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5\section{\CFA Background}
7\CFA is a modern extension to the C programming language.
8As it is an extension of C, there is already a wealth of existing C code and principles that govern the design of the language.
9Among the goals set out in the original design of \CFA, four points stand out \cite{Bilson03}.
11\item The behaviour of standard C code must remain the same when translated by a \CFA compiler as when translated by a C compiler.
12\item Standard C code must be as fast and as small when translated by a \CFA compiler as when translated by a C compiler.
13\item \CFA code must be at least as portable as standard C code.
14\item Extensions introduced by \CFA must be translated in the most efficient way possible.
16Therefore, these design principles must be kept in mind throughout the design and development of new language features.
17In order to appeal to existing C programmers, great care must be taken to ensure that new features naturally feel like C.
18The remainder of this section describes some of the important new features that currently exist in \CFA, to give the reader the necessary context in which the new features presented in this thesis must dovetail. % TODO: harmonize with?
20\subsection{C Background}
22One of the lesser-known features of standard C is \emph{designations}.
23Designations are similar to named parameters in languages such as Python and Scala, except that they only apply to aggregate initializers.
25struct A {
26  int w, x, y, z;
28A a0 = { .x:4 .z:1, .x:8 };
29A a1 = { 1, .y:7, 6 };
30A a2[4] = { [2]:a0, [0]:a1, { .z:3 } };
31// equvialent to
32// A a0 = { 0, 8, 0, 1 };
33// A a1 = { 1, 0, 7, 6 };
34// A a2[4] = { a1, { 0, 0, 0, 3 }, a0, { 0, 0, 0, 0 } };
36Designations allow specifying the field to initialize by name, rather than by position.
37Any field not explicitly initialized is initialized as if it had static storage duration \cite[p.~141]{C11}.
38A designator specifies the current object for initialization, and as such any undesignated subobjects pick up where the last initialization left off.
39For example, in the initialization of @a1@, the initializer of @y@ is @7@, and the unnamed initializer @6@ initializes the next subobject, @z@.
40Later initializers override earlier initializers, so a subobject for which there is more than one initializer is only initailized by its last initializer.
41This can be seen in the initialization of @a0@, where @x@ is designated twice, and thus initialized to @8@.
42Note that in \CFA, designations use a colon separator, rather than an equals sign as in C.
44C also provides \emph{compound literal} expressions, which provide a first-class mechanism for creating unnamed objects.
46struct A { int x, y; };
47int f(A, int);
48int g(int *);
50f((A){ 3, 4 }, (int){ 5 } = 10);
51g((int[]){ 1, 2, 3 });
52g(&(int){ 0 });
54Compound literals create an unnamed object, and result in an lvalue, so it is legal to assign a value into a compound literal or to take its address \cite[p.~86]{C11}.
55Syntactically, compound literals look like a cast operator followed by a brace-enclosed initializer, but semantically are different from a C cast, which only applies basic conversions and is never an lvalue.
59Overloading is the ability to specify multiple entities with the same name.
60The most common form of overloading is function overloading, wherein multiple functions can be defined with the same name, but with different signatures.
61Like in \CC, \CFA allows overloading based both on the number of parameters and on the types of parameters.
62  \begin{cfacode}
63  void f(void);  // (1)
64  void f(int);   // (2)
65  void f(char);  // (3)
67  f('A');        // selects (3)
68  \end{cfacode}
69In this case, there are three @f@ procedures, where @f@ takes either 0 or 1 arguments, and if an argument is provided then it may be of type @int@ or of type @char@.
70Exactly which procedure is executed depends on the number and types of arguments passed.
71If there is no exact match available, \CFA attempts to find a suitable match by examining the C built-in conversion heuristics.
72  \begin{cfacode}
73  void g(long long);
75  g(12345);
76  \end{cfacode}
77In the above example, there is only one instance of @g@, which expects a single parameter of type @long long@.
78Here, the argument provided has type @int@, but since all possible values of type @int@ can be represented by a value of type @long long@, there is a safe conversion from @int@ to @long long@, and so \CFA calls the provided @g@ routine.
80In addition to this form of overloading, \CFA also allows overloading based on the number and types of \emph{return} values.
