User-Defined Operators, Re: Function composition and currying

[Andrew J Bromage]

G'day all.

On Thu, Jul 17, 2003 at 04:46:13PM +0100, Jon Fairbairn wrote:

> Someone mentioned multiplying by a scalar. I think this is a
> good application, but what we need is to agree (somehow) on
> the symbol used. I've used (*.) and (.*), with the dot being
> on the side the scalar is on (on the grounds that . is a
> scalar product elsewhere), but without wide agreement I
> agree that this sort of thing reduces readability, because
> while I can read these programmes, it's harder for everyone
> else.

Yuck. :-)

I've run into the same problem with affine algebra, which has two
types, the Point and the Vector, where a Vector is the difference
between two Points:

	Vector + Vector = Vector
	Vector + Point = Point
	Point + Vector = Point
	Point + Point is an error

	Vector - Vector = Vector
	Point - Vector = Point
	Vector - Point = Point	-- (this rule is a bit controversial)
	Point - Point = Vector

It's not obvious what to call the operators here.

One solution might be to relax the rules about how the types of
operators are resolved.  At the moment, you can define function
names from different modules and all you need to do is qualify
them when you use them.  It's a little odd that you can't do
something similar with operators, though no succinct syntax leaps
to mind.

Of course you could always allow overloading _without_ requiring
module qualification (unless the overloading can't be resolved
using type information).  It'd make type checking NP-hard, but I
seem to recall that it's already more complex than that.

Cheers,
Andrew Bromage