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1%======================================================================
2\chapter{Introduction}
3%======================================================================
4
5\section{\protect\CFA Background}
6\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.
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}.
10\begin{enumerate}
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.
15\end{enumerate}
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.
18These goals ensure existing C code-bases can be converted to \CFA incrementally with minimal effort, and C programmers can productively generate \CFA code without training beyond the features being used.
19Unfortunately, \CC is actively diverging from C, so incremental additions require significant effort and training, coupled with multiple legacy design-choices that cannot be updated.
20
21The current implementation of \CFA is a source-to-source translator from \CFA to GNU C \cite{GCCExtensions}.
22
23The remainder of this section describes some of the important features that currently exist in \CFA, to give the reader the necessary context in which the new features presented in this thesis must dovetail.
24
25\subsection{C Background}
26\label{sub:c_background}
27In the context of this work, the term \emph{object} refers to a region of data storage in the execution environment, the contents of which can represent values \cite[p.~6]{C11}.
28
29One of the lesser-known features of standard C is \emph{designations}.
30Designations are similar to named parameters in languages such as Python and Scala, except that they only apply to aggregate initializers.
31Note 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.
32\begin{cfacode}
33struct A {
34  int w, x, y, z;
35};
36A a0 = { .x:4 .z:1, .x:8 };
37A a1 = { 1, .y:7, 6 };
38A a2[4] = { [2]:a0, [0]:a1, { .z:3 } };
39// equivalent to
40// A a0 = { 0, 8, 0, 1 };
41// A a1 = { 1, 0, 7, 6 };
42// A a2[4] = { a1, { 0, 0, 0, 3 }, a0, { 0, 0, 0, 0 } };
43\end{cfacode}
44Designations allow specifying the field to initialize by name, rather than by position.
45Any field not explicitly initialized is initialized as if it had static storage duration \cite[p.~141]{C11}.
46A designator specifies the current object for initialization, and as such any undesignated sub-objects pick up where the last initialization left off.
47For example, in the initialization of @a1@, the initializer of @y@ is @7@, and the unnamed initializer @6@ initializes the next sub-object, @z@.
48Later initializers override earlier initializers, so a sub-object for which there is more than one initializer is only initialized by its last initializer.
49These semantics can be seen in the initialization of @a0@, where @x@ is designated twice, and thus initialized to @8@.
50
51C also provides \emph{compound literal} expressions, which provide a first-class mechanism for creating unnamed objects.
52\begin{cfacode}
53struct A { int x, y; };
54int f(A, int);
55int g(int *);
56
57f((A){ 3, 4 }, (int){ 5 } = 10);
58g((int[]){ 1, 2, 3 });
59g(&(int){ 0 });
60\end{cfacode}
61Compound 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}.
62Syntactically, 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 coercions and is never an lvalue.
63
64The \CFA translator makes use of several GNU C extensions, including \emph{nested functions} and \emph{attributes}.
65Nested functions make it possible to access data that is lexically in scope in the nested function's body.
66\begin{cfacode}
67int f() {
68  int x = 0;
69  void g() {
70    x++;
71  }
72  g();  // changes x
73}
74\end{cfacode}
75Nested functions come with the usual C caveat that they should not leak into the containing environment, since they are only valid as long as the containing function's stack frame is active.
76
77Attributes make it possible to inform the compiler of certain properties of the code.
78For example, a function can be marked as deprecated, so that legacy APIs can be identified and slowly removed, or as \emph{hot}, so that the compiler knows the function is called frequently and should be aggresively optimized.
79\begin{cfacode}
80__attribute__((deprecated("foo is deprecated, use bar instead")))
81void foo();
82__attribute__((hot)) void bar(); // heavily optimized
83
84foo();  // warning
85bar();
86\end{cfacode}
87
88\subsection{Overloading}
89\label{sub:overloading}
90Overloading is the ability to specify multiple entities with the same name.
91The most common form of overloading is function overloading, wherein multiple functions can be defined with the same name, but with different signatures.
92C provides a small amount of built-in overloading, \eg + is overloaded for the basic types.
93Like in \CC, \CFA allows user-defined overloading based both on the number of parameters and on the types of parameters.
94\begin{cfacode}
95void f(void);  // (1)
96void f(int);   // (2)
97void f(char);  // (3)
98
99f('A');        // selects (3)
100\end{cfacode}
101In 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@.
102Exactly which procedure is executed depends on the number and types of arguments passed.
103If there is no exact match available, \CFA attempts to find a suitable match by examining the C built-in conversion heuristics.
104The \CFA expression resolution algorithm uses a cost function to determine the interpretation that uses the fewest conversions and polymorphic type bindings.
105\begin{cfacode}
106void g(long long);
107
108g(12345);
109\end{cfacode}
110In the above example, there is only one instance of @g@, which expects a single parameter of type @long long@.
