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Existential Pontification and Generalized Abstract Digressions

Modelling IO: MonadIO and beyond

The MonadIO problem is, at the surface, a simple one: we would like to take some function signature that contains IO, and replace all instances of IO with some other IO-backed monad m. The MonadIO typeclass itself allows us to transform a value of form IO a to m a (and, by composition, any function with an IO a as the result). This interface is uncontroversial and quite flexible; it’s been in the bootstrap libraries ever since it was created in 2001 (originally in base, though it migrated to transformers later). However, it was soon discovered that when there were many functions with forms like IO a -> IO a, which we wanted to convert into m a -> m a; MonadIO had no provision for handling arguments in the negative position of functions. This was particularly troublesome in the case of exception handling, where these higher-order functions were primitive. Thus, the community began searching for a new type class which captured more of IO.

While the semantics of lift were well understood (by the transformer laws), it wasn’t clear what a more powerful mechanism looked like. So, early attacks at the problem took the approach of picking a few distinguished functions which we wanted, placing them in a typeclass, and manually implementing lifted versions of them. This lead to the development of the already existing MonadError class into a more specialized MonadCatchIO class. However, Anders Kaseorg realized that there was a common pattern to the implementation of the lifted versions of these functions, which he factored out into the MonadMorphIO class. This approach was refined into the MonadPeelIO and MonadTransControlIO typeclasses. However, only MonadError was in the core, and it had failed to achieve widespread acceptance due to some fundamental problems.

I believe it is important and desirable for the community of library writers to converge on one of these type classes, for the primary reason that it is important for them to implement exception handling properly, a task which is impossible to do if you want to export an interface that requires only MonadIO. I fully expected monad-control to be the “winner”, being the end at a long lineage of type classes. However, I think it would be more accurate to describe MonadError and MonadCatchIO as one school of thought, and MonadMorphIO, MOnadPeelIO and MonadTransControlIO as another.

In this blog post, I’d like to examine and contrast these two schools of thought. A type class is an interface: it defines operations that some object supports, as well as laws that this object abides by. The utility in a type class is both in its generality (the ability to support multiple implementations with one interface) as well as its precision (the restriction on permissible implementations by laws, making it easier to reason about code that uses an interface). This is the essential tension: and these two schools have very different conclusions about how it should be resolved.

Modelling exceptions

This general technique can be described as picking a few functions to generalize in a type class. Since a type class with less functions is preferable to one with more (for generality reasons), MonadError and MonadCatchIO have a very particular emphasis on exceptions:

class (Monad m) => MonadError e m | m -> e where
  throwError :: e -> m a
  catchError :: m a -> (e -> m a) -> m a

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

Unfortunately, these functions are marred by some problems:

  • MonadError encapsulates an abstract notion of errors which does not necessarily include asynchronous exceptions. That is to say, catchError undefined h will not necessarily run the exception handler h.
  • MonadError is inadequate for robust handling of asynchronous exceptions, because it does not contain an interface for mask; this makes it difficult to write bracketing functions robustly.
  • MonadCatchIO explicitly only handles asynchronous exceptions, which means any pure error handling is not handled by it. This is the “finalizers are sometimes skipped” problem.
  • MonadCatchIO, via the MonadIO constraint, requires the API to support lifting arbitrary IO actions to the monad (whereas a monad designer may create a restricted IO backed monad, limiting what IO actions the user has access to.)
  • MonadCatchIO exports the outdated block and unblock function, while modern code should use mask instead.
  • MonadCatchIO exports an instance for the ContT transformer. However, continuations and exceptions are known to have nontrivial interactions which require extra care to handle properly.

In some sense, MonadError is a non-sequitur, because it isn’t tied to IO at all; perfectly valid instances of it exist for non-IO backed monads as well. MonadCatchIO is closer; the latter three points are not fatal ones could be easily accounted for:

class MonadException m where
  throwM  :: Exception e => e -> m a
  catch   :: Exception e => m a -> (e -> m a) -> m a
  mask    :: ((forall a. m a -> m a) -> m b) -> m b

(With a removal of the ContT instance.) However, the “finalizers are sometimes skipped” problem is a bit more problematic. In effect, it is the fact that there may exist zeros which a given instance of MonadCatchIO may not know about. It has been argued that these zeros are none of MonadCatchIO’s business; one inference you might draw from this is that if you have short-circuiting which you would like to respect finalizers installed using MonadException, it should be implemented using asynchronous exceptions. In other words, ErrorT is a bad idea.

However, there is another perspective you can take: MonadException is not tied just to asynchronous exceptions, but any zero-like value which obeys the same laws that exceptions obey. The semantics of these exceptions are described in the paper Asynchronous Exceptions in Haskell. They specify exactly the interaction of masking, throw and catch, as well as how interrupts can be introduced by other threads. In this view, whether or not this behavior is prescribed by the RTS or by passing pure values around is an implementation detail: as long as an instance is written properly, zeros will be properly handled. This also means that it is no longer acceptable to provide a MonadException instance for ErrorT e, unless we also have an underlying MonadException for the inner monad: we can’t forget about exceptions on the lower layers!

There is one last problem with this approach: once the primitives have been selected, huge swaths of the standard library have to be redefined by “copy pasting” their definitions but having them refer to the generalized versions. This is a significant practical hurdle for implementing a library based on this principle: it’s simply not enough to tack a liftIO to the beginning of a function!

I think an emphasis on the semantics of the defined type class will be critical for the future of this lineage of typeclasses; this is an emphasis that hasn’t really existed in the past. From this perspective, we define with our typeclass not only a way to access otherwise inaccessible functions in IO, but also how these functions should behave. We are, in effect, modeling a subset of IO. I think Conal Elliott would be proud.

