assignments @x = z.0@ and @y = z.1@ are executed.
 A mass assignment assigns the value $R$ to each $L_i$. For a mass assignment to be valid, @?=?(&$L_i$, $R$)@ must be a well-typed expression. This rule differs from C cascading assignment (\eg{} @a=b=c@) in that conversions are applied to $R$ in each individual assignment, which prevents data loss from the chain of conversions that can happen during a cascading assignment. For example, @[y, x] = 3.14@ performs the assignments @y = 3.14@ and @x = 3.14@, which results in the value @3.14@ in @y@ and the value @3@ in @x@. On the other hand, the C cascading assignment @y = x = 3.14@ performs the assignments @x = 3.14@ and @y = x@, which results in the value @3@ in @x@, and as a result the value @3@ in @y@ as well.
+A mass assignment assigns the value $R$ to each $L_i$. For a mass assignment to be valid, @?=?(&$L_i$, $R$)@ must be a well-typed expression. This rule differs from C cascading assignment (\eg @a=b=c@) in that conversions are applied to $R$ in each individual assignment, which prevents data loss from the chain of conversions that can happen during a cascading assignment. For example, @[y, x] = 3.14@ performs the assignments @y = 3.14@ and @x = 3.14@, which results in the value @3.14@ in @y@ and the value @3@ in @x@. On the other hand, the C cascading assignment @y = x = 3.14@ performs the assignments @x = 3.14@ and @y = x@, which results in the value @3@ in @x@, and as a result the value @3@ in @y@ as well.
 Both kinds of tuple assignment have parallel semantics, such that each value on the left side and right side is evaluated \emph{before} any assignments occur. As a result, it is possible to swap the values in two variables without explicitly creating any temporary variables or calling a function:
 …
 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. This definition allows cascading tuple assignment and use of tuple assignment in other expression contexts, an occasionally useful idiom to keep code succinct and reduce repetition.
 % In \CFA{}, tuple assignment is an expression where the result type is the type of the left-hand side of the assignment, as in normal assignment. That is, a tuple assignment produces the value of the left-hand side after assignment. These semantics allow cascading tuple assignment to work out naturally in any context where a tuple is permitted. These semantics are a change from the original tuple design in {K-W C} \citep{Till89}, wherein tuple assignment was a statement that allows cascading assignments as a special case. This decision was made in an attempt to fix what was seen as a problem with assignment, wherein it can be used in many different locations, such as in function-call argument position. While permitting assignment as an expression does introduce the potential for subtle complexities, it is impossible to remove assignment expressions from \CFA{} without affecting backwards compatibility with C. Furthermore, there are situations where permitting assignment as an expression improves readability by keeping code succinct and reducing repetition, and complicating the definition of tuple assignment puts a greater cognitive burden on the user. In another language, tuple assignment as a statement could be reasonable, but it would be inconsistent for tuple assignment to be the only kind of assignment in \CFA{} that is not an expression.
+% In \CFA, tuple assignment is an expression where the result type is the type of the left-hand side of the assignment, as in normal assignment. That is, a tuple assignment produces the value of the left-hand side after assignment. These semantics allow cascading tuple assignment to work out naturally in any context where a tuple is permitted. These semantics are a change from the original tuple design in {K-W C}~\citep{Till89}, wherein tuple assignment was a statement that allows cascading assignments as a special case. This decision was made in an attempt to fix what was seen as a problem with assignment, wherein it can be used in many different locations, such as in function-call argument position. While permitting assignment as an expression does introduce the potential for subtle complexities, it is impossible to remove assignment expressions from \CFA without affecting backwards compatibility with C. Furthermore, there are situations where permitting assignment as an expression improves readability by keeping code succinct and reducing repetition, and complicating the definition of tuple assignment puts a greater cognitive burden on the user. In another language, tuple assignment as a statement could be reasonable, but it would be inconsistent for tuple assignment to be the only kind of assignment in \CFA that is not an expression.
