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Monads and monad transformers

Monads are used everywhere in Haskell. Monads in general represent computations, and specific monads represent computations capable of specific features. For example, there is a monad that encapsulates stateful computations, a monad that encapsulates computations which may fail (and recover from failure) and a monad that encapsulates computations which perform I/O. When writing applications in Haskell, we often wish to use a combination of these features all at once. The most common way to do this is to use monad transformers. Monad transformers are monad "constructors" that take an existing monad and return a new monad that has all the features of the original monad in addition to any features that were added by the monad transformer. Haskell applications often use a custom monad which consists of a stack of (standard) monad transformers layered on top of some base monad. The standard monad transformers are provided by the transformers package, which at the time of writing has 676 reverse dependencies on Hackage. For the "monad transformer stack" design pattern to be usable, quite a lot of type class machinery is required. As it stands, some of this machinery lives in the transformers package ( MonadTrans , MonadIO ), while the rest is provided by the mtl (monad transformer library) package ( MonadReader , MonadState , etc.: the documentation of this package refers to these sorts of type classes as "monad interfaces"). However, the type class machinery provided by these packages is limited in many important respects and it doesn't allow us to do many of the things we might expect to be able to do.

Limitations of the existing machinery

lift is not powerful enough

One of the most glaring weaknesses of the existing type class machinery is that the lift operation provided by MonadTrans is not very powerful. It's only capable of lifting very simple types of operations up from the inner monad. Consider the local operation from the MonadReader interface: local :: MonadReader r m => (r -> r) -> m a -> m a It should be possible to automatically lift local through every conceivable monad transformer, even ContT . However, with lift alone, it is impossible. The MonadTrans class clearly needs at least one more operation in addition to lift to allow this. And while it should be possible to automatically lift local through every possible monad transformer, there are some operations which can be lifted through most monad transformers, but not all. These sorts of operations are often called "control" operations. One example is catch from the MonadException interface: catch :: (Exception e, MonadException m) => m a -> (e -> m a) -> m a catch can be lifted through most monad transformers, but not ContT . Given that there is a class of monad transformers through which control operations can be lifted, one would expect there to be a type class (a subclass of MonadTrans ) for such monad transformers, but none is provided by the transformers library. There are other packages which define such classes, some of which are discussed below, but none of them are standard.

Non-modularity, code duplication

Imagine you are designing a monad transformer Foo . A common design pattern would be to define a type constructor FooT :: (* -> *) -> * -> * in the module Control.Monad.Trans.Foo , and a function runFooT :: FooT m a -> m a . Let's say that your monad transformer adds a single operation, getFoo , to the transformed monad: getFoo :: Monad m => FooT m Foo getFoo , defined in this way, will only work when FooT is at the top of the transformer stack, but we would like it would work on any monad built from a transformer stack containing FooT anywhere in the stack. The common design pattern achieves this by defining in the Control.Monad.Foo.Class module a MonadFoo class like the following: class Monad m => MonadFoo m where getFoo :: m Foo instance Monad m => MonadFoo (FooT m) where getFoo = FooT $ return Foo So now we have a class that represents every monad that supports the getFoo operation, and we have an instance for FooT . But where are the instances for other monads which support getFoo (i.e., monads built on top of FooT )? You might expect there to be an instance like: instance (MonadTrans t, Monad (t m), MonadFoo m) => MonadFoo (t m) where getFoo = lift getFoo But this is not what is generally done. There are two reasons for this: one is that lift is not powerful enough to lift all types of operations, so for many interfaces it isn't possible to define a universal pass-through instance that can lift all the required operations through an arbitrary monad transformer (although our MonadFoo interface happens to only contain getFoo which is simple enough for lift ). The second reason is that such instances require the OverlappingInstances extension, which is considered far too controversial to be made a requirement for such a core part of the Haskell ecosystem (the monad transfomer library). So instead what monad transformer authors generally do is create pass-through instances for each of the monad transformers in the transformers library: instance MonadFoo m => MonadFoo (ReaderT r m) where getFoo = lift getFoo instance MonadFoo m => MonadFoo (StateT s m) where getFoo = lift getFoo ...and so on. This is a lot of code duplication. If you have n monad transformers and m monad interfaces, you need to define O(n * m) instances to ensure that each monad interface can pass through each transformer. This means n identical instances for each monad interface (or at least they would be identical if there was a sufficiently powerful complement to lift ). But the code duplication isn't the worst part: the worst part is how this destroys modularity. It means that every third-party monad interface can only be lifted through the standard monad transformers. If you want to lift a third party monad interface through a third party monad transformer, your only hope is to define an orphan instance, which means your application will break if any of the libraries you depend on ever define this instance themselves.

Redundant type classes

The transformers package includes the MonadIO interface. It provides a single operation, liftIO . This is unsatisfactory in a lot of ways. Firstly, liftIO suffers from the same lack of power as lift : only very simple types of IO operations can be lifted with liftIO . Secondly: while obviously it's particularly useful to be able to lift operations from IO through an arbitrary stack of monad transformers, and it makes sense to have a type class for the class of monads capable of performing I/O (including IO itself), there's no theoretical reason why IO should be a special case like this. It should be equally valid to have a MonadST class that represents all monad stacks that have ST as their base monad, but obviously it would be ridiculous to have to define a new type class for every possible base monad. Instead all that's needed is a class like the following: class MonadBase b m | m -> b where liftBase :: b a -> m a Indeed the transformers-base package does define such a class. However, that means there are two incompatible ways of expressing the same constraint: MonadIO m and MonadBase IO m . It would be better to do away with MonadIO completely, or at least redefine it as a synonym for MonadBase IO . However, even this is unsatisfactory, at least on its own. If lift is for lifting operations from the monad just beneath the top of the stack, and liftBase is for lifting operations from the monad at the very bottom of the stack, what operation do we have for lifting operations from every monad in between? What we really want is a fully polymorphic lift that can lift operations from any monad anywhere in the stack. Such an operation would unify lift , liftIO , liftBase and friends into a single operation that could do all of these things and more.

