## Lvalues and References ##
C defines the notion of a _lvalue_, essentially an addressable object, as well 
as a number of type _qualifiers_, `const`, `volatile`, and `restrict`. 
As these type qualifiers are generally only meaningful to the type system as 
applied to lvalues, the two concepts are closely related. 
A const lvalue cannot be modified, the compiler cannot assume that a volatile 
lvalue will not be concurrently modified by some other part of the system, and 
a restrict lvalue must have pointer type, and the compiler may assume that no 
other pointer in scope aliases that pointer (this is solely a performance 
optimization, and may be ignored by implementers).
_Lvalue-to-rvalue conversion_, which takes an lvalue of type `T` and converts 
it to an expression result of type `T` (commonly called an _rvalue_ of type 
`T`) also strips all the qualifiers from the lvalue, as an expression result 
is a value, not an addressable object that can have properties like 
immutability. 
Though lvalue-to-rvalue conversion strips the qualifiers from lvalues, 
derived rvalue types such as pointer types may include qualifiers; 
`const int *` is a distinct type from `int *`, though the latter is safely 
convertable to the former. 
In general, any number of qualifiers can be safely added to the 
pointed-to-type of a pointer type, e.g. `int *` converts safely to 
`const int *` and `volatile int *`, both of which convert safely to 
`const volatile int *`.

Since lvalues are precicely "addressable objects", in C, only lvalues can be 
used as the operand of the `&` address-of operator. 
Similarly, only modifiable lvalues may be used as the assigned-to 
operand of the mutating operators: assignment, compound assignment 
(e.g. `+=`), and increment and decrement; roughly speaking, lvalues without 
the `const` qualifier are modifiable, but lvalues of incomplete types, array 
types, and struct or union types with const members are also not modifiable. 
Lvalues are produced by the following expressions: object identifiers 
(function identifiers are not considered to be lvalues), the result of the `*` 
dereference operator applied to an object pointer, the result of a member 
expression `s.f` if the left argument `s` is an lvalue (note that the 
preceding two rules imply that the result of indirect member expressions 
`s->f` are always lvalues, by desugaring to `(*s).f`), and the result of the 
indexing operator `a[i]` (similarly by its desugaring to `*((a)+(i))`). 
Somewhat less obviously, parenthesized lvalue expressions, string literals, 
and compound literals (e.g. `(struct foo){ 'x', 3.14, 42 }`) are also lvalues.

All of the conversions described above are defined in standard C, but Cforall 
requires further features from its type system. 
In particular, to allow overloading of the `*?` and `?[?]` dereferencing and 
indexing operators, Cforall requires a way to declare that the functions 
defining these operators return lvalues, and since C functions never return 
lvalues and for syntactic reasons we wish to distinguish functions which 
return lvalues from functions which return pointers, this is of necessity an 
extension to standard C. 
In the current design, an `lvalue` qualifier can be added to function return 
types (and only to function return types), the effect of which is to return a 
pointer which is implicitly dereferenced by the caller.
C++ includes the more general concept of _references_, which are typically 
implemented as implicitly dereferenced pointers as well. 
Another use case which C++ references support is providing a way to pass 
function parameters by reference (rather than by value) with a natural 
syntax; Cforall in its current state has no such mechanism. 
As an example, consider the following (currently typical) copy-constructor 
signature and call:

	void ?{}(T *lhs, T rhs);
	
	T x;
	T y = { x };

Note that the right-hand argument is passed by value, and would in fact be 
copied twice in the course of the constructor call `T y = { x };` (once into 
the parameter by C's standard `memcpy` semantics, once again in the body of 
the copy constructor, though it is possible that return value optimization 
will elide the `memcpy`-style copy).
However, to pass by reference using the existing pointer syntax, the example 
above would look like this:

	void ?{}(T *lhs, const T *rhs);
	
	T x;
	T y = { &x };

This example is not even as bad as it could be; assuming pass-by-reference is 
the desired semantics for the `?+?` operator, that implies the following 
design today:

	T ?+?(const T *lhs, const T *rhs);
	
	T a, b;
	T c = &a + &b,

In addition to `&a + &b` being unsightly and confusing syntax to add `a` and 
`b`, it also introduces a possible ambiguity with pointer arithmetic on `T*` 
which can only be resolved by return-type inference.

Pass-by-reference and marking functions as returning lvalues instead of the 
usual rvalues are actually closely related concepts, as obtaining a reference 
to pass depends on the referenced object being addressable, i.e. an lvalue, 
and lvalue return types are effectively return-by-reference. 
Cforall should also unify the concepts, with a parameterized type for 
"reference to `T`", which I will write `T&`. 

