Re: Equality operator overloading in ADA 83

[Mats Weber <Mats.Weber@elca-matrix.ch>]

> >OK, but then if I redefine "<" on a scalar type, should ">=" change?
> >After all, ">=" is (or could be) defined as "not <".
> 
> Only for totally-ordered sets.  It is useful to redefine "<" and ">" to model
> partial orderings, in which case >= is not equivalent a < b.

If it's done right, the definition of "=" and "<" is enough to construct
the others, even for non-totally ordered sets. Just don't make the
mistake of making "<" defined as not ">=":

a <= b means a < b or a = b
a > b  means b < a
a >= b meanss a > b or a = b

The case where this does not work is when "<=" is not an ordering
relation (in the mathematical sense). Non-total orders such as set
inclusion work perfectly.

And yes, I think that there should be an automatic redefinition in Ada
once "=" and one of "<", ">", ">=", "<=" are defined (but I realize it's
too late now, this should have been done in Ada 83).