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  • doc/rob_thesis/intro.tex

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    55\section{\CFA Background}
    66\label{s:background}
    7 \CFA is a modern extension to the C programming language.
     7\CFA \footnote{Pronounced ``C-for-all'', and written \CFA or Cforall.} is a modern non-object-oriented extension to the C programming language.
    88As it is an extension of C, there is already a wealth of existing C code and principles that govern the design of the language.
    99Among the goals set out in the original design of \CFA, four points stand out \cite{Bilson03}.
     
    1616Therefore, these design principles must be kept in mind throughout the design and development of new language features.
    1717In order to appeal to existing C programmers, great care must be taken to ensure that new features naturally feel like C.
    18 The 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?
     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.
    1919
    2020\subsection{C Background}
     
    2929A a1 = { 1, .y:7, 6 };
    3030A a2[4] = { [2]:a0, [0]:a1, { .z:3 } };
    31 // equvialent to
     31// equivalent to
    3232// A a0 = { 0, 8, 0, 1 };
    3333// A a1 = { 1, 0, 7, 6 };
     
    3636Designations allow specifying the field to initialize by name, rather than by position.
    3737Any field not explicitly initialized is initialized as if it had static storage duration \cite[p.~141]{C11}.
    38 A designator specifies the current object for initialization, and as such any undesignated subobjects pick up where the last initialization left off.
    39 For example, in the initialization of @a1@, the initializer of @y@ is @7@, and the unnamed initializer @6@ initializes the next subobject, @z@.
    40 Later initializers override earlier initializers, so a subobject for which there is more than one initializer is only initailized by its last initializer.
    41 This can be seen in the initialization of @a0@, where @x@ is designated twice, and thus initialized to @8@.
    42 Note that in \CFA, designations use a colon separator, rather than an equals sign as in C.
     38A designator specifies the current object for initialization, and as such any undesignated sub-objects 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 sub-object, @z@.
     40Later initializers override earlier initializers, so a sub-object for which there is more than one initializer is only initialized by its last initializer.
     41These semantics 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, because this syntax is one of the few places that conflicts with the new language features.
    4343
    4444C also provides \emph{compound literal} expressions, which provide a first-class mechanism for creating unnamed objects.
     
    9191
    9292There are times when a function should logically return multiple values.
    93 Since 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.
     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 to package multiple return-values.
    9494\begin{cfacode}
    9595int f(int * ret) {        // returns a value through parameter ret
     
    102102\end{cfacode}
    103103The 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.
     104The latter approach:
    104105\begin{cfacode}
    105106struct A {
     
    112113... res3.x ... res3.y ... // use result values
    113114\end{cfacode}
    114 The 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.
     115requires the caller to either learn the field names of the structure or learn the names of helper routines to access the individual return values.
    115116Both solutions are syntactically unnatural.
    116117
    117 In \CFA, it is possible to directly declare a function returning mutliple values.
    118 This provides important semantic information to the caller, since return values are only for output.
    119 \begin{cfacode}
    120 [int, int] f() {       // don't need to create a new type
     118In \CFA, it is possible to directly declare a function returning multiple values.
     119This extension provides important semantic information to the caller, since return values are only for output.
     120\begin{cfacode}
     121[int, int] f() {       // no new type
    121122  return [123, 37];
    122123}
    123124\end{cfacode}
    124 However, the ability to return multiple values requires a syntax for accepting the results from a function.
     125However, the ability to return multiple values is useless without a syntax for accepting the results from the function.
     126
    125127In standard C, return values are most commonly assigned directly into local variables, or are used as the arguments to another function call.
    126128\CFA allows both of these contexts to accept multiple return values.
     
    148150  g(f());             // selects (2)
    149151  \end{cfacode}
    150 In this example, the only possible call to @f@ that can produce the two @int@s required by @g@ is the second option.
    151 A similar reasoning holds for assigning into multiple variables.
     152In this example, the only possible call to @f@ that can produce the two @int@s required for assigning into the variables @x@ and @y@ is the second option.
     153A similar reasoning holds calling the function @g@.
    152154
    153155In \CFA, overloading also applies to operator names, known as \emph{operator overloading}.
     
    166168  bool ?<?(A x, A y);
    167169  \end{cfacode}
    168 Notably, the only difference in this example is syntax.
     170Notably, the only difference is syntax.
    169171Most of the operators supported by \CC for operator overloading are also supported in \CFA.
    170172Of notable exception are the logical operators (e.g. @||@), the sequence operator (i.e. @,@), and the member-access operators (e.g. @.@ and \lstinline{->}).
     
