Product category (sort of)

ProductCat.hs

-- Product category instance

import Prelude hiding ((.),id)
import Control.Category

data Product c d x y = Product (c x y) (d x y)
  deriving (Eq,Show)

instance (Category c,Category d) => Category (Product c d) where
  id = Product id id
  (Product e f).(Product g h) = Product (e.g) (f.h)

app :: Product (->) (->) a b -> (a,a) -> (b,b)
app (Product f g) (x,y) = (f x,g y)

main :: IO ()
main = do
  let f = (+1)
  let g = (*2)
  let gfxfg = Product f g >>> Product g f
  print $ app gfxfg (3,4)