Other (partial) solutions

hoist

The pipes package contains a module Control.MFunctor which exports the following class: class MFunctor t where hoist :: Monad m => (forall b. m b -> n b) -> t m a -> t n a The documentation describes MFunctor as "a functor in the category of monads". Its hoist operation lifts a homomorphism between monads to a homomorphism between inner monads wrapped by the same transformer. The combination of hoist and lift is powerful enough to define a universal pass-through instance for the MonadReader interface discussed above: instance (MonadTrans t, MFunctor t, Monad (t m), MonadReader r m) => MonadReader r (t m) where ask = lift ask local f = hoist (local f) The crucial question then is: is hoist the missing operation from MonadTrans ? Can every type that is currently an instance of MonadTrans be made an instance of MFunctor too? The answer, unfortunately, is no. Once again, ContT proves too stubborn, and won't permit an instance of MFunctor . However, the idea behind MFunctor / hoist is "close", and it certainly seems to be on the right track.

mmtl

There is an alternative to mtl on Hackage called mmtl : the modular monad transformer library. It's an old package, and it no longer builds with recent versions of GHC, but it's worth studying. Its version of the MonadTrans class contains an extra operation tmap : class MonadTrans t where lift :: Monad m => m a -> t m a tmap :: (Monad m, Monad n) => (forall b. m b -> n b) -> (forall b. n b -> m b) -> t m a -> t n a This tmap operation is very similar to the hoist operation in the pipes package. It lifts an isomorphism between monads to a homomorphism between inner monads wrapped by the same transformer. (In addition to the morphism between monads that hoist takes, tmap also takes that morphism's inverse. In other words, tmap is less powerful than hoist , because it can only lift morphisms which have an inverse, while hoist can lift any moprhism.) This type of operation is sometimes called an invariant functor: if hoist is "a functor in the category of monads", then tmap is "an invariant functor in the category of monads". Invariant functors from the category of Hask can be represented by the following type class: class Invariant f where invmap :: (a -> b) -> (b -> a) -> f a -> f b This class is defined in the invariant package. What's interesting is that the documentation of Invariant states that it's possible to define an instance of Invariant (i.e., an invariant functor from the category of Hask ) for every * -> * type parametric in the argument. If we translate this to the category of monads, that means that it's possible to define an invariant functor (i.e., tmap ) for every (* -> *) -> * -> * type parametric in the argument: this is exactly what monad transformers are. So unlike hoist , it's possible to define tmap for every possible monad transfomer, even ContT . The crucial question for us now is: is tmap powerful enough to lift local ? Can we define a universal pass-through instance of MonadReader ? The answer is yes! instance (MonadTrans t, Monad (t m), MonadReader r m) => MonadReader r (t m) where ask = lift ask local f m = lift ask >>= \r -> tmap (local f) (local (const r)) m As with hoist above, we pass local f to tmap to lift the morphism into the transformed monad. The tricky part though is that tmap also requires us to give it the inverse of local f . How can we get the inverse of local f ? It could be local g if we knew a function g which was the inverse of f (such that g . f = id ), but we don't. However, given that we know that local f just applies a transfomation f to the environment r of a reader monad, we can cheat by using const r (where r is value in the environment prior to running local , which we obtain by ask ing the inner monad using lift ask ) as the function we pass to local . This leaves us with tmap (local f) (local (const r)) , which does the job. (Although const r is not the inverse of f , we know that r is the value applied to f by local , which means that the invariant local (const r) . local f = id holds true.) So what is the problem with mmtl then? Well, as stated above, it has bitrotted to the point where it no longer builds with recent versions of GHC. But it also defines its own versions of all the monad transformers from transformers . transformers has 676 reverse dependencies on Hackage, and the types that are defined in that package are used everywhere in the Haskell ecosystem. No matter how much of an improvement a package is on transformers , it will never take off unless it remains compatible with it. The proof of this is that mmtl has only three reverse dependencies on Hackage. Also, remember we mentioned above that while local should be able to be automatically lifted through every monad transformer, there should also be a subclass of monad transformers which can lift control operations like catch ? mmtl does not do anything to provide this class (although we are free to build it on top of mmtl ourselves).