81This extension is a feature that is not available in \CC, but is available in other programming languages such as Ada \cite{Ada95}.
82  \begin{cfacode}
83  int g();         // (1)
84  double g();      // (2)
86  int x = g();     // selects (1)
87  \end{cfacode}
88Here, the only difference between the signatures of the different versions of @g@ is in the return values.
89The result context is used to select an appropriate routine definition.
90In this case, the result of @g@ is assigned into a variable of type @int@, so \CFA prefers the routine that returns a single @int@, because it is an exact match.
92There are times when a function should logically return multiple values.
93Since a function in standard C can only return a single value, a programmer must either take in additional return values by address, or the function's designer must create a wrapper structure t0 package multiple return-values.
95int f(int * ret) {        // returns a value through parameter ret
96  *ret = 37;
97  return 123;
100int res1, res2;           // allocate return value
101int res1 = g(&res2);      // explicitly pass storage
103The former solution is awkward because it requires the caller to explicitly allocate memory for $n$ result variables, even if they are only temporary values used as a subexpression, or even not used at all.
105struct A {
106  int x, y;
108struct A g() {            // returns values through a structure
109  return (struct A) { 123, 37 };
111struct A res3 = g();
112... res3.x ... res3.y ... // use result values
114The latter approach requires the caller to either learn the field names of the structure or learn the names of helper routines to access the individual return values.
115Both solutions are syntactically unnatural.
117In \CFA, it is possible to directly declare a function returning mutliple values.
118This provides important semantic information to the caller, since return values are only for output.
120[int, int] f() {       // don't need to create a new type
121  return [123, 37];
124However, the ability to return multiple values requires a syntax for accepting the results from a function.
125In standard C, return values are most commonly assigned directly into local variables, or are used as the arguments to another function call.
126\CFA allows both of these contexts to accept multiple return values.
128int res1, res2;
129[res1, res2] = f();    // assign return values into local variables
131void g(int, int);
132g(f());                // pass both return values of f to g
134As seen in the example, it is possible to assign the results from a return value directly into local variables.
135These local variables can be referenced naturally, without requiring any unpacking as in structured return values.
136Perhaps more interesting is the fact that multiple return values can be passed to multiple parameters seamlessly, as in the call @g(f())@.
137In this call, the return values from @f@ are linked to the parameters of @g@ so that each of the return values is passed directly to the corresponding parameter of @g@, without any explicit storing, unpacking, or additional naming.
139An extra quirk introduced by multiple return values is in the resolution of function calls.
140  \begin{cfacode}
141  int f();            // (1)
142  [int, int] f();     // (2)
144  void g(int, int);
146  int x, y;
147  [x, y] = f();       // selects (2)
148  g(f());             // selects (2)
149  \end{cfacode}
150In this example, the only possible call to @f@ that can produce the two @int@s required by @g@ is the second option.
151A similar reasoning holds for assigning into multiple variables.
153In \CFA, overloading also applies to operator names, known as \emph{operator overloading}.
154Similar to function overloading, a single operator is given multiple meanings by defining new versions of the operator with different signatures.
155In \CC, this can be done as follows
156  \begin{cppcode}
157  struct A { int i; };
158  int operator+(A x, A y);
159  bool operator<(A x, A y);
160  \end{cppcode}
162In \CFA, the same example can be written as follows.
163  \begin{cfacode}
164  struct A { int i; };
165  int ?+?(A x, A y);
166  bool ?<?(A x, A y);
167  \end{cfacode}
168Notably, the only difference in this example is syntax.
169Most of the operators supported by \CC for operator overloading are also supported in \CFA.
170Of notable exception are the logical operators (e.g. @||@), the sequence operator (i.e. @,@), and the member-access operators (e.g. @.@ and \lstinline{->}).
172Finally, \CFA also permits overloading variable identifiers.
173This feature is not available in \CC.
174  \begin{cfacode} % TODO: pick something better than x? max, zero, one?
175  struct Rational { int numer, denom; };
176  int x = 3;               // (1)
177  double x = 1.27;         // (2)
178  Rational x = { 4, 11 };  // (3)
180  void g(double);
182  x += 1;                  // chooses (1)
183  g(x);                    // chooses (2)
184  Rational y = x;          // chooses (3)
185  \end{cfacode}
186In this example, there are three definitions of the variable @x@.
