source: doc/papers/general/Paper.tex @ 3fd3bda

\documentclass[AMA,STIX1COL]{WileyNJD-v2}

\articletype{RESEARCH ARTICLE}%

\received{26 April 2016}
\revised{6 June 2016}
\accepted{6 June 2016}

\raggedbottom

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\title{\texorpdfstring{\protect\CFA : Adding Modern Programming Language Features to C}{Cforall : Adding Modern Programming Language Features to C}}

\author[1]{Aaron Moss}
\author[1]{Robert Schluntz}
\author[1]{Peter A. Buhr*}

\address[1]{\orgdiv{David R. Cheriton School of Computer Science}, \orgname{University of Waterloo}, \orgaddress{\state{Ontario}, \country{Canada}}}

\corres{*Peter A. Buhr, \email{pabuhr{\char`\@}uwaterloo.ca}}
\presentaddress{David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, N2L 3G1, Canada}


\abstract[Summary]{
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.
Nevertheless, 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 but failed to honour C programming-style; for instance, adding object-oriented or functional programming with garbage collection is a non-starter for many C developers.
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 programmers.
This paper presents a quick tour of \CFA features showing how their design avoids shortcomings of similar features in C and other C-like languages.
Finally, experimental results are presented to validate several of the new features.
}%

\keywords{generic types, tuple types, variadic types, polymorphic functions, C, Cforall}


\begin{document}
\linenumbers                                            % comment out to turn off line numbering

\maketitle


\section{Introduction}

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.
The TIOBE~\cite{TIOBE} ranks the top 5 most \emph{popular} programming languages as: Java 15\%, \Textbf{C 12\%}, \Textbf{\CC 5.5\%}, Python 5\%, \Csharp 4.5\% = 42\%, where the next 50 languages are less than 4\% each with a long tail.
The top 3 rankings over the past 30 years are:
\begin{center}
\setlength{\tabcolsep}{10pt}
\lstDeleteShortInline@%
\begin{tabular}{@{}rccccccc@{}}
                & 2018  & 2013  & 2008  & 2003  & 1998  & 1993  & 1988  \\ \hline
Java    & 1             & 2             & 1             & 1             & 18    & -             & -             \\
\Textbf{C}& \Textbf{2} & \Textbf{1} & \Textbf{2} & \Textbf{2} & \Textbf{1} & \Textbf{1} & \Textbf{1} \\
\CC             & 3             & 4             & 3             & 3             & 2             & 2             & 5             \\
\end{tabular}
\lstMakeShortInline@%
\end{center}
Love it or hate it, C is extremely popular, highly used, and one of the few systems languages.
In many cases, \CC is often used solely as a better C.
Nonetheless, C, first standardized over thirty years ago, lacks many features that make programming in more modern languages safer and more productive.

\CFA (pronounced ``C-for-all'', and written \CFA or Cforall) is an evolutionary extension of the C programming language that aims to add modern language features to C while maintaining both source compatibility with C and a familiar programming model for programmers.
The four key design goals for \CFA~\cite{Bilson03} are:
(1) The behaviour of standard C code must remain the same when translated by a \CFA compiler as when translated by a C compiler;
(2) Standard C code must be as fast and as small when translated by a \CFA compiler as when translated by a C compiler;
(3) \CFA code must be at least as portable as standard C code;
(4) Extensions introduced by \CFA must be translated in the most efficient way possible.
These goals ensure existing C code-bases can be converted to \CFA incrementally with minimal effort, and C programmers can productively generate \CFA code without training beyond the features being used.
\CC is used similarly, but has the disadvantages of multiple legacy design-choices that cannot be updated and active divergence of the language model from C, requiring significant effort and training to incrementally add \CC to a C-based project.

\CFA is currently implemented as a source-to-source translator from \CFA to the gcc-dialect of C~\cite{GCCExtensions}, allowing it to leverage the portability and code optimizations provided by gcc, meeting goals (1)--(3).
Ultimately, a compiler is necessary for advanced features and optimal performance.
All features discussed in this paper are working, unless otherwise stated as under construction.

Finally, it is impossible to describe a programming language without usages before definitions.
Therefore, syntax and semantics appear before explanations;
hence, patience is necessary until details are presented.


\section{Polymorphic Functions}

\CFA introduces both ad-hoc and parametric polymorphism to C, with a design originally formalized by Ditchfield~\cite{Ditchfield92}, and first implemented by Bilson~\cite{Bilson03}.
Shortcomings are identified in existing approaches to generic and variadic data types in C-like languages and how these shortcomings are avoided in \CFA.
Specifically, the solution is both reusable and type-checked, as well as conforming to the design goals of \CFA with ergonomic use of existing C abstractions.
The new constructs are empirically compared with C and \CC approaches via performance experiments in Section~\ref{sec:eval}.


\subsection{Name Overloading}
\label{s:NameOverloading}

\begin{quote}
There are only two hard things in Computer Science: cache invalidation and \emph{naming things} -- Phil Karlton
\end{quote}
C already has a limited form of ad-hoc polymorphism in the form of its basic arithmetic operators, which apply to a variety of different types using identical syntax. 
\CFA extends the built-in operator overloading by allowing users to define overloads for any function, not just operators, and even any variable;
Section~\ref{sec:libraries} includes a number of examples of how this overloading simplifies \CFA programming relative to C. 
Code generation for these overloaded functions and variables is implemented by the usual approach of mangling the identifier names to include a representation of their type, while \CFA decides which overload to apply based on the same ``usual arithmetic conversions'' used in C to disambiguate operator overloads.
As an example:

\begin{cfa}
int max = 2147483647;                                   $\C[4in]{// (1)}$
double max = 1.7976931348623157E+308;   $\C{// (2)}$
int max( int a, int b ) { return a < b ? b : a; }  $\C{// (3)}$
double max( double a, double b ) { return a < b ? b : a; }  $\C{// (4)}\CRT$
max( 7, -max );                                         $\C[2.75in]{// uses (3) and (1), by matching int from constant 7}$
max( max, 3.14 );                                       $\C{// uses (4) and (2), by matching double from constant 3.14}$
max( max, -max );                                       $\C{// ERROR: ambiguous}$
int m = max( max, -max );                       $\C{// uses (3) and (1) twice, by matching return type}\CRT$
\end{cfa}

\CFA maximizes the ability to reuse names to aggressively address the naming problem.
In some cases, hundreds of names can be reduced to tens, resulting in a significant cognitive reduction.
In the above, the name @max@ has a consistent meaning, and a programmer only needs to remember the single concept: maximum.
To prevent significant ambiguities, \CFA uses the return type in selecting overloads, \eg in the assignment to @m@, the compiler use @m@'s type to unambiguously select the most appropriate call to function @max@ (as does Ada).
As is shown later, there are a number of situations where \CFA takes advantage of available type information to disambiguate, where other programming languages generate ambiguities.

\Celeven added @_Generic@ expressions, which is used in preprocessor macros to provide a form of ad-hoc polymorphism;
however, this polymorphism is both functionally and ergonomically inferior to \CFA name overloading. 
The macro wrapping the generic expression imposes some limitations;
\eg, it cannot implement the example above, because the variables @max@ are ambiguous with the functions @max@. 
Ergonomic limitations of @_Generic@ include the necessity to put a fixed list of supported types in a single place and manually dispatch to appropriate overloads, as well as possible namespace pollution from the dispatch functions, which must all have distinct names.
For backwards compatibility, \CFA supports @_Generic@ expressions, but it is an unnecessary mechanism. \TODO{actually implement that}

% http://fanf.livejournal.com/144696.html
% http://www.robertgamble.net/2012/01/c11-generic-selections.html
% https://abissell.com/2014/01/16/c11s-_generic-keyword-macro-applications-and-performance-impacts/


\subsection{\texorpdfstring{\protect\lstinline{forall} Functions}{forall Functions}}
\label{sec:poly-fns}

The signature feature of \CFA is parametric-polymorphic functions~\cite{forceone:impl,Cormack90,Duggan96} with functions generalized using a @forall@ clause (giving the language its name):
\begin{cfa}
`forall( otype T )` T identity( T val ) { return val; }
int forty_two = identity( 42 );         $\C{// T is bound to int, forty\_two == 42}$
\end{cfa}
This @identity@ function can be applied to any complete \newterm{object type} (or @otype@).
The type variable @T@ is transformed into a set of additional implicit parameters encoding sufficient information about @T@ to create and return a variable of that type.
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, \eg for a pointer, the type parameter can be declared as a \newterm{data type} (or @dtype@).

In \CFA, the polymorphic runtime-cost is spread over each polymorphic call, because more arguments are passed to polymorphic functions;
the experiments in Section~\ref{sec:eval} show this overhead is similar to \CC virtual-function calls.
A design advantage is that, unlike \CC template-functions, \CFA polymorphic-functions are compatible with C \emph{separate compilation}, preventing compilation and code bloat.

Since bare polymorphic-types provide a restricted set of available operations, \CFA provides a \newterm{type assertion}~\cite[pp.~37-44]{Alphard} mechanism to provide further type information, where type assertions may be variable or function declarations that depend on a polymorphic type-variable.
For example, the function @twice@ can be defined using the \CFA syntax for operator overloading:
\begin{cfa}
forall( otype T `| { T ?+?(T, T); }` ) T twice( T x ) { return x `+` x; }  $\C{// ? denotes operands}$
int val = twice( twice( 3.7 ) );
\end{cfa}
which works for any type @T@ with a matching addition operator.
The polymorphism is achieved by creating a wrapper function for calling @+@ with @T@ bound to @double@, then passing this function to the first call of @twice@.
There is now the option of using the same @twice@ and converting the result to @int@ on assignment, or creating another @twice@ with type parameter @T@ bound to @int@ because \CFA uses the return type~\cite{Cormack81,Baker82,Ada} in its type analysis.
The first approach has a late conversion from @double@ to @int@ on the final assignment, while the second has an eager conversion to @int@.
\CFA minimizes the number of conversions and their potential to lose information, so it selects the first approach, which corresponds with C-programmer intuition.

Crucial to the design of a new programming language are the libraries to access thousands of external software features.
Like \CC, \CFA inherits a massive compatible library-base, where other programming languages must rewrite or provide fragile inter-language communication with C.
A simple example is leveraging the existing type-unsafe (@void *@) C @bsearch@ to binary search a sorted float array:
\begin{cfa}
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 = 5.0, vals[10] = { /* 10 sorted float values */ };
double * val = (double *)bsearch( &key, vals, 10, sizeof(vals[0]), comp ); $\C{// search sorted array}$
\end{cfa}
which can be augmented simply with a generalized, type-safe, \CFA-overloaded wrappers:
\begin{cfa}
forall( otype T | { int ?<?( T, T ); } ) T * bsearch( T key, const T * arr, size_t size ) {
        int comp( const void * t1, const void * t2 ) { /* as above with double changed to T */ }
        return (T *)bsearch( &key, arr, size, sizeof(T), comp );
}
forall( otype T | { int ?<?( T, T ); } ) unsigned int bsearch( T key, const T * arr, size_t size ) {
        T * result = bsearch( key, arr, size ); $\C{// call first version}$
        return result ? result - arr : size; $\C{// pointer subtraction includes sizeof(T)}$
}
double * val = bsearch( 5.0, vals, 10 ); $\C{// selection based on return type}$
int posn = bsearch( 5.0, vals, 10 );
\end{cfa}
The nested function @comp@ provides the hidden interface from typed \CFA to untyped (@void *@) C, plus the cast of the result.
Providing a hidden @comp@ function in \CC is awkward as lambdas do not use C calling-conventions and template declarations cannot appear at block scope.
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 template @bsearch@.

\CFA has replacement libraries condensing hundreds of existing C functions into tens of \CFA overloaded functions, all without rewriting the actual computations (see Section~\ref{sec:libraries}).
For example, it is possible to write a type-safe \CFA wrapper @malloc@ based on the C @malloc@:
\begin{cfa}
forall( dtype T | sized(T) ) T * malloc( void ) { return (T *)malloc( sizeof(T) ); }
int * ip = malloc();                                            $\C{// select type and size from left-hand side}$
double * dp = malloc();
struct S {...} * sp = malloc();
\end{cfa}
where the return type supplies the type/size of the allocation, which is impossible in most type systems.

Call-site inferencing and nested functions provide a localized form of inheritance.
For example, the \CFA @qsort@ only sorts in ascending order using @<@.
However, it is trivial to locally change this behaviour:
\begin{cfa}
forall( otype T | { int ?<?( T, T ); } ) void qsort( const T * arr, size_t size ) { /* use C qsort */ }
{
        int ?<?( double x, double y ) { return x `>` y; } $\C{// locally override behaviour}$
        qsort( vals, size );                                    $\C{// descending sort}$
}
\end{cfa}
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 local environments, adding and modifying appropriate functions, to maximize reuse of other existing functions and types.

Under construction is a mechanism to distribute @forall@ over routines/types, where each block declaration is prefixed with the initial @forall@ clause significantly reducing duplication (see @stack@ examples in Section~\ref{sec:eval}):
\begin{cfa}
forall( otype `T` ) {                                                   $\C{// forall block}$
        struct stack { stack_node(`T`) * head; };       $\C{// generic type}$
        void push( stack(`T`) & s, `T` value ) ...      $\C{// generic operations}$
        T pop( stack(`T`) & s ) ...
}
\end{cfa}


\subsection{Traits}

\CFA provides \newterm{traits} to name a group of type assertions, where the trait name allows specifying the same set of assertions in multiple locations, preventing repetition mistakes at each function declaration:
\begin{cfa}
trait `summable`( otype T ) {
        void ?{}( T *, zero_t );                                $\C{// constructor from 0 literal}$
        T ?+?( T, T );                                                  $\C{// assortment of additions}$
        T ?+=?( T *, T );
        T ++?( T * );
        T ?++( T * );
};
forall( otype T `| summable( T )` ) T sum( T a[$\,$], size_t size ) {  // use trait
        `T` total = { `0` };                                    $\C{// instantiate T from 0 by calling its constructor}$
        for ( unsigned int i = 0; i < size; i += 1 ) total `+=` a[i]; $\C{// select appropriate +}$
        return total;
}
\end{cfa}

In fact, the set of @summable@ trait operators is incomplete, as it is missing assignment for type @T@, but @otype@ is syntactic sugar for the following implicit trait:
\begin{cfa}
trait otype( dtype T | sized(T) ) {  // sized is a 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{cfa}
Given the information provided for an @otype@, variables of polymorphic type can be treated as if they were a complete type: stack-allocatable, default or copy-initialized, assigned, and deleted.

In summation, the \CFA type-system uses \newterm{nominal typing} for concrete types, matching with the C type-system, and \newterm{structural typing} for polymorphic types.
Hence, trait names play no part in type equivalence;
the names are simply macros for a list of polymorphic assertions, which are expanded at usage sites.
Nevertheless, trait names form a logical subtype-hierarchy with @dtype@ at the top, where traits often contain overlapping assertions, \eg operator @+@.
Traits are used like interfaces in Java or abstract base-classes in \CC, but without the nominal inheritance-relationships.
Instead, each polymorphic function (or generic type) defines the structural type needed for its execution (polymorphic type-key), and this key is fulfilled at each call site from the lexical environment, which is similar to Go~\cite{Go} interfaces.
Hence, new lexical scopes and nested functions are used extensively to create local subtypes, as in the @qsort@ example, without having to manage a nominal-inheritance hierarchy.
(Nominal inheritance can be approximated with traits using marker variables or functions, as is done in Go.)

% Nominal inheritance can be simulated with traits using marker variables or functions:
% \begin{cfa}
% trait nominal(otype T) {
%     T is_nominal;
% };
% int is_nominal;                                                               $\C{// int now satisfies the nominal trait}$
% \end{cfa}
%
% Traits, however, are significantly more powerful than nominal-inheritance interfaces; most notably, traits may be used to declare a relationship \emph{among} multiple types, a property that may be difficult or impossible to represent in nominal-inheritance type systems:
% \begin{cfa}
% trait pointer_like(otype Ptr, otype El) {
%     lvalue El *?(Ptr);                                                $\C{// Ptr can be dereferenced into a modifiable value of type El}$
% }
% struct list {
%     int value;
%     list * next;                                                              $\C{// may omit "struct" on type names as in \CC}$
% };
% typedef list * list_iterator;
%
% lvalue int *?( list_iterator it ) { return it->value; }
% \end{cfa}
% 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.


\section{Generic Types}

A significant shortcoming of standard C is the lack of reusable type-safe abstractions for generic data structures and algorithms.
Broadly speaking, there are three approaches to implement abstract 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, \eg the C standard-library functions @bsearch@ and @qsort@, which allow reuse of code with common functionality.
However, basing all polymorphism on @void *@ eliminates the type-checker's ability to ensure that argument types are properly matched, often requiring a number of extra function parameters, pointer indirection, and dynamic allocation that is not otherwise needed.
A third approach to generic code is to use preprocessor macros, which does allow the generated code to be both generic and type-checked, but errors may be difficult to interpret.
Furthermore, writing and using preprocessor macros is unnatural and inflexible.