 \subsection{Casting}
 In C, the cast operator is used to explicitly convert between types. In \CFA{}, the cast operator has a secondary use as type ascription. That 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:
+In C, the cast operator is used to explicitly convert between types. In \CFA, the cast operator has a secondary use as type ascription. That 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:
 \begin{lstlisting}
 int f();     // (1)
 …
 \end{lstlisting}
 Since casting is a fundamental operation in \CFA{}, casts should be given a meaningful interpretation in the context of tuples. Taking a look at standard C provides some guidance with respect to the way casts should work with tuples:
+Since casting is a fundamental operation in \CFA, casts should be given a meaningful interpretation in the context of tuples. Taking a look at standard C provides some guidance with respect to the way casts should work with tuples:
 \begin{lstlisting}
 int f();
 …
 Since @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)]@).
 Note 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.}. As such, (4) is invalid because the cast target type contains 4 components, while the source type contains only 3. Similarly, (5) is invalid because the cast @([int, int, int])(g().1)@ is invalid. That is, it is invalid to cast @[int, int]@ to @[int, int, int]@.
+Note 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.}. As such, (4) is invalid because the cast target type contains 4 components, while the source type contains only 3. Similarly, (5) is invalid because the cast @([int, int, int])(g().1)@ is invalid. That is, it is invalid to cast @[int, int]@ to @[int, int, int]@.
 \subsection{Polymorphism}
 Tuples also integrate with \CFA{} polymorphism as a special sort of generic type. Due to the implicit flattening and structuring conversions involved in argument passing, @otype@ and @dtype@ parameters are restricted to matching only with non-tuple types.
+Tuples also integrate with \CFA polymorphism as a special sort of generic type. Due to the implicit flattening and structuring conversions involved in argument passing, @otype@ and @dtype@ parameters are restricted to matching only with non-tuple types.
 \begin{lstlisting}
 forall(otype T, dtype U)
 …
 \end{lstlisting}
 Flattening and restructuring conversions are also applied to tuple types in polymorphic type assertions. Previously in \CFA{}, it has been assumed that assertion arguments must match the parameter type exactly, modulo polymorphic specialization (\ie{} no implicit conversions are applied to assertion arguments). In the example below:
+Flattening and restructuring conversions are also applied to tuple types in polymorphic type assertions. Previously in \CFA, it has been assumed that assertion arguments must match the parameter type exactly, modulo polymorphic specialization (\ie no implicit conversions are applied to assertion arguments). In the example below:
 \begin{lstlisting}
 int f([int, double], double);
 …
 If assertion arguments must match exactly, then the call to @g@ cannot be resolved, since the expected type of @f@ is flat, while the only @f@ in scope requires a tuple type. Since tuples are fluid, this requirement reduces the usability of tuples in polymorphic code. To ease this pain point, function parameter and return lists are flattened for the purposes of type unification, which allows the previous example to pass expression resolution.
 This relaxation is made possible by extending the existing thunk generation scheme, as described by \citet{Bilson03}. Now, whenever 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:
+This relaxation is made possible by extending the existing thunk generation scheme, as described by~\citet{Bilson03}. Now, whenever 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:
 \begin{lstlisting}
 int _thunk(int _p0, double _p1, double _p2) {
 …
 \subsection{Variadic Tuples}
 To define variadic functions, \CFA{} adds a new kind of type parameter, @ttype@. Matching against a @ttype@ (``tuple type'') parameter consumes all remaining argument components and packages them into a tuple, binding to the resulting tuple of types. In a given parameter list, there should be at most one @ttype@ parameter that must occur last, otherwise the call can never resolve, given the previous rule. This idea essentially matches normal variadic semantics, with a strong feeling of similarity to \CCeleven{} variadic templates. As such, @ttype@ variables are also referred to as \emph{argument} or \emph{parameter packs} in this paper.
