zhaw-fup/Exercises/exercise-4/Solution.hs

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2024-06-16 09:08:56 +00:00
--------------------
-- 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