\CC, Java, and other languages use \newterm{generic types} to produce type-safe abstract data-types.
\CFA also implements generic types that integrate efficiently and naturally with the existing polymorphic functions, while retaining backwards compatibility with C and providing separate compilation.
However, for known concrete parameters, the generic-type definition can be inlined, like \CC templates.

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:
\begin{cfa}
forall( otype R, otype S ) struct pair {
        R first;
        S second;
};
forall( otype T ) T value( pair( const char *, T ) p ) { return p.second; } $\C{// dynamic}$
forall( dtype F, otype T ) T value( pair( F *, T * ) p ) { return *p.second; } $\C{// dtype-static (concrete)}$

pair( const char *, int ) p = { "magic", 42 }; $\C{// concrete}$
int i = value( p );
pair( void *, int * ) q = { 0, &p.second }; $\C{// concrete}$
i = value( q );
double d = 1.0;
pair( double *, double * ) r = { &d, &d }; $\C{// concrete}$
d = value( r );
\end{cfa}

\CFA classifies generic types as either \newterm{concrete} or \newterm{dynamic}.
Concrete types have a fixed memory layout regardless of type parameters, while dynamic types vary in memory layout depending on their type parameters.
A \newterm{dtype-static} type has polymorphic parameters but is still concrete.
Polymorphic pointers are an example of dtype-static types, \eg @forall(dtype T) T *@ is a polymorphic type, but for any @T@, @T *@  is a fixed-sized pointer, and therefore, can be represented by a @void *@ in code generation.

\CFA generic types also allow checked argument-constraints.
For example, the following declaration of a sorted set-type ensures the set key supports equality and relational comparison:
\begin{cfa}
forall( otype Key | { _Bool ?==?(Key, Key); _Bool ?<?(Key, Key); } ) struct sorted_set;
\end{cfa}


\subsection{Concrete Generic-Types}

The \CFA translator template-expands concrete generic-types into new structure types, affording maximal inlining.
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 structure declarations where appropriate.
A function declaration that accepts or returns a concrete generic-type produces a declaration for the instantiated structure in the same scope, which all callers may reuse.
For example, the concrete instantiation for @pair( const char *, int )@ is:
\begin{cfa}
struct _pair_conc0 {
        const char * first;
        int second;
};
\end{cfa}

A concrete generic-type with dtype-static parameters is also expanded to a structure type, but this type is used for all matching instantiations.
In the above example, the @pair( F *, T * )@ parameter to @value@ is such a type; its expansion is below and it is used as the type of the variables @q@ and @r@ as well, with casts for member access where appropriate:
\begin{cfa}
struct _pair_conc1 {
        void * first;
        void * second;
};
\end{cfa}


\subsection{Dynamic Generic-Types}

Though \CFA implements concrete generic-types efficiently, it also has a fully general system for 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-types also have an \newterm{offset array} containing structure-member offsets.
A dynamic generic-@union@ needs no such offset array, as all members are at offset 0, but size and alignment are still necessary.
Access to members of a dynamic structure is provided at runtime via base-displacement addressing with the structure pointer and the member offset (similar to the @offsetof@ macro), moving a compile-time offset calculation to runtime.

The 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 the generic type is complete (\ie 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, the body of the second @value@ function is implemented as:
\begin{cfa}
_assign_T( _retval, p + _offsetof_pair[1] ); $\C{// return *p.second}$
\end{cfa}
@_assign_T@ is passed in as an implicit parameter from @otype T@, and takes two @T *@ (@void *@ in the generated code), a destination and a source; @_retval@ is the pointer to a caller-allocated buffer for the return value, the usual \CFA method to handle dynamically-sized return types.
@_offsetof_pair@ is the offset array passed into @value@; this array is generated at the call site as:
\begin{cfa}
size_t _offsetof_pair[] = { offsetof( _pair_conc0, first ), offsetof( _pair_conc0, second ) }
\end{cfa}

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 structure and associated accessor and mutator functions in a header file, with the actual implementations in a separately-compiled @.c@ file.
\CFA supports this pattern for generic types, but the caller does not know the actual layout or size of the dynamic generic-type, and only holds it by a pointer.
The \CFA translator automatically generates \newterm{layout functions} for cases where the size, alignment, and offset array of a generic struct cannot be passed into a function from that function's caller.
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 structure (un@sized@ parameters are forbidden 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@.
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)@ likely has a pointer to the vector as its only explicit parameter, but uses 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 solely on the @forall@'s type parameters.
This design allows opaque forward declarations of generic types, \eg @forall(otype T)@ @struct Box@ -- like in C, all uses of @Box(T)@ can be separately compiled, and callers from other translation units know the proper calling conventions to use.
If the definition of a structure type is included in deciding whether a generic type is dynamic or concrete, some further types may be recognized as dtype-static (\eg @forall(otype T)@ @struct unique_ptr { T * p }@ does not depend on @T@ for its layout, but the existence of an @otype@ parameter means that it \emph{could}.), but preserving separate compilation (and the associated C compatibility) in the existing design is judged to be an appropriate trade-off.


\subsection{Applications}
\label{sec:generic-apps}

The reuse of dtype-static structure instantiations enables useful programming patterns at zero runtime cost.
The most important such pattern is using @forall(dtype T) T *@ as a type-checked replacement for @void *@, \eg creating a lexicographic comparison for pairs of pointers used by @bsearch@ or @qsort@:
\begin{cfa}
forall( dtype T ) int lexcmp( pair( T *, T * ) * a, pair( T *, T * ) * b, int (* cmp)( T *, T * ) ) {
        return cmp( a->first, b->first ) ? : cmp( a->second, b->second );
}
\end{cfa}
Since @pair( T *, T * )@ is a concrete type, there are no implicit parameters passed to @lexcmp@, so the generated code is identical to a function written in standard C using @void *@, yet the \CFA version is type-checked to ensure the fields of both pairs and the arguments to the comparison function match in type.

Another useful pattern enabled by reused dtype-static type instantiations is zero-cost \newterm{tag-structures}.
Sometimes information is only used for type-checking and can be omitted at runtime, \eg:
\begin{cfa}
forall( dtype Unit ) struct scalar { unsigned long value; };
struct metres {};
struct litres {};

forall( dtype U ) scalar(U) ?+?( scalar(U) a, scalar(U) b ) {
        return (scalar(U)){ a.value + b.value };
}
scalar(metres) half_marathon = { 21093 };
scalar(litres) swimming_pool = { 2500000 };
scalar(metres) marathon = half_marathon + half_marathon;
scalar(litres) two_pools = swimming_pool + swimming_pool;
marathon + swimming_pool;                                       $\C{// compilation ERROR}$
\end{cfa}
@scalar@ is a dtype-static type, so all uses have a single structure definition, containing @unsigned long@, and can share the same implementations of common functions like @?+?@.
These implementations may even be separately compiled, unlike \CC template functions.
However, the \CFA type-checker ensures matching types are used by all calls to @?+?@, preventing nonsensical computations like adding a length to a volume.


\section{Tuples}
\label{sec:tuples}

In many languages, functions can return at most one value;
however, many operations have multiple outcomes, some exceptional.
Consider C's @div@ and @remquo@ functions, which return the quotient and remainder for a division of integer and float values, respectively.
\begin{cfa}
typedef struct { int quo, rem; } div_t;         $\C{// from include stdlib.h}$
div_t div( int num, int den );
double remquo( double num, double den, int * quo );
div_t qr = div( 13, 5 );                                        $\C{// return quotient/remainder aggregate}$
int q;
double r = remquo( 13.5, 5.2, &q );                     $\C{// return remainder, alias quotient}$
\end{cfa}
@div@ aggregates the quotient/remainder in a structure, while @remquo@ aliases a parameter to an argument.
Both approaches are awkward.
Alternatively, a programming language can directly support returning multiple values, \eg in \CFA:
\begin{cfa}
[ int, int ] div( int num, int den );           $\C{// return two integers}$
[ double, double ] div( double num, double den ); $\C{// return two doubles}$
int q, r;                                                                       $\C{// overloaded variable names}$
double q, r;
[ q, r ] = div( 13, 5 );                                        $\C{// select appropriate div and q, r}$
[ q, r ] = div( 13.5, 5.2 );                            $\C{// assign into tuple}$
\end{cfa}
This approach is straightforward to understand and use;
therefore, why do few programming languages support this obvious feature or provide it awkwardly?
To answer, there are complex consequences that cascade through multiple aspects of the language, especially the type-system.
This section show these consequences and how \CFA handles them.


\subsection{Tuple Expressions}

The addition of multiple-return-value functions (MRVF) are \emph{useless} without a syntax for accepting multiple values at the call-site.
The simplest mechanism for capturing the return values is variable assignment, allowing the values to be retrieved directly.
As such, \CFA allows assigning multiple values from a function into multiple variables, using a square-bracketed list of lvalue expressions (as above), called a \newterm{tuple}.

However, functions also use \newterm{composition} (nested calls), with the direct consequence that MRVFs must also support composition to be orthogonal with single-returning-value functions (SRVF), \eg:
\begin{cfa}
printf( "%d %d\n", div( 13, 5 ) );                      $\C{// return values seperated into arguments}$
\end{cfa}
Here, the values returned by @div@ are composed with the call to @printf@ by flattening the tuple into separate arguments.
However, the \CFA type-system must support significantly more complex composition:
\begin{cfa}
[ int, int ] foo$\(_1\)$( int );                        $\C{// overloaded foo functions}$
[ double ] foo$\(_2\)$( int );
void bar( int, double, double );
`bar`( foo( 3 ), foo( 3 ) );
\end{cfa}
The type-resolver only has the tuple return-types to resolve the call to @bar@ as the @foo@ parameters are identical, which involves unifying the possible @foo@ functions with @bar@'s parameter list.
No combination of @foo@s are an exact match with @bar@'s parameters, so the resolver applies C conversions.
The minimal cost is @bar( foo@$_1$@( 3 ), foo@$_2$@( 3 ) )@, giving (@int@, {\color{ForestGreen}@int@}, @double@) to (@int@, {\color{ForestGreen}@double@}, @double@) with one {\color{ForestGreen}safe} (widening) conversion from @int@ to @double@ versus ({\color{red}@double@}, {\color{ForestGreen}@int@}, {\color{ForestGreen}@int@}) to ({\color{red}@int@}, {\color{ForestGreen}@double@}, {\color{ForestGreen}@double@}) with one {\color{red}unsafe} (narrowing) conversion from @double@ to @int@ and two safe conversions.


\subsection{Tuple Variables}

An important observation from function composition is that new variable names are not required to initialize parameters from an MRVF.
\CFA also allows declaration of tuple variables that can be initialized from an MRVF, since it can be awkward to declare multiple variables of different types, \eg:
\begin{cfa}
[ int, int ] qr = div( 13, 5 );                         $\C{// tuple-variable declaration and initialization}$
[ double, double ] qr = div( 13.5, 5.2 );
\end{cfa}
where the tuple variable-name serves the same purpose as the parameter name(s).
Tuple variables can be composed of any types, except for array types, since array sizes are generally unknown in C.

One way to access the tuple-variable components is with assignment or composition:
\begin{cfa}
[ q, r ] = qr;                                                          $\C{// access tuple-variable components}$
printf( "%d %d\n", qr );
\end{cfa}
\CFA also supports \newterm{tuple indexing} to access single components of a tuple expression:
\begin{cfa}
[int, int] * p = &qr;                                           $\C{// tuple pointer}$
int rem = qr`.1`;                                                       $\C{// access remainder}$
int quo = div( 13, 5 )`.0`;                                     $\C{// access quotient}$
p`->0` = 5;                                                                     $\C{// change quotient}$
bar( qr`.1`, qr );                                                      $\C{// pass remainder and quotient/remainder}$
rem = [div( 13, 5 ), 42]`.0.1`;                         $\C{// access 2nd component of 1st component}$
\end{cfa}


\subsection{Flattening and Restructuring}

In function call contexts, tuples support implicit flattening and restructuring conversions.
Tuple flattening recursively expands a tuple into the list of its basic components.
Tuple structuring packages a list of expressions into a value of tuple type, \eg:
\begin{cfa}
int f( int, int );
int g( [int, int] );
int h( int, [int, int] );
[int, int] x;
int y;
f( x );                                                                         $\C{// flatten}$
g( y, 10 );                                                                     $\C{// structure}$
h( x, y );                                                                      $\C{// flatten and structure}$
\end{cfa}
In the call to @f@, @x@ is implicitly flattened so the components of @x@ are passed as the two arguments.
In the call to @g@, the values @y@ and @10@ are structured into a single argument of type @[int, int]@ to match the parameter type of @g@.
Finally, in the call to @h@, @x@ is flattened to yield an argument list of length 3, of which the first component of @x@ is passed as the first parameter of @h@, and the second component of @x@ and @y@ are structured into the second argument of type @[int, int]@.
The flexible structure of tuples permits a simple and expressive function call syntax to work seamlessly with both SRVF and MRVF, and with any number of arguments of arbitrarily complex structure.


\subsection{Tuple Assignment}

An assignment where the left side is a tuple type is called \newterm{tuple assignment}.
There are two kinds of tuple assignment depending on whether the right side of the assignment operator has a tuple type or a non-tuple type, called \newterm{multiple} and \newterm{mass assignment}, respectively.
\begin{cfa}
int x = 10;
double y = 3.5;
[int, double] z;
z = [x, y];                                                                     $\C{// multiple assignment}$
[x, y] = z;                                                                     $\C{// multiple assignment}$
z = 10;                                                                         $\C{// mass assignment}$
[y, x] = 3.14;                                                          $\C{// mass assignment}$
\end{cfa}
Both kinds of tuple assignment have parallel semantics, so that each value on the left and right side is evaluated 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, \eg, @[x, y] = [y, x]@.
This semantics means mass assignment differs from C cascading assignment (\eg @a = b = c@) in that conversions are applied in each individual assignment, which prevents data loss from the chain of conversions that can happen during a cascading assignment.
For example, @[y, x] = 3.14@ performs the assignments @y = 3.14@ and @x = 3.14@, yielding @y == 3.14@ and @x == 3@;
whereas, C cascading assignment @y = x = 3.14@ performs the assignments @x = 3.14@ and @y = x@, yielding @3@ in @y@ and @x@.
Finally, 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 example shows mass, multiple, and cascading assignment used in one expression:
\begin{cfa}
void f( [int, int] );
f( [x, y] = z = 1.5 );                                          $\C{// assignments in parameter list}$
\end{cfa}


\subsection{Member Access}

It is also possible to access multiple fields from a single expression using a \newterm{member-access}.
The result is a single tuple-valued expression whose type is the tuple of the types of the members, \eg:
\begin{cfa}
struct S { int x; double y; char * z; } s;
s.[x, y, z] = 0;
\end{cfa}
Here, the mass assignment sets all members of @s@ to zero.
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, drop, and duplicate components).
\begin{cfa}
[int, int, long, double] x;
void f( double, long );
x.[0, 1] = x.[1, 0];                                            $\C{// rearrange: [x.0, x.1] = [x.1, x.0]}$
f( x.[0, 3] );                                                          $\C{// drop: f(x.0, x.3)}$
[int, int, int] y = x.[2, 0, 2];                        $\C{// duplicate: [y.0, y.1, y.2] = [x.2, x.0.x.2]}$
\end{cfa}
It is also possible for a member access to contain other member accesses, \eg:
\begin{cfa}
struct A { double i; int j; };
struct B { int * k; short l; };
struct C { int x; A y; B z; } v;
v.[x, y.[i, j], z.k];                                           $\C{// [v.x, [v.y.i, v.y.j], v.z.k]}$
\end{cfa}


\begin{comment}
\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:
\begin{cfa}
int f();     // (1)
double f();  // (2)

f();       // ambiguous - (1),(2) both equally viable
(int)f();  // choose (2)
\end{cfa}

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{cfa}
int f();
void g();

(void)f();  // (1)
(int)g();  // (2)
\end{cfa}
In C, (1) is a valid cast, which calls @f@ and discards its result.
On the other hand, (2) is invalid, because @g@ does not produce a result, so requesting an @int@ to materialize from nothing is nonsensical.
Generalizing these principles, any cast wherein the number of components increases as a result of the cast is invalid, while casts that have the same or fewer number of components may be valid.

Formally, a cast to tuple type is valid when $T_n \leq S_m$, where $T_n$ is the number of components in the target type and $S_m$ is the number of components in the source type, and for each $i$ in $[0, n)$, $S_i$ can be cast to $T_i$.
Excess elements ($S_j$ for all $j$ in $[n, m)$) are evaluated, but their values are discarded so that they are not included in the result expression.
This approach follows naturally from the way that a cast to @void@ works in C.