MonadCatchIO

One of the first packages that attempted to deal with the "catch" problem to gain widespread adoption on Hackage was MonadCatchIO-{mtl,transformers} . It defines a type class MonadCatchIO specifically for the purpose of lifting the catch operation through monad transformer stacks: class MonadIO m => MonadCatchIO m where catch :: Exception e => m a -> (e -> m a) -> m a block :: m a -> m a unblock :: m a -> m a (It also includes the (deprecated) operations block and unblock for dealing with asynchronous exceptions, but we'll ignore asynchronous exceptions for the moment and focus on catch .) While MonadCatchIO succeeds at being the class of monads into which catch can be lifted, that is all it is. If we want to lift from IO (or indeed any monad) any other control operation, we need to define a separate type class just for lifting that operation. That is unacceptable. What we're really looking for is the class of monad transformers through which control operations can be lifted, but MonadCatchIO doesn't get us any closer to that. Another problem with MonadCatchIO is with the bracket operation it provides, defined in terms of catch . Consider the following example: foo = runMaybeT $ bracket (lift (putStrLn "init")) (\() -> lift (putStrLn "close")) (\() -> lift (putStrLn "running") >> mzero) Running foo in GHCi, you might expect it to produce the following output: >>> foo init running close Nothing However, instead the following is produced: >>> foo init running Nothing The finaliser was never run. What this shows is that the naive implementation of the bracket family of operations is deficient when lifted through a monad transformer stack containing one or more short-circuiting monad transformers. (The short-circuiting monad transformers provided by the transformers package are ErrorT , ListT and MaybeT ). This hereafter is referred to as "the bracket problem".

monad-control

There is another family of packages in this solution space; monad-peel and monad-control . ( monad-control started as a faster replacement for monad-peel , but its design has diverged from the original monad-peel design over time.) They both provide a subclass of MonadTrans called MonadTransControl ( monad-peel calls it MonadTransPeel ), and this is the type class that we've been looking for! It represents the subclass of monad transformers through which control operations can be automatically lifted. The latest version of monad-control implements MonadTransControl as follows: class MonadTrans t => MonadTransControl t where data StT t :: * -> * restoreT :: Monad m => m (StT t a) -> t m a liftWith :: Monad m => ((forall n b. Monad n => t n b -> n (StT t b)) -> m a) -> t m a Where to begin? The first thing to note is the associated data type StT . For a given monad transformer t , StT t represents the "state" added that t adds to the monad it wraps. For example, StT MaybeT a =~ Maybe a and StT (ErrorT e) a =~ Either e a . A good rule of thumb for figuring out what StT t is for a given transformer t is to look at the definition of t : data {t} m a = {t} { run{t} :: m (Foo a) } If t is defined as above, then StT t a =~ Foo a . In general, StT t will be the type of everything "inside" the m in the definition of the transformer. The trick is to extract the component of "monadic state" added by t which is independent of the underlying monad m . The next thing to note is restoreT , which is pretty simple. It just takes the "monadic state of t " ( StT t a ) wrapped in m , and "restores" it to a value of t m a . For most transformers, restoreT is trivial: e.g., for MaybeT , restoreT =~ MaybeT , modulo the unwrapping of the StT value. It's the liftWith operation where the real "magic" of the monad-control package happens. It's a CPS-style operation which takes a function which takes a function, to which liftWith passes an operation (usually called run ) of type forall n b. Monad n => t n b -> n (StT t b) . run is basically the inverse of lift : if lift wraps a transformer t around a monadic action, run peels a transformer off a monadic action, storing its monadic state in an StT t value inside m . The type variable n in the signature of run is usually instantiated to m , but it's type is polymorphic over all monads to statically ensure that there are no remaining side effects in m in the resulting action. Using something like MonadTransControl , it's possible to define a universal pass-through instance for the MonadException interface as follows: instance (MonadTransControl t, Monad (t m), MonadException m) => MonadException (t m) where throw = lift . throw catch m h = do st <- liftWith (\run -> catch (run m) (run . h)) restoreT (return st) The monad-control package also includes a class MonadBaseControl , which is a subclass of the MonadBase class from transformers-base (described above): class MonadBase i m => MonadBaseControl i m | m -> i where data StM m :: * -> * restoreM :: StM m a -> m a liftBaseWith :: ((forall b. m b -> i (StM m b)) -> i a) -> m a ( MonadBaseControl is to MonadBase as MonadTransControl is to MonadTrans . While lift lifts operations from the monad just beneath the top of the transformer stack, liftBase lifts operations from the monad at the very bottom of the stack. lift and liftBase can only lift very basic types of operations, liftWith and liftBaseWith can lift much more complicated types of operations. MonadBaseControl uses the same technique to achieve this with liftBaseWith as MonadTransControl uses with liftWith .) MonadBaseControl is used extensively in the lifted-base package, whose author is also the author of monad-control . It re-exports many of the IO operations in the base package, but lifted to work with any monad built from a transformer stack with IO as its base monad. This includes a version of bracket , defined as follows: bracket :: MonadBaseControl IO m => m a -> (a -> m b) -> (a -> m c) -> m c bracket before after thing = do st <- liftBaseWith $ \run -> E.bracket (run before) (\st -> run $ restoreM st >>= after) (\st -> run $ restoreM st >>= thing) restoreM st Let's see if this version of bracket can handle the bracket problem correctly: foo = runMaybeT $ bracket (lift (putStrLn "init")) (\() -> lift (putStrLn "close")) (\() -> lift (putStrLn "running") >> mzero) >>> foo init running close Nothing Success! But this success comes at a cost. Consider a more complicated example: bar :: IO (Maybe (), Int) bar = flip runStateT 0 $ runMaybeT $ bracket (do liftBase $ putStrLn "init" modify (+1)) (\() -> do modify (+16) liftBase $ putStrLn "close" modify (+32) mzero modify (+64)) (\() -> do modify (+2) liftBase $ putStrLn "body" modify (+4) mzero modify (+8)) (Adding a different power of two with each modify operation is equivalent to setting a different bit of the state. By looking at the final value of the state we can see exactly which modify operations were run.) We would expect the following to output: >>> bar init body close (Nothing,55) Instead, however, we get: >>> bar init body close (Nothing,7) While monad-control 's bracket operation manages to run the finaliser even in the presence of a short-circuiting monad transformer, the reason it is able to do this so is because it liberally discards the monadic state of the outer transformers. The finaliser is run with the monadic state that existed after the initialiser finished, not the monadic state after the "body" (which is what one would expect). Additionally, the monadic state after the finaliser is discarded, so the final monadic state after bracket completes is the monadic state that existed after the "body" exited, not after the finaliser exited. This makes sense if you look at the definition of bracket above: bracket discards any potentially "zero" (i.e., short-circuiting) monadic state that could prevent the finaliser from being run. While this solution "works", the above example shows that it can lead to incorrect results as shown above. We do not consider that monad-control solves the bracket problem satisfactorily.

