Roman Cheplyaka

Taking advantage of type synonyms in monad-control

December 26, 2014

Bas van Dijk has recently released monad-control-, the main purpose of which is to replace associated data types with associated type synonyms. The change caused minor breakages here and there, so people might wonder whether and why it was worth it. Let me show you a simple example that demonstrates the difference.

Let’s say we are writing a web application. wai defines an application as

type Application =
  Request ->
  (Response -> IO ResponseReceived) ->
  IO ResponseReceived

Our web app will need a database connection, which we’ll pass using the ReaderT transformer:

type ApplicationM m =
  Request ->
  (Response -> m ResponseReceived) ->
  m ResponseReceived

myApp :: ApplicationM (ReaderT DbConnection IO)

However, warp can only run an Application, not ApplicationM:

run :: Port -> Application -> IO ()

Can we build runM :: Port -> ApplicationM m -> m () on top of the simple run function? Solving the problems like this one is exactly the purpose of monad-control.

Here’s how such a function might look like:

  :: (MonadBaseControl IO m)
  => Port -> ApplicationM m -> m ()
runM port app = do
  liftBaseWith $ \runInIO ->
    run port $ \req ack -> runInIO $ app req (liftBase . ack)

What’s going on here? liftBaseWith, like liftM or liftBase, allows to run a primitive monadic action in a complex monad stack. The difference is that it also gives us a function, here named runInIO, which lets to “lower” complex actions to primitive ones. Here we use runInIO to translate the return value of our app, m (), into a basic IO () value that the run function can digest.

All is well, except…

Could not deduce (StM m ResponseReceived ~ ResponseReceived)
Expected type: IO ResponseReceived
  Actual type: IO (StM m ResponseReceived)
Relevant bindings include
  runInIO :: RunInBase m IO
In the expression: runInIO $ app req (liftBase . ack)

The type of runInIO is forall a . m a -> IO (StM m a) (a.k.a. RunInBase m IO), while we would like a simple forall a . m a -> IO a. The purpose of StM is to encompass any “output effects”, such as state or error.

In our case, we don’t have any “output effects” (nor would we be allowed to), so StM (ReaderT DbConnection IO) ResponseReceived is really isomorphic to ResponseReceived.

In monad-control 0.x, StM used to be an associated data family, and its constructors for the standard monad transformers were hidden. Even though we knew that the above two types were isomorphic, we still couldn’t resolve the error nicely.

Not anymore! Since in monad-control 1.0 StM is an associated type synonym, StM (ReaderT DbConnection IO) ResponseReceived and ResponseReceived are not just hypothetically isomorphic; they are literally the same type. After we add the corresponding equality constraint to runM

  :: (MonadBaseControl IO m, StM m ResponseReceived ~ ResponseReceived)
  => Port -> ApplicationM m -> m ()

our app compiles!

This example is not just an isolated case. The general problem with monad-control is that it is all too easy to discard the output effects as Edward Yang shows.

Monads for which StM m a ~ a provide a “safe subset” of monad-control. Let’s call them “stateless” monads.

Previously, it was hard to tell apart stateless and stateful monads because the output effects or absence thereof hid behind the opaque StM data family.

Now not only is it transparent when the output effects are absent, but we can actually encode that fact right in the type system! As an example, Mitsutoshi Aoe and I are experimenting with a safe lifted async module.

One may wonder if this subset is too boring, since it only includes monads that are isomorphic to a reader transformer over the base monad. While that is technically true, there are a lot of things you can do with a reader. The ZoomT and CustomWriterT transformers that I described in another article, as well as the Proxied transformer they’re based upon, are stateless and thus safe to use with monad-control.

Another common example of a stateless monad transformer is a ReaderT holding a reference (such as IORef, TVar, or MVar). This is commonly used to maintain a shared state in multithreaded server applications, so it is fortunate that we can fork threads and catch exceptions inside such monads.