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    55\section{\CFA Background}
    66\label{s:background}
    7 \CFA \footnote{Pronounced ``C-for-all'', and written \CFA or Cforall.} is a modern non-object-oriented extension to the C programming language.
     7\CFA is a modern 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.
     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?
    1919
    2020\subsection{C Background}
     
    2929A a1 = { 1, .y:7, 6 };
    3030A a2[4] = { [2]:a0, [0]:a1, { .z:3 } };
    31 // equivalent to
     31// equvialent 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 sub-objects 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 sub-object, @z@.
    40 Later initializers override earlier initializers, so a sub-object for which there is more than one initializer is only initialized by its last initializer.
    41 These semantics 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, because this syntax is one of the few places that conflicts with the new language features.
     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.
    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 to 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 t0 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.
    104 The latter approach:
    105104\begin{cfacode}
    106105struct A {
     
    113112... res3.x ... res3.y ... // use result values
    114113\end{cfacode}
    115 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.
     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.
    116115Both solutions are syntactically unnatural.
    117116
    118 In \CFA, it is possible to directly declare a function returning multiple values.
    119 This 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
     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.
     119\begin{cfacode}
     120[int, int] f() {       // don't need to create a new type
    122121  return [123, 37];
    123122}
    124123\end{cfacode}
    125 However, the ability to return multiple values is useless without a syntax for accepting the results from the function.
    126 
     124However, the ability to return multiple values requires a syntax for accepting the results from a function.
    127125In standard C, return values are most commonly assigned directly into local variables, or are used as the arguments to another function call.
    128126\CFA allows both of these contexts to accept multiple return values.
     
    150148  g(f());             // selects (2)
    151149  \end{cfacode}
    152 In 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.
    153 A similar reasoning holds calling the function @g@.
     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.
    154152
    155153In \CFA, overloading also applies to operator names, known as \emph{operator overloading}.
     
    168166  bool ?<?(A x, A y);
    169167  \end{cfacode}
    170 Notably, the only difference is syntax.
     168Notably, the only difference in this example is syntax.
    171169Most of the operators supported by \CC for operator overloading are also supported in \CFA.
    172170Of notable exception are the logical operators (e.g. @||@), the sequence operator (i.e. @,@), and the member-access operators (e.g. @.@ and \lstinline{->}).
     
    174172Finally, \CFA also permits overloading variable identifiers.
    175173This feature is not available in \CC.
    176   \begin{cfacode}
     174  \begin{cfacode} % TODO: pick something better than x? max, zero, one?
    177175  struct Rational { int numer, denom; };
    178176  int x = 3;               // (1)
     
    188186In this example, there are three definitions of the variable @x@.
    189187Based on the context, \CFA attempts to choose the variable whose type best matches the expression context.
    190 When used judiciously, this feature allows names like @MAX@, @MIN@, and @PI@ to apply across many types.
    191188
    192189Finally, the values @0@ and @1@ have special status in standard C.
     
    200197}
    201198\end{cfacode}
    202 Every 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.
     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.
    203200Due 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}.}.
    204 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.
     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.
    205202  \begin{cfacode}
    206203  // lvalue is similar to returning a reference in C++
     
    296293This 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.
    297294
    298 An interesting application of return-type resolution and polymorphism is with type-safe @malloc@.
    299 \begin{cfacode}
    300 forall(dtype T | sized(T))
    301 T * malloc() {
    302   return (T*)malloc(sizeof(T)); // call C malloc
    303 }
    304 int * x = malloc();     // malloc(sizeof(int))
    305 double * y = malloc();  // malloc(sizeof(double))
    306 
    307 struct S { ... };
    308 S * s = malloc();       // malloc(sizeof(S))
    309 \end{cfacode}
    310 The 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.
    311 In 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 
    313295\section{Invariants}
    314 An \emph{invariant} is a logical assertion that is true for some duration of a program's execution.
     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.
    315300Invariants help a programmer to reason about code correctness and prove properties of programs.
    316301
    317302In object-oriented programming languages, type invariants are typically established in a constructor and maintained throughout the object's lifetime.
    318 These assertions are typically achieved through a combination of access control modifiers and a restricted interface.
     303This is typically achieved through a combination of access control modifiers and a restricted interface.
    319304Typically, 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.
    320305It 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.
     
    322307In C, the @assert@ macro is often used to ensure invariants are true.
    323308Using @assert@, the programmer can check a condition and abort execution if the condition is not true.
    324 This powerful tool forces the programmer to deal with logical inconsistencies as they occur.
     309This is a powerful tool that forces the programmer to deal with logical inconsistencies as they occur.
    325310For 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.
    326311\begin{cfacode}
     
    369354\end{dcode}
    370355The D compiler is able to assume that assertions and invariants hold true and perform optimizations based on those assumptions.
    371 Note, these invariants are internal to the type's correct behaviour.
    372 
    373 Types also have external invariants with the state of the execution environment, including the heap, the open-file table, the state of global variables, etc.
    374 Since 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.
     356
     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.
    375359
    376360\section{Resource Management}
     
    382366The program stack grows and shrinks automatically with each function call, as needed for local variables.
    383367However, 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@.
    384 This 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.
    385 Once 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.
     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.
    386370This implicit convention is provided only through documentation about the expectations of functions.
    387371
    388372In other languages, a hybrid situation exists where resources escape the allocation block, but ownership is precisely controlled by the language.
    389 This 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.
    390 This 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.
     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.
    391375
    392376For 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.
     
