Add polynomials

#!/usr/local/bin/runhugs
 
module Main where
 
type Poly = [(Int,Int)] 
-- assume sorted by increasing exponent. 
-- data Rational =  (Poly, Poly)
 
 
-- an interesting thing to observe: 
-- when adding, the null polynomial is zero. 
-- when multiplying it is one.  This concept emerges implicitly 
-- in these definitions. 
 
addPoly :: Poly -> Poly -> Poly
addPoly [] ys = ys
addPoly xs [] = xs
addPoly ((a,b):xs) ((c,d):ys)
    | a == c  = ((a,b+d):(addPoly xs ys))
    | a < c = ((a,b):(addPoly xs ((c,d):ys)))
    | a > c = ((c,d):(addPoly ((a,b):xs) ys))
 
addManyPolys :: [Poly] -> Poly
addManyPolys ps = foldl 0 addPoly ps
 
multiply :: [Int] -> [Int] -> [Int]
--multiply polynomials together. 
multiply [] ys = ys
multiply xs [] = xs
multiply ((a,b):xs) ((c,d):ys) 
 
 
main = do
       putStr $ show $ addPoly [(0,1),(2,1)] [(0,1)]