Polynomial in Haskell troubles with map

Question

I need to multiply a polynomial by a number using map. I´ve been trying for a long time and I´m already getting crazy. I´ve tried two ways getting this errors:

data Pol = P [(Float,Int)] deriving Show

prodEsc :: Pol -> Float -> Pol
prodEsc (P a) n = P (prodAux a n)

--First try:
prodAux :: [(Float,Int)] -> Float -> [(Float,Int)]
prodAux [] _ = []
prodAux ((c,g):xs) n = map (\ (c,g) n -> (c*n,g)) xs 

--error:
ERROR file:.\Febrero 2011.hs:21 - Type error in explicitly typed binding
*** Term           : prodAux
*** Type           : [(Float,Int)] -> Float -> [Float -> (Float,Int)]
*** Does not match : [(Float,Int)] -> Float -> [(Float,Int)]

--Second try:
prodAux :: [(Float,Int)] -> Float -> [(Float,Int)]
prodAux [] _ = []
prodAux (x:xs) n = map (opera x n) (x:xs)

opera :: (Float,Int) -> Float -> (Float,Int)
opera (c,g) n = (c*n,g)

--error:
ERROR file:.\Febrero 2011.hs:23 - Type error in application
*** Expression     : map (opera x n) (x : xs)
*** Term           : opera x n
*** Type           : (Float,Int)
*** Does not match : (Float,Int) -> a

Could anyone help me please?.

Thank you so much!!

Answer 1

When you're using map, you don't need to do your own pattern matching on whether the list is empty or not. So I strongly suspect that instead of

prodAux [] _ = []
prodAux ((c,g):xs) n = map (\ (c,g) n -> (c*n,g)) xs 

you mean simply

prodAux xs n = map (\ (c,g) -> (c*n,g)) xs

Otherwise you would be throwing away the first (c,g) pair, which does not appear to make much sense.

Answer 2

Your first try is right. Just remove the n from the lambda. It is already in scope and not needed:

prodAux :: [(Float,Int)] -> Float -> [(Float,Int)]
prodAux [] _ = []
prodAux ((c,g):xs) n = map (\ (c,g) -> (c*n,g)) xs

map has the type (a -> b) -> [a] -> [b]. this means, that it takes a list of something and applies a function to every element. This function has to have exactly one argument: The element to operate over.