Combining contravariant functors?

gistfile1.hs

type Prop  = String
type Value = String

newtype ChartConf = Conf { toList :: [(Prop, Value)] } deriving Show
newtype Charter a = Charter { runCharter :: a -> ChartConf }

instance Monoid ChartConf where
  mempty = Conf []
  c1 `mappend` c2 = Conf $ toList c1 `mappend` toList c2

c1 :: Charter [Int]
c1 = Charter $ \ xs -> Conf [("length", (show . length) xs)]

c2 :: Charter String
c2 = Charter $ \ str -> Conf [("rev", reverse str)]

x :: (Charter a, c -> a) -> (Charter b, c -> b) -> Charter c
(a, f) `x` (b, g) = Charter $ \ x -> runCharter a (f x) `mappend` runCharter b (g x)

c3 = (c1, fst) `x` (c2, snd)

z = runCharter ((c3, fstsnd) `x` (c2, third)) $ payload

fstsnd (x,y,z) = (x,y)
third  (x,y,z) = z

payload = ([1..10], "foo", "foobar")