Changeset 3fe98b7


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Timestamp:
Apr 13, 2017, 1:17:57 PM (4 years ago)
Author:
Aaron Moss <a3moss@…>
Branches:
aaron-thesis, arm-eh, cleanup-dtors, deferred_resn, demangler, jacob/cs343-translation, jenkins-sandbox, master, new-ast, new-ast-unique-expr, new-env, no_list, persistent-indexer, resolv-new, with_gc
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cceab8a
Parents:
d9dd3d1 (diff), 5103d7a (diff)
Note: this is a merge changeset, the changes displayed below correspond to the merge itself.
Use the (diff) links above to see all the changes relative to each parent.
Message:

Merge branch 'master' of plg.uwaterloo.ca:software/cfa/cfa-cc

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1 edited

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  • doc/generic_types/generic_types.tex

    rd9dd3d1 r3fe98b7  
    8787
    8888% inline code @...@
    89 \lstMakeShortInline@
     89\lstMakeShortInline@%
    9090
    9191% ACM Information
     
    151151The 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.
    152152The \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@%
    154154\begin{center}
    155155\setlength{\tabcolsep}{10pt}
     
    164164\end{tabular}
    165165\end{center}
    166 \lstMakeShortInline@
     166\lstMakeShortInline@%
    167167Love it or hate it, C is extremely popular, highly used, and one of the few system's languages.
    168168In many cases, \CC is often used solely as a better C.
     
    251251
    252252Finally, \CFA allows variable overloading:
    253 \lstDeleteShortInline@
     253\lstDeleteShortInline@%
    254254\par\smallskip
    255255\begin{tabular}{@{}l@{\hspace{\parindent}}|@{\hspace{\parindent}}l@{}}
     
    266266\end{lstlisting}
    267267\end{tabular}
    268 \lstMakeShortInline@
    269268\smallskip\par\noindent
     269\lstMakeShortInline@%
    270270Hence, the single name @MAX@ replaces all the C type-specific names: @SHRT_MAX@, @INT_MAX@, @DBL_MAX@.
    271271As 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.
     
    273273\begin{lstlisting}
    274274int x;
    275 if (x)        // if (x != 0)
    276         x++;    //   x += 1;
     275if (x) x++                                                                      $\C{// if (x != 0) x += 1;}$
    277276\end{lstlisting}
    278277Every 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.
     
    343342% int is_nominal;                                                               $\C{// int now satisfies the nominal trait}$
    344343% \end{lstlisting}
    345 % 
     344%
    346345% 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:
    347346% \begin{lstlisting}
     
    354353% };
    355354% typedef list *list_iterator;
    356 % 
     355%
    357356% lvalue int *?( list_iterator it ) { return it->value; }
    358357% \end{lstlisting}
     
    377376forall( otype T ) T value( pair( const char *, T ) p ) { return p.second; }
    378377forall( dtype F, otype T ) T value_p( pair( F *, T * ) p ) { return *p.second; }
    379 
    380378pair( const char *, int ) p = { "magic", 42 };
    381379int magic = value( p );
     
    493491scalar(metres) marathon = half_marathon + half_marathon;
    494492scalar(litres) two_pools = swimming_pool + swimming_pool;
    495 marathon + swimming_pool;                       $\C{// compilation ERROR}$
     493marathon + swimming_pool;                                       $\C{// compilation ERROR}$
    496494\end{lstlisting}
    497495@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 @?+?@.
     
