How do I use the Church encoding for Free Monads?

Question

I\'ve been using the Free datatype in Control.Monad.Free from the free package. Now I\'m trying to convert it to use F in

Answer 1

Your

matchF
  :: Functor f
  => (a -> r)
  -> (f (F f a) -> r)
  -> F f a
  -> r

looks like the Scott-encoded Free monad. The Church-encoded version is just

matchF
  :: Functor f
  => (a -> r)
  -> (f r -> r)
  -> F f a
  -> r
matchF kp kf f = runF f kp kf

Here are Church- and Scott-encoded lists for comparison:

newtype Church a = Church { runChurch :: forall r. (a -> r       -> r) -> r -> r }
newtype Scott  a = Scott  { runScott  :: forall r. (a -> Scott a -> r) -> r -> r }