source: doc/theses/aaron_moss_PhD/phd/generic-types.tex @ a332d432

\chapter{Generic Types}
\label{generic-chap}

A significant shortcoming in 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 for the reuse of 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 otherwise not 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 in such code may be difficult to locate and debug. 
Furthermore, writing and using preprocessor macros is unnatural and inflexible.
Figure~\ref{bespoke-generic-fig} demonstrates the bespoke approach for a simple linked list with !insert! and !head! operations, while Figure~\ref{void-generic-fig} and Figure~\ref{macro-generic-fig} show the same example using !void*!- and !#define!-based polymorphism, respectively.

\begin{figure}
        \begin{cfa}
                struct int_list { int value; struct int_list* next; };

                void int_list_insert( struct int_list** ls, int x ) {
                        struct int_list* node = malloc(sizeof(struct int_list));
                        node->value = x; node->next = *ls;
                        *ls = node;
                }

                int int_list_head( const struct int_list* ls ) { return ls->value; }

                $\C[\textwidth]{// all code must be duplicated for every generic instantiation}$

                struct string_list { const char* value; struct string_list* next; };

                void string_list_insert( struct string_list** ls, const char* x ) {
                        struct string_list* node = malloc(sizeof(struct string_list));
                        node->value = x; node->next = *ls;
                        *ls = node;
                }

                const char* string_list_head( const struct string_list* ls )
                        { return ls->value; }

                $\C[\textwidth]{// use is efficient and idiomatic}$

                int main() {
                        struct int_list* il = NULL;
                        int_list_insert( &il, 42 );
                        printf("%d\n", int_list_head(il));
                        
                        struct string_list* sl = NULL;
                        string_list_insert( &sl, "hello" );
                        printf("%s\n", string_list_head(sl));
                }
        \end{cfa}

        \caption{Bespoke code for linked list implementation.} \label{bespoke-generic-fig}
\end{figure}

\begin{figure}
        \begin{cfa}
                // single code implementation

                struct list { void* value; struct list* next; };

                $\C[\textwidth]{// internal memory management requires helper functions}$

                void list_insert( struct list** ls, void* x, void* (*copy)(void*) ) {
                        struct list* node = malloc(sizeof(struct list));
                        node->value = copy(x); node->next = *ls;
                        *ls = node;
                }

                void* list_head( const struct list* ls ) { return ls->value; }

                $\C[\textwidth]{// helpers duplicated per type}$

                void* int_copy(void* x) {
                        int* n = malloc(sizeof(int));
                        *n = *(int*)x;
                        return n;
                }

                void* string_copy(void* x) { return strdup((const char*)x); }

                int main() {
                        struct list* il = NULL;
                        int i = 42;
                        list_insert( &il, &i, int_copy );
                        printf("%d\n", *(int*)list_head(il));  $\C[2in]{// unsafe type cast}$
                        
                        struct list* sl = NULL;
                        list_insert( &sl, "hello", string_copy );
                        printf("%s\n", (char*)list_head(sl));  $\C[2in]{// unsafe type cast}$
                }
        \end{cfa}

        \caption{\lstinline{void*}-polymorphic code for linked list implementation.} \label{void-generic-fig}
\end{figure}

\begin{figure}
        \begin{cfa}
                $\C[\textwidth]{// code is nested in macros}$

                #define list(N) N ## _list

                #define list_insert(N) N ## _list_insert

                #define list_head(N) N ## _list_head

                #define define_list(N, T) $\C[0.25in]{ \textbackslash }$
                        struct list(N) { T value; struct list(N)* next; }; $\C[0.25in]{ \textbackslash }$
                        $\C[0.25in]{ \textbackslash }$
                        void list_insert(N)( struct list(N)** ls, T x ) { $\C[0.25in]{ \textbackslash }$
                                struct list(N)* node = malloc(sizeof(struct list(N))); $\C[0.25in]{ \textbackslash }$
                                node->value = x; node->next = *ls; $\C[0.25in]{ \textbackslash }$
                                *ls = node; $\C[0.25in]{ \textbackslash }$
                        } $\C[0.25in]{ \textbackslash }$
                        $\C[0.25in]{ \textbackslash }$
                        T list_head(N)( const struct list(N)* ls ) { return ls->value; }

                define_list(int, int); $\C[3in]{// defines int\_list}$
                define_list(string, const char*); $\C[3in]{// defines string\_list}$