layers ' solution

Monad layers

The most fundamental type class in layers , and its replacement for MonadTrans , is MonadLayer . Unlike MonadTrans , which is instantiated with types of kind (* -> *) -> * -> * (i.e., monad constructors), MonadLayer is instantiated on normal monads (of kind * -> * ). Simply put, a monad m can be an instance of MonadLayer if it is built ("layered") on top of some inner monad Inner m . ( Inner m is an associated type that must be provided by instances MonadLayer .) It looks like the following: class (Monad m, Monad (Inner m)) => MonadLayer m where type Inner m :: * -> * layer :: Inner m a -> m a ( layer is the MonadLayer equivalent to lift .) Note that unlike monad transformers, monad layers are not necessarily parametric in their inner monad. This means that the class of layers, in addition to including all valid monad transformers, also includes monads which are implemented on top of some fixed inner monad. For example, it's common to define an Application monad in terms of some transformer stack based on IO , and then use liftIO to lift IO computations into the Application monad. Application could look like the following: newtype Application a = Application (StateT AppState IO a) deriving (Functor, Applicative, Monad, MonadState) While it clearly isn't a monad transformer (it doesn't even have the right kind), it's clearly in some sense a "layer" around IO , and we would like to be able to lift computations from IO to the Application monad. MonadLayer allows us to express this (without resorting to hacks like MonadIO ): instance MonadLayer Application where type Inner Application = IO layer = Application . layer (This definition makes use of the MonadLayer instance for StateT provided by the layers package.)

Transformers as polymorphic layers

Every monad transformer can be made an instance of MonadLayer , but not all monad layers are monad transformers. For this reason it might be useful to have a subclass of MonadLayer that represents all the monad layers which are monad transformers. (A monad layer is a monad transformer if it is (parametrically) polymorphic in its inner monad.) layers provides such a type class: class (MonadLayer m, m ~ Outer m (Inner m)) => MonadTrans m where type Outer m :: (* -> *) -> * -> * This MonadTrans class is a bit different to the one from transformers . Like MonadLayer (of which it is a subclass), it is instantiated on monads ( * -> * ) rather than monad constructors ( (* -> *) -> * -> * ). It has an associated type Outer m which points to the monad constructor from which m is composed. The superclass equality constraint on the MonadTrans class m ~ Outer m (Inner m) ensures that m really is a composition of the monad constructor Outer m and the inner monad Inner m , making this class pretty much equivalent to the MonadTrans class from transformers . If GHC supported QuantifiedConstraints and ImplicationConstraints (which it doesn't due to GHC bugs #2893 and #5927 respectively (though it seems possible that these could be fixed some day)), it would be tempting to reformulate MonadTrans to be instantiated directly on types t of kind (* -> *) -> * -> * , just like the MonadTrans class from transformers . To ensure that such a MonadTrans class would still be a "subclass" of MonadLayer , it would need to have the constraint (forall m. Monad m => (MonadLayer (t m), Inner (t m) ~ m)) in its superclass context. However, this would exclude some instances which are currently permitted. For example, if it was done right (and if there existed a CommutativeMonad type class), the monad instance of ListT would look something like instance CommutativeMonad m => Monad (ListT m) . This in turn would mean that ListT 's MonadLayer instance would have the constraint CommutativeMonad m in its context, meaning that the constraint forall m. Monad m => (MonadLayer (ListT m), Inner (ListT m) ~ m) would not be satisfied, preventing ListT from being made an instance of MonadTrans . This in turn could be solved by adding an associated type of kind (* -> *) -> Constraint (which would default to Monad ) to the MonadTrans class and modifying the superclass constraint accordingly, but it would be kind of messy. This is how it would look: class (forall m. MonadConstraint t m => (MonadLayer (t m), Inner (t m) ~ m))) => MonadTrans t where type MonadConstraint t :: (* -> *) -> Constraint type MonadConstraint t = Monad