For example, in
\begin{cfa}
[int, int, int] f();
[int, [int, int], int] g();

([int, double])f();           $\C{// (1)}$
([int, int, int])g();         $\C{// (2)}$
([void, [int, int]])g();      $\C{// (3)}$
([int, int, int, int])g();    $\C{// (4)}$
([int, [int, int, int]])g();  $\C{// (5)}$
\end{cfa}

(1) discards the last element of the return value and converts the second element to @double@.
Since @int@ is effectively a 1-element tuple, (2) discards the second component of the second element of the return value of @g@.
If @g@ is free of side effects, this expression is equivalent to @[(int)(g().0), (int)(g().1.0), (int)(g().2)]@.
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 requires 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]@.
\end{comment}


\subsection{Polymorphism}

Tuples also integrate with \CFA polymorphism as a kind 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, \eg:
\begin{cfa}
forall( otype T, dtype U ) void f( T x, U * y );
f( [5, "hello"] );
\end{cfa}
where @[5, "hello"]@ is flattened, giving argument list @5, "hello"@, and @T@ binds to @int@ and @U@ binds to @const char@.
Tuples, however, may contain polymorphic components.
For example, a plus operator can be written to sum two triples.
\begin{cfa}
forall( otype T | { T ?+?( T, T ); } ) [T, T, T] ?+?( [T, T, T] x, [T, T, T] y ) {
        return [x.0 + y.0, x.1 + y.1, x.2 + y.2];
}
[int, int, int] x;
int i1, i2, i3;
[i1, i2, i3] = x + ([10, 20, 30]);
\end{cfa}

Flattening and restructuring conversions are also applied to tuple types in polymorphic type assertions.
\begin{cfa}
int f( [int, double], double );
forall( otype T, otype U | { T f( T, U, U ); } ) void g( T, U );
g( 5, 10.21 );
\end{cfa}
Hence, function parameter and return lists are flattened for the purposes of type unification allowing the example to pass expression resolution.
This relaxation is possible by extending the thunk scheme described by Bilson~\cite{Bilson03}.
% 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{cfa}
% int _thunk( int _p0, double _p1, double _p2 ) { return f( [_p0, _p1], _p2 ); }
% \end{cfa}
% so the thunk provides flattening and structuring conversions to inferred functions, improving the compatibility of tuples and polymorphism.
% These thunks are generated locally using gcc nested-functions, rather hoisting them to the external scope, so they can easily access local state.


\subsection{Variadic Tuples}
\label{sec:variadic-tuples}

To define variadic functions, \CFA adds a new kind of type parameter, @ttype@ (tuple type).
Matching against a @ttype@ 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 must be at most one @ttype@ parameter that occurs last, which matches normal variadic semantics, with a strong feeling of similarity to \CCeleven variadic templates.
As such, @ttype@ variables are also called \newterm{argument packs}.

Like variadic templates, @ttype@ polymorphic functions are primarily manipulated via 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.
For example, a generalized @sum@ function:
\begin{cfa}
int sum$\(_0\)$() { return 0; }
forall( ttype Params | { int sum( Params ); } ) int sum$\(_1\)$( int x, Params rest ) {
        return x + sum( rest );
}
sum( 10, 20, 30 );
\end{cfa}
Since @sum@\(_0\) does not accept any arguments, it is not a valid candidate function for the call @sum(10, 20, 30)@.
In order to call @sum@\(_1\), @10@ is matched with @x@, and the argument resolution moves on to the argument pack @rest@, which consumes the remainder of the argument list and @Params@ is bound to @[20, 30]@.
The process continues until @Params@ is bound to @[]@, requiring an assertion @int sum()@, which matches @sum@\(_0\) and terminates the recursion.
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))@.

It is reasonable to take the @sum@ function a step further to enforce a minimum number of arguments:
\begin{cfa}
int sum( int x, int y ) { return x + y; }
forall( ttype Params | { int sum( int, Params ); } ) int sum( int x, int y, Params rest ) {
        return sum( x + y, rest );
}
\end{cfa}
One more step permits the summation of any summable type with all arguments of the same type:
\begin{cfa}
trait summable( otype T ) {
        T ?+?( T, T );
};
forall( otype R | summable( R ) ) R sum( R x, R y ) {
        return x + y;
}
forall( otype R, ttype Params | summable(R) | { R sum(R, Params); } ) R sum(R x, R y, Params rest) {
        return sum( x + y, rest );
}
\end{cfa}
Unlike C variadic functions, it is unnecessary to hard code the number and expected types.
Furthermore, this code is extendable for any user-defined type with a @?+?@ operator.
Summing arbitrary heterogeneous lists is possible with similar code by adding the appropriate type variables and addition operators.

It is also possible to write a type-safe variadic print function to replace @printf@:
\begin{cfa}
struct S { int x, y; };
forall( otype T, ttype Params | { void print(T); void print(Params); } ) void print(T arg, Params rest) {
        print(arg);  print(rest);
}
void print( const char * x ) { printf( "%s", x ); }
void print( int x ) { printf( "%d", x ); }
void print( S s ) { print( "{ ", s.x, ",", s.y, " }" ); }
print( "s = ", (S){ 1, 2 }, "\n" );
\end{cfa}
This example showcases a variadic-template-like decomposition of the provided argument list.
The individual @print@ functions allow printing a single element of a type.
The polymorphic @print@ allows printing any list of types, where as each individual type has a @print@ function.
The individual print functions can be used to build up more complicated @print@ functions, such as @S@, which cannot be done with @printf@ in C.
This mechanism is used to seamlessly print tuples in the \CFA I/O library (see Section~\ref{s:IOLibrary}).

Finally, it is possible to use @ttype@ polymorphism to provide arbitrary argument forwarding functions.
For example, it is possible to write @new@ as a library function:
\begin{cfa}
forall( otype R, otype S ) void ?{}( pair(R, S) *, R, S );
forall( dtype T, ttype Params | sized(T) | { void ?{}( T *, Params ); } ) T * new( Params p ) {
        return ((T *)malloc()){ p };                    $\C{// construct into result of malloc}$
}
pair( int, char ) * x = new( 42, '!' );
\end{cfa}
The @new@ function provides the combination of type-safe @malloc@ with a \CFA constructor call, making it impossible to forget constructing 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.


\subsection{Implementation}

Tuples are implemented in the \CFA translator via a transformation into \newterm{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, \eg:
\begin{cfa}
[int, int] f() {
        [double, double] x;
        [int, double, int] y;
}
\end{cfa}
is transformed into:
\begin{cfa}
forall( dtype T0, dtype T1 | sized(T0) | sized(T1) ) struct _tuple2 {
        T0 field_0;                                                             $\C{// generated before the first 2-tuple}$
        T1 field_1;
};
_tuple2(int, int) f() {
        _tuple2(double, double) x;
        forall( dtype T0, dtype T1, dtype T2 | sized(T0) | sized(T1) | sized(T2) ) struct _tuple3 {
                T0 field_0;                                                     $\C{// generated before the first 3-tuple}$
                T1 field_1;
                T2 field_2;
        };
        _tuple3(int, double, int) y;
}
\end{cfa}
{\sloppy
Tuple expressions are then simply converted directly into compound literals, \eg @[5, 'x', 1.24]@ becomes @(_tuple3(int, char, double)){ 5, 'x', 1.24 }@.
\par}%

\begin{comment}
Since tuples are essentially structures, tuple indexing expressions are just field accesses:
\begin{cfa}
void f(int, [double, char]);
[int, double] x;

x.0+x.1;
printf("%d %g\n", x);
f(x, 'z');
\end{cfa}
Is transformed into:
\begin{cfa}
void f(int, _tuple2(double, char));
_tuple2(int, double) x;

x.field_0+x.field_1;
printf("%d %g\n", x.field_0, x.field_1);
f(x.field_0, (_tuple2){ x.field_1, 'z' });
\end{cfa}
Note that due to flattening, @x@ used in the argument position is converted into the list of its fields.
In the call to @f@, the second and third argument components are structured into a tuple argument.
Similarly, tuple member expressions are recursively expanded into a list of member access expressions.

Expressions that may contain side effects are made into \newterm{unique expressions} before being expanded by the flattening conversion.
Each unique expression is assigned an identifier and is guaranteed to be executed exactly once:
\begin{cfa}
void g(int, double);
[int, double] h();
g(h());
\end{cfa}
Internally, this expression is converted to two variables and an expression:
\begin{cfa}
void g(int, double);
[int, double] h();

_Bool _unq0_finished_ = 0;
[int, double] _unq0;
g(
        (_unq0_finished_ ? _unq0 : (_unq0 = f(), _unq0_finished_ = 1, _unq0)).0,
        (_unq0_finished_ ? _unq0 : (_unq0 = f(), _unq0_finished_ = 1, _unq0)).1,
);
\end{cfa}
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.
\end{comment}


\section{Control Structures}

\CFA identifies inconsistent, problematic, and missing control structures in C, and extends, modifies, and adds control structures to increase functionality and safety.


\subsection{\texorpdfstring{\protect\lstinline{if} Statement}{if Statement}}

The @if@ expression allows declarations, similar to @for@ declaration expression:
\begin{cfa}
if ( int x = f() ) ...                                          $\C{// x != 0}$
if ( int x = f(), y = g() ) ...                         $\C{// x != 0 \&\& y != 0}$
if ( int x = f(), y = g(); `x < y` ) ...        $\C{// relational expression}$
\end{cfa}
Unless a relational expression is specified, each variable is compared not equal to 0, which is the standard semantics for the @if@ expression, and the results are combined using the logical @&&@ operator.\footnote{\CC only provides a single declaration always compared not equal to 0.}
The scope of the declaration(s) is local to the @if@ statement but exist within both the ``then'' and ``else'' clauses.


\subsection{\texorpdfstring{\protect\lstinline{switch} Statement}{switch Statement}}

There are a number of deficiencies with the C @switch@ statements: enumerating @case@ lists, placement of @case@ clauses, scope of the switch body, and fall through between case clauses.

C has no shorthand for specifying a list of case values, whether the list is non-contiguous or contiguous\footnote{C provides this mechanism via fall through.}.
\CFA provides a shorthand for a non-contiguous list:
\begin{cquote}
\lstDeleteShortInline@%
\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
\begin{cfa}
case 2, 10, 34, 42:
\end{cfa}
&
\begin{cfa}
case 2: case 10: case 34: case 42:
\end{cfa}
\end{tabular}
\lstMakeShortInline@%
\end{cquote}
for a contiguous list:\footnote{gcc has the same mechanism but awkward syntax, \lstinline@2 ...42@, because a space is required after a number, otherwise the period is a decimal point.}
\begin{cquote}
\lstDeleteShortInline@%
\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
\begin{cfa}
case 2~42:
\end{cfa}
&
\begin{cfa}
case 2: case 3: ... case 41: case 42:
\end{cfa}
\end{tabular}
\lstMakeShortInline@%
\end{cquote}
and a combination:
\begin{cfa}
case -12~-4, -1~5, 14~21, 34~42:
\end{cfa}

C allows placement of @case@ clauses \emph{within} statements nested in the @switch@ body (called Duff's device~\cite{Duff83});
\begin{cfa}
switch ( i ) {
  case 0:
        for ( int i = 0; i < 10; i += 1 ) {
                ...
  `case 1:`             // no initialization of loop index
                ...
        }
}
\end{cfa}
\CFA precludes this form of transfer \emph{into} a control structure because it causes undefined behaviour, especially with respect to missed initialization, and provides very limited functionality.

C allows placement of declaration within the @switch@ body and unreachable code at the start, resulting in undefined behaviour:
\begin{cfa}
switch ( x ) {
        `int y = 1;`                                                    $\C{// unreachable initialization}$
        `x = 7;`                                                                $\C{// unreachable code without label/branch}$
  case 0:
        ...
        `int z = 0;`                                                    $\C{// unreachable initialization, cannot appear after case}$
        z = 2;
  case 1:
        `x = z;`                                                                $\C{// without fall through, z is undefined}$
}
\end{cfa}
\CFA allows the declaration of local variables, \eg @y@, at the start of the @switch@ with scope across the entire @switch@ body, \ie all @case@ clauses.
\CFA disallows the declaration of local variable, \eg @z@, directly within the @switch@ body, because a declaration cannot occur immediately after a @case@ since a label can only be attached to a statement, and the use of @z@ is undefined in @case 1@ as neither storage allocation nor initialization may have occurred.

C @switch@ provides multiple entry points into the statement body, but once an entry point is selected, control continues across \emph{all} @case@ clauses until the end of the @switch@ body, called \newterm{fall through};
@case@ clauses are made disjoint by the @break@ statement.
While fall through \emph{is} a useful form of control flow, it does not match well with programmer intuition, resulting in errors from missing @break@ statements.
For backwards compatibility, \CFA provides a \emph{new} control structure, @choose@, which mimics @switch@, but reverses the meaning of fall through (see Figure~\ref{f:ChooseSwitchStatements}), similar to Go.

\begin{figure}
\centering
\lstDeleteShortInline@%
\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
\begin{cfa}
`choose` ( day ) {
  case Mon~Thu:  // program

  case Fri:  // program
        wallet += pay;
        `fallthrough;`
  case Sat:  // party
        wallet -= party;

  case Sun:  // rest

  default:  // error
}
\end{cfa}
&
\begin{cfa}
switch ( day ) {
  case Mon: case Tue: case Wed: case Thu:  // program
        `break;`
  case Fri:  // program
        wallet += pay;

  case Sat:  // party
        wallet -= party;
        `break;`
  case Sun:  // rest
        `break;`
  default:  // error
}
\end{cfa}
\end{tabular}
\lstMakeShortInline@%
\caption{\lstinline|choose| versus \lstinline|switch| Statements}
\label{f:ChooseSwitchStatements}
\end{figure}

Finally, Figure~\ref{f:FallthroughStatement} shows @fallthrough@ may appear in contexts other than terminating a @case@ clause, and have an explicit transfer label allowing separate cases but common final-code for a set of cases.
The target label must be below the @fallthrough@, \ie @fallthrough@ cannot form a loop, and the label may not be nested in a control structure, \ie it must be at the same level as the @case@ clauses;
the target label may be case @default@.

\begin{figure}
\centering
\lstDeleteShortInline@%
\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{non-terminator}}  & \multicolumn{1}{c}{\textbf{target label}}     \\
\begin{cfa}
choose ( ... ) {
  case 3:
        if ( ... ) {
                ... `fallthrough;`  // goto case 4
        } else {
                ...
        }
        // implicit break
  case 4:
\end{cfa}
&
\begin{cfa}
choose ( ... ) {
  case 3:
        ... `fallthrough common;`
  case 4:
        ... `fallthrough common;`
  common: // below fallthrough at same level as case clauses
        ...      // common code for cases 3 and 4
        // implicit break
  case 4:
\end{cfa}
\end{tabular}
\lstMakeShortInline@%
\caption{\lstinline|fallthrough| Statement}
\label{f:FallthroughStatement}
\end{figure}

Collectively, these control-structure enhancements reduce programmer burden and increase readability and safety.


\subsection{\texorpdfstring{Labelled \protect\lstinline{continue} / \protect\lstinline{break}}{Labelled continue / break}}

While C provides @continue@ and @break@ statements for altering control flow, both are restricted to one level of nesting for a particular control structure.
Unfortunately, this restriction forces programmers to use @goto@ to achieve the equivalent control-flow for more than one level of nesting.
To prevent having to switch to the @goto@, \CFA extends the @continue@ and @break@ with a target label to support static multi-level exit~\cite{Buhr85}, as in Java.
For both @continue@ and @break@, the target label must be directly associated with a @for@, @while@ or @do@ statement;
for @break@, the target label can also be associated with a @switch@, @if@ or compound (@{}@) statement.
Figure~\ref{f:MultiLevelExit} shows @continue@ and @break@ indicating the specific control structure, and the corresponding C program using only @goto@ and labels.
The innermost loop has 7 exit points, which cause continuation or termination of one or more of the 7 nested control-structures.

\begin{figure}
\lstDeleteShortInline@%
\begin{tabular}{@{\hspace{\parindentlnth}}l@{\hspace{\parindentlnth}}l@{\hspace{\parindentlnth}}l@{}}
\multicolumn{1}{@{\hspace{\parindentlnth}}c@{\hspace{\parindentlnth}}}{\textbf{\CFA}}   & \multicolumn{1}{@{\hspace{\parindentlnth}}c}{\textbf{C}}      \\
\begin{cfa}
`LC:` {
        ... $declarations$ ...
        `LS:` switch ( ... ) {
          case 3:
                `LIF:` if ( ... ) {
                        `LF:` for ( ... ) {
                                `LW:` while ( ... ) {
                                        ... break `LC`; ...
                                        ... break `LS`; ...
                                        ... break `LIF`; ...
                                        ... continue `LF;` ...
                                        ... break `LF`; ...
                                        ... continue `LW`; ...
                                        ... break `LW`; ...
                                } // while
                        } // for
                } else {
                        ... break `LIF`; ...
                } // if
        } // switch
} // compound
\end{cfa}
&
\begin{cfa}
{
        ... $declarations$ ...
        switch ( ... ) {
          case 3:
                if ( ... ) {
                        for ( ... ) {
                                while ( ... ) {
                                        ... goto `LC`; ...
                                        ... goto `LS`; ...
                                        ... goto `LIF`; ...
                                        ... goto `LFC`; ...
                                        ... goto `LFB`; ...
                                        ... goto `LWC`; ...
                                        ... goto `LWB`; ...
                                  `LWC`: ; } `LWB:` ;
                          `LFC:` ; } `LFB:` ;
                } else {
                        ... goto `LIF`; ...
                } `LIF:` ;
        } `LS:` ;
} `LC:` ;
\end{cfa}
&
\begin{cfa}







// terminate compound
// terminate switch
// terminate if
// continue loop
// terminate loop
// continue loop
// terminate loop



// terminate if



\end{cfa}
\end{tabular}
\lstMakeShortInline@%
\caption{Multi-level Exit}
\label{f:MultiLevelExit}
\end{figure}

With respect to safety, both labelled @continue@ and @break@ are a @goto@ restricted in the following ways:
\begin{itemize}
\item
They cannot create a loop, which means only the looping constructs cause looping.
This restriction means all situations resulting in repeated execution are clearly delineated.
\item
They cannot branch into a control structure.
This restriction prevents missing declarations and/or initializations at the start of a control structure resulting in undefined behaviour.
\end{itemize}
The advantage of the labelled @continue@/@break@ is allowing static multi-level exits without having to use the @goto@ statement, and tying control flow to the target control structure rather than an arbitrary point in a program.
Furthermore, the location of the label at the \emph{beginning} of the target control structure informs the reader (eye candy) that complex control-flow is occurring in the body of the control structure.
With @goto@, the label is at the end of the control structure, which fails to convey this important clue early enough to the reader.
Finally, using an explicit target for the transfer instead of an implicit target allows new constructs to be added or removed without affecting existing constructs.
Otherwise, the implicit targets of the current @continue@ and @break@, \ie the closest enclosing loop or @switch@, change as certain constructs are added or removed.