+To define variadic functions, \CFA adds a new kind of type parameter, @ttype@. Matching against a @ttype@ (``tuple type'') parameter consumes all remaining argument components and packages them into a tuple, binding to the resulting tuple of types. In a given parameter list, there should be at most one @ttype@ parameter that must occur last, otherwise the call can never resolve, given the previous rule. This idea essentially matches normal variadic semantics, with a strong feeling of similarity to \CCeleven variadic templates. As such, @ttype@ variables are also referred to as \emph{argument} or \emph{parameter packs} in this paper.
 Like variadic templates, the main way to manipulate @ttype@ polymorphic functions is through recursion. Since nothing is known about a parameter pack by default, assertion parameters are key to doing anything meaningful. Unlike variadic templates, @ttype@ polymorphic functions can be separately compiled.
 …
 Effectively, 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))@.
 As a point of note, this version does not require any form of argument descriptor, since the \CFA{} type system keeps track of all of these details. It might be reasonable to take the @sum@ function a step further to enforce a minimum number of arguments:
+As a point of note, this version does not require any form of argument descriptor, since the \CFA type system keeps track of all of these details. It might be reasonable to take the @sum@ function a step further to enforce a minimum number of arguments:
 \begin{lstlisting}
 int sum(int x, int y){
 …
 Pair(int, char) * x = new(42, '!');
 \end{lstlisting}
 The @new@ function provides the combination of type-safe @malloc@ with a constructor call, so that it becomes impossible to forget to construct dynamically allocated objects. This function provides the type-safety of @new@ in \CC{}, without the need to specify the allocated type again, thanks to return-type inference.
+The @new@ function provides the combination of type-safe @malloc@ with a constructor call, so that it becomes impossible to forget to construct dynamically allocated objects. This function provides the type-safety of @new@ in \CC, without the need to specify the allocated type again, thanks to return-type inference.
 In the call to @new@, @Pair(double, char)@ is selected to match @T@, and @Params@ is expanded to match @[double, char]@. The constructor (1) may be specialized to  satisfy the assertion for a constructor with an interface compatible with @void ?{}(Pair(int, char) *, int, char)@.
 …
 \subsection{Implementation}
 Tuples are implemented in the \CFA{} translator via a transformation into generic types. For each $N$, the first time an $N$-tuple is seen in a scope a generic type with $N$ type parameters is generated. For example:
+Tuples are implemented in the \CFA translator via a transformation into generic types. For each $N$, the first time an $N$-tuple is seen in a scope a generic type with $N$ type parameters is generated. For example:
 \begin{lstlisting}
 [int, int] f() {
 …
 Since argument evaluation order is not specified by the C programming language, this scheme is built to work regardless of evaluation order. The first time a unique expression is executed, the actual expression is evaluated and the accompanying boolean is set to true. Every subsequent evaluation of the unique expression then results in an access to the stored result of the actual expression. Tuple member expressions also take advantage of unique expressions in the case of possible impurity.
 Currently, the \CFA{} translator has a very broad, imprecise definition of impurity, where any function call is assumed to be impure. This 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.
 The various kinds of tuple assignment, constructors, and destructors generate GNU C statement expressions. A 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. The 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. However, 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.
+Currently, the \CFA translator has a very broad, imprecise definition of impurity, where any function call is assumed to be impure. This 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.
+The various kinds of tuple assignment, constructors, and destructors generate GNU C statement expressions. A 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. The 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. However, 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.
