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

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

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

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