111Here, 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.
112
113Overloading solves the problem present in C where there can only be one function with a given name, requiring multiple names for functions that perform the same operation but take in different types.
114This can be seen in the example of the absolute value functions C:
115\begin{cfacode}
116// stdlib.h
117int abs(int);
118long int labs(long int);
119long long int llabs(long long int);
120\end{cfacode}
121In \CFA, the functions @labs@ and @llabs@ are replaced by appropriate overloads of @abs@.
122
123In addition to this form of overloading, \CFA also allows overloading based on the number and types of \emph{return} values.
124This extension is a feature that is not available in \CC, but is available in other programming languages such as Ada \cite{Ada95}.
125\begin{cfacode}
126int g();         // (1)
127double g();      // (2)
128
129int x = g();     // selects (1)
130\end{cfacode}
131Here, the only difference between the signatures of the different versions of @g@ is in the return values.
132The result context is used to select an appropriate routine definition.
133In 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.
134
135Return-type overloading solves similar problems to parameter-list overloading, in that multiple functions that perform similar operations can have the same, but produce different values.
136One use case for this feature is to provide two versions of the @bsearch@ routine:
137\begin{cfacode}
138forall(otype T | { int ?<?( T, T ); })
139T * bsearch(T key, const T * arr, size_t dimension) {
140  int comp(const void * t1, const void * t2) {
141    return *(T *)t1 < *(T *)t2 ? -1 : *(T *)t2 < *(T *)t1 ? 1 : 0;
142  }
143  return (T *)bsearch(&key, arr, dimension, sizeof(T), comp);
144}
145forall(otype T | { int ?<?( T, T ); })
146unsigned int bsearch(T key, const T * arr, size_t dimension) {
147  T *result = bsearch(key, arr, dimension);
148  // pointer subtraction includes sizeof(T)
149  return result ? result - arr : dimension;
150}
151double key = 5.0;
152double vals[10] = { /* 10 floating-point values */ };
153
154double * val = bsearch( 5.0, vals, 10 ); // selection based on return type
155int posn = bsearch( 5.0, vals, 10 );
156\end{cfacode}
157The first version provides a thin wrapper around the C @bsearch@ routine, converting untyped @void *@ to the polymorphic type @T *@, allowing the \CFA compiler to catch errors when the type of @key@, @arr@, and the target at the call-site do not agree.
158The second version provides an alternate return of the index in the array of the selected element, rather than its address.
159
160There are times when a function should logically return multiple values.
161Since 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.
162For example, the first approach:
163\begin{cfacode}
164int f(int * ret) {        // returns a value through parameter ret
165  *ret = 37;
166  return 123;
167}
168
169int res1, res2;           // allocate return value
170int res1 = g(&res2);      // explicitly pass storage
171\end{cfacode}
172is 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.
173The second approach:
174\begin{cfacode}
175struct A {
176  int x, y;
177};
178struct A g() {            // returns values through a structure
179  return (struct A) { 123, 37 };
180}
181struct A res3 = g();
182... res3.x ... res3.y ... // use result values
183\end{cfacode}
184is awkward because the caller has to either learn the field names of the structure or learn the names of helper routines to access the individual return values.
185Both approaches are syntactically unnatural.
186
187In \CFA, it is possible to directly declare a function returning multiple values.
188This extension provides important semantic information to the caller, since return values are only for output.
189\begin{cfacode}
190[int, int] f() {       // no new type
191  return [123, 37];
192}
193\end{cfacode}
194However, the ability to return multiple values is useless without a syntax for accepting the results from the function.
195
196In standard C, return values are most commonly assigned directly into local variables, or are used as the arguments to another function call.
197\CFA allows both of these contexts to accept multiple return values.
198\begin{cfacode}
199int res1, res2;
200[res1, res2] = f();    // assign return values into local variables
201
202void g(int, int);
203g(f());                // pass both return values of f to g
204\end{cfacode}
205As seen in the example, it is possible to assign the results from a return value directly into local variables.
206These local variables can be referenced naturally, without requiring any unpacking as in structured return values.
207Perhaps more interesting is the fact that multiple return values can be passed to multiple parameters seamlessly, as in the call @g(f())@.
208In 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.
209
210An extra quirk introduced by multiple return values is in the resolution of function calls.
211\begin{cfacode}
212int f();            // (1)
213[int, int] f();     // (2)
214
215void g(int, int);
216
217int x, y;
218[x, y] = f();       // selects (2)
219g(f());             // selects (2)
220\end{cfacode}
221In 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.
222A similar reasoning holds calling the function @g@.
223
224This duality between aggregation and aliasing can be seen in the C standard library in the @div@ and @remquo@ functions, which return the quotient and remainder for a division of integer and floating-point values, respectively.