                $\C[\textwidth]{// use is efficient, but syntactically idiosyncratic}$

                int main() {
                        struct list(int)* il = NULL; $\C[3in]{// does not match compiler-visible name}$
                        list_insert(int)( &il, 42 );
                        printf("%d\n", list_head(int)(il));
                        
                        struct list(string)* sl = NULL;
                        list_insert(string)( &sl, "hello" );
                        printf("%s\n", list_head(string)(sl));
                }
        \end{cfa}

        \caption{Macros for generic linked list implementation.} \label{macro-generic-fig}
\end{figure}

\CC{}, Java, and other languages use \emph{generic types} to produce type-safe abstract data types. 
Design and implementation of generic types for \CFA{} is the first major contribution of this thesis, a summary of which is published in \cite{Moss18}. 
\CFA{} generic types integrate efficiently and naturally with the existing polymorphic functions in \CFA{}, while retaining backward compatibility with C in layout and support for separate compilation. 
A generic type can be declared in \CFA{} by placing a !forall! specifier on a !struct! or !union! declaration, and instantiated using a parenthesized list of types after the generic name. 
An example comparable to the C polymorphism examples in Figures~\ref{bespoke-generic-fig}, \ref{void-generic-fig}, and \ref{macro-generic-fig} can be seen in Figure~\ref{cfa-generic-fig} \TODO{test this code}.

\begin{figure}
        \begin{cfa}
                forall(otype T) struct list { T value; list(T)* next; };

                $\C[\textwidth]{// single polymorphic implementation of each function}$
                $\C[\textwidth]{// overloading reduces need for namespace prefixes}$

                forall(otype T) void insert( list(T)** ls, T x ) {
                        list(T)* node = alloc();  $\C{// type-inferring alloc}$
                        (*node){ x, *ls };  $\C{// concise constructor syntax}$
                        *ls = node;
                }

                forall(otype T) T head( const list(T)* ls ) { return ls->value; }

                $\C[\textwidth]{// use is clear and efficient}$

                int main() {
                        list(int)* il = 0;
                        insert( &il, 42 );  $\C{// inferred polymorphic T}$
                        printf("%d\n", head(il));
                        
                        list(const char*)* sl = 0;
                        insert( &sl, "hello" );
                        printf("%s\n", head(sl));
                }
        \end{cfa}

        \caption{\CFA{} generic linked list implementation.} \label{cfa-generic-fig}
\end{figure}

\section{Design}

Though a number of languages have some implementation of generic types, backward compatibility with both C and existing \CFA{} polymorphism presented some unique design constraints for this project. 
The guiding principle was to maintain an unsurprising language model for C programmers without compromising runtime efficiency. 
A key insight for this design was that C already possesses a handful of built-in generic types (\emph{compound types} in the language of the standard\cit{}), notably pointer (!T*!) and array (!T[]!), and that user-definable generics should act similarly.

\subsection{Related Work}

One approach to the design of generic types is that taken by \CC{} templates\cite{C++}. 
The template approach is closely related to the macro-expansion approach to C polymorphism demonstrated in Figure~\ref{macro-generic-fig}, but where the macro-expansion syntax has been given first-class language support. 
Template expansion has the benefit of generating code with near-optimal runtime efficiency, as distinct optimizations can be applied for each instantiation of the template. 
On the other hand, template expansion can also lead to significant code bloat, exponential in the worst case\cit{}, and the costs of increased instruction cache pressure at runtime and wasted developer time when compiling cannot be discounted. 
The most significant restriction of the \CC{} template model is that it breaks separate compilation and C's translation-unit-based encapsulation mechanisms. 
Because a \CC{} template is not actually code, but rather a sort of ``recipe'' to generate code, template code must be visible at its call site to be used. 
Furthermore, \CC{} template code cannot be type-checked without instantiating it, a time consuming process with no hope of improvement until \CC{} concepts\cite{C++Concepts} are standardized in \CCtwenty{}.
C code, by contrast, only needs a !struct! or function declaration to call that function or use (by-pointer) values of that type, a desirable property to maintain for \CFA{}.

