free-composition.hs

import Control.Object

echo' :: Object f (Coyoneda f)
echo' = Object $ Coyoneda (\x -> (x, echo'))

(@>>>@) :: Object f (Coyoneda g) -> Object g (Coyoneda h) -> Object f (Coyoneda h)
Object m @>>>@ Object n = Object $ \f -> case m f of
  Coyoneda k g -> case n g of
    Coyoneda l h -> Coyoneda (\x -> case l x of (y, ogh) -> case k y of (z, ofg) -> (z, ofg @>>>@ ogh)) h
infixr 1 @>>>@