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-- Ex. 1

interleave :: a -> [a] -> [[a]]
interleave x []     = [[x]]
interleave x (y:ys) = [x:y:ys] ++ map (y:) (interleave x ys)

{- interleave 3 [1,2,3]  =>  [[3,1,2,3],[1,3,2,3],[1,2,3,3],[1,2,3,3]] -}

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-- Ex. 2

perms :: [a] -> [[a]]
perms []     = [[]]
perms (x:xs) = [zs | ys <- perms xs, zs <- interleave x ys]

{- perms [1,2,3]  =>  [[1,2,3],[2,1,3],[2,3,1],[1,3,2],[3,1,2],[3,2,1]] -}

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-- Ex. 3

data Matrix a = M [[a]]

instance (Show a) => Show (Matrix a) where
    show (M xs) = concatMap showRow xs where
        showRow = foldr (\x rest -> (show x) ++ " " ++ rest) "\n"

map2 :: (a -> a -> a) -> [a] -> [a] -> [a]
map2 f xs []         = []
map2 f [] ys         = []
map2 f (x:xs) (y:ys) = (f x y):(map2 f xs ys)

matAdd :: (Num a) => Matrix a -> Matrix a -> Matrix a
matAdd (M xs) (M ys) = M (map2 (\x y -> map2 (+) x y) xs ys)


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-- Ex. 4

e :: Double -> Double
e n = foldl (\x y -> x + (1 / (fac y))) 0.0 [0..n] where
    fac 0 = 1
    fac n = n * (fac (n-1))

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