```-- CSE 341, 1999su
-- Assignment 3
-- sample solutions
-- Ken Yasuhara
-- July, 1999

module A3 where

----------------------------------------------------------------------
-- no. 1

squareList :: Num a => [a] -> [a]
squareList = map (\x -> x * x)		-- also:  map (^2)

squareList2 [] = []
squareList2 (x:xs) = (x * x):(squareList2 xs)

-- also:
-- squareList2 l = [x^2 | x <- l]

----------------------------------------------------------------------
-- no. 2

filterGE k l = [ x | x <- l, x >= k ]

-- also:
-- filterGE k [] = []
-- filterGE k (x:xs) | x >= k    = x:(filterGE k xs)
-- 		     | otherwise = filterGE k xs

----------------------------------------------------------------------
-- nos. 3, 4

factors k = [x | x <- [2..k], mod k x == 0] -- also:  k `mod` x == 0
primes = [x | x <- [2..], factors x == [x]]

----------------------------------------------------------------------
-- no. 5

isMember _ [] = False
isMember k (x:xs) | x == k    = True
| otherwise = isMember k xs

union s1 s2 = s1 ++ [x | x <- s2, not (isMember x s1)]

-- also:
-- union [] [] = []
-- union [] xs = xs
-- union xs [] = xs
-- union (x:xs) ys | isMember x ys = union xs (ys)
--                 | otherwise     = union xs (x:ys)

intersection s1 s2 = [ x | x <- s1, isMember x s2 ]

-- also:
-- intersection [] [] = []
-- intersection [] xs = []
-- intersection (x:xs) ys | isMember x ys = x:(intersection xs ys)
-- 			  | otherwise     = intersection xs ys

difference s1 s2 = [ x | x <- s1, not (isMember x s2) ]

-- also:
-- difference [] xs = []
-- difference (x:xs) ys | not (isMember x ys) = x:(difference xs ys)
--                      | otherwise           = difference xs ys

-- end of file

```