A Fresh Look at Comparisons, Take 2

[Yigal Chripun]

Janice Caron wrote:
>>  is it possible (mathematically speaking) to have only one of the
>>  operators defined?
> 
> Only if you allowed opPartialLess to return three values (true, false,
> and can't compare).
> 
> For a /fully/ ordered set, you only need boolean <, because you can
> derive everything else. i.e.
> 
>     (a > b) == (b < a)
>     (a == b) == (!(a < b || b < a))
>     etc.
> 
> but what makes an ordering partial is that there may exist some
> elements, x and y say, for which x and y cannot be ordered. For such
> elements, neither (x < y) nor (x > y) have meaning, and both are
> considered to evaluate to false (because boolean expressions must be
> either true or false).
> 
> So you'd either need both opPartialLess() and opPartialGreater() being
> boolean, or you'd need a single opPartialCmp() which could return an
> enum { LESS, EQUAL, GREATER, UNORDERED }.
> 
> Does that make sense?

Thanks for the explanation :)
I'd prefer in that case either two boolean operators (the first
suggestion) or an opCmp that would throw an exception... (I a purist and
don't like enum return types that indicate errors...)

in any case I think all those strange !<> type comparisons should be
removed from D. they are not intuitive (at least for me).

--Yigal