> find = find_viii
> findBit :: (Bit -> Bool) -> Bit
> findBit p = if p Zero then Zero else One
> branch :: Bit -> Cantor -> Cantor -> Cantor
> branch x l r n |  n == 0    = x
>                    |  odd n     = l ((n-1) `div` 2)
>                    |  otherwise = r ((n-2) `div` 2)
> find_viii :: (Cantor -> Bool) -> Cantor
> find_viii p = branch x l r
>  where x = findBit(x -> forsome(l -> forsome(r -> p(branch x l r))))
>          l = find_viii(l -> forsome(r -> p(branch x l r)))
>          r = find_viii(r -> p(branch x l r))

This doesn’t need the memoization, because the things one needs to remember are bound to variables in the where-clause. Using this algorithm, comparing f’ and g’, and f’ and h’ for equality moves from 6.75 and 3.20 seconds to respectively 0.14 and 0.09 seconds (using the Glasgow interpreter in all cases).