Java\cite{Java8} has another prominent implementation for generic types, introduced in Java~5 and based on a significantly different approach than \CC{}. 
The Java approach has much more in common with the !void*!-polymorphism shown in Figure~\ref{void-generic-fig}; since in Java nearly all data is stored by reference, the Java approach to polymorphic data is to store pointers to arbitrary data and insert type-checked implicit casts at compile-time. 
This process of \emph{type erasure} has the benefit of allowing a single instantiation of polymorphic code, but relies heavily on Java's object model and garbage collector. 
To use this model, a more C-like language such as \CFA{} would be required to dynamically allocate internal storage for variables, track their lifetime, and properly clean them up afterward. 

Cyclone\cite{Grossman06} is another language extending C, and 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, which is tedious and error-prone compared to \CFA{}'s implicit assertion satisfaction. 
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 the \CFA{} terminology discussed in Section~\ref{generic-impl-sec}, all Cyclone polymorphism must be dtype-static. 
While the Cyclone polymorphism design provides the efficiency benefits discussed in Section~\ref{dtype-static-sec} for dtype-static polymorphism, it is more restrictive than the more general model of \CFA{}. 

Many other languages include some form of generic types. 
As a brief survey, ML\cite{ML} was the first language to support parameteric polymorphism, but unlike \CFA{} does not support the use of assertions and traits to constrain type arguments. 
Haskell\cite{Haskell10} combines ML-style polymorphism with the notion of type classes, similar to \CFA{} traits, but requiring an explicit association with their implementing types, unlike \CFA{}. 
Objective-C\cite{obj-c-book} is an extension to C which has had some industrial success; however, it did not support type-checked generics until recently\cite{xcode7}, and it's garbage-collected, message-passing object-oriented model is a radical departure from C.
Go\cite{Go}, and Rust\cite{Rust} are modern compiled languages with abstraction features similar to \CFA{} traits, \emph{interfaces} in Go and \emph{traits} in Rust. 
Go has implicit interface implementation and uses a ``fat pointer'' construct to pass polymorphic objects to functions, similar in principle to \CFA{}'s implicit forall paramters. 
Go does not, however, allow user code to define generic types, restricting Go programmers to the small set of generic types defined by the compiler. 
Rust has powerful abstractions for generic programming, including explicit implemenation of traits and options for both separately-compiled virtual dispatch and template-instantiated static dispatch in functions. 
On the other hand, the safety guarantees of Rust's \emph{lifetime} abstraction and borrow checker impose a distinctly idiosyncratic programming style and steep learning curve; \CFA{}, with its more modest safety features, allows direct ports of C code while maintaining the idiomatic style of the original source. 

\subsection{\CFA{} Generics}

The generic types design in \CFA{} draws inspiration from both \CC{} and Java generics, capturing the better aspects of each. 
Like \CC{} template types, generic !struct!s and !union!s in \CFA{} have macro-expanded storage layouts, but, like Java generics, \CFA{} generic types can be used with separately-compiled polymorphic functions without requiring either the type or function definition to be visible to the other. 
The fact that the storage layout of any instantiation of a \CFA{} generic type is identical to that of the monomorphic type produced by simple macro replacement of the generic type parameters is important to provide consistent and predictable runtime performance, and to not impose any undue abstraction penalty on generic code. 
As an example, consider the following generic type and function \TODO{test this}:

\begin{cfa}
forall( otype R, otype S ) struct pair { R first; S second; };

pair(const char*, int) with_len( const char* s ) {
        return (pair(const char*), int){ s, strlen(s) };
}
\end{cfa}

In this example, !with_len! is defined at the same scope as !pair!, but it could be called from any context that can see the definition of !pair! and a declaration of !with_len!. 
If its return type was !pair(const char*, int)*!, callers of !with_len! would only need the declaration !forall(otype R, otype S) struct pair! to call it, in accordance with the usual C rules for opaque types.