225\begin{cfacode}
226typedef struct { int quo, rem; } div_t; // from stdlib.h
227div_t div( int num, int den );
228double remquo( double num, double den, int * quo );
229div_t qr = div( 13, 5 );            // return quotient/remainder aggregate
230int q;
231double r = remquo( 13.5, 5.2, &q ); // return remainder, alias quotient
232\end{cfacode}
233@div@ aggregates the quotient/remainder in a structure, while @remquo@ aliases a parameter to an argument.
234Alternatively, a programming language can directly support returning multiple values, \eg in \CFA:
235\begin{lstlisting}
236[int, int] div(int num, int den);               // return two integers
237[double, double] div( double num, double den ); // return two doubles
238int q, r;                     // overloaded variable names
239double q, r;
240[q, r] = div(13, 5);          // select appropriate div and q, r
241[q, r] = div(13.5, 5.2);
242\end{lstlisting}
243
244In \CFA, overloading also applies to operator names, known as \emph{operator overloading}.
245Similar to function overloading, a single operator is given multiple meanings by defining new versions of the operator with different signatures.
246In \CC, this can be done as follows
247\begin{cppcode}
248struct A { int i; };
249A operator+(A x, A y);
250bool operator<(A x, A y);
251\end{cppcode}
252
253In \CFA, the same example can be written as follows.
254\begin{cfacode}
255struct A { int i; };
256A ?+?(A x, A y);    // '?'s represent operands
257int ?<?(A x, A y);
258\end{cfacode}
259Notably, the only difference is syntax.
260Most of the operators supported by \CC for operator overloading are also supported in \CFA.
261Of notable exception are the logical operators (\eg @||@), the sequence operator (\ie @,@), and the member-access operators (\eg @.@ and \lstinline{->}).
262
263Finally, \CFA also permits overloading variable identifiers.
264This feature is not available in \CC.
265\begin{cfacode}
266struct Rational { int numer, denom; };
267int x = 3;               // (1)
268double x = 1.27;         // (2)
269Rational x = { 4, 11 };  // (3)
270
271void g(double);
272
273x += 1;                  // chooses (1)
274g(x);                    // chooses (2)
275Rational y = x;          // chooses (3)
276\end{cfacode}
277In this example, there are three definitions of the variable @x@.
278Based on the context, \CFA attempts to choose the variable whose type best matches the expression context.
279When used judiciously, this feature allows names like @MAX@, @MIN@, and @PI@ to apply across many types.
280
281Finally, the values @0@ and @1@ have special status in standard C.
282In particular, the value @0@ is both an integer and a pointer literal, and thus its meaning depends on the context.
283In addition, several operations can be redefined in terms of other operations and the values @0@ and @1@.
284For example,
285\begin{cfacode}
286int x;
287if (x) {  // if (x != 0)
288  x++;    //   x += 1;
289}
290\end{cfacode}
291Every 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.
292Due 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}.}.
293The 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.
294\begin{cfacode}
295// lvalue is similar to returning a reference in C++
296lvalue Rational ?+=?(Rational *a, Rational b);
297Rational ?=?(Rational * dst, zero_t) {
298  return *dst = (Rational){ 0, 1 };
299}
300
301Rational sum(Rational *arr, int n) {
302  Rational r;
303  r = 0;     // use rational-zero_t assignment
304  for (; n > 0; n--) {
305    r += arr[n-1];
306  }
307  return r;
308}
309\end{cfacode}
310This function takes an array of @Rational@ objects and produces the @Rational@ representing the sum of the array.
311Note the use of an overloaded assignment operator to set an object of type @Rational@ to an appropriate @0@ value.
312
313\subsection{Polymorphism}
314\label{sub:polymorphism}
315In its most basic form, polymorphism grants the ability to write a single block of code that accepts different types.
316In particular, \CFA supports the notion of parametric polymorphism.
317Parametric polymorphism allows a function to be written generically, for all values of all types, without regard to the specifics of a particular type.
318For example, in \CC, the simple identity function for all types can be written as:
319\begin{cppcode}
320template<typename T>
321T identity(T x) { return x; }
322\end{cppcode}
323\CC uses the template mechanism to support parametric polymorphism. In \CFA, an equivalent function can be written as:
324\begin{cfacode}
325forall(otype T)
326T identity(T x) { return x; }
327\end{cfacode}
328Once again, the only visible difference in this example is syntactic.
329Fundamental differences can be seen by examining more interesting examples.
330In \CC, a generic sum function is written as follows:
331\begin{cppcode}
332template<typename T>
333T sum(T *arr, int n) {
334  T t;  // default construct => 0
335  for (; n > 0; n--) t += arr[n-1];
336  return t;
337}
338\end{cppcode}
339Here, the code assumes the existence of a default constructor, assignment operator, and an addition operator over the provided type @T@.