187Based on the context, \CFA attempts to choose the variable whose type best matches the expression context.
189Finally, the values @0@ and @1@ have special status in standard C.
190In particular, the value @0@ is both an integer and a pointer literal, and thus its meaning depends on the context.
191In addition, several operations can be redefined in terms of other operations and the values @0@ and @1@.
192For example,
194int x;
195if (x) {  // if (x != 0)
196  x++;    //   x += 1;
199Every 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.
200Due to these rewrite rules, the values @0@ and @1@ have the types \zero and \one in \CFA, which allow for overloading various operations that connect to @0@ and @1@ \footnote{In the original design of \CFA, @0@ and @1@ were overloadable names \cite[p.~7]{cforall}.}.
201The types \zero and \one have special built in implicit conversions to the various integral types, and a conversion to pointer types for @0@, which allows standard C code involving @0@ and @1@ to work as normal.
202  \begin{cfacode}
203  // lvalue is similar to returning a reference in C++
204  lvalue Rational ?+=?(Rational *a, Rational b);
205  Rational ?=?(Rational * dst, zero_t) {
206    return *dst = (Rational){ 0, 1 };
207  }
209  Rational sum(Rational *arr, int n) {
210    Rational r;
211    r = 0;     // use rational-zero_t assignment
212    for (; n > 0; n--) {
213      r += arr[n-1];
214    }
215    return r;
216  }
217  \end{cfacode}
218This function takes an array of @Rational@ objects and produces the @Rational@ representing the sum of the array.
219Note the use of an overloaded assignment operator to set an object of type @Rational@ to an appropriate @0@ value.
223In its most basic form, polymorphism grants the ability to write a single block of code that accepts different types.
224In particular, \CFA supports the notion of parametric polymorphism.
225Parametric polymorphism allows a function to be written generically, for all values of all types, without regard to the specifics of a particular type.
226For example, in \CC, the simple identity function for all types can be written as
227  \begin{cppcode}
228  template<typename T>
229  T identity(T x) { return x; }
230  \end{cppcode}
231\CC uses the template mechanism to support parametric polymorphism. In \CFA, an equivalent function can be written as
232  \begin{cfacode}
233  forall(otype T)
234  T identity(T x) { return x; }
235  \end{cfacode}
236Once again, the only visible difference in this example is syntactic.
237Fundamental differences can be seen by examining more interesting examples.
238In \CC, a generic sum function is written as follows
239  \begin{cppcode}
240  template<typename T>
241  T sum(T *arr, int n) {
242    T t;
243    for (; n > 0; n--) t += arr[n-1];
244    return t;
245  }
246  \end{cppcode}
247Here, the code assumes the existence of a default constructor, assignment operator, and an addition operator over the provided type @T@.
248If any of these required operators are not available, the \CC compiler produces an error message stating which operators could not be found.
250A similar sum function can be written in \CFA as follows
251  \begin{cfacode}
252  forall(otype T | **R**{ T ?=?(T *, zero_t); T ?+=?(T *, T); }**R**)
253  T sum(T *arr, int n) {
254    T t = 0;
255    for (; n > 0; n--) t = t += arr[n-1];
256    return t;
257  }
258  \end{cfacode}
259The first thing to note here is that immediately following the declaration of @otype T@ is a list of \emph{type assertions} that specify restrictions on acceptable choices of @T@.
260In particular, the assertions above specify that there must be a an assignment from \zero to @T@ and an addition assignment operator from @T@ to @T@.
261The existence of an assignment operator from @T@ to @T@ and the ability to create an object of type @T@ are assumed implicitly by declaring @T@ with the @otype@ type-class.
262In addition to @otype@, there are currently two other type-classes.