!with_len! is itself a monomorphic function, returning a type that is structurally identical to !struct { const char* first; int second; }!, and as such could be called from C given an appropriate redeclaration and demangling flags. 
However, the definition of !with_len! depends on a polymorphic function call to the !pair! constructor, which only needs to be written once (in this case, implicitly by the compiler according to the usual \CFA{} constructor generation\cite{Moss18}) and can be re-used for a wide variety of !pair! instantiations. 
Since the parameters to this polymorphic constructor call are all statically known, compiler inlining can eliminate any runtime overhead of this polymorphic call. 

\CFA{} deliberately does not support \CC{}-style partial specializations of generic types. 
A particularly infamous example in the \CC{} standard library is !vector<bool>!, which is represented as a bitstring rather than the array representation of the other !vector! instantiations. 
Complications from this inconsistency (chiefly the fact that a single bit is not addressable, unlike an array element) make the \CC{} !vector! unpleasant to use in generic contexts due to the break in its public interface. 
Rather than attempting to plug leaks in the template specialization abstraction with a detailed method interface, \CFA{} takes the more principled position that two types with an unrelated data layout are in fact unrelated types, and should be handled with different code. 
Of course, to the degree that distinct types are similar enough to share an interface, the \CFA{} !trait! system allows one to be defined, and objects of types implementing that !trait! to be operated on in the same polymorphic functions. 

Since \CFA{} polymorphic functions can operate over polymorphic generic types, functions over such types can be partially or completely specialized using the usual overload selection rules. 
As an example, the !with_len! function above could be an optimization of the following more general function:

\begin{cfa}
forall(otype T, otype I | { I len(T); })
pair(T, I) with_len( T s ) {
        return (pair(T,I)){ s, len(s) };
}
\end{cfa}

\CFA{} generic types also support the type constraints from !forall! functions. 
For example, the following declaration of a sorted set type ensures that the set key implements equality and relational comparison:

\begin{cfa}
forall(otype Key | { int ?==?(Key, Key); int ?<?(Key, Key); }) struct sorted_set;
\end{cfa}

These constraints are implemented by applying equivalent constraints to the compiler-generated constructors for this type.

\section{Implementation} \label{generic-impl-sec}

The ability to use generic types in polymorphic contexts means that the \CFA{} implementation in \CFACC{} must support a mechanism for accessing fields of generic types dynamically at runtime. 
While \CFACC{} could in principle use this same mechanism for accessing fields of all generic types, such an approach would throw away compiler knowledge of static types and impose an unnecessary runtime cost, limiting the utility of the generic type design. 
Instead, my design for generic type support in \CFACC{} distinguishes between \emph{concrete} generic types that have a fixed memory layout regardless of type parameters and \emph{dynamic} generic types that may vary in memory layout depending on their type parameters.
A \emph{dtype-static} type has polymorphic parameters but is still concrete. 
Polymorphic pointers are an example of dtype-static types; given some type variable !T!, T is a polymorphic type, but !T*! has a fixed size and can therefore be represented by a !void*! in code generation. 
In particular, generic types where all parameters are un-!sized! (\ie{} they do not conform to the built-in !sized! trait because the compiler does not know their size and alignment) are always concrete, as there is no possibility for their layout to vary based on type parameters of unknown size and alignment. 
More precisely, a type is concrete if and only if all of its !sized! type parameters are concrete, and a concrete type is dtype-static if any of its type parameters are (possibly recursively) polymorphic. 
To illustrate, the following code using the !pair! type from above \TODO{test this} has each use of !pair! commented with its class:

\begin{cfa}
//dynamic, layout varies based on T
forall(otype T) T value( pair(const char*, T) p ) { return p.second; }

// dtype-static, F* and T* are concrete but recursively polymorphic
forall(dtype F, otype T) T value( pair(F*, T*) ) { return *p.second; }

pair(const char*, int) p = {"magic", 42}; $\C[2.5in]{// concrete}$
int i = value(p);
pair(void*, int*) q = {0, &p.second}; $\C[2.5in]{// concrete}$
i = value(q);
double d = 1.0;
pair(double*, double*) r = {&d, &d}; $\C[2.5in]{// concrete}$
d = value(r);
\end{cfa}

