Write functions genUnion and genIntersect for generalized list union and list intersection. The functions should be of type [[a]] -> [a]. Note that genIntersect is undefined on the empty list of lists.

Solution 1 - 1st attempt:
genUnion :: Eq a => [[a]] -> [a]
genUnion [] = []
genUnion (x:xs) = gu2 x xs where
  gu2 :: Eq a => [a] -> [[a]] -> [a]
  gu2 xs [] = xs
  gu2 xs (y:ys) = gu2 (u2 xs y) ys where
    u2 :: Eq a => [a] -> [a] -> [a]
    u2 xs [] = xs
    u2 xs (y:ys)
      | elem y xs = u2 xs ys
      | otherwise = u2 (xs++[y]) ys

genIntersect :: Eq a => [[a]] -> [a]
genIntersect [] = error "general intersection is undefined on the empty list of lists"
genIntersect (x:xs) = gi2 x xs where
  gi2 :: Eq a => [a] -> [[a]] -> [a]
  gi2 xs [] = xs
  gi2 xs (y:ys) = gi2 (i2 xs y) ys where
    i2 :: Eq a => [a] -> [a] -> [a]
    i2 [] _ = []
    i2 (x:xs) ys
      | elem x ys = x : i2 xs ys
      | otherwise = i2 xs ys

Solution 2 - much nicer:
genUnion' :: Eq a => [[a]] -> [a]
genUnion' [] = []
genUnion' (x:xs) = union x (genUnion' xs)      

genIntersect' :: Eq a => [[a]] -> [a]
genIntersect' [] = error "general intersection is undefined on the empty list of lists"
genIntersect' [xs] = xs
genIntersect' (x:xs) = intersect x (genIntersect' xs)

# posted by rot13(Unafba Pune) @ 11:27 PM