Invariant functors

The MonadLayer and MonadTrans classes we showed in the last two sections were not quite complete: we omitted one method from each of them for the sake of the discussion. Here are the complete definitions of both of these classes: class (Monad m, Monad (Inner m)) => MonadLayer m where type Inner m :: * -> * layer :: Inner m a -> m a layerInvmap :: (forall b. Inner m b -> Inner m b) -> (forall b. Inner m b -> Inner m b) -> m a -> m a class (MonadLayer m, m ~ Outer m (Inner m)) => MonadTrans m where type Outer m :: (* -> *) -> * -> * transInvmap :: (MonadTrans n, Outer n ~ Outer m) => (forall b. Inner m b -> Inner n b) -> (forall b. Inner n b -> Inner m b) -> m a -> n a We've added the layerInvmap and transInvmap operations to MonadLayer and MonadTrans respectively. transInvmap corresponds exactly to the tmap function described in the mmtl section above. (Its name refers to the fact that monad transformers (should) be invariant functors in the category of monads. (Re-read the mmtl section above if you've forgotten what this means.)) layerInvmap is like a restricted version of transInvmap where the inner monad is fixed: this is because monad layers are not necessarily parametric in their inner monad. It might then seem that layerInvmap is useless, but it can still be useful to apply a transformation to the underlying monad which does not change its type. For example, local f is such a transformation. This means that layerInvmap (unlike layer on its own) is powerful enough to define a universal pass-through instance for any MonadReader through any MonadLayer .

Functorial layers

While layerInvmap and transInvmap are useful, they can only lift from the inner monad morphisms which have an inverse. Sometimes we might want to lift morphisms which do not have an inverse. However, not all monad layers/monad transformers are capable of lifting such morphisms through them, so we need new subclasses of MonadLayer and MonadTrans to represent monad layers and monad transformers through which such morphisms can be lifted. We call these classes MonadLayerFunctor and MonadTransFunctor . (Their names refer to the fact they represent functors in the category of monads.) The provide the operations layerMap and transMap respectively, the definitions of which are given below: class MonadLayer m => MonadLayerFunctor m where layerMap :: (forall b. Inner m b -> Inner m b) -> m a -> m a class (MonadLayerFunctor m, MonadTrans m) => MonadTransFunctor m where transMap :: (MonadTrans n, Outer n ~ Outer m) => (forall b. Inner m b -> Inner n b) -> m a -> n a

Peelable layers

Is it possible to lift control operations like catch through a monad layer? Yes, if that monad layer provides an instance of MonadLayerControl : class MonadLayerFunctor m => MonadLayerControl m where data LayerState m :: * -> * restore :: LayerState m a -> m a layerControl :: ((forall b. m b -> Inner m (LayerState m b)) -> Inner m a) -> m a The design of MonadLayerControl is very similar to that of MonadTransControl from the monad-control package (discussed above). StT is renamed to LayerState , restoreT to restore and liftWith to layerControl . One of the main differences with MonadLayerControl is that LayerState is parameterised by m :: * -> * rather than t :: (* -> *) -> * -> * (as StT is). This is simply because monad layers don't necessarily have a t . What LayerState m is supposed to represent then is the portion of the monadic state of m that is independent of Inner m . The other big difference between MonadLayerControl and monad-control 's MonadTransControl is with the run operation that layerControl passes to its continuation. MonadLayerControl 's run operation is of type forall b. m b -> Inner m (LayerState m b) : unlike MonadTransControl 's, ours is not polymorphic over all inner monads, so we cannot statically ensure with the type system that there are no remaining side effects in m in the action returned by run . The reason we make this change is because layers are not necessarily parametric in their inner monad, so we cannot express for monad layers the polymorphism used by monad-control 's MonadTransControl . However, we do include our own version of MonadTransControl . It has the operation transControl , which does exactly the same thing as layerControl , but the run operation it passes to its continuation is more polymorphic. We can use the Outer associated type of the MonadTrans class (from which our MonadTransControl is (transitively) descended) to express the polymorphism required to statically ensure that the result of the run operation provided by transControl has no remaining side effects in Outer m . We don't intend for MonadTransControl to ever really be used in practice though. Its main use is as a guide for those who write monad transformers. If you are implementing a monad transformer t , you'll almost certainly want to make t an instance of both MonadLayerControl and MonadTransControl . If it turns out that you can write an instance of MonadLayerControl for t , but not an instance of MonadTransControl , then you'll know that your instance for MonadLayerControl was invalid because it relied on residual side effects in t in the result of its run computation. Without MonadTransControl it is possible that such instances would be distributed in libraries and propogated widely before anybody realised their invalidity, because the type system cannot do so automatically with MonadLayerControl alone. For monad layers which are not monad transformers, we still have to just trust that their instances of MonadLayerControl do the right thing, but in practice most monad layers are monad transformers, so this is not really that bad. Here is the MonadTransControl type class: class (MonadLayerControl m, MonadTrans m) => MonadTransControl m where transControl :: (forall n. (MonadTrans n, Outer n ~ Outer m) => (forall b. n b -> Inner n (LayerState n b)) -> Inner n a) -> m a In case it isn't obvious why MonadLayerControl is a subclass of MonadLayerFunctor rather than MonadLayer , it's because it's possible to define layerMap in terms of layerControl and restore . Given this fact, MonadLayerControl not being a subclass of MonadLayerFunctor makes about as much sense as Monad not being a subclass of Functor (given that fmap can be defined in terms of >>= and return ). Here is layerMap defined in terms of layerControl and restore : layerMap f m = layerControl (\run -> f (run m)) >>= restore

