“MTL style” and “free monad style” are competing ways of implementing classes of effectful operations in Haskell programs. When we use MTL style we specify a type class of monadic operations and give various instances which interpret the operations in different monads. When we use free monad style we specify a
Functor which encodes the monadic operations and we implement various interpretations of that functor in different monads.
After reading an excellent article by Matt Parsons (which advocated the MTL style) I realised that you can have the best of both worlds! The base functor that defines the free monad also gives rise to an MTL style type class.
Inspired by Matthew’s article on the three layer cake pattern in Haskell, we might have the interfaces
class MonadTime m where getCurrentTime :: m UTCTime class MonadLock m where acquireLock :: NominalDiffTime -> Key -> m (Maybe Lock) renewLock :: NominalDiffTime -> Lock -> m (Maybe Lock) releaseLock :: Lock -> m ()
and give them interpretations which can be either effectful or pure mocked versions
acquireLockIO :: NominalDiffTime -> Key -> IO (Maybe Lock) renewLockIO :: NominalDiffTime -> Lock -> IO (Maybe Lock) releaseLockIO :: Lock -> IO () instance MonadTime ((->) UTCTime) where getCurrentTime = id instance MonadTime IO where getCurrentTime = Data.Time.getCurrentTime instance MonadLock IO where acquireLock = acquireLockIO renewLock = renewLockIO releaseLock = releaseLockIO
Instead of defining different classes for different sets of operations let’s define a class once and for all parameterized by a
Functor which carries the operations.
class Monad_ f m where interpret :: forall r. f r -> m r
Then instead of
MonadTime we have
Monad_ Time_ and instead of
MonadLock we have
Monad_ Lock_, where
data Time_ a = GetCurrentTime (UTCTime -> a) data Lock_ a = AcquireLock (Maybe Lock -> a) NominalDiffTime Key | RenewLock (Maybe Lock -> a) NominalDiffTime Lock | ReleaseLock (() -> a) Lock
The way that we write a functor for a class of monadic operations is that we take our collection of operations of the form
class MonadOperations where operation1 :: arg1 -> ... -> argN -> m result ...
and convert it to a sum type of the form
data Operations_ a = Operation1 (result -> a) arg1 ... argN | ...
We can go ahead and give instance definitions for our classes
instance Monad_ Time_ ((->) UTCTime) where interpret = \case GetCurrentTime f -> k0 id f instance Monad_ Time_ IO where interpret = \case GetCurrentTime f -> k0 Data.Time.getCurrentTime f instance Monad_ Lock_ IO where interpret = \case AcquireLock f t k -> k2 acquireLockIO f t k RenewLock f t l -> k2 renewLockIO f t l ReleaseLock f l -> k1 releaseLockIO f l
For each constructor we give its interpretation in the target monad.
k2 are somewhat uninteresting combinators for making this look cleaner.
k0 op f = fmap f op k1 op f a = fmap f (op a) k2 op f a b = fmap f (op a b)
The downside of this new style is that if we want to use direct function calls for our operations we have to wrap them:
-- All these types are inferrable -- with NoMonomorphismRestriction getCurrentTime :: Monad_ Time_ m => m UTCTime getCurrentTime = j0 GetCurrentTime acquireLock :: Monad_ Lock_ m => NominalDiffTime -> Key -> m (Maybe Lock) acquireLock = j2 AcquireLock renewLock :: Monad_ Lock_ m => NominalDiffTime -> Lock -> m (Maybe Lock) renewLock = j2 RenewLock releaseLock :: Monad_ Lock_ m => Lock -> m () releaseLock = j1 ReleaseLock
j2 are combinators for implementing operations conveniently
j0 op = interpret (op id) j1 op a = interpret (op id a) j2 op a b = interpret (op id a b)
Or we could use
j2 AcquireLock etc. directly, but that looks rather bizarre.
The benefit we get is automatic interaction with free monads. The functor of operations that we defined is exactly the base functor of the corresponding free monad. There is a function
freely which interprets
Free f in the MTL style
Monad_ f m
freely :: (Functor f, Monad m, Monad_ f m) => Free f a -> m a freely f = foldFree interpret f
The inverse to
liftF (which is also the
interpret of the
Monad_ f (Free f) instance).
instance Functor f => Monad_ f (Free f) where interpret = liftF
I haven’t measured the performance of this but with a suitable combination of inlining plus
RULEs it feels like it should perform equally well to the MTL style.
This approach doesn’t provide support for non-algebraic operations such as
Writer.pass, but perhaps that’s a good thing.
Implemention of classes of operations in MTL style contains a common pattern parametrized by a functor. Using the parametrized style gives you automatic interchange between MTL style and free monad style so you can have the best of both worlds for free!
I’m probably not the first person to notice this. If anyone knows any prior references please let me know and I’ll add a reference.