    499497However, the \CFA type-checker ensures matching types are used by all calls to @?+?@, preventing nonsensical computations like adding a length to a volume.
    500498
     499
    501500\section{Tuples}
    502501\label{sec:tuples}
    503502
    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{multiple-return-value 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 null-safe. On a related note, C does not provide a standard mechanism to state that a parameter is going to be used as an additional return value, which makes the job of ensuring that a value is returned more difficult for the compiler.
    507 
    508 C does provide a mechanism for variadic functions through manipulation of @va_list@ objects, but it is notoriously type-unsafe. 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 non-variadic 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, floating-point numbers, and structures. In the case where the provided type is not compatible with the argument's actual type after default argument promotions, or if too many arguments are accessed, the behaviour is undefined~\citep{C11}. Furthermore, there is no way to perform the necessary error checks in the @sum@ function at run-time, since type information is not carried into the function body. Since they rely on programmer convention rather than compile-time checks, variadic functions are inherently unsafe.
    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.
     503In many languages, functions can return at most one value;
     504however, many operations have multiple outcomes, some exceptional.
     505Consider C's @div@ and @remquo@ functions, which return the quotient and remainder for a division of integer and floating-point values, respectively.
     506\begin{lstlisting}
     507typedef struct { int quo, rem; } div_t;
     508div_t div( int num, int den );
     509double remquo( double num, double den, int * quo );
     510div_t qr = div( 13, 5 );                                        $\C{// return quotient/remainder aggregate}$
     511int q;
     512double 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.
     515Both approaches are awkward.
     516Alternatively, 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 ); $\C{// return two doubles}$
     520int q, r;                                                                       $\C{// overload variable names}$
     521double 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}
     525Clearly, this approach is straightforward to understand and use;
     526therefore, why do few programming languages support this obvious feature or provide it awkwardly?
     527The answer is that there are complex consequences that cascade through multiple aspects of the language, especially the type-system.
     528This section show these consequences and how \CFA deals with them.
    528529
    529530
    530531\subsection{Tuple Expressions}
    531532
    532 The tuple extensions in \CFA can express multiple return values and variadic function parameters in an efficient and type-safe manner. \CFA introduces \emph{tuple expressions} and \emph{tuple types}. A tuple expression is an expression producing a fixed-size, ordered list of values of heterogeneous types. The type of a tuple expression is the tuple of the subexpression types, or a \emph{tuple type}. In \CFA, a tuple expression is denoted by a comma-separated list of expressions enclosed in square brackets. For example, the expression @[5, 'x', 10.5]@ has type @[int, char, double]@. The previous expression has three \emph{components}. Each component in a tuple expression can be any \CFA expression, including another tuple expression. The order of evaluation of the components in a tuple expression is unspecified, to allow a compiler the greatest flexibility for program optimization. It is, however, guaranteed that each component of a tuple expression is evaluated for side-effects, even if the result is not used. Multiple-return-value functions can equivalently be called \emph{tuple-returning functions}.
    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]@.
     533The addition of multiple-return-value functions (MRVF) are useless without a syntax for accepting multiple values at the call-site.
     534The simplest mechanism for capturing the return values is variable assignment, allowing the values to be retrieved directly.
     535As such, \CFA allows assigning multiple values from a function into multiple variables, using a square-bracketed list of lvalue expressions (as above), called a \emph{tuple}.
     536
     537However, functions also use \emph{composition} (nested calls), with the direct consequence that MRVFs must also support composition to be orthogonal with single-returning-value functions (SRVF), \eg:
     538\begin{lstlisting}
     539printf( "%d %d\n", div( 13, 5 ) );                      $\C{// return values seperated into arguments}$
     540\end{lstlisting}
     541Here, the values returned by @div@ are composed with the call to @printf@.
     542However, the \CFA type-system must support significantly more complex composition:
     543\begin{lstlisting}
     544[ int, int ] foo$\(_1\)$( int );
     545[ double ] foo$\(_2\)$( int );
     546void bar( int, double, double );
     547bar( foo( 3 ), foo( 3 ) );
     548\end{lstlisting}
     549The type-resolver only has the tuple return-types to resolve the call to @bar@ as the @foo@ parameters are identical, which involves unifying the possible @foo@ functions with @bar@'s parameter list.
     550No combination of @foo@s are an exact match with @bar@'s parameters, so the resolver applies C conversions.
     551The minimal cost is @bar( foo@$_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
     556An 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.