Zero-aware layer state

If layers just copies monad-control 's design for MonadLayerControl pretty much verbatim, and monad-control 's solution to the bracket problem produces incorrect results, then how can layers hope to solve the bracket problem any better? The truth is that once again, we omitted a method when we showed you MonadLayerControl class for the sake of the discussion. The full MonadLayerControl class is as follows: class MonadLayerFunctor m => MonadLayerControl m where data LayerState m :: * -> * zero :: LayerState m a -> Bool restore :: LayerState m a -> m a layerControl :: ((forall b. m b -> Inner m (LayerState m b)) -> Inner m a) -> m a zero _ = False The only differnce is that we've added the operation zero . It's very simple: it just takes the LayerState of m and says whether or not it's "zero". For example, in the MonadLayerControl instance for MaybeT , zero is pretty much just isNothing . For ListT , zero is null . A good rule of thumb for implementing zero for a monad layer is to ask, for a given LayerState m a , does this LayerState m a contain a value of type a somewhere that can be extracted from it? If the answer is no, then zero should return True . For example, MaybeT 's zero returns True when its LayerState is Nothing , and ListT 's zero returns True when LayerState is [] . This allows us to solve the bracket problem without discarding the monadic state of the outer layers, because we can directly detect when a short-circuiting monad transformer has short-circuited ("zero'd"). layers defines its version of bracket in terms of the MonadTry interface, which is shown here: class MonadMask m => MonadTry m where mtry :: m a -> m (Either (m a) a) mtry = liftM Right It provides a single operation mtry , which takes a monadic action in m and returns a new monadic value in m which is guaranteed not to short-circuit. If the action m that was given to mtry would have short-circuited, it returns Left m , otherwise it returns Right a , where a is the value returned by the computation m . (The MonadMask you see in the superclass constraint is for dealing with asynchronous exceptions. MonadMask is actually not used anywhere in the MonadException interface, only by MonadTry , for defining bracket and friends. This seems to suggest that mask / bracket and throw / catch are actually orthogonal to one another.) Instances of MonadTry are provided for all the base monads defined in the base and transformers libraries, and the zero operation of MonadLayerControl is used to define a universal pass-through instance for any MonadTry wrapped by a monad layer: instance (MonadLayerControl m, MonadTry (Inner m)) => MonadTry m where mtry m = do ma <- layerControl (\run -> mtry (run m)) case ma of Left m' -> return . Left $ layer m' >>= restore Right a -> if zero a then return . Left $ restore a else liftM Right $ restore a Let's try out the bracket function defined in Control.Monad.Interface.Try. Let's see if it produces the correct result where monad-control could not. bar :: IO (Maybe (), Int) bar = flip runStateT 0 $ runMaybeT $ bracket (do lift $ putStrLn "init" modify (+1)) (\() -> do modify (+16) lift $ putStrLn "close" modify (+32) mzero modify (+64)) (\() -> do modify (+2) lift $ putStrLn "body" modify (+4) mzero modify (+8)) >>> bar init body close (Nothing,55) This is the correct result! Our bracket correctly handles the short-circuiting monad transformer without discarding the monadic state of the other transformers. The bracket problem is solved.

