Using the free monad for observable sharing in DSLs

Remote.hs

{-#LANGUAGE ExistentialQuantification, Rank2Types #-}

-- using free monad for observable sharing

data Free f a = Pure a | Free (f (Free f a))

data RemoteF a =  
    N Int 
  | Ref Int 
  | Ap a a
  | forall t . Let a (forall z . Free RemoteF z -> Remote t z)

type Remote t a = Free RemoteF a

n :: Int -> Remote Int a
n = Free . N

ref :: Int -> Remote (a -> b) a
ref = Free . Ref

ap :: Remote (a -> b) x -> Remote a x -> Remote b x
ap f arg = Free $ Ap f arg

letr :: Remote e x -> (forall z . Remote e z -> Remote t z) -> Remote t x
letr e body = Free $ Let e body

factorial :: Remote (Int -> Int) a
factorial = Free (Ref 0)

example :: Remote Int x
example = letr (n 22) (\e -> ap factorial e)

runBatch :: (forall a . Remote t a) -> IO (Remote t a) 
runBatch = undefined