Exames de Princípios de Programação - FCUL

2018_f1.hs

import Test.QuickCheck

-- Grupo 1

-- a)
encontra :: (a -> Bool) -> [a] -> Maybe a
encontra f xs
    | length matches == 0 = Nothing
    | otherwise = Just (head matches)
    where
        matches = filter f xs

-- b)
fatias :: Int -> [a] -> [[a]]
fatias n xs
    | (length xs) < n = [xs]
    | otherwise = (take n xs) : fatias n (drop n xs)

-- c)
separa :: Eq a => [a] -> [a] -> [[a]]
separa sep [] = []
separa sep str = left : separa sep right
    where
        ok = (flip notElem) sep
        partes = span ok str
        left  = fst partes
        right = dropWhile (not . ok) (snd partes)

-- Grupo 2
data Doc = Vazio
    | Texto String
    | NovaLinha
    | Concat Doc Doc

-- a)
instance Show Doc where
    show Vazio = ""
    show NovaLinha = "\n"
    show (Texto str) = str
    show (Concat a b) = show a ++ show b

-- b)
instance Eq Doc where
    a == b = (show a) == (show b)

-- Grupo 3
-- a)
instance Arbitrary Doc where
    arbitrary = oneof [
        return Vazio,
        return NovaLinha,
        do
            t <- arbitrary :: Gen String
            return $ Texto t,
        do
            a <- arbitrary
            b <- arbitrary
            return $ Concat a b]

-- b)
prop_concat_vazio doc =
    Concat doc Vazio == doc &&
    Concat Vazio doc == doc

prop_concat_assoc a b c=
    (Concat (Concat a b) c) == (Concat a (Concat b c))


-- Grupo 4
???

-- Grupo 5 (Java)
Stream.iterate(0, x -> x + 1).limit(n)
      .filter(x -> x%2 == 1)
      .map(x -> x * x)
      .reduce(0, (a, b) -> a + b);