"Inexact" encapsulates Cauchy sequences.
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)