\subsection{Exception Handling}

The following framework for \CFA exception handling is in place, excluding some runtime type-information and virtual functions.
\CFA provides two forms of exception handling: \newterm{fix-up} and \newterm{recovery} (see Figure~\ref{f:CFAExceptionHandling})~\cite{Buhr92b,Buhr00a}.
Both mechanisms provide dynamic call to a handler using dynamic name-lookup, where fix-up has dynamic return and recovery has static return from the handler.
\CFA restricts exception types to those defined by aggregate type @exception@.
The form of the raise dictates the set of handlers examined during propagation: \newterm{resumption propagation} (@resume@) only examines resumption handlers (@catchResume@); \newterm{terminating propagation} (@throw@) only examines termination handlers (@catch@).
If @resume@ or @throw@ have no exception type, it is a reresume/rethrow, meaning the currently exception continues propagation.
If there is no current exception, the reresume/rethrow results in a runtime error.

\begin{figure}
\begin{cquote}
\lstDeleteShortInline@%
\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{Resumption}}      & \multicolumn{1}{c}{\textbf{Termination}}      \\
\begin{cfa}
`exception R { int fix; };`
void f() {
        R r;
        ... `resume( r );` ...
        ... r.fix // control returns here after handler
}
`try` {
        ... f(); ...
} `catchResume( R r )` {
        ... r.fix = ...; // return correction to raise
} // dynamic return to _Resume
\end{cfa}
&
\begin{cfa}
`exception T {};`
void f() {

        ... `throw( T{} );` ...
        // control does NOT return here after handler
}
`try` {
        ... f(); ...
} `catch( T t )` {
        ... // recover and continue
} // static return to next statement
\end{cfa}
\end{tabular}
\lstMakeShortInline@%
\end{cquote}
\caption{\CFA Exception Handling}
\label{f:CFAExceptionHandling}
\end{figure}

The set of exception types in a list of catch clause may include both a resumption and termination handler:
\begin{cfa}
try {
        ... resume( `R{}` ); ...
} catchResume( `R` r ) { ... throw( R{} ); ... } $\C{\color{red}// H1}$
   catch( `R` r ) { ... }                                       $\C{\color{red}// H2}$

\end{cfa}
The resumption propagation raises @R@ and the stack is not unwound;
the exception is caught by the @catchResume@ clause and handler H1 is invoked.
The termination propagation in handler H1 raises @R@ and the stack is unwound;
the exception is caught by the @catch@ clause and handler H2 is invoked.
The termination handler is available because the resumption propagation did not unwind the stack.

An additional feature is conditional matching in a catch clause:
\begin{cfa}
try {
        ... write( `datafile`, ... ); ...               $\C{// may throw IOError}$
        ... write( `logfile`, ... ); ...
} catch ( IOError err; `err.file == datafile` ) { ... } $\C{// handle datafile error}$
   catch ( IOError err; `err.file == logfile` ) { ... } $\C{// handle logfile error}$
   catch ( IOError err ) { ... }                        $\C{// handler error from other files}$
\end{cfa}
where the throw inserts the failing file-handle into the I/O exception.
Conditional catch cannot be trivially mimicked by other mechanisms because once an exception is caught, handler clauses in that @try@ statement are no longer eligible..

The resumption raise can specify an alternate stack on which to raise an exception, called a \newterm{nonlocal raise}:
\begin{cfa}
resume( $\emph{exception-type}$, $\emph{alternate-stack}$ )
resume( $\emph{alternate-stack}$ )
\end{cfa}
These overloads of @resume@ raise the specified exception or the currently propagating exception (reresume) at another \CFA coroutine or task\footnote{\CFA coroutine and concurrency features are discussed in a separately submitted paper.}~\cite{Delisle18}.
Nonlocal raise is restricted to resumption to provide the exception handler the greatest flexibility because processing the exception does not unwind its stack, allowing it to continue after the handler returns.

To facilitate nonlocal raise, \CFA provides dynamic enabling and disabling of nonlocal exception-propagation.
The constructs for controlling propagation of nonlocal exceptions are the @enable@ and the @disable@ blocks:
\begin{cquote}
\lstDeleteShortInline@%
\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
\begin{cfa}
enable $\emph{exception-type-list}$ {
        // allow non-local raise
}
\end{cfa}
&
\begin{cfa}
disable $\emph{exception-type-list}$ {
        // disallow non-local raise
}
\end{cfa}
\end{tabular}
\lstMakeShortInline@%
\end{cquote}
The arguments for @enable@/@disable@ specify the exception types allowed to be propagated or postponed, respectively.
Specifying no exception type is shorthand for specifying all exception types.
Both @enable@ and @disable@ blocks can be nested, turning propagation on/off on entry, and on exit, the specified exception types are restored to their prior state.
Coroutines and tasks start with non-local exceptions disabled, allowing handlers to be put in place, before non-local exceptions are explicitly enabled.
\begin{cfa}
void main( mytask & t ) {                                       $\C{// thread starts here}$
        // non-local exceptions disabled
        try {                                                                   $\C{// establish handles for non-local exceptions}$
                enable {                                                        $\C{// allow non-local exception delivery}$
                        // task body
                }
        // appropriate catchResume/catch handlers
        }
}
\end{cfa}

Finally, \CFA provides a Java like  @finally@ clause after the catch clauses:
\begin{cfa}
try {
        ... f(); ...
// catchResume or catch clauses
} `finally` {
        // house keeping
}
\end{cfa}
The finally clause is always executed, i.e., if the try block ends normally or if an exception is raised.
If an exception is raised and caught, the handler is run before the finally clause.
Like a destructor (see Section~\ref{s:ConstructorsDestructors}), a finally clause can raise an exception but not if there is an exception being propagated.
Mimicking the @finally@ clause with mechanisms like RAII is non-trivially when there are multiple types and local accesses.


\subsection{\texorpdfstring{\protect\lstinline{with} Statement}{with Statement}}
\label{s:WithStatement}

Grouping heterogeneous data into \newterm{aggregate}s (structure/union) is a common programming practice, and an aggregate can be further organized into more complex structures, such as arrays and containers:
\begin{cfa}
struct S {                                                                      $\C{// aggregate}$
        char c;                                                                 $\C{// fields}$
        int i;
        double d;
};
S s, as[10];
\end{cfa}
However, functions manipulating aggregates must repeat the aggregate name to access its containing fields:
\begin{cfa}
void f( S s ) {
        `s.`c; `s.`i; `s.`d;                                    $\C{// access containing fields}$
}
\end{cfa}
which extends to multiple levels of qualification for nested aggregates.
A similar situation occurs in object-oriented programming, \eg \CC:
\begin{C++}
struct S {
        char c;                                                                 $\C{// fields}$
        int i;
        double d;
        void f() {                                                              $\C{// implicit ``this'' aggregate}$
                `this->`c; `this->`i; `this->`d;        $\C{// access containing fields}$
        }
}
\end{C++}
Object-oriented nesting of member functions in a \lstinline[language=C++]@class/struct@ allows eliding \lstinline[language=C++]@this->@ because of lexical scoping.
However, for other aggregate parameters, qualification is necessary:
\begin{cfa}
struct T { double m, n; };
int S::f( T & t ) {                                                     $\C{// multiple aggregate parameters}$
        c; i; d;                                                                $\C{\color{red}// this--{\textgreater}.c, this--{\textgreater}.i, this--{\textgreater}.d}$
        `t.`m; `t.`n;                                                   $\C{// must qualify}$
}
\end{cfa}

To simplify the programmer experience, \CFA provides a @with@ statement (see Pascal~\cite[\S~4.F]{Pascal}) to elide aggregate qualification to fields by opening a scope containing the field identifiers.
Hence, the qualified fields become variables with the side-effect that it is easier to optimizing field references in a block.
\begin{cfa}
void f( S & this ) `with ( this )` {            $\C{// with statement}$
        c; i; d;                                                                $\C{\color{red}// this.c, this.i, this.d}$
}
\end{cfa}
with the generality of opening multiple aggregate-parameters:
\begin{cfa}
void f( S & s, T & t ) `with ( s, t )` {                $\C{// multiple aggregate parameters}$
        c; i; d;                                                                $\C{\color{red}// s.c, s.i, s.d}$
        m; n;                                                                   $\C{\color{red}// t.m, t.n}$
}
\end{cfa}

In detail, the @with@ statement has the form:
\begin{cfa}
$\emph{with-statement}$:
        'with' '(' $\emph{expression-list}$ ')' $\emph{compound-statement}$
\end{cfa}
and may appear as the body of a function or nested within a function body.
Each expression in the expression-list provides a type and object.
The type must be an aggregate type.
(Enumerations are already opened.)
The object is the implicit qualifier for the open structure-fields.

All expressions in the expression list are open in parallel within the compound statement.
This semantic is different from Pascal, which nests the openings from left to right.
The difference between parallel and nesting occurs for fields with the same name and type:
\begin{cfa}
struct S { int `i`; int j; double m; } s, w;
struct T { int `i`; int k; int m; } t, w;
with ( s, t ) {
        j + k;                                                                  $\C{// unambiguous, s.j + t.k}$
        m = 5.0;                                                                $\C{// unambiguous, t.m = 5.0}$
        m = 1;                                                                  $\C{// unambiguous, s.m = 1}$
        int a = m;                                                              $\C{// unambiguous, a = s.i }$
        double b = m;                                                   $\C{// unambiguous, b = t.m}$
        int c = s.i + t.i;                                              $\C{// unambiguous, qualification}$
        (double)m;                                                              $\C{// unambiguous, cast}$
}
\end{cfa}
For parallel semantics, both @s.i@ and @t.i@ are visible, so @i@ is ambiguous without qualification;
for nested semantics, @t.i@ hides @s.i@, so @i@ implies @t.i@.
\CFA's ability to overload variables means fields with the same name but different types are automatically disambiguated, eliminating most qualification when opening multiple aggregates.
Qualification or a cast is used to disambiguate.

There is an interesting problem between parameters and the function-body @with@, \eg:
\begin{cfa}
void ?{}( S & s, int i ) with ( s ) {           $\C{// constructor}$
        `s.i = i;`  j = 3;  m = 5.5;                    $\C{// initialize fields}$
}
\end{cfa}
Here, the assignment @s.i = i@ means @s.i = s.i@, which is meaningless, and there is no mechanism to qualify the parameter @i@, making the assignment impossible using the function-body @with@.
To solve this problem, parameters are treated like an initialized aggregate:
\begin{cfa}
struct Params {
        S & s;
        int i;
} params;
\end{cfa}
and implicitly opened \emph{after} a function-body open, to give them higher priority:
\begin{cfa}
void ?{}( S & s, int `i` ) with ( s ) `with( $\emph{\color{red}params}$ )` {
        s.i = `i`; j = 3; m = 5.5;
}
\end{cfa}
Finally, a cast may be used to disambiguate among overload variables in a @with@ expression:
\begin{cfa}
with ( w ) { ... }                                                      $\C{// ambiguous, same name and no context}$
with ( (S)w ) { ... }                                           $\C{// unambiguous, cast}$
\end{cfa}
and @with@ expressions may be complex expressions with type reference (see Section~\ref{s:References}) to aggregate:
\begin{cfa}
struct S { int i, j; } sv;
with ( sv ) {                                                           $\C{// implicit reference}$
        S & sr = sv;
        with ( sr ) {                                                   $\C{// explicit reference}$
                S * sp = &sv;
                with ( *sp ) {                                          $\C{// computed reference}$
                        i = 3; j = 4;                                   $\C{\color{red}// sp--{\textgreater}i, sp--{\textgreater}j}$
                }
                i = 2; j = 3;                                           $\C{\color{red}// sr.i, sr.j}$
        }
        i = 1; j = 2;                                                   $\C{\color{red}// sv.i, sv.j}$
}
\end{cfa}


\section{Declarations}

Declarations in C have weaknesses and omissions.
\CFA attempts to correct and add to C declarations, while ensuring \CFA subjectively ``feels like'' C.
An important part of this subjective feel is maintaining C's syntax and procedural paradigm, as opposed to functional and object-oriented approaches in other systems languages such as \CC and Rust.
Maintaining the C approach means that C coding-patterns remain not only useable but idiomatic in \CFA, reducing the mental burden of retraining C programmers and switching between C and \CFA development.
Nevertheless, some features from other approaches are undeniably convenient;
\CFA attempts to adapt these features to the C paradigm.


\subsection{Alternative Declaration Syntax}

C declaration syntax is notoriously confusing and error prone.
For example, many C programmers are confused by a declaration as simple as:
\begin{cquote}
\lstDeleteShortInline@%
\begin{tabular}{@{}ll@{}}
\begin{cfa}
int * x[5]
\end{cfa}
&
\raisebox{-0.75\totalheight}{\input{Cdecl}}
\end{tabular}
\lstMakeShortInline@%
\end{cquote}
Is this an array of 5 pointers to integers or a pointer to an array of 5 integers?
If there is any doubt, it implies productivity and safety issues even for basic programs.
Another example of confusion results from the fact that a function name and its parameters are embedded within the return type, mimicking the way the return value is used at the function's call site.
For example, a function returning a pointer to an array of integers is defined and used in the following way:
\begin{cfa}
int `(*`f`())[`5`]` {...};                                      $\C{// definition}$
 ... `(*`f`())[`3`]` += 1;                                      $\C{// usage}$
\end{cfa}
Essentially, the return type is wrapped around the function name in successive layers (like an onion).
While attempting to make the two contexts consistent is a laudable goal, it has not worked out in practice.

\CFA provides its own type, variable and function declarations, using a different syntax~\cite[pp.~856--859]{Buhr94a}.
The new declarations place qualifiers to the left of the base type, while C declarations place qualifiers to the right.
The qualifiers have the same meaning but are ordered left to right to specify a variable's type.
\begin{cquote}
\lstDeleteShortInline@%
\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{\hspace{2\parindentlnth}}l@{}}
\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
\begin{cfa}
`[5] *` int x1;
`* [5]` int x2;
`[* [5] int]` f( int p );
\end{cfa}
&
\begin{cfa}
int `*` x1 `[5]`;
int `(*`x2`)[5]`;
`int (*`f( int p )`)[5]`;
\end{cfa}
&
\begin{cfa}
// array of 5 pointers to int
// pointer to array of 5 int
// function returning pointer to array of 5 int and taking int
\end{cfa}
\end{tabular}
\lstMakeShortInline@%
\end{cquote}
The only exception is bit field specification, which always appear to the right of the base type.
% Specifically, the character @*@ is used to indicate a pointer, square brackets @[@\,@]@ are used to represent an array or function return value, and parentheses @()@ are used to indicate a function parameter.
However, unlike C, \CFA type declaration tokens are distributed across all variables in the declaration list.
For instance, variables @x@ and @y@ of type pointer to integer are defined in \CFA as follows:
\begin{cquote}
\lstDeleteShortInline@%
\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
\begin{cfa}
`*` int x, y;
int y;
\end{cfa}
&
\begin{cfa}
int `*`x, `*`y;

\end{cfa}
\end{tabular}
\lstMakeShortInline@%
\end{cquote}
The downside of the \CFA semantics is the need to separate regular and pointer declarations.

\begin{comment}
Other examples are:
\begin{cquote}
\lstDeleteShortInline@%
\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{\hspace{2\parindentlnth}}l@{}}
\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{C}}     \\
\begin{cfa}
[ 5 ] int z;
[ 5 ] * char w;
* [ 5 ] double v;
struct s {
        int f0:3;
        * int f1;
        [ 5 ] * int f2;
};
\end{cfa}
&
\begin{cfa}
int z[ 5 ];
char * w[ 5 ];
double (* v)[ 5 ];
struct s {
        int f0:3;
        int * f1;
        int * f2[ 5 ]
};
\end{cfa}
&
\begin{cfa}
// array of 5 integers
// array of 5 pointers to char
// pointer to array of 5 doubles

// common bit field syntax



\end{cfa}
\end{tabular}
\lstMakeShortInline@%
\end{cquote}
\end{comment}

All specifiers (@extern@, @static@, \etc) and qualifiers (@const@, @volatile@, \etc) are used in the normal way with the new declarations and also appear left to right, \eg:
\begin{cquote}
\lstDeleteShortInline@%
\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{\hspace{2\parindentlnth}}l@{}}
\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{C}}     \\
\begin{cfa}
extern const * const int x;
static const * [5] const int y;
\end{cfa}
&
\begin{cfa}
int extern const * const x;
static const int (* const y)[5]
\end{cfa}
&
\begin{cfa}
// external const pointer to const int
// internal const pointer to array of 5 const int
\end{cfa}
\end{tabular}
\lstMakeShortInline@%
\end{cquote}
Specifiers must appear at the start of a \CFA function declaration\footnote{\label{StorageClassSpecifier}
The placement of a storage-class specifier other than at the beginning of the declaration specifiers in a declaration is an obsolescent feature.~\cite[\S~6.11.5(1)]{C11}}.