Fully modular monad interfaces

We said above that one of the problems with the type class machinery provided by (and the design patterns suggested by) transformers and mtl is the lack of modularity possible with them. If you have n monad interfaces and m monad layers, then you need O(n * m) instances. You need to write an instance for each combination of monad transformer and monad interface. In particular, this makes it impossible to use a third-party monad interface with a third-party monad transformer, unless the author of the monad transformer knew of that monad interface and was okay with making their monad transformer depend on the package which provides that monad interface (or vice-versa). We would like for there to only need to be O(n + m) instances, and for it to be possible to use third-party monad interfaces with third-party monad transformers that know nothing about each other. The achieve this, we need what this documentation has so far referred to as "universal pass-through instances". We've shown a few examples of these already, but here is another one just to make it completely clear what we're talking about (this time for MonadCont ): instance (MonadLayerControl m, MonadCont (Inner m)) => MonadCont m where callCC f = layerControl (\run -> callCC $ \c -> run . f $ \a -> layer (run (return a) >>= c)) >>= restore As we said above, there are two reasons why this is not done currently: one is that the lift operation provided by transformers is not powerful enough to define universal pass-through instances for control operations. layers solves this by with the MonadLayerControl interface, whose layerControl operation can lift control operations (such as callCC above). The other reason why this is not done is because these instances require the OverlappingInstances extension. layers doesn't solve this problem, but we just say "fuck it" and use OverlappingInstances anyway. It seems that the main reason that OverlappingInstances is considered evil is that if your code uses relies on an overlapping instance, it's possible for the meaning of your code to change if you import a module which defines a more specific instance which matches the types in your code and the more specific instance behaves differently to the more general instance. While this is definitely bad, we don't think that it will be a problem in practice with layers , as long as people use common sense when writing instances. In order to spell out exactly what we mean by "common sense", let us first note that there are three types of instances that are needed when writing monad transformers and/or monad interfaces the layers way. Monad transformers need to be made instances of MonadLayer and MonadTrans , and if applicable, MonadLayerFunctor , MonadTransFunctor , MonadLayerControl and MonadTransControl . Using StateT as an example, these instances have the form instance Monad m => MonadLayer (StateT s m) where type Inner (StateT s m) = m . The functionality provided by a monad transformer is often abstracted into a monad interface. Again using the example of StateT (and MonadState ), these instances have the form instance Monad m => MonadState s (StateT s m) . To achieve the level of modularity we wish for, monad interfaces need to have universal pass-through instances. This means that an monad which is an instance of a given monad interface is still an instance of that monad interface when wrapped by a monad layer. These instances have the form: instance (MonadLayer m, MonadState s (Inner m)) => MonadState s m . (These are also the only instances that require the OverlappingInstances extension.) Now that we can easily refer to these different types of instances by number, the "common sense" rules that consumers of the layers library need to follow to ensure sensible behaviour are as follows: Every instance of type 3, e.g., the universal pass-through instance for a given monad interface, must be defined in the same module as that monad interface. (The only thing worse than overlapping instances are overlapping orphan instances.) A monad transformer t 's instances of type 2, i.e., of the monad interfaces which encapsulate its functionality, can be defined in either the same module as t 's type 1 instances or in the same module(s) as the monad interface(s), but if the latter, then thatthose module(s) must/ also import the module in which t 's type 1 instances are defined. (Normally this is not an issue because t 's instances of type 1 are defined in the same module as t (or in the same module as MonadLayer in the special case of the monad transformers from the transformers package), but if t 's type 1 instances are orphans then this is relevant.) You should generally not need to define instances for monad layers that do not fit into one of the three types above. One exception is if you are writing a monad transformer t , and you want instances of the monad interface m to be able to pass through t , but you know that the universal pass-through instance of m can only pass-through monad layers which can provide MonadLayerControl , but your t can't, yet you know of a way to define a pass-through instance of m for t . This type of instance is not a problem. The same rules which apply to type 2 instances (these rules are described rule 2 above) apply to these kinds of instances, The only other case where you might want to define an instance that doesn't fall into one of the three types described above is where you are writing a monad transformer t , and you want instances of the monad interface m to be able to pass through t , and the universal pass-through instance of m is able to pass through t , but you have a much more efficient implementation of the pass-through of m through t than the universal one. The same rules which apply to type 2 instances (described in rule 2 above) apply to these kinds of instances, with the additional stipulation that you must make absolutely certain that such instances behaves exactly the same as the universal ones. This is to ensure that the behaviour of a program which uses the universal instance does not change if it switches to the optimised one. However, we strongly recommend against providing such instances unless you are sure that the inefficiency of the universal pass-through instance is causing a noticable degradation in performance. Having said all of that, there are real problems caused by OverlappingInstances that makes layers harder to use than it should be. These are mainly the error messages produced by GHC when it cannot find a solution for constraint which has overlapping instances. For example, attempting to compile the following program produces the following error message: import Control.Monad.Interface.State stupidGet :: Monad m => m Int stupidGet = get >>> runhaskell Main.hs Main.hs:4:9: Overlapping instances for MonadState Int m arising from a use of `get' Matching instances: instance [overlap ok] (Control.Monad.Layer.MonadLayer m, MonadState s (Control.Monad.Layer.Inner m)) => MonadState s m -- Defined in `Control.Monad.Interface.State' instance [overlap ok] (Monad m, Data.Monoid.Monoid w) => MonadState s (Control.Monad.Trans.RWS.Strict.RWST r w s m) -- Defined in `Control.Monad.Interface.State' instance [overlap ok] (Monad m, Data.Monoid.Monoid w) => MonadState s (Control.Monad.Trans.RWS.Lazy.RWST r w s m) -- Defined in `Control.Monad.Interface.State' instance [overlap ok] Monad m => MonadState s (Control.Monad.Trans.State.Strict.StateT s m) -- Defined in `Control.Monad.Interface.State' instance [overlap ok] Monad m => MonadState s (Control.Monad.Trans.State.Lazy.StateT s m) -- Defined in `Control.Monad.Interface.State' (The choice depends on the instantiation of `m' To pick the first instance above, use -XIncoherentInstances when compiling the other instance declarations) In the expression: get In an equation for `stupidGet': stupidGet = get Annoyingly, GHC unhelpfully suggests that we enable the IncoherentInstances extension. Ideally the error message that GHC would produce would simply be: >>> runhaskell Main.hs Main.hs:4:9: Could not deduce (MonadState Int m) arising from a use of `get' from the context (Monad m) bound by the type signature for myGet :: Monad m => m Int at Main.hs:3:10-25 Possible fix: add an instance declaration for (MonadState Int m) In the expression: get In an equation for `stupidGet': stupidGet = get We are unsure whether this could be considered a bug in GHC or whether it's expected behaviour, but either way we are documenting it here so that users who run into this problem can know what to do when they see it. (Sometimes similar messages pop up but are caused by the monomorphism restriction. If you think your types really do satisfy the constraints in question, try either disabling the monomorphism restriction or adding type signatures where appropriate.)

Compatibility with transformers

One of the fatal flaws of earlier attempts to do what we have done with the layers library, such as the modular monad transformer library mmtl , is that they defined their own versions of the monad transformers from transformers . As we have said already in this document, the types defined in the transformers package are used everywhere in the Haskell ecosystem, to the extent that it's simply not possible that a library which seeks to improve the type class machinery for working with compositions of those types will be adopted unless it reuses those types themselves. layers gets this right by reusing the monad transformer and base monad types from the transformers package and not defining any of its own. However, almost as widespread in the Haskell ecosystem as the monad transformers defined in the transformers package are the monad interfaces defined in the mtl package. We unfortunately can't reuse these monad interfaces in the layers package, because we need monad interfaces to have universal pass-through instances, and the mtl monad interfaces do not provide universal pass-through instances. Rule 1 above states that we are only allowed to define a universal pass-through instance for a given monad interface in the same module module as that monad interface, so we can't define them ourselves, and we have no control over modules in mtl package in which those interfaces are defined. The solution the layers package takes is to define its own versions of all of the monad interfaces from the mtl package (as well as some new ones too). However, this isn't nearly as bad as defining our own versions of all of the monad transformers from the transformers package. The reason for that is that a constraint MonadState' s m (where MonadState' is the MonadState defined in the mtl package) should be more or less equivalent to the constraint MonadState s m in the sense that the set of monads m that satisfy the former should be more or less the same as the set of monads m which satisfy the latter. In particular, a monad m built from a stack of monad transformers from the transformers library which satisifes some constraint composed of monad interfaces from the mtl package, is guaranteed to satisfy corresponding constraint composed of equivalent monad interfaces from the layers package.

