I do think something has to be done to have an Eq and Ord with more strict laws.

* Operators in Eq and Ord diverge iff any of their parameters are bottom.

* The default definitions of (/=), (<), (>) and `compare` are law.

* (==) is reflexive and transitive

* (<=) is antisymmetric ((x <= y && y <= x) `implies` (x == y))

* (<=) is 'total' (x <= y || y <= x)

* (<=) is transitive

Currently, reflexivity of (==) is broken in the Prelude (let x = 0/0 in x == x). I know this is for IEEE 754 compliance, but c'mon, this is Haskell, we can have better ways of dealing with NaNs.

-Stijn