263The three type parameter kinds are summarized in \autoref{table:types}
266  \begin{center}
267    \begin{tabular}{|c||c|c|c||c|c|c|}
268                                                                                                    \hline
269    name    & object type & incomplete type & function type & can assign value & can create & has size \\ \hline
270    @otype@ & X           &                 &               & X                & X          & X        \\ \hline
271    @dtype@ & X           & X               &               &                  &            &          \\ \hline
272    @ftype@ &             &                 & X             &                  &            &          \\ \hline
273    \end{tabular}
274  \end{center}
275  \caption{\label{table:types} The different kinds of type parameters in \CFA}
278A major difference between the approaches of \CC and \CFA to polymorphism is that the set of assumed properties for a type is \emph{explicit} in \CFA.
279One of the major limiting factors of \CC's approach is that templates cannot be separately compiled.
280In contrast, the explicit nature of assertions allows \CFA's polymorphic functions to be separately compiled.
282In \CFA, a set of assertions can be factored into a \emph{trait}.
284  trait Addable(otype T) {
285    T ?+?(T, T);
286    T ++?(T);
287    T ?++(T);
288  }
289  forall(otype T | Addable(T)) void f(T);
290  forall(otype T | Addable(T) | { T --?(T); }) T g(T);
291  forall(otype T, U | Addable(T) | { T ?/?(T, U); }) U h(T, U);
293This capability allows specifying the same set of assertions in multiple locations, without the repetition and likelihood of mistakes that come with manually writing them out for each function declaration.
296% TODO: discuss software engineering benefits of ctor/dtors: {pre/post} conditions, invariants
297% an important invariant is the state of the environment (memory, resources)
298% some objects pass their contract to the object user
299An \emph{invariant} is a logical assertion that true for some duration of a program's execution.
300Invariants help a programmer to reason about code correctness and prove properties of programs.
302In object-oriented programming languages, type invariants are typically established in a constructor and maintained throughout the object's lifetime.
303This is typically achieved through a combination of access control modifiers and a restricted interface.
304Typically, data which requires the maintenance of an invariant is hidden from external sources using the \emph{private} modifier, which restricts reads and writes to a select set of trusted routines, including member functions.
305It is these trusted routines that perform all modifications to internal data in a way that is consistent with the invariant, by ensuring that the invariant holds true at the end of the routine call.
307In C, the @assert@ macro is often used to ensure invariants are true.
308Using @assert@, the programmer can check a condition and abort execution if the condition is not true.
309This is a powerful tool that forces the programmer to deal with logical inconsistencies as they occur.
310For production, assertions can be removed by simply defining the preprocessor macro @NDEBUG@, making it simple to ensure that assertions are 0-cost for a performance intensive application.
312struct Rational {
313  int n, d;
315struct Rational create_rational(int n, int d) {
316  assert(d != 0);  // precondition
317  if (d < 0) {
318    n *= -1;
319    d *= -1;
320  }
321  assert(d > 0);  // postcondition
322  // rational invariant: d > 0
323  return (struct Rational) { n, d };
325struct Rational rat_abs(struct Rational r) {
326  assert(r.d > 0); // check invariant, since no access control
327  r.n = abs(r.n);
328  assert(r.d > 0); // ensure function preserves invariant on return value
329  return r;
333Some languages, such as D, provide language-level support for specifying program invariants.
334In addition to providing a C-like @assert@ expression, D allows specifying type invariants that are automatically checked at the end of a constructor, beginning of a destructor, and at the beginning and end of every public member function.
336import std.math;
337struct Rational {
338  invariant {
339    assert(d > 0, "d <= 0");
340  }
341  int n, d;
342  this(int n, int d) {  // constructor
343    assert(d != 0);
344    this.n = n;
345    this.d = d;
346    // implicitly check invariant
347  }
348  Rational abs() {
349    // implicitly check invariant
350    return Rational(std.math.abs(n), d);
351    // implicitly check invariant
352  }
355The D compiler is able to assume that assertions and invariants hold true and perform optimizations based on those assumptions.
357An important invariant is the state of the execution environment, including the heap, the open file table, the state of global variables, etc.
358Since resources are finite, it is important to ensure that objects clean up properly when they are finished, restoring the execution environment to a stable state so that new objects can reuse resources.
360\section{Resource Management}
363Resource management is a problem that pervades every programming language.
365In standard C, resource management is largely a manual effort on the part of the programmer, with a notable exception to this rule being the program stack.
