Operator overloading -- lets collect some use cases

[Don]

Don wrote:
> There's been some interesting discussion about operator overloading over 
> the past six months, but to take the next step, I think we need to 
> ground it in reality. What are the use cases?
> 
> I think that D's existing opCmp() takes care of the plethora of trivial 
> cases where <, >= etc are overloaded. It's the cases where the 
> arithmetic and logical operations are overloaded that are particularly 
> interesting to me.
> 
> The following mathematical cases immediately spring to mind:
> * complex numbers
> * quaternions
> * vectors
> * matrices
> * tensors
> * bigint operations (including bigint, bigfloat,...)
> I think that all of those are easily defensible.
> 
> But I know of very few reasonable non-mathematical uses.
> In C++, I've seen them used for iostreams, regexps, and some stuff that 
> is quite frankly bizarre.
> 
> So, please post any use cases which you consider convincing.

Some observations based on the use cases to date:
(1)
a += b is ALWAYS a = a + b (and likewise for all other operations).
opXXXAssign therefore seems to be a (limited) performance optimisation. 
The compiler should be allowed to synthesize += from +. This would 
almost halve the minimum number of repetitive functions required.

A straightforward first step would be to state in the spec that "the 
compiler is entitled to assume that X+=Y yields the same result as X=X+Y"

(2)
There seems to be a need for abstract syntax trees, which is NOT 
necessarily related to performance. (If we had a 'perfect performance' 
solution for operator overloading, it would not remove the desire for 
abstract syntax trees).
(3)
The array operations ~, [], [..] need further attention. A solution for 
$ is also required.