On 4/6/06, Brian Hulley
What about:
class Eq a where (==), (/=) :: ... class PartialOrd a where (<), (>) :: a->a->Bool x > y = y < x
class (PartialOrd a) => TotalOrd a where x <= y = not (y < x) .... -- => not meaning inheritance but just a restriction on a for use of TotalOrd
A partial order can be defined in either of two ways, both of which require some notion of equality. If it is a weak partial order, you need to require reflexivity, i.e. x=y implies R(x,y). If it is a strong partial order, you need to require irreflexivity. So some notion of equality is necessary in either case. (I think the same is true of preorders, if we want to generalize to that.) So, if such a PartialOrd existed, it really should be between Eq and Ord in the class hierarchy. Steve