366The program stack grows and shrinks automatically with each function call, as needed for local variables.
367However, whenever a program needs a variable to outlive the block it is created in, the storage must be allocated dynamically with @malloc@ and later released with @free@.
368This pattern is extended to more complex objects, such as files and sockets, which also outlive the block where they are created, but at their core is resource management.
369Once allocated storage escapes a block, the responsibility for deallocating the storage is not specified in a function's type, that is, that the return value is owned by the caller.
370This implicit convention is provided only through documentation about the expectations of functions.
372In other languages, a hybrid situation exists where resources escape the allocation block, but ownership is precisely controlled by the language.
373This pattern requires a strict interface and protocol for a data structure, where the protocol consists of a pre-initialization and a post-termination call, and all intervening access is done via interface routines.
374This kind of encapsulation is popular in object-oriented programming languages, and like the stack, it contains a significant portion of resource management cases.
376For example, \CC directly supports this pattern through class types and an idiom known as RAII \footnote{Resource Acquisition is Initialization} by means of constructors and destructors.
377Constructors and destructors are special routines that are automatically inserted into the appropriate locations to bookend the lifetime of an object.
378Constructors allow the designer of a type to establish invariants for objects of that type, since it is guaranteed that every object must be initialized through a constructor.
379In particular, constructors allow a programmer to ensure that all objects are initially set to a valid state.
380On the other hand, destructors provide a simple mechanism for tearing down an object and resetting the environment in which the object lived.
381RAII ensures that if all resources are acquired in a constructor and released in a destructor, there are no resource leaks, even in exceptional circumstances.
382A type with at least one non-trivial constructor or destructor will henceforth be referred to as a \emph{managed type}.
383In the context of \CFA, a non-trivial constructor is either a user defined constructor or an auto generated constructor that calls a non-trivial constructor.
385For the remaining resource ownership cases, programmer must follow a brittle, explicit protocol for freeing resources or an implicit porotocol implemented via the programming language.
387In garbage collected languages, such as Java, resources are largely managed by the garbage collector.
388Still, garbage collectors are typically focus only on memory management.
389There are many kinds of resources that the garbage collector does not understand, such as sockets, open files, and database connections.
390In particular, Java supports \emph{finalizers}, which are similar to destructors.
391Sadly, finalizers come with far fewer guarantees, to the point where a completely conforming JVM may never call a single finalizer. % TODO: citation JVM spec;
392Due to operating system resource limits, this is unacceptable for many long running tasks. % TODO: citation?
393Instead, the paradigm in Java requires programmers manually keep track of all resource \emph{except} memory, leading many novices and experts alike to forget to close files, etc.
394Complicating the picture, uncaught exceptions can cause control flow to change dramatically, leaking a resource which appears on first glance to be closed.
396void write(String filename, String msg) throws Exception {
397  FileOutputStream out = new FileOutputStream(filename);
398  FileOutputStream log = new FileOutputStream(filename);
399  out.write(msg.getBytes());
400  log.write(msg.getBytes());
401  log.close();
402  out.close();
405Any line in this program can throw an exception.
406This leads to a profusion of finally blocks around many function bodies, since it isn't always clear when an exception may be thrown.
408public void write(String filename, String msg) throws Exception {
409  FileOutputStream out = new FileOutputStream(filename);
410  try {
411    FileOutputStream log = new FileOutputStream("log.txt");
412    try {
413      out.write(msg.getBytes());
414      log.write(msg.getBytes());
415    } finally {
416      log.close();
417    }
418  } finally {
419    out.close();
420  }
423In Java 7, a new \emph{try-with-resources} construct was added to alleviate most of the pain of working with resources, but ultimately it still places the burden squarely on the user rather than on the library designer.
424Furthermore, for complete safety this pattern requires nested objects to be declared separately, otherwise resources which can throw an exception on close can leak nested resources. % TODO: cite oracle article
426public void write(String filename, String msg) throws Exception {
427  try (
428    FileOutputStream out = new FileOutputStream(filename);
429    FileOutputStream log = new FileOutputStream("log.txt");
430  ) {
431    out.write(msg.getBytes());
432    log.write(msg.getBytes());
433  } // automatically closes out and log in every exceptional situation
436On the other hand, the Java compiler generates more code if more resources are declared, meaning that users must be more familiar with each type and library designers must provide better documentation.
