Changeset 3fe98b7 for doc/generic_types/generic_types.tex
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doc/generic_types/generic_types.tex
rd9dd3d1 r3fe98b7 87 87 88 88 % inline code @...@ 89 \lstMakeShortInline@ 89 \lstMakeShortInline@% 90 90 91 91 % ACM Information … … 151 151 The C programming language is a foundational technology for modern computing with millions of lines of code implementing everything from commercial operatingsystems to hobby projects. This installation base and the programmers producing it represent a massive softwareengineering investment spanning decades and likely to continue for decades more. 152 152 The \citet{TIOBE} ranks the top 5 most popular programming languages as: Java 16\%, \Textbf{C 7\%}, \Textbf{\CC 5\%}, \CS 4\%, Python 4\% = 36\%, where the next 50 languages are less than 3\% each with a long tail. The top 3 rankings over the past 30 years are: 153 \lstDeleteShortInline@ 153 \lstDeleteShortInline@% 154 154 \begin{center} 155 155 \setlength{\tabcolsep}{10pt} … … 164 164 \end{tabular} 165 165 \end{center} 166 \lstMakeShortInline@ 166 \lstMakeShortInline@% 167 167 Love it or hate it, C is extremely popular, highly used, and one of the few system's languages. 168 168 In many cases, \CC is often used solely as a better C. … … 251 251 252 252 Finally, \CFA allows variable overloading: 253 \lstDeleteShortInline@ 253 \lstDeleteShortInline@% 254 254 \par\smallskip 255 255 \begin{tabular}{@{}l@{\hspace{\parindent}}@{\hspace{\parindent}}l@{}} … … 266 266 \end{lstlisting} 267 267 \end{tabular} 268 \lstMakeShortInline@269 268 \smallskip\par\noindent 269 \lstMakeShortInline@% 270 270 Hence, the single name @MAX@ replaces all the C typespecific names: @SHRT_MAX@, @INT_MAX@, @DBL_MAX@. 271 271 As well, restricted constant overloading is allowed for the values @0@ and @1@, which have special status in C, \eg the value @0@ is both an integer and a pointer literal, so its meaning depends on context. … … 273 273 \begin{lstlisting} 274 274 int x; 275 if (x) // if (x != 0) 276 x++; // x += 1; 275 if (x) x++ $\C{// if (x != 0) x += 1;}$ 277 276 \end{lstlisting} 278 277 Every if statement in C compares the condition with @0@, and every increment and decrement operator is semantically equivalent to adding or subtracting the value @1@ and storing the result. … … 343 342 % int is_nominal; $\C{// int now satisfies the nominal trait}$ 344 343 % \end{lstlisting} 345 % 344 % 346 345 % Traits, however, are significantly more powerful than nominalinheritance 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 nominalinheritance type systems: 347 346 % \begin{lstlisting} … … 354 353 % }; 355 354 % typedef list *list_iterator; 356 % 355 % 357 356 % lvalue int *?( list_iterator it ) { return it>value; } 358 357 % \end{lstlisting} … … 377 376 forall( otype T ) T value( pair( const char *, T ) p ) { return p.second; } 378 377 forall( dtype F, otype T ) T value_p( pair( F *, T * ) p ) { return *p.second; } 379 380 378 pair( const char *, int ) p = { "magic", 42 }; 381 379 int magic = value( p ); … … 493 491 scalar(metres) marathon = half_marathon + half_marathon; 494 492 scalar(litres) two_pools = swimming_pool + swimming_pool; 495 marathon + swimming_pool; $\C{// compilation ERROR}$493 marathon + swimming_pool; $\C{// compilation ERROR}$ 496 494 \end{lstlisting} 497 495 @scalar@ is a dtypestatic type, so all uses have a single structure definition, containing @unsigned long@, and can share the same implementations of common functions like @?+?@. … … 499 497 However, the \CFA typechecker ensures matching types are used by all calls to @?+?@, preventing nonsensical computations like adding a length to a volume. 500 498 499 501 500 \section{Tuples} 502 501 \label{sec:tuples} 503 502 504 The @pair(R, S)@ generic type used as an example in the previous section can be considered a special case of a more general \emph{tuple} data structure. The authors have implemented tuples in \CFA, with a design particularly motivated by two use cases: \emph{multiplereturnvalue functions} and \emph{variadic functions}. 505 506 In standard C, functions can return at most one value. This restriction results in code that emulates functions with multiple return values by \emph{aggregation} or by \emph{aliasing}. In the former situation, the function designer creates a record type that combines all of the return values into a single type. Unfortunately, the designer must come up with a name for the return type and for each of its fields. Unnecessary naming is a common programming language issue, introducing verbosity and a complication of the user's mental model. As such, this technique is effective when used sparingly, but can quickly get out of hand if many functions need to return different combinations of types. In the latter approach, the designer simulates multiple return values by passing the additional return values as pointer parameters. The pointer parameters are assigned inside of the function body to emulate a return. Using this approach, the caller is directly responsible for allocating storage for the additional temporary return values. This responsibility complicates the call site with a sequence of variable declarations leading up to the call. Also, while a disciplined use of @const@ can give clues about whether a pointer parameter is going to be used as an out parameter, it is not immediately obvious from only the function signature whether the callee expects such a parameter to be initialized before the call. Furthermore, while many C functions that accept pointers are designed so that it is safe to pass @NULL@ as a parameter, there are many C functions that are not nullsafe. On a related note, C does not provide a standard mechanism to state that a parameter is going to be used as an additional return value, which makes the job of ensuring that a value is returned more difficult for the compiler. 507 508 C does provide a mechanism for variadic functions through manipulation of @va_list@ objects, but it is notoriously typeunsafe. A variadic function is one that contains at least one parameter, followed by @...