     558As 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 );                         $\C{// tuple-variable declaration and initialization}$
     561[ double, double ] qr = div( 13.5, 5.2 );
     562\end{lstlisting}
     563where the tuple variable-name serves the same purpose as the parameter name(s).
     564Tuple variables can be composed of any types, except for array types, since array sizes are generally unknown.
     565
     566One way to access the tuple-variable components is with assignment or composition:
     567\begin{lstlisting}
     568[ q, r ] = qr;                                                          $\C{// access tuple-variable components}$
     569printf( "%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;                                           $\C{// tuple pointer}$
     574int rem = qr.1;                                                         $\C{// access remainder}$
     575int quo = div( 13, 5 ).0;                                       $\C{// access quotient}$
     576p->0 = 5;                                                                       $\C{// change quotient}$
     577bar( qr.1, qr );                                                        $\C{// pass remainder and quotient/remainder}$
     578rem = [42, div( 13, 5 )].0.1;                           $\C{// access 2nd component of 1st component of tuple expression}$
     579\end{lstlisting}
     580
    551581
    552582\subsection{Flattening and Restructuring}
    553583
    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]);
     584In function call contexts, tuples support implicit flattening and restructuring conversions.
     585Tuple flattening recursively expands a tuple into the list of its basic components.
     586Tuple 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}
     591int f( int, int );
     592int g( [int, int] );
     593int h( int, [int, int] );
    559594[int, int] x;
     595\end{lstlisting}
     596&
     597\begin{lstlisting}
    560598int 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 multiple-return-value functions, and with any number of arguments of arbitrarily complex structure.
    567 
    568 % In {K-W C} \citep{Buhr94a,Till89}, a precursor to \CFA, there were 4 tuple coercions: opening, closing, flattening, and structuring. Opening coerces a tuple value into a tuple of values, while closing converts a tuple of values into a single tuple value. Flattening coerces a nested tuple into a flat tuple, \ie it takes a tuple with tuple components and expands it into a tuple with only non-tuple components. Structuring moves in the opposite direction, \ie it takes a flat tuple value and provides structure by introducing nested tuple components.
    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 non-tuple valued expressions. Then the flattened list of expressions is compared with each value in the function's parameter list. If the parameter's type is not a tuple type, then the current argument value is unified with the parameter type, and on success the next argument and parameter are examined. If the parameter's type is a tuple type, then the structuring conversion takes effect, recursively applying the parameter matching algorithm using the tuple's component types as the parameter list types. Assuming a successful unification, eventually the algorithm gets to the end of the tuple type, which causes all of the matching expressions to be consumed and structured into a tuple expression. For example, in
    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])@.
     599f( x );                 $\C[1in]{// flatten}$
     600g( y, 10 );             $\C{// structure}$
     601h( x, y );              $\C{// flatten and structure}\CRT{}$
     602\end{lstlisting}
     603\end{tabular}
     604\smallskip\par\noindent
     605\lstMakeShortInline@%
     606In the call to @f@, @x@ is implicitly flattened so the components of @x@ are passed as the two arguments.
     607In 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@.
     608Finally, 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]@.
     609The 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
     614An assignment where the left side is a tuple type is called \emph{tuple assignment}.
     615There are two kinds of tuple assignment depending on whether the right side of the assignment operator has a tuple type or a non-tuple type, called \emph{multiple} and \emph{mass assignment}, respectively.
     616\lstDeleteShortInline@%
     617\par\smallskip
     618\begin{tabular}{@{}l@{\hspace{\parindent}}|@{\hspace{\parindent}}l@{}}
     619\begin{lstlisting}
     620int x = 10;
     621double y = 3.5;
     622[int, double] z;
     623
     624\end{lstlisting}
     625&
     626\begin{lstlisting}
     627z = [x, y];             $\C[1in]{// multiple assignment}$
     628[x, y] = z;             $\C{// multiple assignment}$
     629z = 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@%
     635Both kinds of tuple assignment have parallel semantics, so that each value on the left and right side is evaluated before any assignments occur.
     636As 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]@.
     637This 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.
     638For example, @[y, x] = 3.14@ performs the assignments @y = 3.14@ and @x = 3.14@, yielding @y == 3.14@ and @x == 3@;
     639whereas C cascading assignment @y = x = 3.14@ performs the assignments @x = 3.14@ and @y = x@, yielding @3@ in @y@ and @x@.
     640Finally, 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.
     641This example shows mass, multiple, and cascading assignment used in one expression:
     642\begin{lstlisting}
     643void f( [int, int] );
     644f( [x, y] = z = 1.5 );                                          $\C{// assignments in parameter list}$