The new declaration syntax can be used in other contexts where types are required, \eg casts and the pseudo-function @sizeof@:
\begin{cquote}
\lstDeleteShortInline@%
\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
\begin{cfa}
y = (* int)x;
i = sizeof([ 5 ] * int);
\end{cfa}
&
\begin{cfa}
y = (int *)x;
i = sizeof(int * [ 5 ]);
\end{cfa}
\end{tabular}
\lstMakeShortInline@%
\end{cquote}

The syntax of the new function-prototype declaration follows directly from the new function-definition syntax;
as well, parameter names are optional, \eg:
\begin{cfa}
[ int x ] f ( /* void */ );             $\C[2.5in]{// returning int with no parameters}$
[ int x ] f (...);                              $\C{// returning int with unknown parameters}$
[ * int ] g ( int y );                  $\C{// returning pointer to int with int parameter}$
[ void ] h ( int, char );               $\C{// returning no result with int and char parameters}$
[ * int, int ] j ( int );               $\C{// returning pointer to int and int with int parameter}$
\end{cfa}
This syntax allows a prototype declaration to be created by cutting and pasting source text from the function-definition header (or vice versa).
Like C, it is possible to declare multiple function-prototypes in a single declaration, where the return type is distributed across \emph{all} function names in the declaration list, \eg:
\begin{cquote}
\lstDeleteShortInline@%
\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
\begin{cfa}
[double] foo(), foo( int ), foo( double ) {...}
\end{cfa}
&
\begin{cfa}
double foo1( void ), foo2( int ), foo3( double );
\end{cfa}
\end{tabular}
\lstMakeShortInline@%
\end{cquote}
where \CFA allows the last function in the list to define its body.

The syntax for pointers to \CFA functions specifies the pointer name on the right, \eg:
\begin{cfa}
* [ int x ] () fp;                              $\C{// pointer to function returning int with no parameters}$
* [ * int ] ( int y ) gp;               $\C{// pointer to function returning pointer to int with int parameter}$
* [ ] ( int, char ) hp;                 $\C{// pointer to function returning no result with int and char parameters}$
* [ * int, int ] ( int ) jp;    $\C{// pointer to function returning pointer to int and int with int parameter}$
\end{cfa}
Note, a function name cannot be specified:
\begin{cfa}
* [ int x ] f () fp;                    $\C{// function name "f" is disallowed}\CRT$
\end{cfa}

Finally, new \CFA declarations may appear together with C declarations in the same program block, but cannot be mixed within a specific declaration.
Therefore, a programmer has the option of either continuing to use traditional C declarations or take advantage of the new style.
Clearly, both styles need to be supported for some time due to existing C-style header-files, particularly for UNIX-like systems.


\subsection{References}
\label{s:References}

All variables in C have an \newterm{address}, a \newterm{value}, and a \newterm{type};
at the position in the program's memory denoted by the address, there exists a sequence of bits (the value), with the length and semantic meaning of this bit sequence defined by the type.
The C type-system does not always track the relationship between a value and its address;
a value that does not have a corresponding address is called a \newterm{rvalue} (for ``right-hand value''), while a value that does have an address is called a \newterm{lvalue} (for ``left-hand value'').
For example, in @int x; x = 42;@ the variable expression @x@ on the left-hand-side of the assignment is a lvalue, while the constant expression @42@ on the right-hand-side of the assignment is a rvalue.
Despite the nomenclature of ``left-hand'' and ``right-hand'', an expression's classification as lvalue or rvalue is entirely dependent on whether it has an address or not; in imperative programming, the address of a value is used for both reading and writing (mutating) a value, and as such, lvalues can be converted to rvalues and read from, but rvalues cannot be mutated because they lack a location to store the updated value.

Within a lexical scope, lvalue expressions have an \newterm{address interpretation} for writing a value or a \newterm{value interpretation} to read a value.
For example, in @x = y@, @x@ has an address interpretation, while @y@ has a value interpretation.
While this duality of interpretation is useful, C lacks a direct mechanism to pass lvalues between contexts, instead relying on \newterm{pointer types} to serve a similar purpose.
In C, for any type @T@ there is a pointer type @T *@, the value of which is the address of a value of type @T@.
A pointer rvalue can be explicitly \newterm{dereferenced} to the pointed-to lvalue with the dereference operator @*?@, while the rvalue representing the address of a lvalue can be obtained with the address-of operator @&?@.

\begin{cfa}
int x = 1, y = 2, * p1, * p2, ** p3;
p1 = &x;                                                                        $\C{// p1 points to x}$
p2 = &y;                                                                        $\C{// p2 points to y}$
p3 = &p1;                                                                       $\C{// p3 points to p1}$
*p2 = ((*p1 + *p2) * (**p3 - *p1)) / (**p3 - 15);
\end{cfa}

Unfortunately, the dereference and address-of operators introduce a great deal of syntactic noise when dealing with pointed-to values rather than pointers, as well as the potential for subtle bugs because of pointer arithmetic.
For both brevity and clarity, it is desirable for the compiler to figure out how to elide the dereference operators in a complex expression such as the assignment to @*p2@ above.
However, since C defines a number of forms of \newterm{pointer arithmetic}, two similar expressions involving pointers to arithmetic types (\eg @*p1 + x@ and @p1 + x@) may each have well-defined but distinct semantics, introducing the possibility that a programmer may write one when they mean the other, and precluding any simple algorithm for elision of dereference operators.
To solve these problems, \CFA introduces reference types @T &@;
a @T &@ has exactly the same value as a @T *@, but where the @T *@ takes the address interpretation by default, a @T &@ takes the value interpretation by default, as below:

\begin{cfa}
int x = 1, y = 2, & r1, & r2, && r3;
&r1 = &x;                                                                       $\C{// r1 points to x}$
&r2 = &y;                                                                       $\C{// r2 points to y}$
&&r3 = &&r1;                                                            $\C{// r3 points to r2}$
r2 = ((r1 + r2) * (r3 - r1)) / (r3 - 15);       $\C{// implicit dereferencing}$
\end{cfa}

Except for auto-dereferencing by the compiler, this reference example is exactly the same as the previous pointer example.
Hence, a reference behaves like a variable name -- an lvalue expression which is interpreted as a value -- but also has the type system track the address of that value.
One way to conceptualize a reference is via a rewrite rule, where the compiler inserts a dereference operator before the reference variable for each reference qualifier in the reference variable declaration, so the previous example implicitly acts like:

\begin{cfa}
`*`r2 = ((`*`r1 + `*`r2) * (`**`r3 - `*`r1)) / (`**`r3 - 15);
\end{cfa}

References in \CFA are similar to those in \CC, with important improvements, which can be seen in the example above.
Firstly, \CFA does not forbid references to references.
This provides a much more orthogonal design for library implementors, obviating the need for workarounds such as @std::reference_wrapper@.
Secondly, \CFA references are rebindable, whereas \CC references have a fixed address.
\newsavebox{\LstBox}
\begin{lrbox}{\LstBox}
\lstset{basicstyle=\footnotesize\linespread{0.9}\sf}
\begin{cfa}
int & r = *new( int );
...                                                                                     $\C{// non-null reference}$
delete &r;                                                                      $\C{// unmanaged (programmer) memory-management}$
r += 1;                                                                         $\C{// undefined reference}$
\end{cfa}
\end{lrbox}
Rebinding allows \CFA references to be default-initialized (\eg to a null pointer\footnote{
While effort has been made into non-null reference checking in \CC and Java, the exercise seems moot for any non-managed languages (C/\CC), given that it only handles one of many different error situations:
\begin{cquote}
\usebox{\LstBox}
\end{cquote}
}%
) and point to different addresses throughout their lifetime, like pointers.
Rebinding is accomplished by extending the existing syntax and semantics of the address-of operator in C.

In C, the address of a lvalue is always a rvalue, as in general that address is not stored anywhere in memory, and does not itself have an address.
In \CFA, the address of a @T &@ is a lvalue @T *@, as the address of the underlying @T@ is stored in the reference, and can thus be mutated there.
The result of this rule is that any reference can be rebound using the existing pointer assignment semantics by assigning a compatible pointer into the address of the reference, \eg @&r1 = &x;@ above.
This rebinding occurs to an arbitrary depth of reference nesting;
loosely speaking, nested address-of operators produce a nested lvalue pointer up to the depth of the reference. 
These explicit address-of operators can be thought of as ``cancelling out'' the implicit dereference operators, \eg @(&`*`)r1 = &x@ or @(&(&`*`)`*`)r3 = &(&`*`)r1@ or even @(&`*`)r2 = (&`*`)`*`r3@ for @&r2 = &r3@.
More precisely:
\begin{itemize}
\item
if @R@ is an rvalue of type {@T &@$_1 \cdots$@ &@$_r$} where $r \ge 1$ references (@&@ symbols) than @&R@ has type {@T `*`&@$_{\color{red}2} \cdots$@ &@$_{\color{red}r}$}, \\ \ie @T@ pointer with $r-1$ references (@&@ symbols).
        
\item
if @L@ is an lvalue of type {@T &@$_1 \cdots$@ &@$_l$} where $l \ge 0$ references (@&@ symbols) then @&L@ has type {@T `*`&@$_{\color{red}1} \cdots$@ &@$_{\color{red}l}$}, \\ \ie @T@ pointer with $l$ references (@&@ symbols).
\end{itemize}
Since pointers and references share the same internal representation, code using either is equally performant; in fact the \CFA compiler converts references to pointers internally, and the choice between them is made solely on convenience, \eg many pointer or value accesses.

By analogy to pointers, \CFA references also allow cv-qualifiers such as @const@:
\begin{cfa}
const int cx = 5;                                                       $\C{// cannot change cx}$
const int & cr = cx;                                            $\C{// cannot change cr's referred value}$
&cr = &cx;                                                                      $\C{// rebinding cr allowed}$
cr = 7;                                                                         $\C{// ERROR, cannot change cr}$
int & const rc = x;                                                     $\C{// must be initialized, like in \CC}$
&rc = &x;                                                                       $\C{// ERROR, cannot rebind rc}$
rc = 7;                                                                         $\C{// x now equal to 7}$
\end{cfa}
Given that a reference is meant to represent a lvalue, \CFA provides some syntactic shortcuts when initializing references.
There are three initialization contexts in \CFA: declaration initialization, argument/parameter binding, and return/temporary binding.
In each of these contexts, the address-of operator on the target lvalue is elided.
The syntactic motivation is clearest when considering overloaded operator-assignment, \eg @int ?+=?(int &, int)@; given @int x, y@, the expected call syntax is @x += y@, not @&x += y@.

More generally, this initialization of references from lvalues rather than pointers is an instance of a ``lvalue-to-reference'' conversion rather than an elision of the address-of operator;
this conversion is used in any context in \CFA where an implicit conversion is allowed.
Similarly, use of a the value pointed to by a reference in an rvalue context can be thought of as a ``reference-to-rvalue'' conversion, and \CFA also includes a qualifier-adding ``reference-to-reference'' conversion, analogous to the @T *@ to @const T *@ conversion in standard C.
The final reference conversion included in \CFA is ``rvalue-to-reference'' conversion, implemented by means of an implicit temporary.
When an rvalue is used to initialize a reference, it is instead used to initialize a hidden temporary value with the same lexical scope as the reference, and the reference is initialized to the address of this temporary.
\begin{cfa}
struct S { double x, y; };
int i, j;
void f( int & i, int & j, S & s, int v[] );
f( 3, i + j, (S){ 1.0, 7.0 }, (int [3]){ 1, 2, 3 } );   $\C{// pass rvalue to lvalue \(\Rightarrow\) implicit temporary}$
\end{cfa}
This allows complex values to be succinctly and efficiently passed to functions, without the syntactic overhead of explicit definition of a temporary variable or the runtime cost of pass-by-value.
\CC allows a similar binding, but only for @const@ references; the more general semantics of \CFA are an attempt to avoid the \newterm{const hell} problem, in which addition of a @const@ qualifier to one reference requires a cascading chain of added qualifiers.


\subsection{Type Nesting}

Nested types provide a mechanism to organize associated types and refactor a subset of fields into a named aggregate (\eg sub-aggregates @name@, @address@, @department@, within aggregate @employe@).
Java nested types are dynamic (apply to objects), \CC are static (apply to the \lstinline[language=C++]@class@), and C hoists (refactors) nested types into the enclosing scope, meaning there is no need for type qualification.
Since \CFA in not object-oriented, adopting dynamic scoping does not make sense;
instead \CFA adopts \CC static nesting, using the field-selection operator ``@.@'' for type qualification, as does Java, rather than the \CC type-selection operator ``@::@'' (see Figure~\ref{f:TypeNestingQualification}).
\begin{figure}
\centering
\lstDeleteShortInline@%
\begin{tabular}{@{}l@{\hspace{3em}}l|l@{}}
\multicolumn{1}{c@{\hspace{3em}}}{\textbf{C Type Nesting}}      & \multicolumn{1}{c}{\textbf{C Implicit Hoisting}}      & \multicolumn{1}{|c}{\textbf{\CFA}}    \\
\hline
\begin{cfa}
struct S {
        enum C { R, G, B };
        struct T {
                union U { int i, j; };
                enum C c;
                short int i, j;
        };
        struct T t;
} s;

int rtn() {
        s.t.c = R;
        struct T t = { R, 1, 2 };
        enum C c;
        union U u;
}
\end{cfa}
&
\begin{cfa}
enum C { R, G, B };
union U { int i, j; };
struct T {
        enum C c;
        short int i, j;
};
struct S {
        struct T t;
} s;
        






\end{cfa}
&
\begin{cfa}
struct S {
        enum C { R, G, B };
        struct T {
                union U { int i, j; };
                enum C c;
                short int i, j;
        };
        struct T t;
} s;

int rtn() {
        s.t.c = `S.`R;  // type qualification
        struct `S.`T t = { `S.`R, 1, 2 };
        enum `S.`C c;
        union `S.T.`U u;
}
\end{cfa}
\end{tabular}
\lstMakeShortInline@%
\caption{Type Nesting / Qualification}
\label{f:TypeNestingQualification}
\end{figure}
In the C left example, types @C@, @U@ and @T@ are implicitly hoisted outside of type @S@ into the containing block scope.
In the \CFA right example, the types are not hoisted and accessible.


\subsection{Constructors and Destructors}
\label{s:ConstructorsDestructors}

One of the strengths (and weaknesses) of C is memory-management control, allowing resource release to be precisely specified versus unknown release with garbage-collected memory-management.
However, this manual approach is often verbose, and it is useful to manage resources other than memory (\eg file handles) using the same mechanism as memory.
\CC addresses these issues using Resource Aquisition Is Initialization (RAII), implemented by means of \newterm{constructor} and \newterm{destructor} functions;
\CFA adopts constructors and destructors (and @finally@) to facilitate RAII.
While constructors and destructors are a common feature of object-oriented programming-languages, they are an independent capability allowing \CFA to adopt them while retaining a procedural paradigm.
Specifically, \CFA constructors and destructors are denoted by name and first parameter-type versus name and nesting in an aggregate type.
Constructor calls seamlessly integrate with existing C initialization syntax, providing a simple and familiar syntax to C programmers and allowing constructor calls to be inserted into legacy C code with minimal code changes.

In \CFA, a constructor is named @?{}@ and a destructor is named @^?{}@\footnote{%
The symbol \lstinline+^+ is used for the destructor name because it was the last binary operator that could be used in a unary context.}.
The name @{}@ comes from the syntax for the initializer: @struct S { int i, j; } s = `{` 2, 3 `}`@.
Like other \CFA operators, these names represent the syntax used to call the constructor or destructor, \eg @?{}(x, ...)@ or @^{}(x, ...)@.
The constructor and destructor have return type @void@, and the first parameter is a reference to the object type to be constructed or destructed.
While the first parameter is informally called the @this@ parameter, as in object-oriented languages, any variable name may be used.
Both constructors and destructors allow additional parametes after the @this@ parameter for specifying values for initialization/de-initialization\footnote{
Destruction parameters are useful for specifying storage-management actions, such as de-initialize but not deallocate.}.
\begin{cfa}
struct VLA { int len, * data; };
void ?{}( VLA & vla ) with ( vla ) { len = 10;  data = alloc( len ); }  $\C{// default constructor}$
void ^?{}( VLA & vla ) with ( vla ) { free( data ); } $\C{// destructor}$
{
        VLA x;                                                                  $\C{// implicit:  ?\{\}( x );}$
}                                                                                       $\C{// implicit:  ?\^{}\{\}( x );}$
\end{cfa}
@VLA@ is a \newterm{managed type}\footnote{
A managed type affects the runtime environment versus a self-contained type.}: a type requiring a non-trivial constructor or destructor, or with a field of a managed type. 
A managed type is implicitly constructed at allocation and destructed at deallocation to ensure proper interaction with runtime resources, in this case, the @data@ array in the heap. 
For details of the code-generation placement of implicit constructor and destructor calls among complex executable statements see~\cite[\S~2.2]{Schluntz17}.

