Dear all, Several attempts have been made to lift control operations (functions that use monadic actions as input instead of just output) through monad transformers:

MonadCatchIO-transformers[1] provided a type class that allowed to overload some often used control operations (catch, block and unblock). Unfortunately that library was limited to those operations. It was not possible to use, say, alloca in a monad transformer. More importantly however, the library was broken as was explained[2] by Michael Snoyman. In response Michael created the MonadInvertIO type class which solved the problems. Then Anders Kaseorg created the monad-peel library which provided an even nicer implementation. monad-control is a rewrite of monad-peel that uses CPS style operations and exploits the RankNTypes language extension to simplify and speedup most functions. A very preliminary and not yet fully representative, benchmark shows that monad-control is on average about 2.6 times faster than monad-peel: bracket: 2.4 x faster bracket_: 3.1 x faster catch: 1.8 x faster try: 4.0 x faster mask: 2.0 x faster Note that, although the package comes with a test suite that passes, I still consider it highly experimental. API DOCS: http://hackage.haskell.org/package/monad-control INSTALLING: $ cabal update $ cabal install monad-control TESTING: The package contains a copy of the monad-peel test suite written by Anders. You can perform the tests using: $ cabal unpack monad-control $ cd monad-control $ cabal configure -ftest $ cabal test BENCHMARKING: $ darcs get http://bifunctor.homelinux.net/~bas/bench-monad-peel-control/ $ cd bench-monad-peel-control $ cabal configure $ cabal build $ dist/build/bench-monad-peel-control/bench-monad-peel-control DEVELOPING: The darcs repository will be hosted on code.haskell.org ones that server is back online. For the time being you can get the repository from: $ darcs get http://bifunctor.homelinux.net/~bas/monad-control/ TUTORIAL: This short unpolished tutorial will explain how to lift control operations through monad transformers. Our goal is to lift a control operation like: foo ∷ M a → M a where M is some monad, into a transformed monad like 'StateT M': foo' ∷ StateT M a → StateT M a The first thing we need to do is write an instance for the MonadTransControl type class: class MonadTrans t ⇒ MonadTransControl t where liftControl ∷ (Monad m, Monad n, Monad o) ⇒ (Run t n o → m a) → t m a If you ignore the Run argument for now, you'll see that liftControl is identical to the 'lift' method of the MonadTrans type class: class MonadTrans t where lift ∷ Monad m ⇒ m a → t m a So the instance for MonadTransControl will probably look very much like the instance for MonadTrans. Let's see: instance MonadTransControl (StateT s) where liftControl f = StateT $ \s → liftM (\x → (x, s)) (f run) So what is this run function? Let's look at its type: type Run t n o = ∀ b. t n b → n (t o b) The run function executes a transformed monadic action 't n b' in the non-transformed monad 'n'. In our case the 't' will be a StateT computation. The only way to run a StateT computation is to give it some state and the only state we have lying around is the one from the outer computation: 's'. So let's run it on 's': instance MonadTransControl (StateT s) where liftControl f = StateT $ \s → let run t = ... runStateT t s ... in liftM (\x → (x, s)) (f run) Now that we are able to run a transformed monadic action, we're almost done. Look at the type of Run again. The function should leave the result 't o b' in the monad 'n'. This 't o b' computation should contain the final state after running the supplied 't n b' computation. In case of our StateT it should contain the final state s': instance MonadTransControl (StateT s) where liftControl f = StateT $ \s → let run t = liftM (\(x, s') → StateT $ \_ → return (x, s')) (runStateT t s) in liftM (\x → (x, s)) (f run) This final computation, "StateT $ \_ → return (x, s')", can later be used to restore the final state. Now that we have our MonadTransControl instance we can start using it. Recall that our goal was to lift "foo ∷ M a → M a" into our StateT transformer yielding the function "foo' ∷ StateT M a → StateT M a". To define foo', the first thing we need to do is call liftControl: foo' t = liftControl $ \run → ... This captures the current state of the StateT computation and provides us with the run function that allows us to run a StateT computation on this captured state. Now recall the type of liftControl ∷ (Run t n o → m a) → t m a. You can see that in place of the ... we must fill in a value of type 'm a'. In our case this will be a value of type 'M a'. We can construct such a value by calling foo. However, foo