import qualified Control.Monad

data D c a b = D (c a b) (c b a)

apply :: (c a b -> c a2 b2) -> (c b a -> c b2 a2) -> D c a b -> D c a2 b2
apply f1 f2 (D x y) = D (f1 x) (f2 y)

applyBoth = Control.Monad.join apply

f :: Int -> String
f = show

g :: String -> Int
g = read

h :: Int -> Int
h = (*2)

join :: (a -> b) -> (c -> d) -> ((a, c) -> (b, d))
join f g (x, y) = (f x, g y)

x1 = D f g

f1 = join h

y1 = apply f1 f1 x1 -- This compiles
y2 = apply g g x1 where g = f1 -- Also works

z1 = applyBoth f1 x1 -- This fails

main = return ()