     645\end{lstlisting}
     646
    576647
    577648\subsection{Member Access}
    578649
    579 At times, it is desirable to access a single component of a tuple-valued expression without creating unnecessary temporary variables to assign to. Given a tuple-valued expression @e@ and a compile-time 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 pointed-to 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, tuple-index expressions can occur on any tuple-typed expression, including tuple-returning functions, square-bracketed tuple expressions, and other tuple-index expressions, provided the retrieved component is also a tuple. This feature was proposed for {K-W C}, but never implemented~\citep[p.~45]{Till89}.
    593 
    594 It is possible to access multiple fields from a single expression using a \emph{member-access tuple expression}. The result is a single tuple expression whose type is the tuple of the types of the members. For example,
     650It is also possible to access multiple fields from a single expression using a \emph{member-access}.
     651The result is a single tuple-valued expression whose type is the tuple of the types of the members, \eg:
    595652\begin{lstlisting}
    596653struct 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 member-access expression, it is possible to use tuple-index expressions in conjunction with member tuple expressions to manually restructure a tuple (\eg rearrange components, drop components, duplicate components, etc.):
     654s.[x, y, z] = 0;
     655\end{lstlisting}
     656Here, the mass assignment sets all members of @s@ to zero.
     657Since 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).
     658\lstDeleteShortInline@%
     659\par\smallskip
     660\begin{tabular}{@{}l@{\hspace{\parindent}}|@{\hspace{\parindent}}l@{}}
    602661\begin{lstlisting}
    603662[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:
     663void f( double, long );
     664
     665\end{lstlisting}
     666&
     667\begin{lstlisting}
     668x.[0, 1] = x.[1, 0];    $\C[1in]{// rearrange: [x.0, x.1] = [x.1, x.0]}$
     669f( 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@%
     675It is also possible for a member access to contain other member accesses, \eg:
    612676\begin{lstlisting}
    613677struct A { double i; int j; };
    614678struct B { int * k; short l; };
    615679struct 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 side-effecting function.
    619 
    620 \subsection{Tuple Assignment}
    621 
    622 In addition to tuple-index expressions, individual components of tuples can be accessed by a \emph{destructuring assignment} which has a tuple expression with lvalue components on its left-hand side. More generally, an assignment where the left-hand 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 right-hand side of the assignment operator has a tuple type or a non-tuple 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 left-hand side, $R_i$ represent each component of the flattened right-hand side of a multiple assignment, and $R$ represent the right-hand 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 well-typed expression. In the previous example, @[x, y] = z@, @z@ is flattened into @z.0, z.1@, and the assignments @x = z.0@ and @y = z.1@ are executed.
    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 well-typed expression. This rule differs from C cascading assignment (\eg @a=b=c@) in that conversions are applied to $R$ in each individual assignment, which prevents data loss from the chain of conversions that can happen during a cascading assignment. For example, @[y, x] = 3.14@ performs the assignments @y = 3.14@ and @x = 3.14@, which results in the value @3.14@ in @y@ and the value @3@ in @x@. On the other hand, the C cascading assignment @y = x = 3.14@ performs the assignments @x = 3.14@ and @y = x@, which results in the value @3@ in @x@, and as a result the value @3@ in @y@ as well.
    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 left-hand side of the assignment, just like all other assignment expressions in C. This definition allows cascading tuple assignment and use of tuple assignment in other expression contexts, an occasionally useful idiom to keep code succinct and reduce repetition.
    647 % In \CFA, tuple assignment is an expression where the result type is the type of the left-hand side of the assignment, as in normal assignment. That is, a tuple assignment produces the value of the left-hand side after assignment. These semantics allow cascading tuple assignment to work out naturally in any context where a tuple is permitted. These semantics are a change from the original tuple design in {K-W C}~\citep{Till89}, wherein tuple assignment was a statement that allows cascading assignments as a special case. This decision was made in an attempt to fix what was seen as a problem with assignment, wherein it can be used in many different locations, such as in function-call argument position. While permitting assignment as an expression does introduce the potential for subtle complexities, it is impossible to remove assignment expressions from \CFA without affecting backwards compatibility with C. Furthermore, there are situations where permitting assignment as an expression improves readability by keeping code succinct and reducing repetition, and complicating the definition of tuple assignment puts a greater cognitive burden on the user. In another language, tuple assignment as a statement could be reasonable, but it would be inconsistent for tuple assignment to be the only kind of assignment in \CFA that is not an expression.
    648 
     680v.[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}
    649685\subsection{Casting}
    650686
     
