--Matthew Larson Exercise 2.2 10/7/2019

    import Prelude hiding (sum)

    sum :: Num n => [n] -> n
    sum [] = 0
    sum (x:xs) = x + sum xs

    -- | Square a number

    square :: Num n => n -> n
    square x = x^2

    sumProducts :: Num n => [n] -> n

    sumProducts = product . map square

    divisibleBy :: Integral n => n -> n -> Bool
    divisibleBy d n = d `mod` n == 0


    result = sum
           . take 100
           . filter (divisibleBy 2)
           . filter (divisibleBy 3)
           . filter (not . divisibleBy 4)
           . filter (not . divisibleBy 9)
           $ [0..]

    allp :: [a-> Bool] -> Bool -> Bool
    allp [] x = False
    allp (p:ps) x
      | p x = allp ps x
      | otherwise = False

    filterAll :: (a-> [b]) -> (c -> Bool)-> [a]
    filterAll filter . (allp (c:cs)) = c: filterAll filter allp cs