57 lines
1.1 KiB
Haskell
57 lines
1.1 KiB
Haskell
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-- Exercise 1
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prim c g 0 x = c x
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prim c g n x = g (f (n - 1) x) (n - 1) x
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where
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f = prim c g
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m2 :: Integer -> () -> Integer
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m2 n x = prim (\_ -> 0) (\a -> \n -> \x -> a + 2) n x
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-- >>> print (m2 8 ())
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-- 16
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--
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e2 :: Integer -> () -> Integer
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e2 n x = prim (\_ -> 1) (\a -> \n -> \x -> a * 2) n x
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-- >>> print (e2 4 ())
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-- 16
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--
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exp :: Integer -> Integer -> Integer
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exp x n = prim (\_ -> 1) (\a -> \n -> \x -> a * x) n x
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-- >>> print (Main.exp 2 3)
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-- 8
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--
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fact :: Integer -> () -> Integer
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fact n x = prim (\_ -> 1) (\a -> \n -> \x -> a * (n + 1)) n x
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-- >>> print (fact 3 ())
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-- 6
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--
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--------------------
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-- Exercise 2
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--------------------
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f g x
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| x == 0 = g x
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| otherwise = g $ f g (x - 1)
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-- Nicht endrekursiv
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length xs = case xs of
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[] -> 0
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x : xs -> (+1) $ Main.length xs
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-- ist endrekursiv
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length' ls = aux
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$ map ( const 1)
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$ ls
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where
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aux ys = case ys of
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[] -> 0
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[x] -> x
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x : xs -> aux $ map (\y -> (+1) x ) xs
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-- length' und aux sind nicht endrekursiv
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