\CFA also provides syntax for \newterm{initialization} and \newterm{copy}:
\begin{cfa}
void ?{}( VLA & vla, int size, char fill ) with ( vla ) {  $\C{// initialization}$
        len = size;  data = alloc( len, fill );
}
void ?{}( VLA & vla, VLA other ) {                      $\C{// copy, shallow}$
        vla.len = other.len;  vla.data = other.data;
}
\end{cfa}
(Note, the example is purposely simplified using shallow-copy semantics.)
An initialization constructor-call has the same syntax as a C initializer, except the initialization values are passed as arguments to a matching constructor (number and type of paremeters).
\begin{cfa}
VLA va = `{` 20, 0 `}`,  * arr = alloc()`{` 5, 0 `}`; 
\end{cfa}
Note, the use of a \newterm{constructor expression} to initialize the storage from the dynamic storage-allocation.
Like \CC, the copy constructor has two parameters, the second of which is a value parameter with the same type as the first parameter;
appropriate care is taken to not recursively call the copy constructor when initializing the second parameter.

\CFA constructors may be explicitly call, like Java, and destructors may be explicitly called, like \CC.
Explicit calls to constructors double as a \CC-style \emph{placement syntax}, useful for construction of member fields in user-defined constructors and reuse of existing storage allocations.
While existing call syntax works for explicit calls to constructors and destructors, \CFA also provides a more concise \newterm{operator syntax} for both:
\begin{cfa}
{
        VLA  x,            y = { 20, 0x01 },     z = y; $\C{// z points to y}$
        //      ?{}( x );  ?{}( y, 20, 0x01 );  ?{}( z, y ); 
        ^x{};                                                                   $\C{// deallocate x}$
        x{};                                                                    $\C{// reallocate x}$
        z{ 5, 0xff };                                                   $\C{// reallocate z, not pointing to y}$
        ^y{};                                                                   $\C{// deallocate y}$
        y{ x };                                                                 $\C{// reallocate y, points to x}$
        x{};                                                                    $\C{// reallocate x, not pointing to y}$
        // ^?{}(z);  ^?{}(y);  ^?{}(x);
}
\end{cfa}

To provide a uniform type interface for @otype@ polymorphism, the \CFA compiler automatically generates a default constructor, copy constructor, assignment operator, and destructor for all types. 
These default functions can be overridden by user-generated versions. 
For compatibility with the standard behaviour of C, the default constructor and destructor for all basic, pointer, and reference types do nothing, while the copy constructor and assignment operator are bitwise copies;
if default zero-initialization is desired, the default constructors can be overridden. 
For user-generated types, the four functions are also automatically generated. 
@enum@ types are handled the same as their underlying integral type, and unions are also bitwise copied and no-op initialized and destructed. 
For compatibility with C, a copy constructor from the first union member type is also defined.
For @struct@ types, each of the four functions are implicitly defined to call their corresponding functions on each member of the struct. 
To better simulate the behaviour of C initializers, a set of \newterm{field constructors} is also generated for structures. 
A constructor is generated for each non-empty prefix of a structure's member-list to copy-construct the members passed as parameters and default-construct the remaining members.
To allow users to limit the set of constructors available for a type, when a user declares any constructor or destructor, the corresponding generated function and all field constructors for that type are hidden from expression resolution;
similarly, the generated default constructor is hidden upon declaration of any constructor. 
These semantics closely mirror the rule for implicit declaration of constructors in \CC\cite[p.~186]{ANSI98:C++}.

In some circumstance programmers may not wish to have constructor and destructor calls.
In these cases, \CFA provides the initialization syntax \lstinline|S x @= {}|, and the object becomes unmanaged, so implicit constructor and destructor calls are not generated. 
Any C initializer can be the right-hand side of an \lstinline|@=| initializer, \eg \lstinline|VLA a @= { 0, 0x0 }|, with the usual C initialization semantics. 
The point of \lstinline|@=| is to provide a migration path from legacy C code to \CFA, by providing a mechanism to incrementally convert to implicit initialization.


% \subsection{Default Parameters}


\section{Literals}

C already includes limited polymorphism for literals -- @0@ can be either an integer or a pointer literal, depending on context, while the syntactic forms of literals of the various integer and float types are very similar, differing from each other only in suffix.
In keeping with the general \CFA approach of adding features while respecting the ``C-style'' of doing things, C's polymorphic constants and typed literal syntax are extended to interoperate with user-defined types, while maintaining a backwards-compatible semantics.

A simple example is allowing the underscore, as in Ada, to separate prefixes, digits, and suffixes in all \CFA constants, \eg @0x`_`1.ffff`_`ffff`_`p`_`128`_`l@, where the underscore is also the standard separator in C identifiers.
\CC uses a single quote as a separator but it is restricted among digits, precluding its use in the literal prefix or suffix, \eg @0x1.ffff@@`'@@ffffp128l@, and causes problems with most IDEs, which must be extended to deal with this alternate use of the single quote.


\subsection{Integral Suffixes}

Additional integral suffixes are added to cover all the integral types and lengths.
\begin{cquote}
\lstDeleteShortInline@%
\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{\hspace{2\parindentlnth}}l@{}}
\begin{cfa}
20_`hh`     // signed char
21_`hhu`   // unsigned char
22_`h`       // signed short int
23_`uh`     // unsigned short int
24_`z`       // size_t
\end{cfa}
&
\begin{cfa}
20_`L8`      // int8_t
21_`ul8`     // uint8_t
22_`l16`     // int16_t
23_`ul16`   // uint16_t
24_`l32`     // int32_t
\end{cfa}
&
\begin{cfa}
25_`ul32`      // uint32_t
26_`l64`        // int64_t
27_`l64u`      // uint64_t
26_`L128`     // int128
27_`L128u`   // unsigned int128
\end{cfa}
\end{tabular}
\lstMakeShortInline@%
\end{cquote}


\subsection{0/1}

In C, @0@ has the special property that it is the only ``false'' value;
from the standard, any value that compares equal to @0@ is false, while any value that compares unequal to @0@ is true. 
As such, an expression @x@ in any boolean context (such as the condition of an @if@ or @while@ statement, or the arguments to @&&@, @||@, or @?:@\,) can be rewritten as @x != 0@ without changing its semantics.
Operator overloading in \CFA provides a natural means to implement this truth-value comparison for arbitrary types, but the C type system is not precise enough to distinguish an equality comparison with @0@ from an equality comparison with an arbitrary integer or pointer. 
To provide this precision, \CFA introduces a new type @zero_t@ as the type of literal @0@ (somewhat analagous to @nullptr_t@ and @nullptr@ in \CCeleven);
@zero_t@ can only take the value @0@, but has implicit conversions to the integer and pointer types so that C code involving @0@ continues to work. 
With this addition, \CFA rewrites @if (x)@ and similar expressions to @if ((x) != 0)@ or the appropriate analogue, and any type @T@ is ``truthy'' by defining an operator overload @int ?!=?(T, zero_t)@.
\CC makes types truthy by adding a conversion to @bool@;
prior to the addition of explicit cast operators in \CCeleven, this approach had the pitfall of making truthy types transitively convertable to any numeric type;
\CFA avoids this issue.

Similarly, \CFA also has a special type for @1@, @one_t@;
like @zero_t@, @one_t@ has built-in implicit conversions to the various integral types so that @1@ maintains its expected semantics in legacy code for operations @++@ and @--@.
The addition of @one_t@ allows generic algorithms to handle the unit value uniformly for types where it is meaningful.
\TODO{Make this sentence true}
In particular, polymorphic functions in the \CFA prelude define @++x@ and @x++@ in terms of @x += 1@, allowing users to idiomatically define all forms of increment for a type @T@ by defining the single function @T & ?+=(T &, one_t)@;
analogous overloads for the decrement operators are present as well.


\subsection{User Literals}

For readability, it is useful to associate units to scale literals, \eg weight (stone, pound, kilogram) or time (seconds, minutes, hours).
The left of Figure~\ref{f:UserLiteral} shows the \CFA alternative call-syntax (literal argument before function name), using the backquote, to convert basic literals into user literals.
The backquote is a small character, making the unit (function name) predominate.
For examples, the multi-precision integer-type in Section~\ref{s:MultiPrecisionIntegers} has user literals:
{\lstset{language=CFA,moredelim=**[is][\color{red}]{|}{|},deletedelim=**[is][]{`}{`}}
\begin{cfa}
y = 9223372036854775807L|`mp| * 18446744073709551615UL|`mp|;
y = "12345678901234567890123456789"|`mp| + "12345678901234567890123456789"|`mp|;
\end{cfa}
Because \CFA uses a standard function, all types and literals are applicable, as well as overloading and conversions.
}%

The right of Figure~\ref{f:UserLiteral} shows the equivalent \CC version using the underscore for the call-syntax.
However, \CC restricts the types, \eg @unsigned long long int@ and @long double@ to represent integral and floating literals.
After which, user literals must match (no conversions);
hence, it is necessary to overload the unit with all appropriate types.

\begin{figure}
\centering
\lstset{language=CFA,moredelim=**[is][\color{red}]{|}{|},deletedelim=**[is][]{`}{`}}
\lstDeleteShortInline@%
\begin{tabular}{@{}l@{\hspace{\parindentlnth}}l@{}}
\multicolumn{1}{c@{\hspace{\parindentlnth}}}{\textbf{\CFA}}     & \multicolumn{1}{c}{\textbf{\CC}}      \\
\begin{cfa}
struct W {
        double stones;
};
void ?{}( W & w ) { w.stones = 0; }
void ?{}( W & w, double w ) { w.stones = w; }
W ?+?( W l, W r ) {
        return (W){ l.stones + r.stones };
}
W |?`st|(double w) { return (W){ w }; }
W |?`lb|(double w) { return (W){ w/14.0 }; }
W |?`kg|(double w) { return (W){ w*0.16 }; }



int main() {
        W w, heavy = { 20 };
        w = 155|`lb|;
        w = 0b_1111|`st|;
        w = 0_233|`lb|;
        w = 0x_9b_u|`kg|;
        w = 5.5|`st| + 8|`kg| + 25.01|`lb| + heavy;
}
\end{cfa}
&
\begin{cfa}
struct W {
        double stones;
        W() { stones = 0.0; }
        W( double w ) { stones = w; }
};
W operator+( W l, W r ) {
        return W( l.stones + r.stones );
}
W |operator""_st|(unsigned long long int w) {return W(w); }
W |operator""_lb|(unsigned long long int w) {return W(w/14.0); }
W |operator""_kg|(unsigned long long int w) {return W(w*0.16); }
W |operator""_st|(long double w ) { return W( w ); }
W |operator""_lb|(long double w ) { return W( w / 14.0 ); }
W |operator""_kg|(long double w ) { return W( w * 0.16 ); }
int main() {
        W w, heavy = { 20 };
        w = 155|_lb|;
        w = 0b1111|_lb|;       // error, binary unsupported
        w = 0${\color{red}\LstBasicStyle{'}}$233|_lb|;          // quote separator
        w = 0x9b|_kg|;
        w = 5.5d|_st| + 8|_kg| + 25.01|_lb| + heavy;
}
\end{cfa}
\end{tabular}
\lstMakeShortInline@%
\caption{User Literal}
\label{f:UserLiteral}
\end{figure}


\section{Libraries}
\label{sec:libraries}

As stated in Section~\ref{sec:poly-fns}, \CFA inherits a large corpus of library code, where other programming languages must rewrite or provide fragile inter-language communication with C.
\CFA has replacement libraries condensing hundreds of existing C names into tens of \CFA overloaded names, all without rewriting the actual computations.
In many cases, the interface is an inline wrapper providing overloading during compilation but zero cost at runtime.
The following sections give a glimpse of the interface reduction to many C libraries.
In many cases, @signed@/@unsigned@ @char@, @short@, and @_Complex@ functions are available (but not shown) to ensure expression computations remain in a single type, as conversions can distort results.


\subsection{Limits}

C library @limits.h@ provides lower and upper bound constants for the basic types.
\CFA name overloading is used to condense these typed constants, \eg:
\begin{cquote}
\lstDeleteShortInline@%
\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{Definition}}      & \multicolumn{1}{c}{\textbf{Usage}}    \\
\begin{cfa}
const short int `MIN` = -32768;
const int `MIN` = -2147483648;
const long int `MIN` = -9223372036854775808L;
\end{cfa}
&
\begin{cfa}
short int si = `MIN`;
int i = `MIN`;
long int li = `MIN`;
\end{cfa}
\end{tabular}
\lstMakeShortInline@%
\end{cquote}
The result is a significant reduction in names to access typed constants, \eg:
\begin{cquote}
\lstDeleteShortInline@%
\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
\begin{cfa}
MIN

MAX

PI
E
\end{cfa}
&
\begin{cfa}
SCHAR_MIN, CHAR_MIN, SHRT_MIN, INT_MIN, LONG_MIN, LLONG_MIN,
                FLT_MIN, DBL_MIN, LDBL_MIN
SCHAR_MAX, UCHAR_MAX, SHRT_MAX, INT_MAX, LONG_MAX, LLONG_MAX,
                FLT_MAX, DBL_MAX, LDBL_MAX
M_PI, M_PIl
M_E, M_El
\end{cfa}
\end{tabular}
\lstMakeShortInline@%
\end{cquote}


\subsection{Math}

C library @math.h@ provides many mathematical functions.
\CFA function overloading is used to condense these mathematical functions, \eg:
\begin{cquote}
\lstDeleteShortInline@%
\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{Definition}}      & \multicolumn{1}{c}{\textbf{Usage}}    \\
\begin{cfa}
float `log`( float x );
double `log`( double );
double _Complex `log`( double _Complex x );
\end{cfa}
&
\begin{cfa}
float f = `log`( 3.5 );
double d = `log`( 3.5 );
double _Complex dc = `log`( 3.5+0.5I );
\end{cfa}
\end{tabular}
\lstMakeShortInline@%
\end{cquote}
The result is a significant reduction in names to access math functions, \eg:
\begin{cquote}
\lstDeleteShortInline@%
\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
\begin{cfa}
log
sqrt
sin
\end{cfa}
&
\begin{cfa}
logf, log, logl, clogf, clog, clogl
sqrtf, sqrt, sqrtl, csqrtf, csqrt, csqrtl
sinf, sin, sinl, csinf, csin, csinl
\end{cfa}
\end{tabular}
\lstMakeShortInline@%
\end{cquote}
While \Celeven has type-generic math~\cite[\S~7.25]{C11} in @tgmath.h@ to provide a similar mechanism, these macros are limited, matching a function name with a single set of floating type(s).
For example, it is impossible to overload @atan@ for both one and two arguments;
instead the names @atan@ and @atan2@ are required (see Section~\ref{s:NameOverloading}).
The key observation is that only a restricted set of type-generic macros are provided for a limited set of function names, which do not generalize across the type system, as in \CFA.


\subsection{Standard}

C library @stdlib.h@ provides many general functions.
\CFA function overloading is used to condense these utility functions, \eg:
\begin{cquote}
\lstDeleteShortInline@%
\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{Definition}}      & \multicolumn{1}{c}{\textbf{Usage}}    \\
\begin{cfa}
unsigned int `abs`( int );
double `abs`( double );
double abs( double _Complex );
\end{cfa}
&
\begin{cfa}
unsigned int i = `abs`( -1 );
double d = `abs`( -1.5 );
double d = `abs`( -1.5+0.5I );
\end{cfa}
\end{tabular}
\lstMakeShortInline@%
\end{cquote}
The result is a significant reduction in names to access utility functions, \eg:
\begin{cquote}
\lstDeleteShortInline@%
\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
\begin{cfa}
abs
strto
random
\end{cfa}
&
\begin{cfa}
abs, labs, llabs, fabsf, fabs, fabsl, cabsf, cabs, cabsl
strtol, strtoul, strtoll, strtoull, strtof, strtod, strtold
srand48, mrand48, lrand48, drand48
\end{cfa}
\end{tabular}
\lstMakeShortInline@%
\end{cquote}
In additon, there are polymorphic functions, like @min@ and @max@, that work on any type with operators @?<?@ or @?>?@.