There is a lively debate going on about extensions to the original semantics of asynchronous exceptions, allowing for the notion of “recoverable” and “unrecoverable” errors. (It’s nearer to the end of the thread.)

Threading pure effects

This technique can be described as generalizing the a common implementation technique which was used to implement many of the original functions in MonadCatchIO. These are a rather odd set of signatures:

class Monad m => MonadMorphIO m where
  morphIO :: (forall b. (m a -> IO b) -> IO b) -> m a

class MonadIO m => MonadPeelIO m where
  peelIO :: m (m a -> IO (m a))

class MonadBase b m => MonadBaseControl b m | m -> b where
  data StM m :: * -> *
  liftBaseWith :: (RunInBase m b -> b a) -> m a
  restoreM :: StM m a → m a
type RunInBase m b = forall a. m a -> b (StM m a)

The key intuition behind these typeclasses is that they utilize polymorphism in the IO function that is being lifted in order to thread the pure effects of the monad stack on top of IO. You can see this as the universal quantification in morphIO, the return type of peelIO (which is IO (m a), not IO a), and the StM associated type in MonadBaseControl. For example, Int -> StateT s IO a, is equivalent to the type Int -> s -> IO (s, a). We can partially apply this function with the current state to get Int -> IO (s, a); it should be clear then that as long as the IO function we’re lifting lets us smuggle out arbitrary values, we can smuggle out our updated state and reincorporate it when the lifted function finishes. The set of functions which are amenable to this technique are precisely the ones for which this threaded is possible.

As I described in this post, this means that you won’t be able to get any transformer stack effects if they aren’t returned by the function. So perhaps a better word for MonadBaseControl is not that it is unsound (although it does admit strange behavior) but that it is incomplete: it cannot lift all IO functions to a form where the base monad effects and the transformer effects always occur in lockstep.

This has some interesting implications. For example, this forgetfulness is in fact precisely the reason why a lifted bracketing function will always run no matter if there are other zeros: finally by definition is only aware of asynchronous exceptions. This makes monad-control lifted functions very explicitly only handling asynchronous exceptions: a lifted catch function will not catch an ErrorT zero. However, if you manually implement finally using lifted versions of the more primitive functions, finalizers may be dropped.

It also suggests an alternate implementation strategy for monad-control: rather than thread the state through the return type of a function, it could instead be embedded in a hidden IORef, and read out at the end of the computation. In effect, we would like to embed the semantics of the pure monad transformer stack inside IO. Some care must be taken in the forkIO case, however: the IORefs need to also be duplicated appropriately, in order to maintain thread locality, or MVars used instead, in order to allow coherent non-local communication.

It is well known that MonadBaseControl does not admit a reasonable instance for ContT. Mikhail Vorozhtsov has argued that this is too restrictive. The difficulty is that while unbounded continuations do not play nice with exceptions, limited use of continuation passing style can be combined with exceptions in a sensible way. Unfortunately, monad-control makes no provision for this case: the function it asks a user to implement is too powerful. It seems the typeclasses explicitly modeling a subset of IO are, in some sense, more general! It also highlights the fact that these type classes are first and foremost driven by an abstraction of a common implementation pattern, rather than any sort of semantics.


I hope this essay has made clear why I think of MonadBaseControl as an implementation strategy, and not as a reasonable interface to program against. MonadException is a more reasonable interface, which has a semantics, but faces significant implementation hurdles.

6 Responses to “Modelling IO: MonadIO and beyond”

  1. John Millikin says:

    “””MonadError encapsulates an abstract notion of errors which does not necessarily include asynchronous exceptions. That is to say, catchError undefined h will not necessarily run the exception handler h.”””

    Perhaps I’m misunderstanding this paragraph, but I do not see any connection between ‘undefined’ and asynchronous exceptions.

    ‘undefined’ is ‘error’, which is ‘throwIO’, which throws a synchronous exception. The exception comes from a known location, at a specific time relative to the rest of the computation. Catching synchronous exceptions requires something like ‘evaluate’.

    An asynchronous exception is thrown by ‘throwTo’, and can occur anywhere at any time. They can be delayed by ‘mask’, but will still be thrown eventually.

    Proper exception handling requires handling both synchronous and asynchronous exceptions.

  2. Asynchronous exceptions subsume synchronous exceptions. We can in fact imagine an asynchronous exception as replacing some expression with an appropriate “throw” in its place: it just need not be marked by source code. (This is what the semantics in Asynchronous Exceptions does.) There is also the question of imprecise exceptions, but they can also be essentially thought of in the same way.

  3. Paul R says:

    Lately we have had plenty of insightful readings and libraries about controlling exceptions in Haskell. Unfortunatly, what it seems to show is that Haskell 98 exceptions mechanism is still out of control 14 years later.
    So the question is : does haskell *really* needed exceptions at all ? Could we envision an exception-free base in the future ?

  4. Hey Paul; it’s a good question. I think the answer is yes; in particular, I think asynchronous exceptions are one of those areas where Haskell really has the opportunity to shine (pure code, after all, is the easiest to interrupt of them all.)

  5. John Lato says:

    Hi Edward; I agree that asynchronous exceptions (in the sense John Millikin meant) are probably necessary in Haskell, but I’m not convinced that the broader theoretical definition of async exceptions is necessary.

    In particular, I think a subset of asynchronous exceptions that excludes synchronous exceptions may be the best fit for Haskell.

  6. John Lato: Unfortunately, that doesn’t mean anything to me! It seems to me that if I have asynchronous exceptions, I *must* admit synchronous exceptions (for example, consider interruptible operations like takeMVar, or even a thread throwing an exception at itself!)

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