    672708For example, in
    673709\begin{lstlisting}
    674   [int, int, int] f();
    675   [int, [int, int], int] g();
    676 
    677   ([int, double])f();           $\C{// (1)}$
    678   ([int, int, int])g();         $\C{// (2)}$
    679   ([void, [int, int]])g();      $\C{// (3)}$
    680   ([int, int, int, int])g();    $\C{// (4)}$
    681   ([int, [int, int, int]])g();  $\C{// (5)}$
     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();  $\C{// (5)}$
    682718\end{lstlisting}
    683719
     
    686722
    687723Note that a cast is not a function call in \CFA, so flattening and structuring conversions do not occur for cast expressions\footnote{User-defined conversions have been considered, but for compatibility with C and the existing use of casts as type ascription, any future design for such conversions would require more precise matching of types than allowed for function arguments and parameters.}. As such, (4) is invalid because the cast target type contains 4 components, while the source type contains only 3. Similarly, (5) is invalid because the cast @([int, int, int])(g().1)@ is invalid. That is, it is invalid to cast @[int, int]@ to @[int, int, int]@.
     724\end{comment}
     725
    688726
    689727\subsection{Polymorphism}
    690728
    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 non-tuple 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];
     729Tuples also integrate with \CFA polymorphism as a kind of generic type.
     730Due 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:
     731\begin{lstlisting}
     732forall(otype T, dtype U) void f( T x, U * y );
     733f( [5, "hello"] );
     734\end{lstlisting}
     735where @[5, "hello"]@ is flattened, giving argument list @5, "hello"@, and @T@ binds to @int@ and @U@ binds to @const char@.
     736Tuples, however, may contain polymorphic components.
     737For example, a plus operator can be written to add two triples together.
     738\begin{lstlisting}
     739forall(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];
    705741}
    706742[int, int, int] x;
     
