programing_in_Haskell_5.hs

-- 5-1
sum [x^2 | x<-[1..100]]
-- 5-2
replicate' :: Int -> a -> [a]
replicate' n a = [a | _ <- [1..n]]
-- 5-3
-- n以下の要素のピタゴラス数のリストを返す
pyths :: Int -> [(Int, Int, Int)]
pyths n = [(x, y, z) | x <- [1..n], y <- [1..n], z <- [1..n], x^2 + y^2 == z^2]
-- 5-4
-- 与えられた上限までに含まれる完全数全てを算出する関数perfects
factors :: Int -> [Int]
factors n = [x | x <- [ 1 .. n], n `mod` x == 0]
perfects :: Int -> [Int]
perfects n = [ x | x <- [1..n], x == sum(init (factors x))]
-- 5-6
find :: Eq a => a -> [(a, b)] -> [b]
find k t = [ v | (k', v) <- t, k == k']
-- > find 'b' [('a', 1), ('b', 2), ('c', 3), ('d', 4)]
-- [2, 4]
-- > zip ['a', 'b', 'c'] [1, 2, 3, 4]
-- [('a',1),('b',2),('c',3)]
positions :: Eq a => a -> [a] -> [Int]
--positions x xs = [i | (x', i) <- zip xs [0..], x == x']
positions x xs = find x (zip xs [0..])
-- ghci > positions False [True, False, True, False]
-- [1, 3]