@ as the last token in the parameter list. In particular, some form of \emph{argument descriptor} is needed to inform the function of the number of arguments and their types, commonly a format string or counter parameter. It is important to note that both of these mechanisms are inherently redundant, because they require the user to specify information that the compiler knows explicitly. This required repetition is error prone, because it is easy for the user to add or remove arguments without updating the argument descriptor. In addition, C requires the programmer to hard code all of the possible expected types. As a result, it is cumbersome to write a variadic function that is open to extension. For example, consider a simple function that sums $N$ @int@s: 509 \begin{lstlisting} 510 int sum(int N, ...) { 511 va_list args; 512 va_start(args, N); // must manually specify last nonvariadic argument 513 int ret = 0; 514 while(N) { 515 ret += va_arg(args, int); // must specify type 516 N; 517 } 518 va_end(args); 519 return ret; 520 } 521 522 sum(3, 10, 20, 30); // must keep initial counter argument in sync 523 \end{lstlisting} 524 525 The @va_list@ type is a special C data type that abstracts variadic argument manipulation. The @va_start@ macro initializes a @va_list@, given the last named parameter. Each use of the @va_arg@ macro allows access to the next variadic argument, given a type. Since the function signature does not provide any information on what types can be passed to a variadic function, the compiler does not perform any error checks on a variadic call. As such, it is possible to pass any value to the @sum@ function, including pointers, floatingpoint numbers, and structures. In the case where the provided type is not compatible with the argument's actual type after default argument promotions, or if too many arguments are accessed, the behaviour is undefined~\citep{C11}. Furthermore, there is no way to perform the necessary error checks in the @sum@ function at runtime, since type information is not carried into the function body. Since they rely on programmer convention rather than compiletime checks, variadic functions are inherently unsafe. 526 527 In practice, compilers can provide warnings to help mitigate some of the problems. For example, GCC provides the @format@ attribute to specify that a function uses a format string, which allows the compiler to perform some checks related to the standard format specifiers. Unfortunately, this attribute does not permit extensions to the format string syntax, so a programmer cannot extend it to warn for mismatches with custom types. 503 In many languages, functions can return at most one value; 504 however, many operations have multiple outcomes, some exceptional. 505 Consider C's @div@ and @remquo@ functions, which return the quotient and remainder for a division of integer and floatingpoint values, respectively. 506 \begin{lstlisting} 507 typedef struct { int quo, rem; } div_t; 508 div_t div( int num, int den ); 509 double remquo( double num, double den, int * quo ); 510 div_t qr = div( 13, 5 ); $\C{// return quotient/remainder aggregate}$ 511 int q; 512 double r = remquo( 13.5, 5.2, &q ); $\C{// return remainder, alias quotient}$ 513 \end{lstlisting} 514 @div@ aggregates the quotient/remainder in a structure, while @remquo@ aliases a parameter to an argument. 515 Both approaches are awkward. 516 Alternatively, a programming language can directly support returning multiple values, \eg in \CFA: 517 \begin{lstlisting} 518 [ int, int ] div( int num, int den ); $\C{// return two integers}$ 519 [ double, double ] div( double num, double den ); $\C{// return two doubles}$ 520 int q, r; $\C{// overload variable names}$ 521 double q, r; 522 [ q, r ] = div( 13, 5 ); $\C{// select appropriate div and q, r}$ 523 [ q, r ] = div( 13.5, 5.2 ); 524 \end{lstlisting} 525 Clearly, this approach is straightforward to understand and use; 526 therefore, why do few programming languages support this obvious feature or provide it awkwardly? 527 The answer is that there are complex consequences that cascade through multiple aspects of the language, especially the typesystem. 528 This section show these consequences and how \CFA deals with them. 528 529 529 530 530 531 \subsection{Tuple Expressions} 531 532 532 The tuple extensions in \CFA can express multiple return values and variadic function parameters in an efficient and typesafe manner. \CFA introduces \emph{tuple expressions} and \emph{tuple types}. A tuple expression is an expression producing a fixedsize, ordered list of values of heterogeneous types. The type of a tuple expression is the tuple of the subexpression types, or a \emph{tuple type}. In \CFA, a tuple expression is denoted by a commaseparated list of expressions enclosed in square brackets. For example, the expression @[5, 'x', 10.5]@ has type @[int, char, double]@. The previous expression has three \emph{components}. Each component in a tuple expression can be any \CFA expression, including another tuple expression. The order of evaluation of the components in a tuple expression is unspecified, to allow a compiler the greatest flexibility for program optimization. It is, however, guaranteed that each component of a tuple expression is evaluated for sideeffects, even if the result is not used. Multiplereturnvalue functions can equivalently be called \emph{tuplereturning functions}. 533 534 \CFA allows declaration of \emph{tuple variables}, variables of tuple type. For example: 535 \begin{lstlisting} 536 [int, char] most_frequent(const char * ); 537 538 const char* str = "hello, world!"; 539 [int, char] freq = most_frequent(str); 540 printf("%s  %d %c\n", str, freq); 541 \end{lstlisting} 542 In this example, the type of the @freq@ and the return type of @most_frequent@ are both tuple types. Also of note is how the tuple expression @freq@ is implicitly flattened into separate @int@ and @char@ arguments to @printf@; this code snippet could have been shortened by replacing the last two lines with @printf("%s  %d %c\n", str, most_frequent(str));@ using exactly the same mechanism. 543 544 In addition to variables of tuple type, it is also possible to have pointers to tuples, and arrays of tuples. Tuple types can be composed of any types, except for array types, since arrays are not of fixed size, which makes tuple assignment difficult when a tuple contains an array. 545 \begin{lstlisting} 546 [double, int] di; 547 [double, int] * pdi 548 [double, int] adi[10]; 549 \end{lstlisting} 550 This example declares a variable of type @[double, int]@, a variable of type pointer to @[double, int]@, and an array of ten @[double, int]@. 