340If any of these required operators are not available, the \CC compiler produces an error message stating which operators could not be found.
341
342A similar sum function can be written in \CFA as follows:
343\begin{cfacode}
344forall(otype T | **R**{ T ?=?(T *, zero_t); T ?+=?(T *, T); }**R**)
345T sum(T *arr, int n) {
346  T t = 0;
347  for (; n > 0; n--) t = t += arr[n-1];
348  return t;
349}
350\end{cfacode}
351The 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@.
352In particular, the assertions above specify that there must be an assignment from \zero to @T@ and an addition assignment operator from @T@ to @T@.
353The 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.
354In addition to @otype@, there are currently two other type-classes.
355
356@dtype@, short for \emph{data type}, serves as the top type for object types; any object type, complete or incomplete, can be bound to a @dtype@ type variable.
357To contrast, @otype@, short for \emph{object type}, is a @dtype@ with known size, alignment, and an assignment operator, and thus bind only to complete object types.
358With this extra information, complete objects can be used in polymorphic code in the same way they are used in monomorphic code, providing familiarity and ease of use.
359The third type-class is @ftype@, short for \emph{function type}, matching only function types.
360The three type parameter kinds are summarized in \autoref{table:types}
361
362\begin{table}[h!]
363  \begin{center}
364    \begin{tabular}{|c||c|c|c||c|c|c|}
365                                                                                                    \hline
366    name    & object type & incomplete type & function type & can assign & can create & has size \\ \hline
367    @otype@ & X           &                 &               & X                & X          & X        \\ \hline
368    @dtype@ & X           & X               &               &                  &            &          \\ \hline
369    @ftype@ &             &                 & X             &                  &            &          \\ \hline
370    \end{tabular}
371  \end{center}
372  \caption{\label{table:types} The different kinds of type parameters in \protect\CFA}
373\end{table}
374
375A 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.
376One of the major limiting factors of \CC's approach is that templates cannot be separately compiled.
377In contrast, the explicit nature of assertions allows \CFA's polymorphic functions to be separately compiled, as the function prototype states all necessary requirements separate from the implementation.
378For example, the prototype for the previous sum function is
379\begin{cfacode}
380forall(otype T | **R**{ T ?=?(T *, zero_t); T ?+=?(T *, T); }**R**)
381T sum(T *arr, int n);
382\end{cfacode}
383With this prototype, a caller in another translation unit knows all of the constraints on @T@, and thus knows all of the operations that need to be made available to @sum@.
384
385In \CFA, a set of assertions can be factored into a \emph{trait}.
386\begin{cfacode}
387trait Addable(otype T) {
388  T ?+?(T, T);
389  T ++?(T);
390  T ?++(T);
391}
392forall(otype T | Addable(T)) void f(T);
393forall(otype T | Addable(T) | { T --?(T); }) T g(T);
394forall(otype T, U | Addable(T) | { T ?/?(T, U); }) U h(T, U);
395\end{cfacode}
396This 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.
397
398An interesting application of return-type resolution and polymorphism is a polymorphic version of @malloc@.
399\begin{cfacode}
400forall(dtype T | sized(T))
401T * malloc() {
402  return (T*)malloc(sizeof(T)); // call C malloc
403}
404int * x = malloc();     // malloc(sizeof(int))
405double * y = malloc();  // malloc(sizeof(double))
406
407struct S { ... };
408S * s = malloc();       // malloc(sizeof(S))
409\end{cfacode}
410The 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.
411In 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.
412
413\subsection{Planned Features}
414
415One of the planned features \CFA is \emph{reference types}.
416At a high level, the current proposal is to add references as a way to cleanup pointer syntax.
417With references, it will be possible to store any address, as with a pointer, with the key difference being that references are automatically dereferenced.
418\begin{cfacode}
419int x = 0;
420int * p = &x;  // needs &
421int & ref = x; // no &
422
423printf("%d %d\n", *p, ref); // pointer needs *, ref does not
424\end{cfacode}
425
426It is possible to add new functions or shadow existing functions for the duration of a scope, using normal C scoping rules.
427One application of this feature is to reverse the order of @qsort@.
428\begin{cfacode}
429forall(otype T | { int ?<?( T, T ); })
430void qsort(const T * arr, size_t size) {
431  int comp(const void * t1, const void * t2) {
432    return *(T *)t1 < *(T *)t2 ? -1 : *(T *)t2 < *(T *)t1 ? 1 : 0;
433  }
434  qsort(arr, dimension, sizeof(T), comp);
435
436}
437double vals[10] = { ... };
438qsort(vals, 10);                // ascending order
439{
440  int ?<?(double x, double y) { // locally override behaviour
441    return x > y;
442  }
443  qsort(vals, 10);              // descending sort
444}
445\end{cfacode}
446Currently, there is no way to \emph{remove} a function from consideration from the duration of a scope.
