[Haskell] ListMap example

[jeff polakow]

Hello,

  Why is the following not an arrow?

newtype ListMap i o = LM ([i] -> [o]
instance Arrow ListMap where
  pure f = LM (map f)
  LM f >>> LM g = LM (g . f)
  first (LM f) = LM ((uncurry zip) . (cross f id) . unzip)

thanks,
  Jeff