533 The addition of multiplereturnvalue functions (MRVF) are useless without a syntax for accepting multiple values at the callsite. 534 The simplest mechanism for capturing the return values is variable assignment, allowing the values to be retrieved directly. 535 As such, \CFA allows assigning multiple values from a function into multiple variables, using a squarebracketed list of lvalue expressions (as above), called a \emph{tuple}. 536 537 However, functions also use \emph{composition} (nested calls), with the direct consequence that MRVFs must also support composition to be orthogonal with singlereturningvalue functions (SRVF), \eg: 538 \begin{lstlisting} 539 printf( "%d %d\n", div( 13, 5 ) ); $\C{// return values seperated into arguments}$ 540 \end{lstlisting} 541 Here, the values returned by @div@ are composed with the call to @printf@. 542 However, the \CFA typesystem must support significantly more complex composition: 543 \begin{lstlisting} 544 [ int, int ] foo$\(_1\)$( int ); 545 [ double ] foo$\(_2\)$( int ); 546 void bar( int, double, double ); 547 bar( foo( 3 ), foo( 3 ) ); 548 \end{lstlisting} 549 The typeresolver only has the tuple returntypes to resolve the call to @bar@ as the @foo@ parameters are identical, which involves unifying the possible @foo@ functions with @bar@'s parameter list. 550 No combination of @foo@s are an exact match with @bar@'s parameters, so the resolver applies C conversions. 551 The minimal cost is @bar( foo@$_1$@( 3 ), foo@$_2$@( 3 ) )@, giving (@int@, {\color{green}@int@}, @double@) to (@int@, {\color{green}@double@}, @double@) with one {\color{green}safe} (widening) conversion from @int@ to @double@ versus ({\color{red}@double@}, {\color{green}@int@}, {\color{green}@int@}) to ({\color{red}@int@}, {\color{green}@double@}, {\color{green}@double@}) with one {\color{red}unsafe} (narrowing) conversion from @double@ to @int@ and two safe conversions. 552 553 554 \subsection{Tuple Variables} 555 556 An important observation from function composition is that new variable names are not required to initialize parameters from an MRVF. 557 \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. 558 As a consequence, \CFA allows declaration of \emph{tuple variables} that can be initialized from an MRVF, \eg: 559 \begin{lstlisting} 560 [ int, int ] qr = div( 13, 5 ); $\C{// tuplevariable declaration and initialization}$ 561 [ double, double ] qr = div( 13.5, 5.2 ); 562 \end{lstlisting} 563 where the tuple variablename serves the same purpose as the parameter name(s). 564 Tuple variables can be composed of any types, except for array types, since array sizes are generally unknown. 565 566 One way to access the tuplevariable components is with assignment or composition: 567 \begin{lstlisting} 568 [ q, r ] = qr; $\C{// access tuplevariable components}$ 569 printf( "%d %d\n", qr ); 570 \end{lstlisting} 571 \CFA also supports \emph{tuple indexing} to access single components of a tuple expression: 572 \begin{lstlisting} 573 [int, int] * p = &qr; $\C{// tuple pointer}$ 574 int rem = qr.1; $\C{// access remainder}$ 575 int quo = div( 13, 5 ).0; $\C{// access quotient}$ 576 p>0 = 5; $\C{// change quotient}$ 577 bar( qr.1, qr ); $\C{// pass remainder and quotient/remainder}$ 578 rem = [42, div( 13, 5 )].0.1; $\C{// access 2nd component of 1st component of tuple expression}$ 579 \end{lstlisting} 580 551 581 552 582 \subsection{Flattening and Restructuring} 553 583 554 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. 555 \begin{lstlisting} 556 int f(int, int); 557 int g([int, int]); 558 int h(int, [int, int]); 584 In function call contexts, tuples support implicit flattening and restructuring conversions. 585 Tuple flattening recursively expands a tuple into the list of its basic components. 586 Tuple structuring packages a list of expressions into a value of tuple type, \eg: 587 \lstDeleteShortInline@% 588 \par\smallskip 589 \begin{tabular}{@{}l@{\hspace{\parindent}}@{\hspace{\parindent}}l@{}} 590 \begin{lstlisting} 591 int f( int, int ); 592 int g( [int, int] ); 593 int h( int, [int, int] ); 559 594 [int, int] x; 595 \end{lstlisting} 596 & 597 \begin{lstlisting} 560 598 int y; 561 562 f(x); // flatten 563 g(y, 10); // structure 564 h(x, y); // flatten & structure 565 \end{lstlisting} 566 In \CFA, each of these calls is valid. In the call to @f@, @x@ is implicitly flattened so that the components of @x@ are passed as the two arguments to @f@. For the call to @g@, the values @y@ and @10@ are structured into a single argument of type @[int, int]@ to match the type of the parameter of @g@. Finally, in the call to @h@, @y@ is flattened to yield an argument list of length 3, of which the first component of @x@ is passed as the first parameter of @h@, and the second component of @x@ and @y@ are structured into the second argument of type @[int, int]@. The flexible structure of tuples permits a simple and expressive function call syntax to work seamlessly with both single and multiplereturnvalue functions, and with any number of arguments of arbitrarily complex structure. 567 568 % In {KW C} \citep{Buhr94a,Till89}, a precursor to \CFA, there were 4 tuple coercions: opening, closing, flattening, and structuring. Opening coerces a tuple value into a tuple of values, while closing converts a tuple of values into a single tuple value. Flattening coerces a nested tuple into a flat tuple, \ie it takes a tuple with tuple components and expands it into a tuple with only nontuple components. Structuring moves in the opposite direction, \ie it takes a flat tuple value and provides structure by introducing nested tuple components. 