Church-encoded Freer Monad

This Oleg's Freer monad but Church-encoded.

• Because it's the Freer monad, FFC g is a Monad for any g even if it isn't a functor.
• Because it's Church-encoded, it reassociates left-nested binds: (m >>= f) >>= g immediately reassociates to m >>= \x -> f x >>= g

It's just continuations

Start with Oleg's "Freer monad"

data Freer g a where
  FPure   :: a -> Freer g a
  FImpure :: g x -> (x -> Freer g a) -> Freer g a

Church encode it to get

data FFC g a =
  FFC { unFFC :: forall r . (a -> r) -> (forall x . g x -> (x -> r) -> r) -> r }

Now flip the two arguments around and note that Cont t b = (b -> t) -> t

data FFC g a =
  FFC { unFFC :: forall r . (forall x . g x -> Cont r x) -> Cont r a }

So, the Freer monad is just an interpreter for 'g' into the continuation monad.