\subsection{Concrete Generic Types}

The \CFACC{} translator template expands concrete generic types into new structure types, affording maximal inlining. 
To enable interoperation among equivalent instantiations of a generic type, \CFACC{} saves the set of instantiations currently in scope and reuses the generated structure declarations where appropriate. 
In particular, tuple types are implemented as a single compiler-generated generic type definition per tuple arity, and can be instantiated and reused according to the usual rules for generic types. 
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. 
As an example, the concrete instantiation for !pair(const char*, int)! is\footnote{This omits the field name mangling performed by \CFACC{} for overloading purposes.\label{mangle-foot}}

\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 example above, the !pair(F*, T*)! parameter to !value! is such a type; its expansion is below\footref{mangle-foot}, 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}

In addition to this efficient implementation of concrete generic types, \CFA{} also offers flexibility with powerful support for dynamic generic types. 
In the pre-existing compiler design, !otype! (and all !sized!) type parameters come with implicit size and alignment parameters provided by the caller. 
The design for generic types presented here adds an \emph{offset array} containing structure-member offsets for dynamic generic !struct! types. 
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 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 passed or returned by value from a polymorphic function, \CFACC{} can safely assume that 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 above is implemented as 

\begin{cfa}
_assign_T( _retval, p + _offsetof_pair[1] ); $\C[2in]{// return *p.second}$
\end{cfa}

Here, !_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, and !_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}

\subsubsection{Layout Functions}

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 \texttt{.c} file. 
\CFA{} supports this pattern for generic types, implying that the caller of a polymorphic function may not know the actual layout or size of a dynamic generic type and only holds it by pointer. 
\CFACC{} automatically generates \emph{layout functions} for cases where the size, alignment, and offset array of a generic struct cannot be passed into a function from that functions'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 not passed because they are forbidden from being used in a context that affects layout by C's usual rules about incomplete types. 
Similarly, the layout function can only safely be called from a context where the generic type definition is visible, because otherwise the caller will not know how large to allocate the array of member offsets. 

The C standard does not specify a memory layout for structs, but the POSIX ABI for x86\cit{} does; this memory layout is common for C implementations, but is a platform-specific issue for porting \CFA{}. 
This algorithm, sketched below in pseudo-\CFA{}, is a straightforward mapping of consecutive fields into the first properly-aligned offset in the !struct! layout; layout functions for !union! types omit the offset array and simply calculate the maximum size and alignment over all union variants. 
Since \CFACC{} generates a distinct layout function for each type, constant-folding and loop unrolling are applied.

\begin{cfa}
forall(dtype T1, dtype T2, ... | sized(T1) | sized(T2) | ...)
void layout(size_t* size, size_t* align, size_t* offsets) {
        // initialize values
        *size = 0; *align = 1;
        // set up members
        for ( int i = 0; i < n_fields; ++i ) {
                // pad to alignment
                size_t off_align = *size % alignof(field[i]);
                if ( off_align != 0 ) { *size += alignof(field[i]) - off_align; }
                // mark member, increase size, and fix alignment
                offsets[i] = *size;
                *size += sizeof(field[i]);
                if ( *align < alignof(field[i]) ) { *align = alignof(field[i]); }
        }
        // final padding to alignment
        size_t off_align = *size % *align;
        if ( off_align != 0 ) { *size += *align - off_align; }
}
\end{cfa}

Results of layout function calls are cached so that they are only computed once per type per function. 
Layout functions also allow generic types to be used in a function definition without reflecting them in the function signature, an important implemenation-hiding constraint of the design. 
For instance, a function that strips duplicate values from an unsorted !list(T)! likely has a reference to the list 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, providing as an argument the layout of !T! implicitly passed into that function.

Whether a type is concrete, dtype-static, or dynamic is decided solely on the basis of the type arguments and !forall! clause type paramters. 
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. 
In an alternate design where 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{} !Box! could be defined with a body !{ T* p; }!, and would thus not depend on !T! for its layout. 
However, the existence of an !otype! parameter !T! means that !Box! \emph{could} depend on !T! for its layout if this definition is not visible, and we judged preserving separate compilation (and the associated C compatibility) in the implemented design to be an acceptable trade-off.

