Definir la funci\u00f3n<\/p>\n
\n sumaSiTodosJustos :: (Num a, Eq a) => [Maybe a] -> Maybe a\n<\/pre>\ntal que (sumaSiTodosJustos xs) es justo la suma de todos los elementos de xs si todos son justos (es decir, si Nothing no pertenece a xs) y Nothing en caso contrario. Por ejemplo,<\/p>\n
\n sumaSiTodosJustos [Just 2, Just 5] == Just 7\n sumaSiTodosJustos [Just 2, Just 5, Nothing] == Nothing\n<\/pre>\nSoluciones<\/h4>\n\nimport Data.Maybe (catMaybes, isJust, fromJust)\nimport Test.QuickCheck (quickCheck)\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nsumaSiTodosJustos1 :: (Num a, Eq a) => [Maybe a] -> Maybe a\nsumaSiTodosJustos1 xs\n | todosJustos xs = Just (sum [x | (Just x) <- xs])\n | otherwise = Nothing\n\n-- (todosJustos xs) se verifica si todos los elementos de xs son justos\n-- (es decir, si Nothing no pertenece a xs) y Nothing en caso\n-- contrario. Por ejemplo,\n-- todosJustos [Just 2, Just 5] == True\n-- todosJustos [Just 2, Just 5, Nothing] == False\n\n-- 1\u00aa definici\u00f3n de todosJustos:\ntodosJustos1 :: Eq a => [Maybe a] -> Bool\ntodosJustos1 = notElem Nothing\n\n-- 2\u00aa definici\u00f3n de todosJustos:\ntodosJustos :: Eq a => [Maybe a] -> Bool\ntodosJustos = all isJust\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nsumaSiTodosJustos2 :: (Num a, Eq a) => [Maybe a] -> Maybe a\nsumaSiTodosJustos2 xs\n | todosJustos xs = Just (sum [fromJust x | x <- xs])\n | otherwise = Nothing\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\nsumaSiTodosJustos3 :: (Num a, Eq a) => [Maybe a] -> Maybe a\nsumaSiTodosJustos3 xs\n | todosJustos xs = Just (sum (map fromJust xs))\n | otherwise = Nothing\n\n-- 4\u00aa soluci\u00f3n\n\nsumaSiTodosJustos4 :: (Num a, Eq a) => [Maybe a] -> Maybe a\nsumaSiTodosJustos4 xs\n | todosJustos xs = Just (sum (catMaybes xs))\n | otherwise = Nothing\n\n-- 5\u00aa soluci\u00f3n\n-- ===========\n\nsumaSiTodosJustos5 :: (Num a, Eq a) => [Maybe a] -> Maybe a\nsumaSiTodosJustos5 xs = suma (sequence xs)\n where suma Nothing = Nothing\n suma (Just ys) = Just (sum ys)\n\n-- Nota. En la soluci\u00f3n anterior se usa la funci\u00f3n\n-- sequence :: Monad m => [m a] -> m [a]\n-- tal que (sequence xs) es la m\u00f3nada obtenida evaluando cada una de las\n-- de xs de izquierda a derecha. Por ejemplo,\n-- sequence [Just 2, Just 5] == Just [2,5]\n-- sequence [Just 2, Nothing] == Nothing\n-- sequence [[2,4],[5,7]] == [[2,5],[2,7],[4,5],[4,7]]\n-- sequence [[2,4],[5,7],[6]] == [[2,5,6],[2,7,6],[4,5,6],[4,7,6]]\n-- sequence [[2,4],[5,7],[]] == []\n\n-- 6\u00aa soluci\u00f3n\n-- ===========\n\nsumaSiTodosJustos6 :: (Num a, Eq a) => [Maybe a] -> Maybe a\nsumaSiTodosJustos6 xs = fmap sum (sequence xs)\n\n-- 7\u00aa soluci\u00f3n\n-- ===========\n\nsumaSiTodosJustos7 :: (Num a, Eq a) => [Maybe a] -> Maybe a\nsumaSiTodosJustos7 = fmap sum . sequence\n\n-- Equivalencia de las definiciones\n-- ================================\n\n-- La propiedad es\nprop_sumaSiTodosJustos :: [Maybe Integer] -> Bool\nprop_sumaSiTodosJustos xs =\n all (== sumaSiTodosJustos1 xs)\n [sumaSiTodosJustos2 xs,\n sumaSiTodosJustos3 xs,\n sumaSiTodosJustos4 xs,\n sumaSiTodosJustos5 xs,\n sumaSiTodosJustos6 xs,\n sumaSiTodosJustos7 xs]\n\nverifica_sumaSiTodosJustos :: IO ()\nverifica_sumaSiTodosJustos =\n quickCheck prop_sumaSiTodosJustos\n\n-- La comprobaci\u00f3n es\n-- \u03bb> verifica_sumaSiTodosJustos\n-- +++ OK, passed 100 tests.\n<\/pre>\n