438% D has constructors and destructors that are worth a mention (under classes)
439%  also
440% these are declared in the struct, so they're closer to C++ than to CFA, at least syntactically. Also do not allow for default constructors
441% D has a GC, which already makes the situation quite different from C/C++
442The programming language, D, also manages resources with constructors and destructors \cite{D}.
443In D, @struct@s are stack allocated and managed via scoping like in \CC, whereas @class@es are managed automatically by the garbage collector.
444Like Java, using the garbage collector means that destructors may never be called, requiring the use of finally statements to ensure dynamically allocated resources that are not managed by the garbage collector, such as open files, are cleaned up.
445Since D supports RAII, it is possible to use the same techniques as in \CC to ensure that resources are released in a timely manner.
446Finally, D provides a scope guard statement, which allows an arbitrary statement to be executed at normal scope exit with \emph{success}, at exceptional scope exit with \emph{failure}, or at normal and exceptional scope exit with \emph{exit}. % cite?
447It has been shown that the \emph{exit} form of the scope guard statement can be implemented in a library in \CC. % cite:
449% TODO: discussion of lexical scope vs. dynamic
450% see Peter's suggestions
451% RAII works in both cases. Guaranteed to work in stack case, works in heap case if root is deleted (but it's dangerous to rely on this, because of exceptions)
455In mathematics, tuples are finite-length sequences which, unlike sets, allow duplicate elements.
456In programming languages, tuples are a construct that provide fixed-sized heterogeneous lists of elements.
457Many programming languages have tuple constructs, such as SETL, \KWC, ML, and Scala.
459\KWC, a predecessor of \CFA, introduced tuples to C as an extension of the C syntax, rather than as a full-blown data type \cite{Till89}.
460In particular, Till noted that C already contains a tuple context in the form of function parameter lists.
461The main contributions of that work were in the form of adding tuple contexts to assignment in the form of multiple assignment and mass assignment (discussed in detail in section \ref{s:TupleAssignment}), function return values (see section \ref{s:MRV_Functions}), and record field access (see section \ref{s:MemberAccessTuple}).
462Adding tuples to \CFA has previously been explored by Esteves \cite{Esteves04}.
464The design of tuples in \KWC took much of its inspiration from SETL.
465SETL is a high-level mathematical programming language, with tuples being one of the primary data types.
466Tuples in SETL allow a number of operations, including subscripting, dynamic expansion, and multiple assignment.
468\CCeleven introduced @std::tuple@ as a library variadic template struct.
469Tuples are a generalization of @std::pair@, in that they allow for arbitrary length, fixed-size aggregation of heterogeneous values.
471tuple<int, int, int> triple(10, 20, 30);
472get<1>(triple); // access component 1 => 30
474tuple<int, double> f();
475int i;
476double d;
477tie(i, d) = f(); // assign fields of return value into local variables
479tuple<int, int, int> greater(11, 0, 0);
480triple < greater; // true
482Tuples are simple data structures with few specific operations.
483In particular, it is possible to access a component of a tuple using @std::get<N>@.
484Another interesting feature is @std::tie@, which creates a tuple of references, which allows assigning the results of a tuple-returning function into separate local variables, without requiring a temporary variable.
485Tuples also support lexicographic comparisons, making it simple to write aggregate comparators using @std::tie@.
487There is a proposal for \CCseventeen called \emph{structured bindings}, that introduces new syntax to eliminate the need to pre-declare variables and use @std::tie@ for binding the results from a function call. % TODO: cite
489tuple<int, double> f();
490auto [i, d] = f(); // unpacks into new variables i, d
492tuple<int, int, int> triple(10, 20, 30);
493auto & [t1, t2, t3] = triple;
494t2 = 0; // changes triple
496struct S { int x; double y; };
497S s = { 10, 22.5 };
498auto [x, y] = s; // unpack s
500Structured bindings allow unpacking any struct with all public non-static data members into fresh local variables.