Polymorphic, universal lift s

Notice that we renamed what is called lift in transformers to layer . This is because one of the goals of layers is to unify all operations which are called lift (e.g., liftIO , liftBase and lift itself) into a single, universal lift . The lift operation from the MonadTrans interface is a little different to the other lifts however, and we felt we should change the name to reflect that. A more accurate name would be wrap , or as we call it, layer . Take liftIO as an example. What we mean when we use liftIO is "Listen, monad, I know you know how to do IO . I don't care if IO is one monad beneath the top of your stack or ten, I don't even care if you are IO itself, I just know you understand IO and that you can figure out the rest yourself." liftBase is generally used similarly. lift on the other hand means "wrap this monadic action in exactly one monad transformer". A useful operation no doubt, but it isn't really the same thing. Anyway, if liftBase means "lift this operation from the base of the monad stack through an arbitrary number of monad transformers", and liftIO is a special case of liftBase where the base monad is always IO , is it possible to define a lift that can lift operations from any monad anywhere in the stack? If so, then as well as being more powerful than liftBase , it would also be able to do what layer does, because another way of understanding layer is as an operation which means "lift this operation from the monad just beneath the top of the stack", and a lift which can lift operations from any monad anywhere in the stack can surely lift operations from the monad just beneath the top of the stack as well. layers provides such a lift function, using type class MonadLift : class (Monad i, Monad m) => MonadLift i m where lift :: i a -> m a instance Monad m => MonadLift m m where lift = id instance (MonadLayer m, MonadLift i (Inner m)) => MonadLift i m where lift = layer . lift (In other words, a monadic operation in the monad i can be lifted into the monad m if i = m , or if m is a layer and operations from i can be lifted into the inner monad of m .) Let's demonstrate why layers ' lift is nice. Imagine you have the following code (using transformers ' lift ): main = flip evalStateT 0 $ do modify (+1) x <- get lift $ print x >>> runhaskell Main.hs 1 Perfect! But now let's say that for some reason you wanted to add a load of redundant IdentityT transformers to your monad stack. main = flip evalStateT 0 $ runIdentityT $ runIdentityT $ runIdentityT $ do modify (+1) x <- get lift $ print x >>> runhaskell Main.hs Main.hs:6:58: Couldn't match type `IO' with `Control.Monad.Trans.Identity.IdentityT (Control.Monad.Trans.Identity.IdentityT (Control.Monad.Trans.State.Lazy.StateT b0 m0))' Expected type: Control.Monad.Trans.Identity.IdentityT (Control.Monad.Trans.Identity.IdentityT (Control.Monad.Trans.State.Lazy.StateT b0 m0)) () Actual type: IO () In the second argument of `($)', namely `runIdentityT $ do { modify (+ 1); x <- get; lift $ print x }' In the second argument of `($)', namely `runIdentityT $ runIdentityT $ do { modify (+ 1); x <- get; lift $ print x }' In the second argument of `($)', namely `runIdentityT $ runIdentityT $ runIdentityT $ do { modify (+ 1); x <- get; lift $ print x }' What an ugly error message! It is the result of the lift from transformers not being polymorphic enough. This means that in practice, adding an IdentityT transformer in the middle of an existing transformer stack breaks code written for that stack. This seems wrong because adding (or removing) IdentityT from a transformer stack should be a no-op. To get the above code working using transformers ' lift , we would have to change lift to lift . lift . lift . lift , which is still brittle and prone to breakage if we in any way modify the transformer stack again. layers ' polymorphic lift does not have this problem. If we change the lift in the above code to be the lift from layers rather than from transformers , it just works: >>> runhaskell Main.hs 1 In addition to lift , which is not very powerful by itself, layers also defines liftInvmap , liftMap and liftControl , which are analogous to layerInvmap , layerMap and layerControl respectively. All of these are trivial except for liftControl , which doesn't work in quite the same way as its layerControl counterpart. It is defined as follows: class MonadLiftFunctor i m => MonadLiftControl i m where liftControl :: ((forall b. m b -> i (m b)) -> i a) -> m a instance Monad m => MonadLiftControl m m where liftControl f = f (liftM return) instance (MonadLayerControl m, MonadLiftControl i (Inner m)) => MonadLiftControl i m where liftControl f = layerControl $ \runLayer -> liftControl $ \run -> f $ liftM (\m -> layer (lift m) >>= restore) . run . runLayer Unlike MonadLayerControl , MonadLiftControl doesn't use an associated data type for the layer state. Part of the reason for this is that associated data types and overlapping instances do not play well together (see GHC bug #4259). However, we still copied monad-control - just an earlier version! monad-control 0.2 did not use associated data types either, and if you look at version 0.3 the transformers-base which depended on it, you will find a type class MonadBaseControl which is pretty much exactly equivalent to MonadLiftControl , except for the fact that MonadLiftControl is not just restricted to the base monad of a transformer stack.

References