447For example, it may be desirable to eliminate assignment from a scope, to reduce accidental mutation.
448To address this desire, \emph{deleted functions} are a planned feature for \CFA.
449\begin{cfacode}
450forall(otype T) void f(T *);
451
452int x = 0;
453f(&x);  // might modify x
454{
455  int ?=?(int *, int) = delete;
456  f(&x);   // error, no assignment for int
457}
458\end{cfacode}
459Now, if the deleted function is chosen as the best match, the expression resolver emits an error.
460
461\section{Invariants}
462An \emph{invariant} is a logical assertion that is true for some duration of a program's execution.
463Invariants help a programmer to reason about code correctness and prove properties of programs.
464
465\begin{sloppypar}
466In object-oriented programming languages, type invariants are typically established in a constructor and maintained throughout the object's lifetime.
467These assertions are typically achieved through a combination of access-control modifiers and a restricted interface.
468Typically, 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.
469It 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.
470\end{sloppypar}
471
472In C, the @assert@ macro is often used to ensure invariants are true.
473Using @assert@, the programmer can check a condition and abort execution if the condition is not true.
474This powerful tool forces the programmer to deal with logical inconsistencies as they occur.
475For 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.
476\begin{cfacode}
477struct Rational {
478  int n, d;
479};
480struct Rational create_rational(int n, int d) {
481  assert(d != 0);  // precondition
482  if (d < 0) {
483    n *= -1;
484    d *= -1;
485  }
486  assert(d > 0);  // postcondition
487  // rational invariant: d > 0
488  return (struct Rational) { n, d };
489}
490struct Rational rat_abs(struct Rational r) {
491  assert(r.d > 0); // check invariant, since no access control
492  r.n = abs(r.n);
493  assert(r.d > 0); // ensure function preserves invariant on return value
494  return r;
495}
496\end{cfacode}
497
498Some languages, such as D, provide language-level support for specifying program invariants.
499In 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.
500\begin{dcode}
501import std.math;
502struct Rational {
503  invariant {
504    assert(d > 0, "d <= 0");
505  }
506  int n, d;
507  this(int n, int d) {  // constructor
508    assert(d != 0);
509    this.n = n;
510    this.d = d;
511    // implicitly check invariant
512  }
513  Rational abs() {
514    // implicitly check invariant
515    return Rational(std.math.abs(n), d);
516    // implicitly check invariant
517  }
518}
519\end{dcode}
520The D compiler is able to assume that assertions and invariants hold true and perform optimizations based on those assumptions.
521Note, these invariants are internal to the type's correct behaviour.
522
523Types also have external invariants with the state of the execution environment, including the heap, the open-file table, the state of global variables, etc.
524Since 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.
525
526\section{Resource Management}
527\label{s:ResMgmt}
528
529Resource management is a problem that pervades every programming language.
530
531In 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.
532The program stack grows and shrinks automatically with each function call, as needed for local variables.
533However, 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@.
534This 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.
535Once 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.
536This implicit convention is provided only through documentation about the expectations of functions.
537
538In other languages, a hybrid situation exists where resources escape the allocation block, but ownership is precisely controlled by the language.
539This 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.
540This 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.
541
542For 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.
543Constructors and destructors are special routines that are automatically inserted into the appropriate locations to bookend the lifetime of an object.
544Constructors 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.
545In particular, constructors allow a programmer to ensure that all objects are initially set to a valid state.
546On the other hand, destructors provide a simple mechanism for tearing down an object and resetting the environment in which the object lived.
547RAII ensures that if all resources are acquired in a constructor and released in a destructor, there are no resource leaks, even in exceptional circumstances.
548A type with at least one non-trivial constructor or destructor is henceforth referred to as a \emph{managed type}.
549In 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.
550
551For the remaining resource ownership cases, a programmer must follow a brittle, explicit protocol for freeing resources or an implicit protocol enforced by the programming language.
552
553In garbage collected languages, such as Java, resources are largely managed by the garbage collector.
554Still, garbage collectors typically focus only on memory management.
555There are many kinds of resources that the garbage collector does not understand, such as sockets, open files, and database connections.
556In particular, Java supports \emph{finalizers}, which are similar to destructors.
557Unfortunately, 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.
558Due to operating-system resource-limits, this is unacceptable for many long running programs.
559Instead, 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.
560Complicating the picture, uncaught exceptions can cause control flow to change dramatically, leaking a resource that appears on first glance to be released.
561\begin{javacode}
562void write(String filename, String msg) throws Exception {
563  FileOutputStream out = new FileOutputStream(filename);
564  FileOutputStream log = new FileOutputStream(filename);
565  out.write(msg.getBytes());
566  log.write(msg.getBytes());
567  log.close();
568  out.close();
569}
570\end{javacode}
571Any 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.