501The use of @&@ allows declaring new variables as references, which is something that cannot be done with @std::tie@, since \CC references do not support rebinding.
502This extension requires the use of @auto@ to infer the types of the new variables, so complicated expressions with a non-obvious type must documented with some other mechanism.
503Furthermore, structured bindings are not a full replacement for @std::tie@, as it always declares new variables.
505Like \CC, D provides tuples through a library variadic template struct.
506In D, it is possible to name the fields of a tuple type, which creates a distinct type.
507\begin{dcode} % TODO: cite
508Tuple!(float, "x", float, "y") point2D;
509Tuple!(float, float) float2;  // different types
511point2D[0]; // access first element
512point2D.x;  // access first element
514float f(float x, float y) {
515  return x+y;
520Tuples are 0-indexed and can be subscripted using an integer or field name, if applicable.
521The @expand@ method produces the components of the tuple as a list of separate values, making it possible to call a function that takes $N$ arguments using a tuple with $N$ components.
523Tuples are a fundamental abstraction in most functional programming languages, such as Standard ML.
524A function in SML always accepts exactly one argument.
525There are two ways to mimic multiple argument functions: the first through currying and the second by accepting tuple arguments.
527fun fact (n : int) =
528  if (n = 0) then 1
529  else n*fact(n-1)
531fun binco (n: int, k: int) =
532  real (fact n) / real (fact k * fact (n-k))
534Here, the function @binco@ appears to take 2 arguments, but it actually takes a single argument which is implicitly decomposed via pattern matching.
535Tuples are a foundational tool in SML, allowing the creation of arbitrarily complex structured data types.
537Scala, like \CC, provides tuple types through the standard library.
538Scala provides tuples of size 1 through 22 inclusive through generic data structures.
539Tuples support named access and subscript access, among a few other operations.
541val a = new Tuple3[Int, String, Double](0, "Text", 2.1)  // explicit creation
542val b = (6, 'a', 1.1f)       // syntactic sugar for Tuple3[Int, Char, Float]
543val (i, _, d) = triple       // extractor syntax, ignore middle element
545println(a._2)                // named access => print "Text"
546println(b.productElement(0)) // subscript access => print 6
548In Scala, tuples are primarily used as simple data structures for carrying around multiple values or for returning multiple values from a function.
549The 22-element restriction is an odd and arbitrary choice, but in practice it doesn't cause problems since large tuples are uncommon.
550Subscript access is provided through the @productElement@ method, which returns a value of the top-type @Any@, since it is impossible to receive a more precise type from a general subscripting method due to type erasure.
551The disparity between named access beginning at @_1@ and subscript access starting at @0@ is likewise an oddity, but subscript access is typically avoided since it discards type information.
552Due to the language's pattern matching facilities, it is possible to extract the values from a tuple into named variables, which is a more idiomatic way of accessing the components of a tuple.
555\Csharp has similarly strange limitations, allowing tuples of size up to 7 components. % TODO: cite
556The officially supported workaround for this shortcoming is to nest tuples in the 8th component.
557\Csharp allows accessing a component of a tuple by using the field @Item$N$@ for components 1 through 7, and @Rest@ for the nested tuple.
560% TODO: cite 5.3
561In Python, tuples are immutable sequences that provide packing and unpacking operations.
562While the tuple itself is immutable, and thus does not allow the assignment of components, there is nothing preventing a component from being internally mutable.
563The components of a tuple can be accessed by unpacking into multiple variables, indexing, or via field name, like D.
564Tuples support multiple assignment through a combination of packing and unpacking, in addition to the common sequence operations.
566% TODO: cite
567Swift, like D, provides named tuples, with components accessed by name, index, or via extractors.
568Tuples are primarily used for returning multiple values from a function.
569In Swift, @Void@ is an alias for the empty tuple, and there are no single element tuples.
571\section{Variadic Functions}
573In statically-typed programming languages, functions are typically defined to receive a fixed number of arguments of specified types.
574Variadic argument functions provide the ability to define a function that can receive a theoretically unbounded number of arguments.
576C provides a simple implementation of variadic functions.
577A function whose parameter list ends with @, ...@ is a variadic function.
578Among the most common variadic functions is @printf@.