569 570 In \CFA, the design has been simplified to require only the two conversions previously described, which trigger only in function call and return situations. Specifically, the expression resolution algorithm examines all of the possible alternatives for an expression to determine the best match. In resolving a function call expression, each combination of function value and list of argument alternatives is examined. Given a particular argument list and function value, the list of argument alternatives is flattened to produce a list of nontuple valued expressions. Then the flattened list of expressions is compared with each value in the function's parameter list. If the parameter's type is not a tuple type, then the current argument value is unified with the parameter type, and on success the next argument and parameter are examined. If the parameter's type is a tuple type, then the structuring conversion takes effect, recursively applying the parameter matching algorithm using the tuple's component types as the parameter list types. Assuming a successful unification, eventually the algorithm gets to the end of the tuple type, which causes all of the matching expressions to be consumed and structured into a tuple expression. For example, in 571 \begin{lstlisting} 572 int f(int, [double, int]); 573 f([5, 10.2], 4); 574 \end{lstlisting} 575 There is only a single definition of @f@, and 3 arguments with only single interpretations. First, the argument alternative list @[5, 10.2], 4@ is flattened to produce the argument list @5, 10.2, 4@. Next, the parameter matching algorithm begins, with $P =~$@int@ and $A =~$@int@, which unifies exactly. Moving to the next parameter and argument, $P =~$@[double, int]@ and $A =~$@double@. This time, the parameter is a tuple type, so the algorithm applies recursively with $P' =~$@double@ and $A =~$@double@, which unifies exactly. Then $P' =~$@int@ and $A =~$@double@, which again unifies exactly. At this point, the end of $P'$ has been reached, so the arguments @10.2, 4@ are structured into the tuple expression @[10.2, 4]@. Finally, the end of the parameter list $P$ has also been reached, so the final expression is @f(5, [10.2, 4])@. 599 f( x ); $\C[1in]{// flatten}$ 600 g( y, 10 ); $\C{// structure}$ 601 h( x, y ); $\C{// flatten and structure}\CRT{}$ 602 \end{lstlisting} 603 \end{tabular} 604 \smallskip\par\noindent 605 \lstMakeShortInline@% 606 In the call to @f@, @x@ is implicitly flattened so the components of @x@ are passed as the two arguments. 607 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@. 608 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]@. 609 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. 610 611 612 \subsection{Tuple Assignment} 613 614 An assignment where the left side is a tuple type is called \emph{tuple assignment}. 615 There are two kinds of tuple assignment depending on whether the right side of the assignment operator has a tuple type or a nontuple type, called \emph{multiple} and \emph{mass assignment}, respectively. 616 \lstDeleteShortInline@% 617 \par\smallskip 618 \begin{tabular}{@{}l@{\hspace{\parindent}}@{\hspace{\parindent}}l@{}} 619 \begin{lstlisting} 620 int x = 10; 621 double y = 3.5; 622 [int, double] z; 623 624 \end{lstlisting} 625 & 626 \begin{lstlisting} 627 z = [x, y]; $\C[1in]{// multiple assignment}$ 628 [x, y] = z; $\C{// multiple assignment}$ 629 z = 10; $\C{// mass assignment}$ 630 [y, x] = 3.14; $\C{// mass assignment}\CRT{}$ 631 \end{lstlisting} 632 \end{tabular} 633 \smallskip\par\noindent 634 \lstMakeShortInline@% 635 Both kinds of tuple assignment have parallel semantics, so that each value on the left and right side is evaluated before any assignments occur. 636 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]@. 637 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. 638 For example, @[y, x] = 3.14@ performs the assignments @y = 3.14@ and @x = 3.14@, yielding @y == 3.14@ and @x == 3@; 639 whereas C cascading assignment @y = x = 3.14@ performs the assignments @x = 3.14@ and @y = x@, yielding @3@ in @y@ and @x@. 640 Finally, tuple assignment is an expression where the result type is the type of the lefthand side of the assignment, just like all other assignment expressions in C. 641 This example shows mass, multiple, and cascading assignment used in one expression: 642 \begin{lstlisting} 643 void f( [int, int] ); 644 f( [x, y] = z = 1.5 ); $\C{// assignments in parameter list}$ 645 \end{lstlisting} 646 576 647 577 648 \subsection{Member Access} 578 649 579 At times, it is desirable to access a single component of a tuplevalued expression without creating unnecessary temporary variables to assign to. Given a tuplevalued expression @e@ and a compiletime constant integer $i$ where $0 \leq i < n$, where $n$ is the number of components in @e@, @e.i@ accesses the $i$\textsuperscript{th} component of @e@. For example, 580 \begin{lstlisting} 581 [int, double] x; 582 [char *, int] f(); 583 void g(double, int); 584 [int, double] * p; 585 586 int y = x.0; // access int component of x 587 y = f().1; // access int component of f 588 p>0 = 5; // access int component of tuple pointedto by p 589 g(x.1, x.0); // rearrange x to pass to g 590 double z = [x, f()].0.1; // access second component of first component of tuple expression 591 \end{lstlisting} 592 As seen above, tupleindex expressions can occur on any tupletyped expression, including tuplereturning functions, squarebracketed tuple expressions, and other tupleindex expressions, provided the retrieved component is also a tuple. This feature was proposed for {KW C}, but never implemented~\citep[p.~45]{Till89}. 593 594 It is possible to access multiple fields from a single expression using a \emph{memberaccess tuple expression}. The result is a single tuple expression whose type is the tuple of the types of the members. For example, 650 It is also possible to access multiple fields from a single expression using a \emph{memberaccess}. 651 The result is a single tuplevalued expression whose type is the tuple of the types of the members, \eg: 595 652 \begin{lstlisting} 596 653 struct S { int x; double y; char * z; } s; 597 s.[x, y, z]; 598 \end{lstlisting} 599 Here, the type of @s.[x, y, z]@ is @[int, double, char *]@. A member tuple expression has the form @a.[x, y, z];@ where @a@ is an expression with type @T@, where @T@ supports member access expressions, and @x, y, z@ are all members of @T@ with types @T$_x$@, @T$_y$@, and @T$_z$@ respectively. Then the type of @a.[x, y, z]@ is @[T$_x$, T$_y$, T$_z$]@. 600 601 Since tuple index expressions are a form of memberaccess expression, it is possible to use tupleindex expressions in conjunction with member tuple expressions to manually restructure a tuple (\eg rearrange components, drop components, duplicate components, etc.): 654 s.