--------------------
-- Exercise 1
--------------------
prim c g 0 x = c x
prim c g n x = g (f (n - 1) x) (n - 1) x
    where
        f = prim c g

m2 :: Integer -> () -> Integer
m2 n x = prim (\_ -> 0) (\a -> \n -> \x -> a + 2) n x

-- >>> print (m2 8 ())
-- 16
--

e2 :: Integer -> () -> Integer
e2 n x = prim (\_ -> 1) (\a -> \n -> \x -> a * 2) n x
-- >>> print (e2 4 ())
-- 16
--

exp :: Integer -> Integer -> Integer
exp x n = prim (\_ -> 1) (\a -> \n -> \x -> a * x) n x
-- >>> print (Main.exp 2 3)
-- 8
--

fact :: Integer -> () -> Integer
fact n x = prim (\_ -> 1) (\a -> \n -> \x -> a * (n + 1)) n x
-- >>> print (fact 3 ())
-- 6
--

--------------------
-- Exercise 2
--------------------
f g x
    | x == 0 = g x
    | otherwise = g $ f g (x - 1)
-- Nicht endrekursiv

length xs = case xs of
    [] -> 0
    x : xs -> (+1) $ Main.length xs
-- ist endrekursiv

length' ls = aux
    $ map ( const 1)
    $ ls
    where
        aux ys = case ys of
            [] -> 0
            [x] -> x
            x : xs -> aux $ map (\y -> (+1) x ) xs
-- length' und aux sind nicht endrekursiv