572\begin{javacode}
573public void write(String filename, String msg) throws Exception {
574  FileOutputStream out = new FileOutputStream(filename);
575  try {
576    FileOutputStream log = new FileOutputStream("log.txt");
577    try {
578      out.write(msg.getBytes());
579      log.write(msg.getBytes());
580    } finally {
581      log.close();
582    }
583  } finally {
584    out.close();
585  }
586}
587\end{javacode}
588In 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.
589Furthermore, 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 \footnote{Since close is only guaranteed to be called on objects declared in the try-list and not objects passed as constructor parameters, the @B@ object may not be closed in @new A(new B())@ if @A@'s close raises an exception.} \cite{TryWithResources}.
590\begin{javacode}
591public void write(String filename, String msg) throws Exception {
592  try (  // try-with-resources
593    FileOutputStream out = new FileOutputStream(filename);
594    FileOutputStream log = new FileOutputStream("log.txt");
595  ) {
596    out.write(msg.getBytes());
597    log.write(msg.getBytes());
598  } // automatically closes out and log in every exceptional situation
599}
600\end{javacode}
601Variables 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.
602Depending 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 automatically guarded and conditionally executed to prevent null-pointer exceptions.
603
604While 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.
605In particular, a variable has ownership over its associated value, which is freed automatically when the owner goes out of scope.
606Furthermore, values are \emph{moved} by default on assignment, rather than copied, which invalidates the previous variable binding.
607\begin{rustcode}
608struct S {
609  x: i32
610}
611let s = S { x: 123 };
612let z = s;           // move, invalidate s
613println!("{}", s.x); // error, s has been moved
614\end{rustcode}
615Types can be made copyable by implementing the @Copy@ trait.
616
617Rust allows multiple unowned views into an object through references, also known as borrows, provided that a reference does not outlive its referent.
618A mutable reference is allowed only if it is the only reference to its referent, preventing data race errors and iterator invalidation errors.
619\begin{rustcode}
620let mut x = 10;
621{
622  let y = &x;
623  let z = &x;
624  println!("{} {}", y, z); // prints 10 10
625}
626{
627  let y = &mut x;
628  // let z1 = &x;     // not allowed, have mutable reference
629  // let z2 = &mut x; // not allowed, have mutable reference
630  *y = 5;
631  println!("{}", y); // prints 5
632}
633println!("{}", x); // prints 5
634\end{rustcode}
635Since references are not owned, they do not release resources when they go out of scope.
636There is no runtime cost imposed on these restrictions, since they are enforced at compile-time.
637
638Rust provides RAII through the @Drop@ trait, allowing arbitrary code to execute when the object goes out of scope, providing automatic clean up of auxiliary resources, much like a \CC program.
639\begin{rustcode}
640struct S {
641  name: &'static str
642}
643
644impl Drop for S {  // RAII for S
645  fn drop(&mut self) {  // destructor
646    println!("dropped {}", self.name);
647  }
648}
649
650{
651  let x = S { name: "x" };
652  let y = S { name: "y" };
653} // prints "dropped y" "dropped x"
654\end{rustcode}
655
656% D has constructors and destructors that are worth a mention (under classes) https://dlang.org/spec/spec.html
657%  also https://dlang.org/spec/struct.html#struct-constructor
658% 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
659% D has a GC, which already makes the situation quite different from C/C++
660The programming language D also manages resources with constructors and destructors \cite{D}.
661In D, @struct@s are stack allocatable and managed via scoping like in \CC, whereas @class@es are managed automatically by the garbage collector.
662Like 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.
663Since D supports RAII, it is possible to use the same techniques as in \CC to ensure that resources are released in a timely manner.
664Finally, 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
665It has been shown that the \emph{exit} form of the scope guard statement can be implemented in a library in \CC \cite{ExceptSafe}.
666
667To provide managed types in \CFA, new kinds of constructors and destructors are added to \CFA and discussed in Chapter 2.
668
669\section{Tuples}
670\label{s:Tuples}
671In mathematics, tuples are finite-length sequences which, unlike sets, are ordered and allow duplicate elements.
672In programming languages, tuples provide fixed-sized heterogeneous lists of elements.
673Many programming languages have tuple constructs, such as SETL, \KWC, ML, and Scala.
674
675\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}.
676In particular, Till noted that C already contains a tuple context in the form of function parameter lists.
677The 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}).
678Adding tuples to \CFA has previously been explored by Esteves \cite{Esteves04}.
679
680The design of tuples in \KWC took much of its inspiration from SETL \cite{SETL}.
681SETL is a high-level mathematical programming language, with tuples being one of the primary data types.
