Solve first few tasks

Exercises/exercise-4/Solution.hs

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+--------------------
+-- 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
+