    396380On the other hand, destructors provide a simple mechanism for tearing down an object and resetting the environment in which the object lived.
    397381RAII ensures that if all resources are acquired in a constructor and released in a destructor, there are no resource leaks, even in exceptional circumstances.
    398 A type with at least one non-trivial constructor or destructor is henceforth referred to as a \emph{managed type}.
    399 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.
    400 
    401 For the remaining resource ownership cases, programmer must follow a brittle, explicit protocol for freeing resources or an implicit protocol implemented via the programming language.
     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.
     384
     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.
    402386
    403387In garbage collected languages, such as Java, resources are largely managed by the garbage collector.
     
    405389There are many kinds of resources that the garbage collector does not understand, such as sockets, open files, and database connections.
    406390In particular, Java supports \emph{finalizers}, which are similar to destructors.
    407 Sadly, 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.
    408 Due to operating-system resource-limits, this is unacceptable for many long running programs.
    409 Instead, 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.
    410 Complicating the picture, uncaught exceptions can cause control flow to change dramatically, leaking a resource that appears on first glance to be released.
     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; http://stackoverflow.com/a/2506514/2386739
     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.
    411395\begin{javacode}
    412396void write(String filename, String msg) throws Exception {
     
    419403}
    420404\end{javacode}
    421 Any 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.
     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.
    422407\begin{javacode}
    423408public void write(String filename, String msg) throws Exception {
     
    437422\end{javacode}
    438423In 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.
    439 Furthermore, 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}.
     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 http://www.oracle.com/technetwork/articles/java/trywithresources-401775.html?
    440425\begin{javacode}
    441426public void write(String filename, String msg) throws Exception {
    442   try (  // try-with-resources
     427  try (
    443428    FileOutputStream out = new FileOutputStream(filename);
    444429    FileOutputStream log = new FileOutputStream("log.txt");
     
    449434}
    450435\end{javacode}
    451 Variables 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.
    452 Depending 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 
    454 While 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.
    455 In particular, a variable has ownership over its associated value, which is freed automatically when the owner goes out of scope.
    456 Furthermore, values are \emph{moved} by default on assignment, rather than copied, which invalidates the previous variable binding.
    457 \begin{rustcode}
    458 struct S {
    459   x: i32
    460 }
    461 let s = S { x: 123 };
    462 let z = s;           // move, invalidate s
    463 println!("{}", s.x); // error, s has been moved
    464 \end{rustcode}
    465 Types can be made copyable by implementing the @Copy@ trait.
    466 
    467 Rust allows multiple unowned views into an object through references, also known as borrows, provided that a reference does not outlive its referent.
    468 A 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}
    470 let 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 }
    483 println!("{}", x); // prints 5
    484 \end{rustcode}
    485 Since references are not owned, they do not release resources when they go out of scope.
    486 There is no runtime cost imposed on these restrictions, since they are enforced at compile-time.
    487 
    488 Rust 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}
    490 struct S {
    491   name: &'static str
    492 }
    493 
    494 impl 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}
     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.
    505437
    506438% D has constructors and destructors that are worth a mention (under classes) https://dlang.org/spec/spec.html
     
    510442The programming language, D, also manages resources with constructors and destructors \cite{D}.
    511443In D, @struct@s are stack allocated and managed via scoping like in \CC, whereas @class@es are managed automatically by the garbage collector.
    512 Like 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.
     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.
    513445Since D supports RAII, it is possible to use the same techniques as in \CC to ensure that resources are released in a timely manner.
    514 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}. % https://dlang.org/spec/statement.html#ScopeGuardStatement
    515 It has been shown that the \emph{exit} form of the scope guard statement can be implemented in a library in \CC \cite{ExceptSafe}.
    516 
    517 To provide managed types in \CFA, new kinds of constructors and destructors are added to \CFA and discussed in Chapter 2.
     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? https://dlang.org/spec/statement.html#ScopeGuardStatement
     447It 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)
    518452
    519453\section{Tuples}
    520454\label{s:Tuples}
    521 In mathematics, tuples are finite-length sequences which, unlike sets, are ordered and allow duplicate elements.
    522 In programming languages, tuples provide fixed-sized heterogeneous lists of elements.
     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.
    523457Many programming languages have tuple constructs, such as SETL, \KWC, ML, and Scala.
    524458
     
    528462Adding tuples to \CFA has previously been explored by Esteves \cite{Esteves04}.
    529463
    530 The design of tuples in \KWC took much of its inspiration from SETL \cite{SETL}.
     464The design of tuples in \KWC took much of its inspiration from SETL.
    531465SETL is a high-level mathematical programming language, with tuples being one of the primary data types.
    532466Tuples in SETL allow a number of operations, including subscripting, dynamic expansion, and multiple assignment.
     