[x, y, z] = 0; 655 \end{lstlisting} 656 Here, the mass assignment sets all members of @s@ to zero. 657 Since tupleindex expressions are a form of memberaccess expression, it is possible to use tupleindex expressions in conjunction with member tuple expressions to manually restructure a tuple (\eg rearrange, drop, and duplicate components). 658 \lstDeleteShortInline@% 659 \par\smallskip 660 \begin{tabular}{@{}l@{\hspace{\parindent}}@{\hspace{\parindent}}l@{}} 602 661 \begin{lstlisting} 603 662 [int, int, long, double] x; 604 void f(double, long); 605 606 f(x.[0, 3]); // f(x.0, x.3) 607 x.[0, 1] = x.[1, 0]; // [x.0, x.1] = [x.1, x.0] 608 [long, int, long] y = x.[2, 0, 2]; 609 \end{lstlisting} 610 611 It is possible for a member tuple expression to contain other member access expressions: 663 void f( double, long ); 664 665 \end{lstlisting} 666 & 667 \begin{lstlisting} 668 x.[0, 1] = x.[1, 0]; $\C[1in]{// rearrange: [x.0, x.1] = [x.1, x.0]}$ 669 f( x.[0, 3] ); $\C{// drop: f(x.0, x.3)}\CRT{}$ 670 [int, int, int] y = x.[2, 0, 2]; // duplicate: [y.0, y.1, y.2] = [x.2, x.0. x.2] 671 \end{lstlisting} 672 \end{tabular} 673 \smallskip\par\noindent 674 \lstMakeShortInline@% 675 It is also possible for a member access to contain other member accesses, \eg: 612 676 \begin{lstlisting} 613 677 struct A { double i; int j; }; 614 678 struct B { int * k; short l; }; 615 679 struct C { int x; A y; B z; } v; 616 v.[x, y.[i, j], z.k]; 617 \end{lstlisting} 618 This expression is equivalent to @[v.x, [v.y.i, v.y.j], v.z.k]@. That is, the aggregate expression is effectively distributed across the tuple, which allows simple and easy access to multiple components in an aggregate, without repetition. It is guaranteed that the aggregate expression to the left of the @.@ in a member tuple expression is evaluated exactly once. As such, it is safe to use member tuple expressions on the result of a sideeffecting function. 619 620 \subsection{Tuple Assignment} 621 622 In addition to tupleindex expressions, individual components of tuples can be accessed by a \emph{destructuring assignment} which has a tuple expression with lvalue components on its lefthand side. More generally, an assignment where the lefthand side of the assignment operator has a tuple type is called \emph{tuple assignment}. There are two kinds of tuple assignment depending on whether the righthand side of the assignment operator has a tuple type or a nontuple type, called \emph{multiple assignment} and \emph{mass assignment}, respectively. 623 \begin{lstlisting} 624 int x; 625 double y; 626 [int, double] z; 627 [y, x] = 3.14; // mass assignment 628 [x, y] = z; // multiple assignment 629 z = 10; // mass assignment 630 z = [x, y]; // multiple assignment 631 \end{lstlisting} 632 Let $L_i$ for $i$ in $[0, n)$ represent each component of the flattened lefthand side, $R_i$ represent each component of the flattened righthand side of a multiple assignment, and $R$ represent the righthand side of a mass assignment. 633 634 For a multiple assignment to be valid, both tuples must have the same number of elements when flattened. Multiple assignment assigns $R_i$ to $L_i$ for each $i$. 635 That is, @?=?(&$L_i$, $R_i$)@ must be a welltyped expression. In the previous example, @[x, y] = z@, @z@ is flattened into @z.0, z.1@, and the assignments @x = z.0@ and @y = z.1@ are executed. 636 637 A mass assignment assigns the value $R$ to each $L_i$. For a mass assignment to be valid, @?=?(&$L_i$, $R$)@ must be a welltyped expression. This rule differs from C cascading assignment (\eg @a=b=c@) in that conversions are applied to $R$ in each individual assignment, which prevents data loss from the chain of conversions that can happen during a cascading assignment. For example, @[y, x] = 3.14@ performs the assignments @y = 3.14@ and @x = 3.14@, which results in the value @3.14@ in @y@ and the value @3@ in @x@. On the other hand, the C cascading assignment @y = x = 3.14@ performs the assignments @x = 3.14@ and @y = x@, which results in the value @3@ in @x@, and as a result the value @3@ in @y@ as well. 638 639 Both kinds of tuple assignment have parallel semantics, such that each value on the left side and right side is evaluated \emph{before} any assignments occur. As a result, it is possible to swap the values in two variables without explicitly creating any temporary variables or calling a function: 640 \begin{lstlisting} 641 int x = 10, y = 20; 642 [x, y] = [y, x]; 643 \end{lstlisting} 644 After executing this code, @x@ has the value @20@ and @y@ has the value @10@. 645 646 Tuple assignment is an expression where the result type is the type of the lefthand side of the assignment, just like all other assignment expressions in C. This definition allows cascading tuple assignment and use of tuple assignment in other expression contexts, an occasionally useful idiom to keep code succinct and reduce repetition. 647 % In \CFA, tuple assignment is an expression where the result type is the type of the lefthand side of the assignment, as in normal assignment. That is, a tuple assignment produces the value of the lefthand side after assignment. These semantics allow cascading tuple assignment to work out naturally in any context where a tuple is permitted. These semantics are a change from the original tuple design in {KW C}~\citep{Till89}, wherein tuple assignment was a statement that allows cascading assignments as a special case. This decision was made in an attempt to fix what was seen as a problem with assignment, wherein it can be used in many different locations, such as in functioncall argument position. While permitting assignment as an expression does introduce the potential for subtle complexities, it is impossible to remove assignment expressions from \CFA without affecting backwards compatibility with C. Furthermore, there are situations where permitting assignment as an expression improves readability by keeping code succinct and reducing repetition, and complicating the definition of tuple assignment puts a greater cognitive burden on the user. In another language, tuple assignment as a statement could be reasonable, but it would be inconsistent for tuple assignment to be the only kind of assignment in \CFA that is not an expression. 648 680 v.[x, y.