Hi Café,

Below I describe what I call «demarcating monad transformer». It works great for my purposes, though the construction feels a bit awkward.
Perhaps, this is just an instance of a general case. For details and example, see [1] (single module package).

Recently I got a challenge of manipulating transformed monadic values. In my case the value was of type t (Free f) a (or MonadFree m => t m a).
The challange itself was to provide a function:

transform :: (Functor f, MonadTrans t) => (forall b. f b -> t (Free f) b) -> t (Free f) a -> t (Free f) a

The type t (Free f) a for my purposes can be read as «a program with low-level API specified with functor f and extra features specified with monad transformer t».
transform takes a “basic transformation” phi and an abstract program p and applies phi whenever p “executes” command of free functor f.

It turns out that this function is impossible (try StateT). The point is that you can't “get inside” of transformed monadic value.

So I came up with idea of «demarcating» monad transformer. By «demarcating» I mean separating pure monadic computations (lifted m a) from transformed ones (t m a).

Such separation can be made explicit with the help of free monads:

data DemarcateF t m next
    = forall b. DemarcateMonad   (m b) (b -> next)  -- "pure" monadic computation
    | forall b. DemarcateTrans (t m b) (b -> next)  -- transformed monadic computation

instance Functor (Demarcate t m) where ...

-- getting monad for free
newtype Demarcate t m a = Demarcate { unDemarcate :: Free (DemarcateF t m) a }

instance Monad (Demarcate t m) where ...
instance MonadTrans (Demarcate t) where ...

With that I can define transform functions:

-- transform arbitrary monadic computation
transformDemarcateM :: (forall b. m b -> Demarcate t m b) -> Demarcate t m a -> Demarcate t m a

-- transform free monadic actions
transformDemarcateFree :: (forall b. f b -> Demarcate t (Free f) b) -> Demarcate t (Free f) a -> Demarcate t (Free f) a
transformDemarcateFree phi = transformDemarcateM (iterM phi)

The complete code is available at [1]. Check out examples/simple.hs for a use case.

Now the questions are:

• has anyone else encountered such a challenge?
• is this solution an instance of a more general pattern?
• is it sensible to use Demarcate t m a when m is not a free monad?
• how Demarcate may affect the performance?

Thanks in advance,
Nick

[1] https://github.com/fizruk/demarcate