    536470\begin{cppcode}
    537471tuple<int, int, int> triple(10, 20, 30);
    538 get<1>(triple); // access component 1 => 20
     472get<1>(triple); // access component 1 => 30
    539473
    540474tuple<int, double> f();
     
    548482Tuples are simple data structures with few specific operations.
    549483In particular, it is possible to access a component of a tuple using @std::get<N>@.
    550 Another 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.
     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.
    551485Tuples also support lexicographic comparisons, making it simple to write aggregate comparators using @std::tie@.
    552486
    553 There 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.
     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 http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2015/p0144r0.pdf
    554488\begin{cppcode}
    555489tuple<int, double> f();
     
    566500Structured bindings allow unpacking any struct with all public non-static data members into fresh local variables.
    567501The 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.
    568 This 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.
     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.
    569503Furthermore, structured bindings are not a full replacement for @std::tie@, as it always declares new variables.
    570504
    571505Like \CC, D provides tuples through a library variadic template struct.
    572506In D, it is possible to name the fields of a tuple type, which creates a distinct type.
    573 % http://dlang.org/phobos/std_typecons.html
    574 \begin{dcode}
     507\begin{dcode} % TODO: cite http://dlang.org/phobos/std_typecons.html
    575508Tuple!(float, "x", float, "y") point2D;
    576 Tuple!(float, float) float2;  // different type from point2D
     509Tuple!(float, float) float2;  // different types
    577510
    578511point2D[0]; // access first element
     
    588521The @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.
    589522
    590 Tuples are a fundamental abstraction in most functional programming languages, such as Standard ML \cite{sml}.
     523Tuples are a fundamental abstraction in most functional programming languages, such as Standard ML.
    591524A function in SML always accepts exactly one argument.
    592525There are two ways to mimic multiple argument functions: the first through currying and the second by accepting tuple arguments.
     
    602535Tuples are a foundational tool in SML, allowing the creation of arbitrarily complex structured data types.
    603536
    604 Scala, like \CC, provides tuple types through the standard library \cite{Scala}.
     537Scala, like \CC, provides tuple types through the standard library.
    605538Scala provides tuples of size 1 through 22 inclusive through generic data structures.
    606539Tuples support named access and subscript access, among a few other operations.
     
    614547\end{scalacode}
    615548In Scala, tuples are primarily used as simple data structures for carrying around multiple values or for returning multiple values from a function.
    616 The 22-element restriction is an odd and arbitrary choice, but in practice it does not cause problems since large tuples are uncommon.
     549The 22-element restriction is an odd and arbitrary choice, but in practice it doesn't cause problems since large tuples are uncommon.
    617550Subscript 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.
    618551The 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.
     
    620553
    621554
    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
     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
    623556The officially supported workaround for this shortcoming is to nest tuples in the 8th component.
    624557\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.
    625558
    626 In Python \cite{Python}, tuples are immutable sequences that provide packing and unpacking operations.
     559
     560% TODO: cite 5.3 https://docs.python.org/3/tutorial/datastructures.html
     561In Python, tuples are immutable sequences that provide packing and unpacking operations.
    627562While the tuple itself is immutable, and thus does not allow the assignment of components, there is nothing preventing a component from being internally mutable.
    628563The components of a tuple can be accessed by unpacking into multiple variables, indexing, or via field name, like D.
    629564Tuples support multiple assignment through a combination of packing and unpacking, in addition to the common sequence operations.
    630565
    631 Swift \cite{Swift}, like D, provides named tuples, with components accessed by name, index, or via extractors.
     566% TODO: cite https://developer.apple.com/library/content/documentation/Swift/Conceptual/Swift_Programming_Language/Types.html#//apple_ref/doc/uid/TP40014097-CH31-ID448
     567Swift, like D, provides named tuples, with components accessed by name, index, or via extractors.
    632568Tuples are primarily used for returning multiple values from a function.
    633569In Swift, @Void@ is an alias for the empty tuple, and there are no single element tuples.
    634 
    635 Tuples comparable to those described above are added to \CFA and discussed in Chapter 3.
    636570
    637571\section{Variadic Functions}
     
    647581printf("%d %g %c %s", 10, 3.5, 'X', "a string");
    648582\end{cfacode}
    649 Through 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.
     583Through the use of a format string, @printf@ allows C programmers to print any of the standard C data types.
    650584Still, @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.
    651585
     
    707641A parameter pack matches 0 or more elements, which can be types or expressions depending on the context.
    708642Like other templates, variadic template functions rely on an implicit set of constraints on a type, in this example a @print@ routine.
    709 That 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.
     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.
    710644
    711645Recent \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.
     
    738672Unfortunately, Java's use of nominal inheritance means that types must explicitly inherit from classes or interfaces in order to be considered a subclass.
    739673The combination of these two issues greatly restricts the usefulness of variadic functions in Java.
    740 
    741 Type-safe variadic functions are added to \CFA and discussed in Chapter 4.
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