opCmp, [partial/total/pre]orders, custom floating point types etc.

[John Colvin via Digitalmars-d]

On Tuesday, 12 January 2016 at 18:36:32 UTC, Ilya Yaroshenko 
wrote:
> On Tuesday, 12 January 2016 at 18:27:15 UTC, John Colvin wrote:
>> Background:
>> Some important properties for binary relations on sets that 
>> are somewhat similar to the normal ≤/≥ on the real numbers or 
>> integers are:
>>
>> [...]
>
> http://dlang.org/phobos/std_math.html#.cmp ? --Ilya

That doesn't solve the whole problem, because std.math.cmp isn't 
the default comparator you can't use a totally ordered float type 
as a drop-in for the builtin float types.

A more interesting question it bring up though is:
does the approach of imposing a (somewhat arbitrary) total order 
work for other types where you would normally use a less "strict" 
ordering? Does it work well for missing data representations?