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.

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