Firstly, assignment to a function parameter as part of a function call and 
local variable initialization have almost identical semantics, so should be 
treated similarly for the reference type too; this implies we should be able 
to declare local variables of reference type, as in the following:

	int x = 42;
	int& r = x; // r is now an alias for x

Unlike in C++, we would like to have the capability to re-bind references 
after initialization, as this allows the attractive syntax of references to 
support some further useful code patterns, such as first initializing a 
reference after its declaration. 
Constant references to `T` (`T& const`) should not be re-bindable. 

One option for re-binding references is to use a dedicated operator, as in the 
code example below:

	int i = 42, j = 7;
	int& r = i;  // bind r to i
	r = j;       // set i (== r) to 7
	r := j;      // rebind r to j using the new := rebind operator
	i = 42;      // reset i (!= r) to 42
	assert( r == 7 );

Another option for reference rebind is to modify the semantics of the `&` 
address-of operator. 
In standard C, the address-of operator never returns an lvalue, but for an 
object of type `T`, returns a `T*`. 
If the address-of operator returned an lvalue for references, this would 
allow reference rebinding using the usual pointer assignment syntax; 
that is, if address-of a `T&` returned a `T*&` then the following works:

    int i = 42; j = 7;
    int& r = i;  // bind r to i
    r = j;       // set i (== r) to 7
    &r = &j;     // rebind r to j using the newly mutable "address-of reference"
    i = 42;      // reset i (!= r) to 42
    assert( r == 7 );

This change (making addresses of references mutable) allows use of existing 
operators defined over pointers, as well as elegant handling of nested 
references-to-references.

The semantics and restrictions of `T&` are effectively the semantics of an 
lvalue of type `T`, and by this analogy there should be a safe, qualifier 
dropping conversion from `const volatile restrict T&` (and every other 
qualifier combination on the `T` in `T&`) to `T`. 
With this conversion, the resolver may type most expressions that C would 
call "lvalue of type `T`" as `T&`. 
There's also an obvious argument that lvalues of a (possibly-qualified) type 
`T` should be convertable to references of type `T`, where `T` is also 
so-qualified (e.g. lvalue `int` to `int&`, lvalue `const char` to 
`const char&`). 
By similar arguments to pointer types, qualifiers should be addable to the 
referred-to type of a reference (e.g. `int&` to `const int&`). 
As a note, since pointer arithmetic is explictly not defined on `T&`, 
`restrict T&` should be allowable and would have alias-analysis rules that 
are actually comprehensible to mere mortals.

Using pass-by-reference semantics for function calls should not put syntactic 
constraints on how the function is called; particularly, temporary values 
should be able to be passed by reference. 
The mechanism for this pass-by-reference would be to store the value of the 
temporary expression into a new unnamed temporary, and pass the reference of 
that temporary to the function.
As an example, the following code should all compile and run:

	void f(int& x) { printf("%d\n", x++); }
	
	int i = 7, j = 11;
	const int answer = 42;
	
	f(i);      // (1)
	f(42);     // (2)
	f(i + j);  // (3)
	f(answer); // (4)

The semantics of (1) are just like C++'s, "7" is printed, and `i` has the 
value 8 afterward. 
For (2), "42" is printed, and the increment of the unnamed temporary to 43 is 
not visible to the caller; (3) behaves similarly, printing "19", but not 
changing `i` or `j`. 
(4) is a bit of an interesting case; we want to be able to support named 
constants like `answer` that can be used anywhere the constant expression 
they're replacing (like `42`) could go; in this sense, (4) and (2) should have 
the same semantics. 
However, we don't want the mutation to the `x` parameter to be visible in 
`answer` afterward, because `answer` is a constant, and thus shouldn't change. 
The solution to this is to allow chaining of the two lvalue conversions; 
`answer` has the type `const int&`, which can be converted to `int` by the 
lvalue-to-rvalue conversion (which drops the qualifiers), then up to `int&` 
by the temporary-producing rvalue-to-lvalue conversion. 
Thus, an unnamed temporary is inserted, initialized to `answer` (i.e. 42), 
mutated by `f`, then discarded; "42" is printed, just as in case (2), and 
`answer` still equals 42 after the call, because it was the temporary that was 
mutated, not `answer`.
It may be somewhat surprising to C++ programmers that `f(i)` mutates `i` while 
`f(answer)` does not mutate `answer` (though `f(answer)` would be illegal in 
C++, leading to the dreaded "const hell"), but the behaviour of this rule can 
be determined by examining local scope with the simple rule "non-`const` 
references to `const` variables produce temporaries", which aligns with 
programmer intuition that `const` variables cannot be mutated.

To bikeshed syntax for `T&`, there are three basic options: language 
keywords (`lvalue T` is already in Cforall), compiler-supported "special" 
generic types (e.g. `ref(T)`), or sigils (`T&` is familiar to C++ 
programmers). 
Keyword or generic based approaches run the risk of name conflicts with 
existing code, while any sigil used would have to be carefully chosen to not 
create parsing conflicts.