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

factRD :: Int -> Int 
factRD(x) -> 1 | x<=1
factRD(x) -> x*factRD(x-1) | x>1

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

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