module Convolution ( convolve ) where
ip :: Num a => [a] -> [a] -> a
ip [] ys = 0
ip xs [] = 0
ip (x:xs) (y:ys) = x*y + ip xs ys

pad :: [a] -> [a] -> [a]
pad x y = (replicate ((length y) - 1) 0) ++ x

heads :: [a] -> [[a]]
heads [x] = [[x]]
heads xs= xs : heads (init xs)

convolve :: (Num a) => [a] -> [a] -> [a]
convolve _ [] = []
convolve [] _ = []
convolve as bs = 
   let  padas = pad as bs
        padbs = pad bs as
   in zipWith (ip) (init $ tails padas)  (heads $ reverse padbs)

-- To compile an executable a [[main]] definition is needed for input and output.  
-- I don't want to think about this right now .