\subsection{Applications of Dtype-static Types} \label{dtype-static-sec}

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 function for pairs of pointers.

\begin{cfa}
forall(dtype T)
int lexcmp( pair(T*, T*)* a, pair(T*, T*)* b, int (*cmp)(T*, T*) ) {
        int c = cmp( a->first, b->first );
        return c ? c : cmp( a->second, b->second );
}
\end{cfa}

Since !pair(T*, T*)! is a concrete type, there are no implicit parameters passed to !lexcmp!; hence, the generated code is identical to a function written in standard C using !void*!, yet the \CFA{} version is type-checked to ensure members of both pairs and arguments to the comparison function match in type.

Another useful pattern enabled by reused dtype-static type instantiations is zero-cost \emph{tag structures}. 
Sometimes, information is only used for type checking and can be omitted at runtime. 
In the example below, !scalar! is a dtype-static type; hence, 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.

\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 = { 21098 };
scalar(litres) pool = { 2500000 };
scalar(metres) marathon = half_marathon + half_marathon;
`marathon + pool;` $\C[4in]{// compiler ERROR, mismatched types}$
\end{cfa}

\section{Performance Experiments} \label{generic-performance-sec}

\TODO{pull benchmarks from Moss et al.}

\section{Future Work}

The generic types design presented here is already sufficiently expressive to implement a variety of useful library types. 
However, some other features based on this design could further improve \CFA{}. 

The most pressing addition is the ability to have non-type generic parameters. 
C already supports fixed-length array types, \eg{} !int[10]!; these types are essentially generic types with unsigned integer parameters, and allowing \CFA{} users the capability to build similar types is a requested feature. 
More exotically, the ability to have these non-type parameters depend on dynamic runtime values rather than static compile-time constants opens up interesting opportunities for type-checking problematic code patterns. 
For example, if a collection iterator was parameterized over the pointer to the collection it was drawn from, then a sufficiently powerful static analysis pass could ensure that that iterator was only used for that collection, eliminating one source of hard-to-find bugs. 

The implementation mechanisms behind this generic types design can also be used to add new features to \CFA{}. 
One such potential feature would be to add \emph{field assertions} to the existing function and variable assertions on polymorphic type variables. 
Implementation of these field assertions would be based on the same code that supports member access by dynamic offset calculation for dynamic generic types. 
Simulating field access can already be done more flexibly in \CFA{} by declaring a trait containing an accessor function to be called from polymorphic code, but these accessor functions impose some overhead both to write and call, and directly providing field access via an implicit offset parameter would be both more concise and more efficient. 
Of course, there are language design trade-offs to such an approach, notably that providing the two similar features of field and function assertions would impose a burden of choice on programmers writing traits, with field assertions more efficient, but function assertions more general; given this open design question we have deferred a decision on field assertions until we have more experience using \CFA{}.
If field assertions are included in the language, a natural extension would be to provide a structural inheritance mechanism for every !struct! type that simply turns the list of !struct! fields into a list of field assertions, allowing monomorphic functions over that type to be generalized to polymorphic functions over other similar types with added or reordered fields.
\CFA{} could also support a packed or otherwise size-optimized representation for generic types based on a similar mechanism --- the layout function would need to be re-written, but nothing in the use of the offset arrays implies that the field offsets need be monotonically increasing.

With respect to the broader \CFA{} polymorphism design, the experimental results in Section~\ref{generic-performance-sec} demonstrate that though the runtime impact of \CFA{}'s dynamic virtual dispatch is low, it is not as low as the static dispatch of \CC{} template inlining. 
However, rather than subject all \CFA{} users to the compile-time costs of ubiquitous template expansion, we are considering more targeted mechanisms for performance-sensitive code. 
Two promising approaches are are an !inline! annotation at polymorphic function call sites to create a template specialization of the function (provided the code is visible) or placing a different !inline! annotation on polymorphic function definitions to instantiate a specialized version of the function for some set of types. 
These approaches are not mutually exclusive and allow performance optimizations to be applied only when necessary, without suffering global code bloat. 
In general, the \CFA{} team believes that separate compilation works well with loaded hardware caches by producing smaller code, which may offset the benefit of larger inlined code.