682Tuples in SETL allow a number of operations, including subscripting, dynamic expansion, and multiple assignment.
683
684\CCeleven introduced @std::tuple@ as a library variadic template struct.
685Tuples are a generalization of @std::pair@, in that they allow for arbitrary length, fixed-size aggregation of heterogeneous values.
686\begin{cppcode}
687tuple<int, int, int> triple(10, 20, 30);
688get<1>(triple); // access component 1 => 20
689
690tuple<int, double> f();
691int i;
692double d;
693tie(i, d) = f(); // assign fields of return value into local variables
694
695tuple<int, int, int> greater(11, 0, 0);
696triple < greater; // true
697\end{cppcode}
698Tuples are simple data structures with few specific operations.
699In particular, it is possible to access a component of a tuple using @std::get<N>@.
700Another 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.
701Tuples also support lexicographic comparisons, making it simple to write aggregate comparators using @std::tie@.
702
703There 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.
704\begin{cppcode}
705tuple<int, double> f();
706auto [i, d] = f(); // unpacks into new variables i, d
707
708tuple<int, int, int> triple(10, 20, 30);
709auto & [t1, t2, t3] = triple;
710t2 = 0; // changes middle element of triple
711
712struct S { int x; double y; };
713S s = { 10, 22.5 };
714auto [x, y] = s; // unpack s
715\end{cppcode}
716Structured bindings allow unpacking any structure with all public non-static data members into fresh local variables.
717The 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.
718This 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.
719Furthermore, structured bindings are not a full replacement for @std::tie@, as it always declares new variables.
720
721Like \CC, D provides tuples through a library variadic-template structure.
722In D, it is possible to name the fields of a tuple type, which creates a distinct type.
723% http://dlang.org/phobos/std_typecons.html
724\begin{dcode}
725Tuple!(float, "x", float, "y") point2D;
726Tuple!(float, float) float2;  // different type from point2D
727
728point2D[0]; // access first element
729point2D.x;  // access first element
730
731float f(float x, float y) {
732  return x+y;
733}
734
735f(point2D.expand);
736\end{dcode}
737Tuples are 0-indexed and can be subscripted using an integer or field name, if applicable.
738The @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.
739
740Tuples are a fundamental abstraction in most functional programming languages, such as Standard ML \cite{sml}.
741A function in SML always accepts exactly one argument.
742There are two ways to mimic multiple argument functions: the first through currying and the second by accepting tuple arguments.
743\begin{smlcode}
744fun fact (n : int) =
745  if (n = 0) then 1
746  else n*fact(n-1)
747
748fun binco (n: int, k: int) =
749  real (fact n) / real (fact k * fact (n-k))
750\end{smlcode}
751Here, the function @binco@ appears to take 2 arguments, but it actually takes a single argument which is implicitly decomposed via pattern matching.
752Tuples are a foundational tool in SML, allowing the creation of arbitrarily-complex structured data-types.
753
754Scala, like \CC, provides tuple types through the standard library \cite{Scala}.
755Scala provides tuples of size 1 through 22 inclusive through generic data structures.
756Tuples support named access and subscript access, among a few other operations.
757\begin{scalacode}
758val a = new Tuple3(0, "Text", 2.1) // explicit creation
759val b = (6, 'a', 1.1f)       // syntactic sugar: Tuple3[Int, Char, Float]
760val (i, _, d) = triple       // extractor syntax, ignore middle element
761
762println(a._2)                // named access => print "Text"
763println(b.productElement(0)) // subscript access => print 6
764\end{scalacode}
765In Scala, tuples are primarily used as simple data structures for carrying around multiple values or for returning multiple values from a function.
766The 22-element restriction is an odd and arbitrary choice, but in practice it does not cause problems since large tuples are uncommon.
767Subscript 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.
768The 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.
769Due 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.
770
771
772\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
773The officially supported workaround for this shortcoming is to nest tuples in the 8th component.
774\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.
775
776In Python \cite{Python}, tuples are immutable sequences that provide packing and unpacking operations.
777While the tuple itself is immutable, and thus does not allow the assignment of components, there is nothing preventing a component from being internally mutable.
778The components of a tuple can be accessed by unpacking into multiple variables, indexing, or via field name, like D.
779Tuples support multiple assignment through a combination of packing and unpacking, in addition to the common sequence operations.
780
781Swift \cite{Swift}, like D, provides named tuples, with components accessed by name, index, or via extractors.
782Tuples are primarily used for returning multiple values from a function.
783In Swift, @Void@ is an alias for the empty tuple, and there are no single element tuples.
784
785Tuples comparable to those described above are added to \CFA and discussed in Chapter 3.
786
787\section{Variadic Functions}
788\label{sec:variadic_functions}
789In statically-typed programming languages, functions are typically defined to receive a fixed number of arguments of specified types.
