--------------------
-- 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

-- sieve :: ( a -> a -> Bool ) -> [ a ] -> [ a ]
-- sieve pred xs = case xs of
--     [] -> []
--     x : xs -> x :( sieve pred $ filter ( pred x ) xs )
sieve :: (a -> a -> Bool) -> [a] -> [a]
sieve pred xs = realSieve [] xs
    where
        realSieve acc [] = acc
        realSieve acc (x : xs) = realSieve (acc ++ [x]) (filter (pred x) xs)

-- >>> sieve (\ x -> \ y -> y > x) [1, 2, 3, 1, 2, 9, 7]
-- [1,2,3,9]
--