    172174Finally, \CFA also permits overloading variable identifiers.
    173175This feature is not available in \CC.
    174   \begin{cfacode} % TODO: pick something better than x? max, zero, one?
     176  \begin{cfacode}
    175177  struct Rational { int numer, denom; };
    176178  int x = 3;               // (1)
     
    186188In this example, there are three definitions of the variable @x@.
    187189Based on the context, \CFA attempts to choose the variable whose type best matches the expression context.
     190When used judiciously, this feature allows names like @MAX@, @MIN@, and @PI@ to apply across many types.
    188191
    189192Finally, the values @0@ and @1@ have special status in standard C.
     
    197200}
    198201\end{cfacode}
    199 Every if statement in C compares the condition with @0@, and every increment and decrement operator is semantically equivalent to adding or subtracting the value @1@ and storing the result.
     202Every if- and iteration-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.
    200203Due 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}.}.
    201 The 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.
     204The 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.
    202205  \begin{cfacode}
    203206  // lvalue is similar to returning a reference in C++
     
    293296This 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.
    294297
     298An interesting application of return-type resolution and polymorphism is with type-safe @malloc@.
     299\begin{cfacode}
     300forall(dtype T | sized(T))
     301T * malloc() {
     302  return (T*)malloc(sizeof(T)); // call C malloc
     303}
     304int * x = malloc();     // malloc(sizeof(int))
     305double * y = malloc();  // malloc(sizeof(double))
     306
     307struct S { ... };
     308S * s = malloc();       // malloc(sizeof(S))
     309\end{cfacode}
     310The built-in trait @sized@ ensures that size and alignment information for @T@ is available in the body of @malloc@ through @sizeof@ and @_Alignof@ expressions respectively.
     311In calls to @malloc@, the type @T@ is bound based on call-site information, allowing \CFA code to allocate memory without the potential for errors introduced by manually specifying the size of the allocated block.
     312
    295313\section{Invariants}
    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
    299 An \emph{invariant} is a logical assertion that true for some duration of a program's execution.
     314An \emph{invariant} is a logical assertion that is true for some duration of a program's execution.
    300315Invariants help a programmer to reason about code correctness and prove properties of programs.
    301316
    302317In object-oriented programming languages, type invariants are typically established in a constructor and maintained throughout the object's lifetime.
    303 This is typically achieved through a combination of access control modifiers and a restricted interface.
     318These assertions are typically achieved through a combination of access control modifiers and a restricted interface.
    304319Typically, 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.
    305320It 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.
     
    307322In C, the @assert@ macro is often used to ensure invariants are true.
    308323Using @assert@, the programmer can check a condition and abort execution if the condition is not true.
    309 This is a powerful tool that forces the programmer to deal with logical inconsistencies as they occur.
     324This powerful tool forces the programmer to deal with logical inconsistencies as they occur.
    310325For 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.
    311326\begin{cfacode}
     
    354369\end{dcode}
    355370The D compiler is able to assume that assertions and invariants hold true and perform optimizations based on those assumptions.
    356 
    357 An important invariant is the state of the execution environment, including the heap, the open file table, the state of global variables, etc.
    358 Since 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.
     371Note, these invariants are internal to the type's correct behaviour.
     372
     373Types also have external invariants with the state of the execution environment, including the heap, the open-file table, the state of global variables, etc.
     374Since resources are finite and shared (concurrency), 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.
    359375
    360376\section{Resource Management}
     
    366382The program stack grows and shrinks automatically with each function call, as needed for local variables.
    367383However, 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@.
    368 This 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.
    369 Once 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.
     384This pattern is extended to more complex objects, such as files and sockets, which can also outlive the block where they are created, and thus require their own resource management.
     385Once allocated storage escapes\footnote{In garbage collected languages, such as Java, escape analysis \cite{Choi:1999:EAJ:320385.320386} is used to determine when dynamically allocated objects are strictly contained within a function, which allows the optimizer to allocate them on the stack.} 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.
    370386This implicit convention is provided only through documentation about the expectations of functions.
    371387
    372388In other languages, a hybrid situation exists where resources escape the allocation block, but ownership is precisely controlled by the language.
    373 This 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.
    374 This kind of encapsulation is popular in object-oriented programming languages, and like the stack, it contains a significant portion of resource management cases.
     389This pattern requires a strict interface and protocol for a data structure, consisting of a pre-initialization and a post-termination call, and all intervening access is done via interface routines.
     390This kind of encapsulation is popular in object-oriented programming languages, and like the stack, it takes care of a significant portion of resource management cases.
    375391
    376392For 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.
     
