Binary Search in Haskell

BinarySearch.hs

module BinarySearch(binarySearch, discreteBinarySearch, continuousBinarySearch) where

binarySearch :: ((a -> a -> Bool), (a -> a -> a)) -> (a, a) -> (a -> Bool) -> Maybe a
binarySearch (closeEnough, mid) (x0, x1) f = if y0 == y1 then Nothing else Just (iter x0 x1 y0 y1) where
    (y0, y1) = (f x0, f x1)
    iter x0 x1 y0 y1 = if closeEnough x0 x1
        then (if y0 then x0 else x1)
        else
            let
                xm = mid x0 x1
                ym = f xm
            in
                if ym /= y0
                    then iter x0 xm y0 ym
                    else iter xm x1 ym y1

discreteBinarySearch :: (Integral a) => (a, a) -> (a -> Bool) -> Maybe a
discreteBinarySearch = binarySearch ((\a -> \b -> abs(a - b) <= 1), (\a -> \b -> (a + b) `div` 2))

continuousBinarySearch :: (Floating a, Ord a) => a -> (a, a) -> (a -> Bool) -> Maybe a
continuousBinarySearch eps = binarySearch ((\a -> \b -> abs(a - b) <= eps), (\a -> \b -> (a + b) / 2))

main = do
    print $ continuousBinarySearch 1e-6 (0, 1e6) ((>=2) . (**2))
    print $ discreteBinarySearch (0, 10000) ((>=25) . (^2))