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)