 \section{Related Work}
 \CC{} is the existing language it is most natural to compare \CFA{} to, as they are both more modern extensions to C with backwards source compatibility. The most fundamental difference in approach between \CC{} and \CFA{} is their approach to this C compatibility. \CC{} does provide fairly strong source backwards compatibility with C, but is a dramatically more complex language than C, and imposes a steep learning curve to use many of its extension features. For instance, in a break from general C practice, template code is typically written in header files, with a variety of subtle restrictions implied on its use by this choice, while the other polymorphism mechanism made available by \CC{}, class inheritance, requires programmers to learn an entirely new object-oriented programming paradigm; the interaction between templates and inheritance is also quite complex. \CFA{}, by contrast, has a single facility for polymorphic code, one which supports separate compilation and the existing procedural paradigm of C code. A major difference between the approaches of \CC{} and \CFA{} to polymorphism is that the set of assumed properties for a type is \emph{explicit} in \CFA{}. One of the major limiting factors of \CC{}'s approach is that templates cannot be separately compiled, and, until concepts \citep{C++Concepts} are standardized (currently anticipated for \CCtwenty{}), \CC{} provides no way to specify the requirements of a generic function in code beyond compilation errors for template expansion failures. By contrast, the explicit nature of assertions in \CFA{} allows polymorphic functions to be separately compiled, and for their requirements to be checked by the compiler; similarly, \CFA{} generic types may be opaque, unlike \CC{} template classes.
 Cyclone also provides capabilities for polymorphic functions and existential types \citep{Gro06}, similar in concept to \CFA{}'s @forall@ functions and generic types. Cyclone 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. Furthermore, Cyclone's polymorphic functions and types are restricted in that they may only abstract over types with the same layout and calling convention as @void*@, in practice only pointer types and @int@ - in \CFA{} terms, all Cyclone polymorphism must be dtype-static. This design provides the efficiency benefits discussed in Section~\ref{sec:generic-apps} for dtype-static polymorphism, but is more restrictive than \CFA{}'s more general model.
 Go and Rust are both modern, compiled languages with abstraction features similar to \CFA{} traits, \emph{interfaces} in Go and \emph{traits} in Rust. However, both languages represent dramatic departures from C in terms of language model, and neither has the same level of compatibility with C as \CFA{}. Go is a garbage-collected language, imposing the associated runtime overhead, and complicating foreign-function calls with the necessity of accounting for data transfer between the managed Go runtime and the unmanaged C runtime. Furthermore, 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. Rust is not garbage-collected, and thus has a lighter-weight runtime that is more easily interoperable with C. It also possesses much more powerful abstraction capabilities for writing generic code than Go. On the other hand, Rust's borrow-checker, while it does provide strong safety guarantees, is complex and difficult to learn, and imposes a distinctly idiomatic programming style on Rust. \CFA{}, with its more modest safety features, is significantly easier to port C code to, while maintaining the idiomatic style of the original source.
+\CC is the existing language it is most natural to compare \CFA to, as they are both more modern extensions to C with backwards source compatibility. The most fundamental difference in approach between \CC and \CFA is their approach to this C compatibility. \CC does provide fairly strong source backwards compatibility with C, but is a dramatically more complex language than C, and imposes a steep learning curve to use many of its extension features. For instance, in a break from general C practice, template code is typically written in header files, with a variety of subtle restrictions implied on its use by this choice, while the other polymorphism mechanism made available by \CC, class inheritance, requires programmers to learn an entirely new object-oriented programming paradigm; the interaction between templates and inheritance is also quite complex. \CFA, by contrast, has a single facility for polymorphic code, one which supports separate compilation and the existing procedural paradigm of C code. A major difference between the approaches of \CC and \CFA to polymorphism is that the set of assumed properties for a type is \emph{explicit} in \CFA. One of the major limiting factors of \CC's approach is that templates cannot be separately compiled, and, until concepts~\citep{C++Concepts} are standardized (currently anticipated for \CCtwenty), \CC provides no way to specify the requirements of a generic function in code beyond compilation errors for template expansion failures. By contrast, the explicit nature of assertions in \CFA allows polymorphic functions to be separately compiled, and for their requirements to be checked by the compiler; similarly, \CFA generic types may be opaque, unlike \CC template classes.