[i, j], z.k]; $\C{// [v.x, [v.y.i, v.y.j], v.z.k]}$ 681 \end{lstlisting} 682 683 684 \begin{comment} 649 685 \subsection{Casting} 650 686 … … 672 708 For example, in 673 709 \begin{lstlisting} 674 675 676 677 678 679 680 681 710 [int, int, int] f(); 711 [int, [int, int], int] g(); 712 713 ([int, double])f(); $\C{// (1)}$ 714 ([int, int, int])g(); $\C{// (2)}$ 715 ([void, [int, int]])g(); $\C{// (3)}$ 716 ([int, int, int, int])g(); $\C{// (4)}$ 717 ([int, [int, int, int]])g(); $\C{// (5)}$ 682 718 \end{lstlisting} 683 719 … … 686 722 687 723 Note that a cast is not a function call in \CFA, so flattening and structuring conversions do not occur for cast expressions\footnote{Userdefined conversions have been considered, but for compatibility with C and the existing use of casts as type ascription, any future design for such conversions would require more precise matching of types than allowed for function arguments and parameters.}. As such, (4) is invalid because the cast target type contains 4 components, while the source type contains only 3. Similarly, (5) is invalid because the cast @([int, int, int])(g().1)@ is invalid. That is, it is invalid to cast @[int, int]@ to @[int, int, int]@. 724 \end{comment} 725 688 726 689 727 \subsection{Polymorphism} 690 728 691 Tuples also integrate with \CFA polymorphism as a special sort of generic type. Due to the implicit flattening and structuring conversions involved in argument passing, @otype@ and @dtype@ parameters are restricted to matching only with nontuple types. 692 \begin{lstlisting} 693 forall(otype T, dtype U) 694 void f(T x, U * y); 695 696 f([5, "hello"]); 697 \end{lstlisting} 698 In this example, @[5, "hello"]@ is flattened, so that the argument list appears as @5, "hello"@. The argument matching algorithm binds @T@ to @int@ and @U@ to @const char*@, and calls the function as normal. 699 700 Tuples, however, may contain polymorphic components. For example, a plus operator can be written to add two triples of a type together. 701 \begin{lstlisting} 702 forall(otype T  { T ?+?(T, T); }) 703 [T, T, T] ?+?([T, T, T] x, [T, T, T] y) { 704 return [x.0+y.0, x.1+y.1, x.2+y.2]; 729 Tuples also integrate with \CFA polymorphism as a kind of generic type. 730 Due to the implicit flattening and structuring conversions involved in argument passing, @otype@ and @dtype@ parameters are restricted to matching only with nontuple types, \eg: 731 \begin{lstlisting} 732 forall(otype T, dtype U) void f( T x, U * y ); 733 f( [5, "hello"] ); 734 \end{lstlisting} 735 where @[5, "hello"]@ is flattened, giving argument list @5, "hello"@, and @T@ binds to @int@ and @U@ binds to @const char@. 736 Tuples, however, may contain polymorphic components. 737 For example, a plus operator can be written to add two triples together. 738 \begin{lstlisting} 739 forall(otype T  { T ?+?( T, T ); }) [T, T, T] ?+?( [T, T, T] x, [T, T, T] y ) { 740 return [x.0 + y.0, x.1 + y.1, x.2 + y.2]; 705 741 } 706 742 [int, int, int] x; … … 709 745 \end{lstlisting} 710 746 711 Flattening and restructuring conversions are also applied to tuple types in polymorphic type assertions. Previously in \CFA, it has been assumed that assertion arguments must match the parameter type exactly, modulo polymorphic specialization (\ie no implicit conversions are applied to assertion arguments). In the example below: 712 \begin{lstlisting} 713 int f([int, double], double); 714 forall(otype T, otype U  { T f(T, U, U); }) 715 void g(T, U); 716 g(5, 10.21); 717 \end{lstlisting} 718 If assertion arguments must match exactly, then the call to @g@ cannot be resolved, since the expected type of @f@ is flat, while the only @f@ in scope requires a tuple type. Since tuples are fluid, this requirement reduces the usability of tuples in polymorphic code. To ease this pain point, function parameter and return lists are flattened for the purposes of type unification, which allows the previous example to pass expression resolution. 719 720 This relaxation is made possible by extending the existing thunk generation scheme, as described by \citet{Bilson03}. Now, whenever a candidate's parameter structure does not exactly match the formal parameter's structure, a thunk is generated to specialize calls to the actual function: 721 \begin{lstlisting} 722 int _thunk(int _p0, double _p1, double _p2) { 723 return f([_p0, _p1], _p2); 724 } 725 \end{lstlisting} 726 Essentially, this thunk provides flattening and structuring conversions to inferred functions, improving the compatibility of tuples and polymorphism. These thunks take advantage of GCC C nested functions to produce closures that have the usual function pointer signature. 747 Flattening and restructuring conversions are also applied to tuple types in polymorphic type assertions. 748 \begin{lstlisting} 749 int f( [int, double], double ); 750 forall(otype T, otype U  { T f( T, U, U ); }) 751 void g( T, U ); 752 g( 5, 10.21 ); 753 \end{lstlisting} 754 Hence, function parameter and return lists are flattened for the purposes of type unification allowing the example to pass expression resolution. 755 This relaxation is possible by extending the thunk scheme described by \citet{Bilson03}. 756 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: 757 \begin{lstlisting} 758 int _thunk( int _p0, double _p1, double _p2 ) { 759 return f( [_p0, _p1], _p2 ); 760 } 761 \end{lstlisting} 762 so the thunk provides flattening and structuring conversions to inferred functions, improving the compatibility of tuples and polymorphism. 763 These thunks take advantage of GCC C nestedfunctions to produce closures that have the usual function pointer signature. 764 727 765 728 766 \subsection{Variadic Tuples} 729 767 730 To define variadic functions, \CFA adds a new kind of type parameter, @ttype@. Matching against a @ttype@ (``tuple type'') parameter consumes all remaining argument components and packages them into a tuple, binding to the resulting tuple of types. In a given parameter list, there should be at most one @ttype@ parameter that must occur last, otherwise the call can never resolve, given the previous rule. This idea essentially matches normal variadic semantics, with a strong feeling of similarity to \CCeleven variadic templates. As such, @ttype@ variables are also referred to as \emph{argument} or \emph{parameter packs} in this paper. 731 732 Like variadic templates, the main way to manipulate @ttype@ polymorphic functions is through recursion. Since nothing is known about a parameter pack by default, assertion parameters are key to doing anything meaningful. Unlike variadic templates, @ttype@ polymorphic functions can be separately compiled. 