The following shows one example where \CFA \emph{extends} an existing standard C interface to reduce complexity and provide safety.
C/\Celeven provide a number of complex and overlapping storage-management operation to support the following capabilities:
\begin{description}%[topsep=3pt,itemsep=2pt,parsep=0pt]
\item[fill]
an allocation with a specified character.
\item[resize]
an existing allocation to decreased or increased its size.
In either case, new storage may or may not be allocated and, if there is a new allocation, as much data from the existing allocation is copied.
For an increase in storage size, new storage after the copied data may be filled.
\item[align]
an allocation on a specified memory boundary, \eg, an address multiple of 64 or 128 for cache-line purposes.
\item[array]
allocation with a specified number of elements.
An array may be filled, resized, or aligned.
\end{description}
Table~\ref{t:StorageManagementOperations} shows the capabilities provided by C/\Celeven allocation-functions and how all the capabilities can be combined into two \CFA functions.
\CFA storage-management functions extend the C equivalents by overloading, providing shallow type-safety, and removing the need to specify the base allocation-size.
Figure~\ref{f:StorageAllocation} contrasts \CFA and C storage-allocation performing the same operations with the same type safety.

\begin{table}
\centering
\lstDeleteShortInline@%
\lstMakeShortInline~%
\begin{tabular}{@{}r|r|l|l|l|l@{}}
\multicolumn{1}{c}{}&           & \multicolumn{1}{c|}{fill}     & resize        & align & array \\
\hline
C               & ~malloc~                      & no                    & no            & no            & no    \\
                & ~calloc~                      & yes (0 only)  & no            & no            & yes   \\
                & ~realloc~                     & no/copy               & yes           & no            & no    \\
                & ~memalign~            & no                    & no            & yes           & no    \\
                & ~posix_memalign~      & no                    & no            & yes           & no    \\
\hline
C11             & ~aligned_alloc~       & no                    & no            & yes           & no    \\
\hline
\CFA    & ~alloc~                       & yes/copy              & no/yes        & no            & yes   \\
                & ~align_alloc~         & yes                   & no            & yes           & yes   \\
\end{tabular}
\lstDeleteShortInline~%
\lstMakeShortInline@%
\caption{Storage-Management Operations}
\label{t:StorageManagementOperations}
\end{table}

\begin{figure}
\centering
\begin{cquote}
\begin{cfa}[aboveskip=0pt]
size_t  dim = 10;                                                       $\C{// array dimension}$
char fill = '\xff';                                                     $\C{// initialization fill value}$
int * ip;
\end{cfa}
\lstDeleteShortInline@%
\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{C}}        \\
\begin{cfa}
ip = alloc();
ip = alloc( fill );
ip = alloc( dim );
ip = alloc( dim, fill );
ip = alloc( ip, 2 * dim );
ip = alloc( ip, 4 * dim, fill );

ip = align_alloc( 16 );
ip = align_alloc( 16, fill );
ip = align_alloc( 16, dim );
ip = align_alloc( 16, dim, fill );
\end{cfa}
&
\begin{cfa}
ip = (int *)malloc( sizeof( int ) );
ip = (int *)malloc( sizeof( int ) ); memset( ip, fill, sizeof( int ) );
ip = (int *)malloc( dim * sizeof( int ) );
ip = (int *)malloc( sizeof( int ) ); memset( ip, fill, dim * sizeof( int ) );
ip = (int *)realloc( ip, 2 * dim * sizeof( int ) );
ip = (int *)realloc( ip, 4 * dim * sizeof( int ) );
                        memset( ip, fill, 4 * dim * sizeof( int ) );
ip = memalign( 16, sizeof( int ) );
ip = memalign( 16, sizeof( int ) ); memset( ip, fill, sizeof( int ) );
ip = memalign( 16, dim * sizeof( int ) );
ip = memalign( 16, dim * sizeof( int ) ); memset( ip, fill, dim * sizeof( int ) );
\end{cfa}
\end{tabular}
\lstMakeShortInline@%
\end{cquote}
\caption{\CFA versus C Storage-Allocation}
\label{f:StorageAllocation}
\end{figure}

Variadic @new@ (see Section~\ref{sec:variadic-tuples}) cannot support the same overloading because extra parameters are for initialization.
Hence, there are @new@ and @anew@ functions for single and array variables, and the fill value is the arguments to the constructor, \eg:
\begin{cfa}
struct S { int i, j; };
void ?{}( S & s, int i, int j ) { s.i = i; s.j = j; }
S * s = new( 2, 3 );                                            $\C{// allocate storage and run constructor}$
S * as = anew( dim, 2, 3 );                                     $\C{// each array element initialized to 2, 3}$
\end{cfa}
Note, \CC can only initialization array elements via the default constructor.

Finally, the \CFA memory-allocator has \newterm{sticky properties} for dynamic storage: fill and alignment are remembered with an object's storage in the heap.
When a @realloc@ is performed, the sticky properties are respected, so that new storage is correctly aligned and initialized with the fill character.


\subsection{I/O}
\label{s:IOLibrary}

The goal of \CFA I/O is to simplify the common cases, while fully supporting polymorphism and user defined types in a consistent way.
The approach combines ideas from \CC and Python.
The \CFA header file for the I/O library is @fstream@.

The common case is printing out a sequence of variables separated by whitespace.
\begin{cquote}
\lstDeleteShortInline@%
\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}l@{}}
\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{c}{\textbf{\CC}}      \\
\begin{cfa}
int x = 1, y = 2, z = 3;
sout | x `|` y `|` z | endl;
\end{cfa}
&
\begin{cfa}

cout << x `<< " "` << y `<< " "` << z << endl;
\end{cfa}
\\
\begin{cfa}[showspaces=true,aboveskip=0pt,belowskip=0pt]
1` `2` `3
\end{cfa}
&
\begin{cfa}[showspaces=true,aboveskip=0pt,belowskip=0pt]
1 2 3
\end{cfa}
\end{tabular}
\lstMakeShortInline@%
\end{cquote}
The \CFA form has half the characters of the \CC form, and is similar to Python I/O with respect to implicit separators.
Similar simplification occurs for tuple I/O, which prints all tuple values separated by ``\lstinline[showspaces=true]@, @''.
\begin{cfa}
[int, [ int, int ] ] t1 = [ 1, [ 2, 3 ] ], t2 = [ 4, [ 5, 6 ] ];
sout | t1 | t2 | endl;                                  $\C{// print tuples}$
\end{cfa}
\begin{cfa}[showspaces=true,aboveskip=0pt]
1`, `2`, `3 4`, `5`, `6
\end{cfa}
Finally, \CFA uses the logical-or operator for I/O as it is the lowest-priority overloadable operator, other than assignment.
Therefore, fewer output expressions require parenthesis.
\begin{cquote}
\lstDeleteShortInline@%
\begin{tabular}{@{}ll@{}}
\textbf{\CFA:}
&
\begin{cfa}
sout | x * 3 | y + 1 | z << 2 | x == y | (x | y) | (x || y) | (x > z ? 1 : 2) | endl;
\end{cfa}
\\
\textbf{\CC:}
&
\begin{cfa}
cout << x * 3 << y + 1 << `(`z << 2`)` << `(`x == y`)` << (x | y) << (x || y) << (x > z ? 1 : 2) << endl;
\end{cfa}
\\
&
\begin{cfa}[showspaces=true,aboveskip=0pt]
3 3 12 0 3 1 2
\end{cfa}
\end{tabular}
\lstMakeShortInline@%
\end{cquote}
There is a weak similarity between the \CFA logical-or operator and the Shell pipe-operator for moving data, where data flows in the correct direction for input but the opposite direction for output.

The implicit separator character (space/blank) is a separator not a terminator.
The rules for implicitly adding the separator are:
\begin{itemize}
\item
A separator does not appear at the start or end of a line.
\item
A separator does not appear before or after a character literal or variable.
\item
A separator does not appear before or after a null (empty) C string, which is a local mechanism to disable insertion of the separator character.
\item
A separator does not appear before a C string starting with the characters: \lstinline[mathescape=off,basicstyle=\tt]@([{=$@
\item
A separator does not appear after a C string ending with the characters: \lstinline[basicstyle=\tt]@,.;!?)]}%@
\item
{\lstset{language=CFA,deletedelim=**[is][]{`}{`}}
A separator does not appear before or after a C string beginning/ending with the quote or whitespace characters: \lstinline[basicstyle=\tt,showspaces=true]@`'": \t\v\f\r\n@
}%
\end{itemize}
There are functions to set and get the separator string, and manipulators to toggle separation on and off in the middle of output.


\subsection{Multi-precision Integers}
\label{s:MultiPrecisionIntegers}

\CFA has an interface to the GMP multi-precision signed-integers~\cite{GMP}, similar to the \CC interface provided by GMP.
The \CFA interface wraps GMP functions into operator functions to make programming with multi-precision integers identical to using fixed-sized integers.
The \CFA type name for multi-precision signed-integers is @Int@ and the header file is @gmp@.
Figure~\ref{f:GMPInterface} shows a multi-precision factorial-program contrasting the GMP interface in \CFA and C.

\begin{figure}
\centering
\lstDeleteShortInline@%
\begin{tabular}{@{}l@{\hspace{2\parindentlnth}}@{\hspace{2\parindentlnth}}l@{}}
\multicolumn{1}{c@{\hspace{2\parindentlnth}}}{\textbf{\CFA}}    & \multicolumn{1}{@{\hspace{2\parindentlnth}}c}{\textbf{C}}     \\
\begin{cfa}
#include <gmp>
int main( void ) {
        sout | "Factorial Numbers" | endl;
        Int fact = 1;
        sout | 0 | fact | endl;
        for ( unsigned int i = 1; i <= 40; i += 1 ) {
                fact *= i;
                sout | i | fact | endl;
        }
}
\end{cfa}
&
\begin{cfa}
#include <gmp.h>
int main( void ) {
        `gmp_printf`( "Factorial Numbers\n" );
        `mpz_t` fact;  `mpz_init_set_ui`( fact, 1 );
        `gmp_printf`( "%d %Zd\n", 0, fact );
        for ( unsigned int i = 1; i <= 40; i += 1 ) {
                `mpz_mul_ui`( fact, fact, i );
                `gmp_printf`( "%d %Zd\n", i, fact );
        }
}
\end{cfa}
\end{tabular}
\lstMakeShortInline@%
\caption{GMP Interface \CFA versus C}
\label{f:GMPInterface}
\end{figure}


\section{Evaluation}
\label{sec:eval}

Though \CFA provides significant added functionality over C, these features have a low runtime penalty.
In fact, \CFA's features for generic programming can enable faster runtime execution than idiomatic @void *@-based C code.
This claim is demonstrated through a set of generic-code-based micro-benchmarks in C, \CFA, and \CC (see stack implementations in Appendix~\ref{sec:BenchmarkStackImplementation}).
Since all these languages share a subset essentially comprising standard C, maximal-performance benchmarks should show little runtime variance, differing only in length and clarity of source code.
A more illustrative comparison measures the costs of idiomatic usage of each language's features.
Figure~\ref{fig:BenchmarkTest} shows the \CFA benchmark tests for a generic stack based on a singly linked-list.
The benchmark test is similar for the other languages.
The experiment uses element types @int@ and @pair(short, char)@, and pushes $N=40M$ elements on a generic stack, copies the stack, clears one of the stacks, and finds the maximum value in the other stack.

\begin{figure}
\begin{cfa}[xleftmargin=3\parindentlnth,aboveskip=0pt,belowskip=0pt]
int main() {
        int max = 0, val = 42;
        stack( int ) si, ti;

        REPEAT_TIMED( "push_int", N, push( si, val ); )
        TIMED( "copy_int", ti{ si }; )
        TIMED( "clear_int", clear( si ); )
        REPEAT_TIMED( "pop_int", N, int x = pop( ti ); if ( x > max ) max = x; )

        pair( short, char ) max = { 0h, '\0' }, val = { 42h, 'a' };
        stack( pair( short, char ) ) sp, tp;

        REPEAT_TIMED( "push_pair", N, push( sp, val ); )
        TIMED( "copy_pair", tp{ sp }; )
        TIMED( "clear_pair", clear( sp ); )
        REPEAT_TIMED( "pop_pair", N, pair(short, char) x = pop( tp ); if ( x > max ) max = x; )
}
\end{cfa}
\caption{\protect\CFA Benchmark Test}
\label{fig:BenchmarkTest}
\end{figure}

The structure of each benchmark implemented is: C with @void *@-based polymorphism, \CFA with the presented features, \CC with templates, and \CC using only class inheritance for polymorphism, called \CCV.
The \CCV variant illustrates an alternative object-oriented idiom where all objects inherit from a base @object@ class, mimicking a Java-like interface;
hence runtime checks are necessary to safely down-cast objects.
The most notable difference among the implementations is in memory layout of generic types: \CFA and \CC inline the stack and pair elements into corresponding list and pair nodes, while C and \CCV lack such a capability and instead must store generic objects via pointers to separately-allocated objects.
Note that the C benchmark uses unchecked casts as there is no runtime mechanism to perform such checks, while \CFA and \CC provide type-safety statically.

Figure~\ref{fig:eval} and Table~\ref{tab:eval} show the results of running the benchmark in Figure~\ref{fig:BenchmarkTest} and its C, \CC, and \CCV equivalents.
The graph plots the median of 5 consecutive runs of each program, with an initial warm-up run omitted.
All code is compiled at \texttt{-O2} by gcc or g++ 6.3.0, with all \CC code compiled as \CCfourteen.
The benchmarks are run on an Ubuntu 16.04 workstation with 16 GB of RAM and a 6-core AMD FX-6300 CPU with 3.5 GHz maximum clock frequency.

\begin{figure}
\centering
\input{timing}
\caption{Benchmark Timing Results (smaller is better)}
\label{fig:eval}
\end{figure}

\begin{table}
\centering
\caption{Properties of benchmark code}
\label{tab:eval}
\newcommand{\CT}[1]{\multicolumn{1}{c}{#1}}
\begin{tabular}{rrrrr}
                                                                        & \CT{C}        & \CT{\CFA}     & \CT{\CC}      & \CT{\CCV}             \\ \hline
maximum memory usage (MB)                       & 10,001        & 2,502         & 2,503         & 11,253                \\
source code size (lines)                        & 196           & 186           & 125           & 290                   \\
redundant type annotations (lines)      & 27            & 0                     & 2                     & 16                    \\
binary size (KB)                                        & 14            & 257           & 14            & 37                    \\
\end{tabular}
\end{table}

The C and \CCV variants are generally the slowest with the largest memory footprint, because of their less-efficient memory layout and the pointer-indirection necessary to implement generic types;
this inefficiency is exacerbated by the second level of generic types in the pair benchmarks.
By contrast, the \CFA and \CC variants run in roughly equivalent time for both the integer and pair of @short@ and @char@ because the storage layout is equivalent, with the inlined libraries (\ie no separate compilation) and greater maturity of the \CC compiler contributing to its lead.
\CCV is slower than C largely due to the cost of runtime type-checking of down-casts (implemented with @dynamic_cast@);
The outlier in the graph for \CFA, pop @pair@, results from the complexity of the generated-C polymorphic code.
The gcc compiler is unable to optimize some dead code and condense nested calls; a compiler designed for \CFA could easily perform these optimizations.
Finally, the binary size for \CFA is larger because of static linking with the \CFA libraries.

\CFA is also competitive in terms of source code size, measured as a proxy for programmer effort. The line counts in Table~\ref{tab:eval} include implementations of @pair@ and @stack@ types for all four languages for purposes of direct comparison, though it should be noted that \CFA and \CC have pre-written data structures in their standard libraries that programmers would generally use instead. Use of these standard library types has minimal impact on the performance benchmarks, but shrinks the \CFA and \CC benchmarks to 39 and 42 lines, respectively.
The difference between the \CFA and \CC line counts is primarily declaration duplication to implement separate compilation; a header-only \CFA library would be similar in length to the \CC version.
On the other hand, C does not have a generic collections-library in its standard distribution, resulting in frequent reimplementation of such collection types by C programmers.
\CCV does not use the \CC standard template library by construction, and in fact includes the definition of @object@ and wrapper classes for @char@, @short@, and @int@ in its line count, which inflates this count somewhat, as an actual object-oriented language would include these in the standard library;
with their omission, the \CCV line count is similar to C.
We justify the given line count by noting that many object-oriented languages do not allow implementing new interfaces on library types without subclassing or wrapper types, which may be similarly verbose.

Line-count is a fairly rough measure of code complexity;
another important factor is how much type information the programmer must specify manually, especially where that information is not compiler-checked.
Such unchecked type information produces a heavier documentation burden and increased potential for runtime bugs, and is much less common in \CFA than C, with its manually specified function pointer arguments and format codes, or \CCV, with its extensive use of untype-checked downcasts, \eg @object@ to @integer@ when popping a stack.
To quantify this manual typing, the ``redundant type annotations'' line in Table~\ref{tab:eval} counts the number of lines on which the type of a known variable is respecified, either as a format specifier, explicit downcast, type-specific function, or by name in a @sizeof@, struct literal, or @new@ expression.
The \CC benchmark uses two redundant type annotations to create a new stack nodes, while the C and \CCV benchmarks have several such annotations spread throughout their code.
The \CFA benchmark is able to eliminate all redundant type annotations through use of the polymorphic @alloc@ function discussed in Section~\ref{sec:libraries}.