    380396On the other hand, destructors provide a simple mechanism for tearing down an object and resetting the environment in which the object lived.
    381397RAII ensures that if all resources are acquired in a constructor and released in a destructor, there are no resource leaks, even in exceptional circumstances.
    382 A type with at least one non-trivial constructor or destructor will henceforth be referred to as a \emph{managed type}.
    383 In 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.
    384 
    385 For the remaining resource ownership cases, programmer must follow a brittle, explicit protocol for freeing resources or an implicit porotocol implemented via the programming language.
     398A type with at least one non-trivial constructor or destructor is henceforth referred to as a \emph{managed type}.
     399In 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.
     400
     401For the remaining resource ownership cases, programmer must follow a brittle, explicit protocol for freeing resources or an implicit protocol implemented via the programming language.
    386402
    387403In garbage collected languages, such as Java, resources are largely managed by the garbage collector.
     
    389405There are many kinds of resources that the garbage collector does not understand, such as sockets, open files, and database connections.
    390406In particular, Java supports \emph{finalizers}, which are similar to destructors.
    391 Sadly, finalizers come with far fewer guarantees, to the point where a completely conforming JVM may never call a single finalizer. % TODO: citation JVM spec; http://stackoverflow.com/a/2506514/2386739
    392 Due to operating system resource limits, this is unacceptable for many long running tasks. % TODO: citation?
    393 Instead, 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.
    394 Complicating the picture, uncaught exceptions can cause control flow to change dramatically, leaking a resource which appears on first glance to be closed.
     407Sadly, finalizers are only guaranteed to be called before an object is reclaimed by the garbage collector \cite[p.~373]{Java8}, which may not happen if memory use is not contentious.
     408Due to operating-system resource-limits, this is unacceptable for many long running programs.
     409Instead, the paradigm in Java requires programmers to manually keep track of all resources \emph{except} memory, leading many novices and experts alike to forget to close files, etc.
     410Complicating the picture, uncaught exceptions can cause control flow to change dramatically, leaking a resource that appears on first glance to be released.
    395411\begin{javacode}
    396412void write(String filename, String msg) throws Exception {
     
    403419}
    404420\end{javacode}
    405 Any line in this program can throw an exception.
    406 This leads to a profusion of finally blocks around many function bodies, since it isn't always clear when an exception may be thrown.
     421Any line in this program can throw an exception, which leads to a profusion of finally blocks around many function bodies, since it is not always clear when an exception may be thrown.
    407422\begin{javacode}
    408423public void write(String filename, String msg) throws Exception {
     
    422437\end{javacode}
    423438In 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.
    424 Furthermore, 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 http://www.oracle.com/technetwork/articles/java/trywithresources-401775.html?
     439Furthermore, for complete safety this pattern requires nested objects to be declared separately, otherwise resources that can throw an exception on close can leak nested resources \cite{TryWithResources}.
    425440\begin{javacode}
    426441public void write(String filename, String msg) throws Exception {
    427   try (
     442  try (  // try-with-resources
    428443    FileOutputStream out = new FileOutputStream(filename);
    429444    FileOutputStream log = new FileOutputStream("log.txt");
     
    434449}
    435450\end{javacode}
    436 On 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.
     451Variables declared as part of a try-with-resources statement must conform to the @AutoClosable@ interface, and the compiler implicitly calls @close@ on each of the variables at the end of the block.
     452Depending on when the exception is raised, both @out@ and @log@ are null, @log@ is null, or both are non-null, therefore, the cleanup for these variables at the end is appropriately guarded and conditionally executed to prevent null-pointer exceptions.
     453
     454While Rust \cite{Rust} does not enforce the use of a garbage collector, it does provide a manual memory management environment, with a strict ownership model that automatically frees allocated memory and prevents common memory management errors.
     455In particular, a variable has ownership over its associated value, which is freed automatically when the owner goes out of scope.
     456Furthermore, values are \emph{moved} by default on assignment, rather than copied, which invalidates the previous variable binding.
     457\begin{rustcode}
     458struct S {
     459  x: i32
     460}
     461let s = S { x: 123 };
     462let z = s;           // move, invalidate s
     463println!("{}", s.x); // error, s has been moved
     464\end{rustcode}
     465Types can be made copyable by implementing the @Copy@ trait.
     466
     467Rust allows multiple unowned views into an object through references, also known as borrows, provided that a reference does not outlive its referent.
     468A mutable reference is allowed only if it is the only reference to its referent, preventing data race errors and iterator invalidation errors.
     469\begin{rustcode}
     470let mut x = 10;
     471{
     472  let y = &x;
     473  let z = &x;
     474  println!("{} {}", y, z); // prints 10 10
     475}
     476{
     477  let y = &mut x;
     478  // let z1 = &x;     // not allowed, have mutable reference
     479  // let z2 = &mut x; // not allowed, have mutable reference
     480  *y = 5;
     481  println!("{}", y); // prints 5
     482}
     483println!("{}", x); // prints 5
     484\end{rustcode}
     485Since references are not owned, they do not release resources when they go out of scope.
     486There is no runtime cost imposed on these restrictions, since they are enforced at compile-time.
     487
     488Rust provides RAII through the @Drop@ trait, allowing arbitrary code to execute when the object goes out of scope, allowing Rust programs to automatically clean up auxiliary resources much like a \CC program.
     489\begin{rustcode}
     490struct S {
     491  name: &'static str
     492}
     493
     494impl Drop for S {  // RAII for S
     495  fn drop(&mut self) {
     496    println!("dropped {}", self.name);
     497  }
     498}
     499
     500{
     501  let x = S { name: "x" };
     502  let y = S { name: "y" };
     503} // prints "dropped y" "dropped x"
     504\end{rustcode}
    437505
    438506% D has constructors and destructors that are worth a mention (under classes) https://dlang.org/spec/spec.html
     