733 734 For example, the C @sum@ function at the beginning of Section~\ref{sec:tuples} could be written using @ttype@ as: 735 \begin{lstlisting} 736 int sum(){ return 0; } // (0) 737 forall(ttype Params  { int sum(Params); }) 738 int sum(int x, Params rest) { // (1) 739 return x+sum(rest); 740 } 741 sum(10, 20, 30); 742 \end{lstlisting} 743 Since (0) does not accept any arguments, it is not a valid candidate function for the call @sum(10, 20, 30)@. 744 In order to call (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]@. 745 In order to finish the resolution of @sum@, an assertion parameter that matches @int sum(int, int)@ is required. 746 Like in the previous iteration, (0) is not a valid candidate, so (1) is examined with @Params@ bound to @[int]@, requiring the assertion @int sum(int)@. 747 Next, (0) fails, and to satisfy (1) @Params@ is bound to @[]@, requiring an assertion @int sum()@. 748 Finally, (0) matches and (1) fails, which terminates the recursion. 749 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))@. 750 751 As a point of note, this version does not require any form of argument descriptor, since the \CFA type system keeps track of all of these details. It might be reasonable to take the @sum@ function a step further to enforce a minimum number of arguments: 752 \begin{lstlisting} 753 int sum(int x, int y){ 754 return x+y; 755 } 756 forall(ttype Params  { int sum(int, Params); }) 757 int sum(int x, int y, Params rest) { 758 return sum(x+y, rest); 759 } 760 \end{lstlisting} 761 762 One more iteration permits the summation of any summable type, as long as all arguments are the same type: 768 To define variadic functions, \CFA adds a new kind of type parameter, @ttype@ (tuple type). 769 Matching against a @ttype@ parameter consumes all remaining argument components and packages them into a tuple, binding to the resulting tuple of types. 770 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. 771 As such, @ttype@ variables are also called \emph{argument packs}. 772 773 Like variadic templates, the main way to manipulate @ttype@ polymorphic functions is via recursion. 774 Since nothing is known about a parameter pack by default, assertion parameters are key to doing anything meaningful. 775 Unlike variadic templates, @ttype@ polymorphic functions can be separately compiled. 776 For example, a generalized @sum@ function written using @ttype@: 777 \begin{lstlisting} 778 int sum$\(_0\)$() { return 0; } 779 forall(ttype Params  { int sum( Params ); } ) int sum$\(_1\)$( int x, Params rest ) { 780 return x + sum( rest ); 781 } 782 sum( 10, 20, 30 ); 783 \end{lstlisting} 784 Since @sum@\(_0\) does not accept any arguments, it is not a valid candidate function for the call @sum(10, 20, 30)@. 785 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]@. 786 The process continues, @Params@ is bound to @[]@, requiring an assertion @int sum()@, which matches @sum@\(_0\) and terminates the recursion. 787 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))@. 788 789 It is reasonable to take the @sum@ function a step further to enforce a minimum number of arguments: 790 \begin{lstlisting} 791 int sum( int x, int y ) { return x + y; } 792 forall(ttype Params  { int sum( int, Params ); } ) int sum( int x, int y, Params rest ) { 793 return sum( x + y, rest ); 794 } 795 \end{lstlisting} 796 One more step permits the summation of any summable type with all arguments of the same type: 763 797 \begin{lstlisting} 764 798 trait summable(otype T) { 765 T ?+?(T, T);799 T ?+?( T, T ); 766 800 }; 767 forall(otype R  summable(R)) 768 R sum(R x, R y){ 769 return x+y; 770 } 771 forall(otype R, ttype Params 772  summable(R) 773  { R sum(R, Params); }) 774 R sum(R x, R y, Params rest) { 775 return sum(x+y, rest); 776 } 777 \end{lstlisting} 778 Unlike C, it is not necessary to hard code the expected type. This code is naturally open to extension, in that any userdefined type with a @?+?@ operator is automatically able to be used with the @sum@ function. That is to say, the programmer who writes @sum@ does not need full program knowledge of every possible data type, unlike what is necessary to write an equivalent function using the standard C mechanisms. Summing arbitrary heterogeneous lists is possible with similar code by adding the appropriate type variables and addition operators. 779 780 It is also possible to write a typesafe variadic print function which can replace @printf@: 801 forall(otype R  summable( R ) ) R sum( R x, R y ) { 802 return x + y; 803 } 804 forall(otype R, ttype Params  summable(R)  { R sum(R, Params); } ) R sum(R x, R y, Params rest) { 805 return sum( x + y, rest ); 806 } 807 \end{lstlisting} 808 Unlike C variadic functions, it is unnecessary to hard code the number and expected types. 809 Furthermore, this code is extendable so any userdefined type with a @?+?@ operator. 810 Summing arbitrary heterogeneous lists is possible with similar code by adding the appropriate type variables and addition operators. 811 812 It is also possible to write a typesafe variadic print function to replace @printf@: 781 813 \begin{lstlisting} 782 814 struct S { int x, y; }; 783 forall(otype T, ttype Params  784 { void print(T); void print(Params); }) 785 void print(T arg, Params rest) { 786 print(arg); 787 print(rest); 788 } 789 void print(char * x) { printf("%s", x); } 790 void print(int x) { printf("%d", x); } 791 void print(S s) { print("{ ", s.x, ",", s.y, " }"); } 792 793 print("s = ", (S){ 1, 2 }, "\n"); 794 \end{lstlisting} 795 This example function showcases a variadictemplatelike 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, as long as each individual type has a @print@ function. The individual print functions can be used to build up more complicated @print@ functions, such as for @S@, which is something that cannot be done with @printf@ in C. 796 797 It is also possible to use @ttype@ polymorphism to provide arbitrary argument forwarding functions. For example, it is possible to write @new@ as a library function: 798 \begin{lstlisting} 799 struct pair(otype R, otype S); 800 forall(otype R, otype S) 801 void ?{}(pair(R, S) *, R, S); // (1) 802 803 forall(dtype T, ttype Params  sized(T)  { void ?