    709745\end{lstlisting}
    710746
    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.
     747Flattening and restructuring conversions are also applied to tuple types in polymorphic type assertions.
     748\begin{lstlisting}
     749int f( [int, double], double );
     750forall(otype T, otype U | { T f( T, U, U ); })
     751void g( T, U );
     752g( 5, 10.21 );
     753\end{lstlisting}
     754Hence, function parameter and return lists are flattened for the purposes of type unification allowing the example to pass expression resolution.
     755This relaxation is possible by extending the thunk scheme described by \citet{Bilson03}.
     756Whenever 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}
     758int _thunk( int _p0, double _p1, double _p2 ) {
     759        return f( [_p0, _p1], _p2 );
     760}
     761\end{lstlisting}
     762so the thunk provides flattening and structuring conversions to inferred functions, improving the compatibility of tuples and polymorphism.
     763These thunks take advantage of GCC C nested-functions to produce closures that have the usual function pointer signature.
     764
    727765
    728766\subsection{Variadic Tuples}
    729767
    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:
     768To define variadic functions, \CFA adds a new kind of type parameter, @ttype@ (tuple type).
     769Matching against a @ttype@ parameter consumes all remaining argument components and packages them into a tuple, binding to the resulting tuple of types.
     770In 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.
     771As such, @ttype@ variables are also called \emph{argument packs}.
     772
     773Like variadic templates, the main way to manipulate @ttype@ polymorphic functions is via recursion.
     774Since nothing is known about a parameter pack by default, assertion parameters are key to doing anything meaningful.
     775Unlike variadic templates, @ttype@ polymorphic functions can be separately compiled.
     776For example, a generalized @sum@ function written using @ttype@:
     777\begin{lstlisting}
     778int sum$\(_0\)$() { return 0; }
     779forall(ttype Params | { int sum( Params ); } ) int sum$\(_1\)$( int x, Params rest ) {
     780        return x + sum( rest );
     781}
     782sum( 10, 20, 30 );
     783\end{lstlisting}
     784Since @sum@\(_0\) does not accept any arguments, it is not a valid candidate function for the call @sum(10, 20, 30)@.
     785In 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]@.
     786The process continues, @Params@ is bound to @[]@, requiring an assertion @int sum()@, which matches @sum@\(_0\) and terminates the recursion.
     787Effectively, 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
     789It is reasonable to take the @sum@ function a step further to enforce a minimum number of arguments:
     790\begin{lstlisting}
     791int sum( int x, int y ) { return x + y; }
     792forall(ttype Params | { int sum( int, Params ); } ) int sum( int x, int y, Params rest ) {
     793        return sum( x + y, rest );
     794}
     795\end{lstlisting}
     796One more step permits the summation of any summable type with all arguments of the same type:
    763797\begin{lstlisting}
    764798trait summable(otype T) {
    765   T ?+?(T, T);
     799        T ?+?( T, T );
    766800};
    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 user-defined 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 type-safe variadic print function which can replace @printf@:
     801forall(otype R | summable( R ) ) R sum( R x, R y ) {
     802        return x + y;
     803}
     804forall(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}
     808Unlike C variadic functions, it is unnecessary to hard code the number and expected types.
     809Furthermore, this code is extendable so any user-defined type with a @?+?@ operator.
     810Summing arbitrary heterogeneous lists is possible with similar code by adding the appropriate type variables and addition operators.
     811
     812It is also possible to write a type-safe variadic print function to replace @printf@:
    781813\begin{lstlisting}
    782814struct 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 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, 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 type-safe @malloc@ with a constructor call, so that it becomes impossible to forget to construct dynamically allocated objects. This function provides the type-safety of @new@ in \CC, without the need to specify the allocated type again, thanks to return-type inference.
    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)@.
     815forall(otype T, ttype Params | { void print(T); void print(Params); }) void print(T arg, Params rest) {
     816        print(arg);
     817        print(rest);
     818}
     819void print( char * x ) { printf( "%s", x ); }
     820void print( int x ) { printf( "%d", x ); }
     821void print( S s ) { print( "{ ", s.x, ",", s.y, " }" ); }
     822print( "s = ", (S){ 1, 2 }, "\n" );
     823\end{lstlisting}
     824This example showcases a variadic-template-like decomposition of the provided argument list.
     825The individual @print@ functions allow printing a single element of a type.
     826The polymorphic @print@ allows printing any list of types, as long as each individual type has a @print@ function.
     827The 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
     829Finally, it is possible to use @ttype@ polymorphism to provide arbitrary argument forwarding functions.
     830For example, it is possible to write @new@ as a library function:
     831\begin{lstlisting}
     832struct pair( otype R, otype S );
     833forall( otype R, otype S ) void ?{}( pair(R, S) *, R, S );  // (1)
     834forall( 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}
     837pair( int, char ) * x = new( 42, '!' );
     838\end{lstlisting}
     839The @new@ function provides the combination of type-safe @malloc@ with a \CFA constructor call, making it impossible to forget constructing dynamically allocated objects.
     840This function provides the type-safety of @new@ in \CC, without the need to specify the allocated type again, thanks to return-type 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
    813844
    814845\subsection{Implementation}
    815846
    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:
     847Tuples are implemented in the \CFA translator via a transformation into generic types.
     848For each $N$, the first time an $N$-tuple is seen in a scope a generic type with $N$ type parameters is generated. \eg:
    817849\begin{lstlisting}
    818850[int, int] f() {
    819   [double, double] x;
    820   [int, double, int] y;
    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 2-tuple
    827   T0 field_0;
    828   T1 field_1;
     851        [double, double] x;
     852        [int, double, int] y;
     853}
     854\end{lstlisting}
     855is transformed into:
     856\begin{lstlisting}
     857// generated before the first 2-tuple
     858forall(dtype T0, dtype T1 | sized(T0) | sized(T1)) struct _tuple2 {
     859        T0 field_0;
     860        T1 field_1;
    829861};
    830862_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 3-tuple
    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 3-tuple
     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}
    842873Tuple expressions are then simply converted directly into compound literals:
    843874\begin{lstlisting}
    844875[5, 'x', 1.24];
    845876\end{lstlisting}
    846 Becomes:
     877becomes:
    847878\begin{lstlisting}
    848879(_tuple3(int, char, double)){ 5, 'x', 1.24 };
    849880\end{lstlisting}
    850881
     882\begin{comment}
    851883Since tuples are essentially structures, tuple indexing expressions are just field accesses:
    852884\begin{lstlisting}
     
    883915[int, double] _unq0;
    884916g(
    885   (_unq0_finished_ ? _unq0 : (_unq0 = f(), _unq0_finished_ = 1, _unq0)).0,
    886   (_unq0_finished_ ? _unq0 : (_unq0 = f(), _unq0_finished_ = 1, _unq0)).1,
     917        (_unq0_finished_ ? _unq0 : (_unq0 = f(), _unq0_finished_ = 1, _unq0)).0,
     918        (_unq0_finished_ ? _unq0 : (_unq0 = f(), _unq0_finished_ = 1, _unq0)).1,
    887919);
    888920\end{lstlisting}
     
    892924
    893925The 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.
     926\end{comment}
     927
    894928
    895929\section{Evaluation}
    896930
    897931\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 micro-benchmarks 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 un-type-checked 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
    898933
    899934\section{Related Work}
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