    442510The programming language, D, also manages resources with constructors and destructors \cite{D}.
    443511In D, @struct@s are stack allocated and managed via scoping like in \CC, whereas @class@es are managed automatically by the garbage collector.
    444 Like 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.
     512Like Java, using the garbage collector means that destructors are called indeterminately, 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.
    445513Since D supports RAII, it is possible to use the same techniques as in \CC to ensure that resources are released in a timely manner.
    446 Finally, 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? https://dlang.org/spec/statement.html#ScopeGuardStatement
    447 It has been shown that the \emph{exit} form of the scope guard statement can be implemented in a library in \CC. % cite: http://www.drdobbs.com/184403758
    448 
    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)
     514Finally, 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}. % https://dlang.org/spec/statement.html#ScopeGuardStatement
     515It has been shown that the \emph{exit} form of the scope guard statement can be implemented in a library in \CC \cite{ExceptSafe}.
     516
     517To provide managed types in \CFA, new kinds of constructors and destructors are added to \CFA and discussed in Chapter 2.
    452518
    453519\section{Tuples}
    454520\label{s:Tuples}
    455 In mathematics, tuples are finite-length sequences which, unlike sets, allow duplicate elements.
    456 In programming languages, tuples are a construct that provide fixed-sized heterogeneous lists of elements.
     521In mathematics, tuples are finite-length sequences which, unlike sets, are ordered and allow duplicate elements.
     522In programming languages, tuples provide fixed-sized heterogeneous lists of elements.
    457523Many programming languages have tuple constructs, such as SETL, \KWC, ML, and Scala.
    458524
     
    462528Adding tuples to \CFA has previously been explored by Esteves \cite{Esteves04}.
    463529
    464 The design of tuples in \KWC took much of its inspiration from SETL.
     530The design of tuples in \KWC took much of its inspiration from SETL \cite{SETL}.
    465531SETL is a high-level mathematical programming language, with tuples being one of the primary data types.
    466532Tuples in SETL allow a number of operations, including subscripting, dynamic expansion, and multiple assignment.
     
    470536\begin{cppcode}
    471537tuple<int, int, int> triple(10, 20, 30);
    472 get<1>(triple); // access component 1 => 30
     538get<1>(triple); // access component 1 => 20
    473539
    474540tuple<int, double> f();
     
    482548Tuples are simple data structures with few specific operations.
    483549In particular, it is possible to access a component of a tuple using @std::get<N>@.
    484 Another 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.
     550Another interesting feature is @std::tie@, which creates a tuple of references, allowing assignment of the results of a tuple-returning function into separate local variables, without requiring a temporary variable.
    485551Tuples also support lexicographic comparisons, making it simple to write aggregate comparators using @std::tie@.
    486552
    487 There 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 http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2015/p0144r0.pdf
     553There is a proposal for \CCseventeen called \emph{structured bindings} \cite{StructuredBindings}, that introduces new syntax to eliminate the need to pre-declare variables and use @std::tie@ for binding the results from a function call.
    488554\begin{cppcode}
    489555tuple<int, double> f();
     