{}(T *, Params); }) 804 T * new(Params p) { 805 return ((T*)malloc( sizeof(T) )){ p }; // construct into result of malloc 806 } 807 808 pair(int, char) * x = new(42, '!'); 809 \end{lstlisting} 810 The @new@ function provides the combination of typesafe @malloc@ with a constructor call, so that it becomes impossible to forget to construct dynamically allocated objects. This function provides the typesafety of @new@ in \CC, without the need to specify the allocated type again, thanks to returntype inference. 811 812 In the call to @new@, @pair(double, char)@ is selected to match @T@, and @Params@ is expanded to match @[double, char]@. The constructor (1) may be specialized to satisfy the assertion for a constructor with an interface compatible with @void ?{}(pair(int, char) *, int, char)@. 815 forall(otype T, ttype Params  { void print(T); void print(Params); }) void print(T arg, Params rest) { 816 print(arg); 817 print(rest); 818 } 819 void print( char * x ) { printf( "%s", x ); } 820 void print( int x ) { printf( "%d", x ); } 821 void print( S s ) { print( "{ ", s.x, ",", s.y, " }" ); } 822 print( "s = ", (S){ 1, 2 }, "\n" ); 823 \end{lstlisting} 824 This example showcases a variadictemplatelike decomposition of the provided argument list. 825 The individual @print@ functions allow printing a single element of a type. 826 The polymorphic @print@ allows printing any list of types, as long as each individual type has a @print@ function. 827 The individual print functions can be used to build up more complicated @print@ functions, such as for @S@, which is something that cannot be done with @printf@ in C. 828 829 Finally, it is possible to use @ttype@ polymorphism to provide arbitrary argument forwarding functions. 830 For example, it is possible to write @new@ as a library function: 831 \begin{lstlisting} 832 struct pair( otype R, otype S ); 833 forall( otype R, otype S ) void ?{}( pair(R, S) *, R, S ); // (1) 834 forall( dtype T, ttype Params  sized(T)  { void ?{}( T *, Params ); } ) T * new( Params p ) { 835 return ((T*)malloc( sizeof(T) )){ p }; // construct into result of malloc 836 } 837 pair( int, char ) * x = new( 42, '!' ); 838 \end{lstlisting} 839 The @new@ function provides the combination of typesafe @malloc@ with a \CFA constructor call, making it impossible to forget constructing dynamically allocated objects. 840 This function provides the typesafety of @new@ in \CC, without the need to specify the allocated type again, thanks to returntype inference. 841 842 % In the call to @new@, @pair(double, char)@ is selected to match @T@, and @Params@ is expanded to match @[double, char]@. The constructor (1) may be specialized to satisfy the assertion for a constructor with an interface compatible with @void ?{}(pair(int, char) *, int, char)@. 843 813 844 814 845 \subsection{Implementation} 815 846 816 Tuples are implemented in the \CFA translator via a transformation into generic types. For each $N$, the first time an $N$tuple is seen in a scope a generic type with $N$ type parameters is generated. For example: 847 Tuples are implemented in the \CFA translator via a transformation into generic types. 848 For each $N$, the first time an $N$tuple is seen in a scope a generic type with $N$ type parameters is generated. \eg: 817 849 \begin{lstlisting} 818 850 [int, int] f() { 819 820 821 } 822 \end{lstlisting} 823 Is transformed into:824 \begin{lstlisting} 825 forall(dtype T0, dtype T1  sized(T0)  sized(T1)) 826 struct _tuple2 { // generated before the first 2tuple 827 828 851 [double, double] x; 852 [int, double, int] y; 853 } 854 \end{lstlisting} 855 is transformed into: 856 \begin{lstlisting} 857 // generated before the first 2tuple 858 forall(dtype T0, dtype T1  sized(T0)  sized(T1)) struct _tuple2 { 859 T0 field_0; 860 T1 field_1; 829 861 }; 830 862 _tuple2(int, int) f() { 831 _tuple2(double, double) x; 832 forall(dtype T0, dtype T1, dtype T2  sized(T0)  sized(T1)  sized(T2)) 833 struct _tuple3 { // generated before the first 3tuple 834 T0 field_0; 835 T1 field_1; 836 T2 field_2; 837 }; 838 _tuple3_(int, double, int) y; 839 } 840 \end{lstlisting} 841 863 _tuple2(double, double) x; 864 // generated before the first 3tuple 865 forall(dtype T0, dtype T1, dtype T2  sized(T0)  sized(T1)  sized(T2)) struct _tuple3 { 866 T0 field_0; 867 T1 field_1; 868 T2 field_2; 869 }; 870 _tuple3(int, double, int) y; 871 } 872 \end{lstlisting} 842 873 Tuple expressions are then simply converted directly into compound literals: 843 874 \begin{lstlisting} 844 875 [5, 'x', 1.24]; 845 876 \end{lstlisting} 846 Becomes:877 becomes: 847 878 \begin{lstlisting} 848 879 (_tuple3(int, char, double)){ 5, 'x', 1.24 }; 849 880 \end{lstlisting} 850 881 882 \begin{comment} 851 883 Since tuples are essentially structures, tuple indexing expressions are just field accesses: 852 884 \begin{lstlisting} … … 883 915 [int, double] _unq0; 884 916 g( 885 886 917 (_unq0_finished_ ? _unq0 : (_unq0 = f(), _unq0_finished_ = 1, _unq0)).0, 918 (_unq0_finished_ ? _unq0 : (_unq0 = f(), _unq0_finished_ = 1, _unq0)).1, 887 919 ); 888 920 \end{lstlisting} … … 892 924 893 925 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 nontrivial 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 nonstandard 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. 926 \end{comment} 927 894 928 895 929 \section{Evaluation} 896 930 897 931 \TODO{Magnus suggests we need some graphs, it's kind of a done thing that the reviewers will be looking for. Also, we've made some unsubstantiated claims about the runtime performance of \CFA, which some microbenchmarks could help with. I'm thinking a simple stack push and pop, with an idiomatic \lstinline@void*@, \CFA, \CC template and \CC virtual inheritance versions (the void* and virtual inheritance versions likely need to be linked lists, or clumsy in their API  possibly both versions) to test generics, and variadic print to test tuples. We measure SLOC, runtime performance, executable size (making sure to include benchmarks for multiple types in the executable), and possibly manually count the number of places where the programmer must provide untypechecked type information. Appendices don't count against our page limit, so we might want to include the source code for the benchmarks (or at least the relevant implementation details) in one.} 932 898 933 899 934 \section{Related Work}
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