Though it is reasonable to make utilities monadic, they lack a crucial property: laziness.
I have the following datatype:
newtype ArbReal = ArbReal (Word -> Integer)
This represents arbitrary real numbers by being able to compute arbitrary decimal places after the decimal point. For example, to compute pi, let f be the function passed to constructor ArbReal. Then f 0 = 3, f 1 = 31, f 2 = 314, and so on.
I can implement instance Random ArbReal:
instance Random ArbReal where
random g = let
(h, i) = split g
d:digits = randomRs (0 :: Word, 9) h
getNum [] = 0
getNum (d:ds) = toInteger d + 10 * getNum ds
takeDigits n = getNum (reverse (take n digits)) + toInteger (fromEnum (d >= 5))
in (ArbReal (takeDigits . fromIntegral), i)
randomR (lo, hi) g = let
(x, h) = random g
in (lo + x * (hi - lo), h)
But I see no way to implement an instance of UniformRange ArbReal, for it relies on randomRs, which is lazy. Neither ST nor IO is able to contain such laziness.