I have following datatype for representing arbitrary computable numbers:

    newtype Computable = Inexact (Word -> Integer)

"Inexact" encapsulates Cauchy sequences.

min and max will halt:

    instance Ord Computable where

        min (Inexact f) (Inexact g) = Inexact (\n -> min (f n) (g n))

        max (Inexact f) (Inexact g) = Inexact (\n -> max (f n) (g n))

But comparison functions won't halt for same numbers:

        compare (Inexact f) (Inexact g) = go 0 where

            go n = compare (f n) (g n) <> go (n+1)

So in this case, it would be inappropriate to defaultly define min and max.

It would be nice if there was a function for alternately defining comparison functions:

    defaultLessThan :: Ord a => a -> a -> Bool

    defaultLessThan x y = x == y || x == min x y

Then we can let (<=) = defaultLessThan.

Also I have to mention that the "realAbs" function I suggested in January must be the following definition in this regard:

    realAbs x = max x (negate x)