+Cyclone also provides capabilities for polymorphic functions and existential types~\citep{Grossman06}, similar in concept to \CFA's @forall@ functions and generic types. Cyclone 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. Furthermore, Cyclone's polymorphic functions and types are restricted in that they may only abstract over types with the same layout and calling convention as @void*@, in practice only pointer types and @int@ - in \CFA terms, all Cyclone polymorphism must be dtype-static. This design provides the efficiency benefits discussed in Section~\ref{sec:generic-apps} for dtype-static polymorphism, but is more restrictive than \CFA's more general model.
+Go and Rust are both modern, compiled languages with abstraction features similar to \CFA traits, \emph{interfaces} in Go and \emph{traits} in Rust. However, both languages represent dramatic departures from C in terms of language model, and neither has the same level of compatibility with C as \CFA. Go is a garbage-collected language, imposing the associated runtime overhead, and complicating foreign-function calls with the necessity of accounting for data transfer between the managed Go runtime and the unmanaged C runtime. Furthermore, 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. Rust is not garbage-collected, and thus has a lighter-weight runtime that is more easily interoperable with C. It also possesses much more powerful abstraction capabilities for writing generic code than Go. On the other hand, Rust's borrow-checker, while it does provide strong safety guarantees, is complex and difficult to learn, and imposes a distinctly idiomatic programming style on Rust. \CFA, with its more modest safety features, is significantly easier to port C code to, while maintaining the idiomatic style of the original source.
 \section{Conclusion \& Future Work}
 In conclusion, the authors' design for generic types and tuples imposes minimal runtime overhead while still supporting a full range of C features, including separately-compiled modules. There is ongoing work on a wide range of \CFA{} feature extensions, including reference types, exceptions, and concurrent programming primitives. In addition to this work, there are some interesting future directions the polymorphism design could take. Notably, \CC{} template functions trade compile time and code bloat for optimal runtime of individual instantiations of polymorphic functions. \CFA{} polymorphic functions, by contrast, use an approach that is essentially dynamic virtual dispatch. The runtime overhead of this approach is low, but not as low as \CC{} template functions, and it may be beneficial to provide a mechanism for particularly performance-sensitive code to close this gap. Further research is needed, but two promising approaches are to allow an annotation on polymorphic function call sites that tells the translator to create a template-specialization of the function (provided the code is visible in the current translation unit) or placing an annotation on polymorphic function definitions that instantiates a version of the polymorphic function specialized to some set of types. These approaches are not mutually exclusive, and would allow these performance optimizations to be applied only where most useful to increase performance, without suffering the code bloat or loss of generality of a template expansion approach where it is unnecessary.
+In conclusion, the authors' design for generic types and tuples imposes minimal runtime overhead while still supporting a full range of C features, including separately-compiled modules. There is ongoing work on a wide range of \CFA feature extensions, including reference types, exceptions, and concurrent programming primitives. In addition to this work, there are some interesting future directions the polymorphism design could take. Notably, \CC template functions trade compile time and code bloat for optimal runtime of individual instantiations of polymorphic functions. \CFA polymorphic functions, by contrast, use an approach that is essentially dynamic virtual dispatch. The runtime overhead of this approach is low, but not as low as \CC template functions, and it may be beneficial to provide a mechanism for particularly performance-sensitive code to close this gap. Further research is needed, but two promising approaches are to allow an annotation on polymorphic function call sites that tells the translator to create a template-specialization of the function (provided the code is visible in the current translation unit) or placing an annotation on polymorphic function definitions that instantiates a version of the polymorphic function specialized to some set of types. These approaches are not mutually exclusive, and would allow these performance optimizations to be applied only where most useful to increase performance, without suffering the code bloat or loss of generality of a template expansion approach where it is unnecessary.
 \begin{acks}
 …
 \bibliographystyle{ACM-Reference-Format}
 \bibliography{generic_types}
+\bibliography{cfa}
 \end{document}
+% Local Variables: %
+% tab-width: 4 %
+% compile-command: "make" %
+% End: %

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