expects an argument of type 'M a'. Fortunately we can provide one if we convert the supplied 't' computation of type 'StateT M a' to 'M a' using our run function of type ∀ b. StateT M b → M (StateT o b): foo' t = ... liftControl $ \run → foo $ run t However, note that the run function returns the final StateT computation inside M. So the type of the right hand side is now 'StateT M (StateT o b)'. We would like to restore this final state. We can do that using join: foo' t = join $ liftControl $ \run → foo $ run t That's it! Note that because it's so common to join after a liftControl I provide an abstraction for it: control = join ∘ liftControl Allowing you to simplify foo' to: foo' t = control $ \run → foo $ run t Probably the most common control operations that you want to lift through your transformers are IO operations. Think about: bracket, alloca, mask, etc.. For this reason I provide the MonadControlIO type class: class MonadIO m ⇒ MonadControlIO m where liftControlIO ∷ (RunInBase m IO → IO a) → m a Again, if you ignore the RunInBase argument, you will see that liftControlIO is identical to the liftIO method of the MonadIO type class: class Monad m ⇒ MonadIO m where liftIO ∷ IO a → m a Just like Run, RunInBase allows you to run your monadic computation inside your base monad, which in case of liftControlIO is IO: type RunInBase m base = ∀ b. m b → base (m b) The instance for the base monad is trivial: instance MonadControlIO IO where liftControlIO = idLiftControl idLiftControl directly executes f and passes it a run function which executes the given action and lifts the result r into the trivial 'return r' action: idLiftControl ∷ Monad m ⇒ ((∀ b. m b → m (m b)) → m a) → m a idLiftControl f = f $ liftM $ \r -> return r The instances for the transformers are all identical. Let's look at StateT and ReaderT: instance MonadControlIO m ⇒ MonadControlIO (StateT s m) where liftControlIO = liftLiftControlBase liftControlIO instance MonadControlIO m ⇒ MonadControlIO (ReaderT r m) where liftControlIO = liftLiftControlBase liftControlIO The magic function is liftLiftControlBase. This function is used to compose two liftControl operations, the outer provided by a MonadTransControl instance and the inner provided as the argument: liftLiftControlBase ∷ (MonadTransControl t, Monad base, Monad m, Monad (t m)) ⇒ ((RunInBase m base → base a) → m a) → ((RunInBase (t m) base → base a) → t m a) liftLiftControlBase lftCtrlBase = \f → liftControl $ \run → lftCtrlBase $ \runInBase → f $ liftM (join ∘ lift) ∘ runInBase ∘ run Basically it captures the state of the outer monad transformer using liftControl. Then it captures the state of the inner monad using the supplied lftCtrlBase function. If you recall the identical definitions of the liftControlIO methods: 'liftLiftControlBase liftControlIO' you will see that this lftCtrlBase function is the recursive step of liftLiftControlBase. If you use 'liftLiftControlBase liftControlIO' in a stack of monad transformers a chain of liftControl operations is created: liftControl $ \run1 -> liftControl $ \run2 -> liftControl $ \run3 -> ... This will recurse until we hit the base monad. Then liftLiftControlBase will finally run f in the base monad supplying it with a run function that is able to run a 't m a' computation in the base monad. It does this by composing the run and runInBase functions. Note that runInBase is basically the composition: '... ∘ run3 ∘ run2'. However, just composing the run and runInBase functions is not enough. Namely: runInBase ∘ run ∷ ∀ b. t m b → base (m (t m b)) while we need to have ∀ b. t m b → base (t m b). So we need to lift the 'm (t m b)' computation inside t yielding: 't m (t m b)' and then join that to get 't m b'. Now that we have our MonadControlIO instances we can start using them. Let's look at how to lift 'bracket' into a monad supporting MonadControlIO. Before we do that I define a little convenience function similar to 'control': controlIO = join ∘ liftControlIO Bracket just calls controlIO which captures the state of m and provides us with a runInIO function which allows us to run an m computation in IO: bracket ∷ MonadControlIO m ⇒ m a → (a → m b) → (a → m c) → m c bracket before after thing = controlIO $ \runInIO → E.bracket (runInIO before) (\m → runInIO $ m >>= after) (\m → runInIO $ m >>= thing) I welcome any comments, questions or patches. Regards, Bas [1] http://hackage.haskell.org/package/MonadCatchIO-transformers [2] http://docs.yesodweb.com/blog/invertible-monads-exceptions-allocations/ [3] http://hackage.haskell.org/package/monad-peel _______________________________________________ Haskell mailing list Haskell@haskell.org http://www.haskell.org/mailman/listinfo/haskell