factTU :: Int -> Int 
u :: Int -> Int -> Int -> Int
factTU(x) -> u(x, 1, 1)
u(x, i, a) -> a | i>x 
u(x, i, a) -> u(x, i+1, i*a) | i<=x

factTD :: Int -> Int 
d :: Int -> Int -> Int 
factTD(x) -> d(x, 1)
d(x, a) -> a            | x<=0
d(x, a) -> d(x-1, a*x)  | x>0

tailup :: (Int -> Int -> Int) -> Int -> Int -> Int -> Int
tailup(F, i, y, a) -> a                               | i > y
tailup(F, i, y, a) -> tailup(F, i + 1, y, F(i, a))    | i ≤ y

taildown :: (Int -> Int -> Int) -> Int -> Int -> Int -> Int
taildown(F, x, i, a) -> a                             | i < x
taildown(F, x, i, a) -> taildown(F, x, i - 1, F(a,i)) | i ≥ x