1 Jan
2015
1 Jan
'15
10:01 a.m.
On Thu, Jan 01, 2015 at 03:52:26PM +0100, Atze van der Ploeg wrote:
If we do not require that (a <= b) && (a >= b) ==> a == b (where <= is from the total ordering and == is from the equality relation) then it is trivial, take the total ordering forall x y. x <= y that i mentioned earlier.
So the compatiblity with equality (you say field structure) is not besides the point, in fact antisymmetry means that the ordering corresponds to the equality relation.
Clear now or did I misunderstand?
Here is my proposed equality and ordering on the complex numbers: data Complex = Complex (Double, Double) deriving (Eq, Ord) Does this violate any of my requested conditions?