580int printf(const char * fmt, ...);
581printf("%d %g %c %s", 10, 3.5, 'X', "a string");
583Through the use of a format string, @printf@ allows C programmers to print any of the standard C data types.
584Still, @printf@ is extremely limited, since the format codes are specified by the C standard, meaning users cannot define their own format codes to extend @printf@ for new data types or new formatting rules.
586C provides manipulation of variadic arguments through the @va_list@ data type, which abstracts details of the manipulation of variadic arguments.
587Since the variadic arguments are untyped, it is up to the function to interpret any data that is passed in.
588Additionally, the interface to manipulate @va_list@ objects is essentially limited to advancing to the next argument, without any built-in facility to determine when the last argument is read.
589This requires the use of an \emph{argument descriptor} to pass information to the function about the structure of the argument list, including the number of arguments and their types.
590The format string in @printf@ is one such example of an argument descriptor.
592int f(const char * fmt, ...) {
593  va_list args;
594  va_start(args, fmt);  // initialize va_list
595  for (const char * c = fmt; *c != '\0'; ++c) {
596    if (*c == '%') {
597      ++c;
598      switch (*c) {
599        case 'd': {
600          int i = va_arg(args, int);  // have to specify type
601          // ...
602          break;
603        }
604        case 'g': {
605          double d = va_arg(args, double);
606          // ...
607          break;
608        }
609        ...
610      }
611    }
612  }
613  va_end(args);
614  return ...;
617Every case must be handled explicitly, since the @va_arg@ macro requires a type argument to determine how the next set of bytes is to be interpreted.
618Furthermore, if the user makes a mistake, compile-time checking is typically restricted to standard format codes and their corresponding types.
619In general, this means that C's variadic functions are not type-safe, making them difficult to use properly.
621% When arguments are passed to a variadic function, they undergo \emph{default argument promotions}.
622% Specifically, this means that
624\CCeleven added support for \emph{variadic templates}, which add much needed type-safety to C's variadic landscape.
625It is possible to use variadic templates to define variadic functions and variadic data types.
627void print(int);
628void print(char);
629void print(double);
632void f() {}    // base case
634template<typename T, typename... Args>
635void f(const T & arg, const Args &... rest) {
636  print(arg);  // print the current element
637  f(rest...);  // handle remaining arguments recursively
640Variadic templates work largely through recursion on the \emph{parameter pack}, which is the argument with @...@ following its type.
641A parameter pack matches 0 or more elements, which can be types or expressions depending on the context.
642Like other templates, variadic template functions rely on an implicit set of constraints on a type, in this example a @print@ routine.
643That is, it is possible to use the @f@ routine any any type provided there is a corresponding @print@ routine, making variadic templates fully open to extension, unlike variadic functions in C.
645Recent \CC standards (\CCfourteen, \CCseventeen) expand on the basic premise by allowing variadic template variables and providing convenient expansion syntax to remove the need for recursion in some cases, amongst other things.
647% D has variadic templates that deserve a mention
649In Java, a variadic function appears similar to a C variadic function in syntax.
651int sum(int... args) {
652  int s = 0;
653  for (int x : args) {
654    s += x;
655  }
656  return s;
659void print(Object... objs) {
660  for (Object obj : objs) {
661    System.out.print(obj);
662  }
665print("The sum from 1 to 10 is ", sum(1,2,3,4,5,6,7,8,9,10), ".\n");
667The key difference is that Java variadic functions are type-safe, because they specify the type of the argument immediately prior to the ellipsis.
668In Java, variadic arguments are syntactic sugar for arrays, allowing access to length, subscripting operations, and for-each iteration on the variadic arguments, among other things.
669Since the argument type is specified explicitly, the top-type @Object@ can be used to accept arguments of any type, but to do anything interesting on the argument requires a down-cast to a more specific type, landing Java in a similar situation to C in that writing a function open to extension is difficult.
671The other option is to restrict the number of types that can be passed to the function by using a more specific type.
672Unfortunately, Java's use of nominal inheritance means that types must explicitly inherit from classes or interfaces in order to be considered a subclass.
673The combination of these two issues greatly restricts the usefulness of variadic functions in Java.
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