    500566Structured bindings allow unpacking any struct with all public non-static data members into fresh local variables.
    501567The 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.
    502 This 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.
     568This extension requires the use of @auto@ to infer the types of the new variables, so complicated expressions with a non-obvious type must be documented with some other mechanism.
    503569Furthermore, structured bindings are not a full replacement for @std::tie@, as it always declares new variables.
    504570
    505571Like \CC, D provides tuples through a library variadic template struct.
    506572In D, it is possible to name the fields of a tuple type, which creates a distinct type.
    507 \begin{dcode} % TODO: cite http://dlang.org/phobos/std_typecons.html
     573% http://dlang.org/phobos/std_typecons.html
     574\begin{dcode}
    508575Tuple!(float, "x", float, "y") point2D;
    509 Tuple!(float, float) float2;  // different types
     576Tuple!(float, float) float2;  // different type from point2D
    510577
    511578point2D[0]; // access first element
     
    521588The @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.
    522589
    523 Tuples are a fundamental abstraction in most functional programming languages, such as Standard ML.
     590Tuples are a fundamental abstraction in most functional programming languages, such as Standard ML \cite{sml}.
    524591A function in SML always accepts exactly one argument.
    525592There are two ways to mimic multiple argument functions: the first through currying and the second by accepting tuple arguments.
     
    535602Tuples are a foundational tool in SML, allowing the creation of arbitrarily complex structured data types.
    536603
    537 Scala, like \CC, provides tuple types through the standard library.
     604Scala, like \CC, provides tuple types through the standard library \cite{Scala}.
    538605Scala provides tuples of size 1 through 22 inclusive through generic data structures.
    539606Tuples support named access and subscript access, among a few other operations.
     
    547614\end{scalacode}
    548615In Scala, tuples are primarily used as simple data structures for carrying around multiple values or for returning multiple values from a function.
    549 The 22-element restriction is an odd and arbitrary choice, but in practice it doesn't cause problems since large tuples are uncommon.
     616The 22-element restriction is an odd and arbitrary choice, but in practice it does not cause problems since large tuples are uncommon.
    550617Subscript 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.
    551618The 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.
     
    553620
    554621
    555 \Csharp has similarly strange limitations, allowing tuples of size up to 7 components. % TODO: cite https://msdn.microsoft.com/en-us/library/system.tuple(v=vs.110).aspx
     622\Csharp also has tuples, but has similarly strange limitations, allowing tuples of size up to 7 components. % https://msdn.microsoft.com/en-us/library/system.tuple(v=vs.110).aspx
    556623The officially supported workaround for this shortcoming is to nest tuples in the 8th component.
    557624\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.
    558625
    559 
    560 % TODO: cite 5.3 https://docs.python.org/3/tutorial/datastructures.html
    561 In Python, tuples are immutable sequences that provide packing and unpacking operations.
     626In Python \cite{Python}, tuples are immutable sequences that provide packing and unpacking operations.
    562627While the tuple itself is immutable, and thus does not allow the assignment of components, there is nothing preventing a component from being internally mutable.
    563628The components of a tuple can be accessed by unpacking into multiple variables, indexing, or via field name, like D.
    564629Tuples support multiple assignment through a combination of packing and unpacking, in addition to the common sequence operations.
    565630
    566 % TODO: cite https://developer.apple.com/library/content/documentation/Swift/Conceptual/Swift_Programming_Language/Types.html#//apple_ref/doc/uid/TP40014097-CH31-ID448
    567 Swift, like D, provides named tuples, with components accessed by name, index, or via extractors.
     631Swift \cite{Swift}, like D, provides named tuples, with components accessed by name, index, or via extractors.
    568632Tuples are primarily used for returning multiple values from a function.
    569633In Swift, @Void@ is an alias for the empty tuple, and there are no single element tuples.
     634
     635Tuples comparable to those described above are added to \CFA and discussed in Chapter 3.
    570636
    571637\section{Variadic Functions}
     
    581647printf("%d %g %c %s", 10, 3.5, 'X', "a string");
    582648\end{cfacode}
    583 Through the use of a format string, @printf@ allows C programmers to print any of the standard C data types.
     649Through the use of a format string, C programmers can communicate argument type information to @printf@, allowing C programmers to print any of the standard C data types.
    584650Still, @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.
    585651
     
    641707A parameter pack matches 0 or more elements, which can be types or expressions depending on the context.
    642708Like other templates, variadic template functions rely on an implicit set of constraints on a type, in this example a @print@ routine.
    643 That 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.
     709That is, it is possible to use the @f@ routine on any type provided there is a corresponding @print@ routine, making variadic templates fully open to extension, unlike variadic functions in C.
    644710
    645711Recent \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.
     
    672738Unfortunately, Java's use of nominal inheritance means that types must explicitly inherit from classes or interfaces in order to be considered a subclass.
    673739The combination of these two issues greatly restricts the usefulness of variadic functions in Java.
     740
     741Type-safe variadic functions are added to \CFA and discussed in Chapter 4.
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