-- Part a
and :: [Bool] -> Bool
and []        = True
and (False:_) = False
and (_:xs)    = and xs

-- Part b
concat :: [[a]] -> [a]
concat []       = []
concat (xs:xss) = xs ++ concat xss

-- Part c
replicate :: Int -> a -> [a]
replicate 0 _ = []
replicate n a = [a] ++ replicate (n - 1) a

-- Part d
-- For simplicity, assume that the index is valid
-- and that the array is non-empty
(!!) :: [a] -> Int -> a
(x:xs) !! 0 = x
(x:xs) !! n = xs !! (n - 1)

-- Part e
elem :: Eq a => a -> [a] -> Bool
elem _ [] = False
-- Note: ys can be [] which is why (y:ys) matches singletons
elem x (y:ys)
    | x == y = True
    | x /= y = elem x ys