Haskell : Integration on the unit cube

integral.hs

{-# OPTIONS -XFlexibleInstances -XMultiParamTypeClasses #-}

-- integrate on the unit cube
-- first argument indicates approximate error

class Integrable a b where
	int :: b -> (b->a) -> b

instance (Ord a, Floating a) => Integrable a a where
	int e f = within (e / 2) (integrate f 0 1)

instance (Ord b, Floating b, Integrable a b) => Integrable (b->a) b where
	int e f = within e2 $ integrate (\t -> int e2 (f t)) 0 1
			where e2 = e/2

-- example : int 0.00001 (\x y z -> cos x + exp (y + exp z) )

integrate f a b = integ f a b (f a) (f b)

integ f a b fa fb = ( (fa + 4*fm + fb) * (b-a) / 6) : zipWith (+) (integ f a m fa fm) (integ f m b fm fb) 
	where
		m = (a+b) / 2
		fm = f m

within eps (x: ys@(y:xs))	|	abs(x-y) <= eps = y
				|	otherwise = within eps ys