790Variadic argument functions provide the ability to define a function that can receive a theoretically unbounded number of arguments.
791
792C provides a simple implementation of variadic functions.
793A function whose parameter list ends with @, ...@ is a variadic function.
794Among the most common variadic functions is @printf@.
795\begin{cfacode}
796int printf(const char * fmt, ...);
797printf("%d %g %c %s", 10, 3.5, 'X', "a string");
798\end{cfacode}
799Through 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.
800Still, @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.
801
802\begin{sloppypar}
803C provides manipulation of variadic arguments through the @va_list@ data type, which abstracts details of the manipulation of variadic arguments.
804Since the variadic arguments are untyped, it is up to the function to interpret any data that is passed in.
805Additionally, 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.
806This limitation 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.
807The format string in @printf@ is one such example of an argument descriptor.
808\begin{cfacode}
809int f(const char * fmt, ...) {
810  va_list args;
811  va_start(args, fmt);  // initialize va_list
812  for (const char * c = fmt; *c != '\0'; ++c) {
813    if (*c == '%') {
814      ++c;
815      switch (*c) {
816        case 'd': {
817          int i = va_arg(args, int);  // have to specify type
818          // ...
819          break;
820        }
821        case 'g': {
822          double d = va_arg(args, double);
823          // ...
824          break;
825        }
826        ...
827      }
828    }
829  }
830  va_end(args);
831  return ...;
832}
833\end{cfacode}
834Every 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.
835Furthermore, if the user makes a mistake, compile-time checking is typically restricted to standard format codes and their corresponding types.
836In general, this means that C's variadic functions are not type-safe, making them difficult to use properly.
837\end{sloppypar}
838
839% When arguments are passed to a variadic function, they undergo \emph{default argument promotions}.
840% Specifically, this means that
841
842\CCeleven added support for \emph{variadic templates}, which add much needed type-safety to C's variadic landscape.
843It is possible to use variadic templates to define variadic functions and variadic data types.
844\begin{cppcode}
845void print(int);
846void print(char);
847void print(double);
848...
849
850void f() {}    // base case
851
852template<typename T, typename... Args>
853void f(const T & arg, const Args &... rest) {
854  print(arg);  // print the current element
855  f(rest...);  // handle remaining arguments recursively
856}
857\end{cppcode}
858Variadic templates work largely through recursion on the \emph{parameter pack}, which is the argument with @...@ following its type.
859A parameter pack matches 0 or more elements, which can be types or expressions depending on the context.
860Like other templates, variadic template functions rely on an implicit set of constraints on a type, in this example a @print@ routine.
861That 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.
862
863Recent \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.
864
865% D has variadic templates that deserve a mention http://dlang.org/ctarguments.html
866
867In Java, a variadic function appears similar to a C variadic function in syntax.
868\begin{javacode}
869int sum(int... args) {
870  int s = 0;
871  for (int x : args) {
872    s += x;
873  }
874  return s;
875}
876
877void print(Object... objs) {
878  for (Object obj : objs) {
879    System.out.print(obj);
880  }
881}
882
883print("The sum from 1 to 10 is ", sum(1,2,3,4,5,6,7,8,9,10), ".\n");
884\end{javacode}
885The key difference is that Java variadic functions are type-safe, because they specify the type of the argument immediately prior to the ellipsis.
886In 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.
887Since 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.
888
889The other option is to restrict the number of types that can be passed to the function by using a more specific type.
890Unfortunately, Java's use of nominal inheritance means that types must explicitly inherit from classes or interfaces in order to be considered a subclass.
891The combination of these two issues greatly restricts the usefulness of variadic functions in Java.
892
893Type-safe variadic functions are added to \CFA and discussed in Chapter 4.
894
895\section{Contributions}
896\label{s:contributions}
897
898No prior work on constructors or destructors had been done for \CFA.
899I did both the design and implementation work.
900While the overall design is based on constructors and destructors in object-oriented C++, it had to be re-engineered into non-object-oriented \CFA.
901I also had to make changes to the \CFA expression-resolver to integrate constructors and destructors into the type system.
902
903Prior work on the design of tuples for \CFA was done by Till, and some initial implementation work by Esteves.
904I largely took the Till design but added tuple indexing, which exists in a number of programming languages with tuples, simplified the implicit tuple conversions, and integrated with the \CFA polymorphism and assertion satisfaction model.
905I did a new implementation of tuples, and extensively
906augmented initial work by Bilson to incorporate tuples into the \CFA expression-resolver and type-unifier.
907
908No prior work on variadic functions had been done for \CFA.
909I did both the design and implementation work.
910While the overall design is based on variadic templates in C++, my design is novel in the way it is incorporated into the \CFA polymorphism model, and is engineered into \CFA so it dovetails with tuples.
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