import Prelude hiding (zip,unzip,last,lines,take)

-- Zip two lists into a list of pairs:
zip :: [a] -> [b] -> [(a,b)]
zip []     _      = []
zip _      []     = []
zip (x:xs) (y:ys) = (x,y) : zip xs ys

-- Unzip a list of pairs into two lists:
unzip :: [(a,b)] -> ([a],[b])
unzip []         = ([],[])
unzip ((x,y):ps) = let (xs,ys) = unzip ps
                   in (x:xs, y:ys)

-- Computes/returns the last element of a list:
last :: [a] -> Maybe a
last []     = Nothing
last (x:xs@(_:_)) = last xs
last [x]    = Just x

-- Breaks a string into a list of its lines.
lines :: String -> [String]
lines "" = []
lines ('\n':cs) = "" : lines cs
lines (c:cs)    = case lines cs of
                    []     -> [[c]]
                    (l:ls) -> (c:l) : ls

-- Factorial function:
fac :: Integer -> Integer
fac n | n==0      = 1
      | otherwise = n * fac (n-1)

-- Computes a maximal prefix of a list of a given length (first argument):
take :: Int -> [a] -> [a]
take n zs | n==0      = []
          | otherwise = case zs of
                          []     -> []
                          (x:xs) -> x : take (n-1) xs