\section{Related Work}


\subsection{Polymorphism}

\CC provides three disjoint polymorphic extensions to C: overloading, inheritance, and templates.
The overloading is restricted because resolution does not use the return type, inheritance requires learning object-oriented programming and coping with a restricted nominal-inheritance hierarchy, templates cannot be separately compiled resulting in compilation/code bloat and poor error messages, and determining how these mechanisms interact and which to use is confusing.
In contrast, \CFA has a single facility for polymorphic code supporting type-safe separate-compilation of polymorphic functions and generic (opaque) types, which uniformly leverage the C procedural paradigm.
The key mechanism to support separate compilation is \CFA's \emph{explicit} use of assumed type properties.
Until \CC concepts~\cite{C++Concepts} are standardized (anticipated for \CCtwenty), \CC provides no way to specify the requirements of a generic function beyond compilation errors during template expansion;
furthermore, \CC concepts are restricted to template polymorphism.

Cyclone~\cite{Grossman06} also provides capabilities for polymorphic functions and existential types, similar 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 to abstraction over types with the same layout and calling convention as @void *@, \ie only pointer types and @int@.
In \CFA terms, all Cyclone polymorphism must be dtype-static.
While the Cyclone design provides the efficiency benefits discussed in Section~\ref{sec:generic-apps} for dtype-static polymorphism, it is more restrictive than \CFA's general model.
Smith and Volpano~\cite{Smith98} present Polymorphic C, an ML dialect with polymorphic functions, C-like syntax, and pointer types; it lacks many of C's features, however, most notably structure types, and so is not a practical C replacement.

Objective-C~\cite{obj-c-book} is an industrially successful extension to C.
However, Objective-C is a radical departure from C, using an object-oriented model with message-passing.
Objective-C did not support type-checked generics until recently \cite{xcode7}, historically using less-efficient runtime checking of object types.
The GObject~\cite{GObject} framework also adds object-oriented programming with runtime type-checking and reference-counting garbage-collection to C;
these features are more intrusive additions than those provided by \CFA, in addition to the runtime overhead of reference-counting.
Vala~\cite{Vala} compiles to GObject-based C, adding the burden of learning a separate language syntax to the aforementioned demerits of GObject as a modernization path for existing C code-bases.
Java~\cite{Java8} included generic types in Java~5, which are type-checked at compilation and type-erased at runtime, similar to \CFA's.
However, in Java, each object carries its own table of method pointers, while \CFA passes the method pointers separately to maintain a C-compatible layout.
Java is also a garbage-collected, object-oriented language, with the associated resource usage and C-interoperability burdens.

D~\cite{D}, Go, and Rust~\cite{Rust} are modern, compiled languages with abstraction features similar to \CFA traits, \emph{interfaces} in D and Go and \emph{traits} in Rust.
However, each language represents a significant departure from C in terms of language model, and none has the same level of compatibility with C as \CFA.
D and Go are garbage-collected languages, imposing the associated runtime overhead.
The necessity of accounting for data transfer between managed runtimes and the unmanaged C runtime complicates foreign-function interfaces to C.
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.
D restricts garbage collection to its own heap by default, while Rust is not garbage-collected, and thus has a lighter-weight runtime more interoperable with C.
Rust also possesses much more powerful abstraction capabilities for writing generic code than Go.
On the other hand, Rust's borrow-checker provides strong safety guarantees but is complex and difficult to learn and imposes a distinctly idiomatic programming style.
\CFA, with its more modest safety features, allows direct ports of C code while maintaining the idiomatic style of the original source.


\subsection{Tuples/Variadics}

Many programming languages have some form of tuple construct and/or variadic functions, \eg SETL, C, KW-C, \CC, D, Go, Java, ML, and Scala.
SETL~\cite{SETL} is a high-level mathematical programming language, with tuples being one of the primary data types.
Tuples in SETL allow subscripting, dynamic expansion, and multiple assignment.
C provides variadic functions through @va_list@ objects, but the programmer is responsible for managing the number of arguments and their types, so the mechanism is type unsafe.
KW-C~\cite{Buhr94a}, a predecessor of \CFA, introduced tuples to C as an extension of the C syntax, taking much of its inspiration from SETL.
The main contributions of that work were adding MRVF, tuple mass and multiple assignment, and record-field access.
\CCeleven introduced @std::tuple@ as a library variadic template structure.
Tuples are a generalization of @std::pair@, in that they allow for arbitrary length, fixed-size aggregation of heterogeneous values.
Operations include @std::get<N>@ to extract values, @std::tie@ to create a tuple of references used for assignment, and lexicographic comparisons.
\CCseventeen proposes \emph{structured bindings}~\cite{Sutter15} to eliminate pre-declaring variables and use of @std::tie@ for binding the results.
This extension requires the use of @auto@ to infer the types of the new variables, so complicated expressions with a non-obvious type must be documented with some other mechanism.
Furthermore, structured bindings are not a full replacement for @std::tie@, as it always declares new variables.
Like \CC, D provides tuples through a library variadic-template structure.
Go does not have tuples but supports MRVF.
Java's variadic functions appear similar to C's but are type-safe using homogeneous arrays, which are less useful than \CFA's heterogeneously-typed variadic functions.
Tuples are a fundamental abstraction in most functional programming languages, such as Standard ML~\cite{sml} and~\cite{Scala}, which decompose tuples using pattern matching.


\subsection{C Extensions}

\CC is the best known C-based language, and is similar to \CFA in that both are extensions to C with source and runtime backwards compatibility.
Specific difference between \CFA and \CC have been identified in prior sections, with a final observation that \CFA has equal or fewer tokens to express the same notion in many cases.
The key difference in design philosophies is that \CFA is easier for C programmers to understand by maintaining a procedural paradigm and avoiding complex interactions among extensions.
\CC, on the other hand, has multiple overlapping features (such as the three forms of polymorphism), many of which have complex interactions with its object-oriented design. 
As a result, \CC has a steep learning curve for even experienced C programmers, especially when attempting to maintain performance equivalent to C legacy-code.

There are several other C extension-languages with less usage and even more dramatic changes than \CC. 
Objective-C and Cyclone are two other extensions to C with different design goals than \CFA, as discussed above. 
Other languages extend C with more focused features. 
$\mu$\CC~\cite{uC++book}, CUDA~\cite{Nickolls08}, ispc~\cite{Pharr12}, and Sierra~\cite{Leissa14} add concurrent or data-parallel primitives to C or \CC;
data-parallel features have not yet been added to \CFA, but are easily incorporated within its design, while concurrency primitives similar to those in $\mu$\CC have already been added~\cite{Delisle18}.
Finally, CCured~\cite{Necula02} and Ironclad \CC~\cite{DeLozier13} attempt to provide a more memory-safe C by annotating pointer types with garbage collection information; type-checked polymorphism in \CFA covers several of C's memory-safety issues, but more aggressive approaches such as annotating all pointer types with their nullability or requiring runtime garbage collection are contradictory to \CFA's backwards compatibility goals.


\begin{comment}
\subsection{Control Structures / Declarations / Literals}

Java has default fall through like C/\CC.
Pascal/Ada/Go/Rust do not have default fall through.
\Csharp does not have fall through but still requires a break.
Python uses dictionary mapping. \\
\CFA choose is like Rust match.

Java has labelled break/continue. \\
Languages with and without exception handling.

Alternative C declarations. \\
Different references \\
Constructors/destructors

0/1 Literals \\
user defined: D, Objective-C
\end{comment}


\section{Conclusion and Future Work}

The goal of \CFA is to provide an evolutionary pathway for large C development-environments to be more productive and safer, while respecting the talent and skill of C programmers.
While other programming languages purport to be a better C, they are in fact new and interesting languages in their own right, but not C extensions.
The purpose of this paper is to introduce \CFA, and showcase language features that illustrate the \CFA type-system and approaches taken to achieve the goal of evolutionary C extension.
The contributions are a powerful type-system using parametric polymorphism and overloading, generic types, tuples, advanced control structures, and extended declarations, which all have complex interactions.
The work is a challenging design, engineering, and implementation exercise.
On the surface, the project may appear as a rehash of similar mechanisms in \CC.
However, every \CFA feature is different than its \CC counterpart, often with extended functionality, better integration with C and its programmers, and always supporting separate compilation.
All of these new features are being used by the \CFA development-team to build the \CFA runtime-system.
Finally, we demonstrate that \CFA performance for some idiomatic cases is better than C and close to \CC, showing the design is practically applicable.

There is ongoing work on a wide range of \CFA features, including arrays with size, runtime type-information, virtual functions, user-defined conversions, concurrent primitives, and modules.
While all examples in the paper compile and run, a public beta-release of \CFA will take another 8--12 months to finalize these extensions.
There are also interesting future directions for the polymorphism design.
Notably, \CC template functions trade compile time and code bloat for optimal runtime of individual instantiations of polymorphic functions.
\CFA polymorphic functions use dynamic virtual-dispatch;
the runtime overhead of this approach is low, but not as low as inlining, and it may be beneficial to provide a mechanism for performance-sensitive code.
Two promising approaches are an @inline@ annotation at polymorphic function call sites to create a template-specialization of the function (provided the code is visible) or placing an @inline@ annotation on polymorphic function-definitions to instantiate a specialized version for some set of types (\CC template specialization).
These approaches are not mutually exclusive and allow performance optimizations to be applied only when necessary, without suffering global code-bloat.
In general, we believe separate compilation, producing smaller code, works well with loaded hardware-caches, which may offset the benefit of larger inlined-code.


\section{Acknowledgments}

The authors would like to recognize the design assistance of Glen Ditchfield, Richard Bilson, Thierry Delisle, Andrew Beach and Brice Dobry on the features described in this paper, and thank Magnus Madsen for feedback on the writing.
This work is supported by a corporate partnership with Huawei Ltd.\ (\url{http://www.huawei.com}), and Aaron Moss and Peter Buhr are partially funded by the Natural Sciences and Engineering Research Council of Canada.


\bibliography{pl}


\appendix

\section{Benchmark Stack Implementation}
\label{sec:BenchmarkStackImplementation}

Throughout, @/***/@ designates a counted redundant type annotation; code reformatted for brevity.

\smallskip\noindent
C
\begin{cfa}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
struct stack_node {
        void * value;
        struct stack_node * next;
};
struct stack { struct stack_node* head; };
void clear_stack( struct stack * s, void (*free_el)( void * ) ) {
        for ( struct stack_node * next = s->head; next; ) {
                struct stack_node * crnt = next;
                next = crnt->next;
                free_el( crnt->value );
                free( crnt );
        }
        s->head = NULL;
}
struct stack new_stack() { return (struct stack){ NULL }; /***/ }
void copy_stack( struct stack * s, const struct stack * t, void * (*copy)( const void * ) ) {
        struct stack_node ** crnt = &s->head;
        for ( struct stack_node * next = t->head; next; next = next->next ) {
                *crnt = malloc( sizeof(struct stack_node) ); /***/
                (*crnt)->value = copy( next->value );
                crnt = &(*crnt)->next;
        }
        *crnt = NULL;
}
struct stack * assign_stack( struct stack * s, const struct stack * t, 
                void * (*copy_el)( const void * ), void (*free_el)( void * ) ) {
        if ( s->head == t->head ) return s;
        clear_stack( s, free_el ); /***/
        copy_stack( s, t, copy_el ); /***/
        return s;
}
_Bool stack_empty( const struct stack * s ) { return s->head == NULL; }
void push_stack( struct stack * s, void * v ) {
        struct stack_node * n = malloc( sizeof(struct stack_node) ); /***/
        *n = (struct stack_node){ v, s->head }; /***/
        s->head = n;
}
void * pop_stack( struct stack * s ) {
        struct stack_node * n = s->head;
        s->head = n->next;
        void * v = n->value;
        free( n );
        return v;
}
\end{cfa}

\medskip\noindent
\CFA
\begin{cfa}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
forall( otype T ) struct stack_node {
        T value;
        stack_node(T) * next;
};
forall( otype T ) struct stack { stack_node(T) * head; };
forall( otype T ) void clear( stack(T) & s ) with( s ) {
        for ( stack_node(T) * next = head; next; ) {
                stack_node(T) * crnt = next;
                next = crnt->next;
                ^(*crnt){};
                free(crnt);
        }
        head = 0;
}
forall( otype T ) void ?{}( stack(T) & s ) { (s.head){ 0 }; }
forall( otype T ) void ?{}( stack(T) & s, stack(T) t ) {
        stack_node(T) ** crnt = &s.head;
        for ( stack_node(T) * next = t.head; next; next = next->next ) {
                *crnt = alloc();
                ((*crnt)->value){ next->value };
                crnt = &(*crnt)->next;
        }
        *crnt = 0;
}
forall( otype T ) stack(T) ?=?( stack(T) & s, stack(T) t ) {
        if ( s.head == t.head ) return s;
        clear( s );
        s{ t };
        return s;
}
forall( otype T ) void ^?{}( stack(T) & s) { clear( s ); }
forall( otype T ) _Bool empty( const stack(T) & s ) { return s.head == 0; }
forall( otype T ) void push( stack(T) & s, T value ) with( s ) {
        stack_node(T) * n = alloc();
        (*n){ value, head };
        head = n;
}
forall( otype T ) T pop( stack(T) & s ) with( s ) {
        stack_node(T) * n = head;
        head = n->next;
        T v = n->value;
        ^(*n){};
        free( n );
        return v;
}
\end{cfa}

\begin{comment}
forall( otype T ) {
        struct stack_node {
                T value;
                stack_node(T) * next;
        };
        struct stack { stack_node(T) * head; };
        void clear( stack(T) & s ) with( s ) {
                for ( stack_node(T) * next = head; next; ) {
                        stack_node(T) * crnt = next;
                        next = crnt->next;
                        ^(*crnt){};
                        free(crnt);
                }
                head = 0;
        }
        void ?{}( stack(T) & s ) { (s.head){ 0 }; }
        void ?{}( stack(T) & s, stack(T) t ) {
                stack_node(T) ** crnt = &s.head;
                for ( stack_node(T) * next = t.head; next; next = next->next ) {
                        *crnt = alloc();
                        ((*crnt)->value){ next->value };
                        crnt = &(*crnt)->next;
                }
                *crnt = 0;
        }
        stack(T) ?=?( stack(T) & s, stack(T) t ) {
                if ( s.head == t.head ) return s;
                clear( s );
                s{ t };
                return s;
        }
        void ^?{}( stack(T) & s) { clear( s ); }
        _Bool empty( const stack(T) & s ) { return s.head == 0; }
        void push( stack(T) & s, T value ) with( s ) {
                stack_node(T) * n = alloc();
                (*n){ value, head };
                head = n;
        }
        T pop( stack(T) & s ) with( s ) {
                stack_node(T) * n = head;
                head = n->next;
                T v = n->value;
                ^(*n){};
                free( n );
                return v;
        }
}
\end{comment}

\medskip\noindent
\CC
\begin{cfa}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
template<typename T> struct stack {
        struct node {
                T value;
                node * next;
                node( const T & v, node * n = nullptr ) : value( v ), next( n ) {}
        };
        node * head;
        stack() : head( nullptr ) {}
        stack( const stack<T> & o ) { copy( o ); }
        void clear() {
                for ( node * next = head; next; ) {
                        node * crnt = next;
                        next = crnt->next;
                        delete crnt;
                }
                head = nullptr;
        }
        void copy( const stack<T> & o ) {
                node ** crnt = &head;
                for ( node * next = o.head; next; next = next->next ) {
                        *crnt = new node{ next->value }; /***/
                        crnt = &(*crnt)->next;
                }
                *crnt = nullptr;
        }
        ~stack() { clear(); }
        stack & operator= ( const stack<T> & o ) {
                if ( this == &o ) return *this;
                clear();
                copy( o );
                return *this;
        }
        bool empty() const { return head == nullptr; }
        void push( const T & value ) { head = new node{ value, head };  /***/ }
        T pop() {
                node * n = head;
                head = n->next;
                T v = std::move( n->value );
                delete n;
                return v;
        }
};
\end{cfa}

\medskip\noindent
\CCV
\begin{cfa}[xleftmargin=2\parindentlnth,aboveskip=0pt,belowskip=0pt]
struct stack {
        struct node {
                ptr<object> value;
                node * next;
                node( const object & v, node * n = nullptr ) : value( v.new_copy() ), next( n ) {}
        };
        node * head;
        void clear() {
                for ( node * next = head; next; ) {
                        node * crnt = next;
                        next = crnt->next;
                        delete crnt;
                }
                head = nullptr;
        }
        void copy( const stack & o ) {
                node ** crnt = &head;
                for ( node * next = o.head; next; next = next->next ) {
                        *crnt = new node{ *next->value }; /***/
                        crnt = &(*crnt)->next;
                }
                *crnt = nullptr;
        }
        stack() : head( nullptr ) {}
        stack( const stack & o ) { copy( o ); }
        ~stack() { clear(); }
        stack & operator= ( const stack & o ) {
                if ( this == &o ) return *this;
                clear();
                copy( o );
                return *this;
        }
        bool empty() const { return head == nullptr; }
        void push( const object & value ) { head = new node{ value, head }; /***/ }
        ptr<object> pop() {
                node * n = head;
                head = n->next;
                ptr<object> v = std::move( n->value );
                delete n;
                return v;
        }
};
\end{cfa}


\end{document}

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