mtl is not a monad transformer library — contrary to popular conception. I believe that this commonly spread myth is due in part to some rather peculiar branding choices (the name of the library) and in part to some historical accidents (mtl was, in the distant and pre-historic past, indeed a monad transformer library).
What is mtl? It is a library of interfaces you can provide to your own types, in the form of typeclasses. It abstracts over different design patterns for different types, in the form of typeclasses. Just like Functor abstracts over “things that can be fmapped”. mtl provides typeclasses abstracting over many useful patterns that many types satisfy — patterns involving different sorts of “effects”.
MonadError is a generic interface over things where you can throw “errors” of a specific type
e, and “catch” them. It offers two methods:
throwError :: e -> m a, and
catchError :: m a -> (e -> m a) -> m a, which does what you’d expect from an error monad.
Now, we have a generic interface to work on all specfic type error-throwing Monads. The
Either type comes to mind as an obvious candidate:
instance MonadError e (Either e) where throwError = Left catchError s f = case s of Right _ -> s Left e -> f e
But there are definitely other instances possible. How about for
IOExceptions, in specific?
instance MonadError IOException IO where throwError = ioError catchErrror = catch -- will not catch non-IOExceptions
This is great, because we can now write code generic over all specific-type error things!
Error behavior…for free!
If we’re clever enough, we can actually imbue any arbitrary Monad
m with rudimentary, basic, “dumb” error handling by using the
ExceptT type. An
ExceptT e m behaves just like our original Monad
m in every way…except now, we have access to rudmentary implementations of side-channels of
This is pretty useful…to be able to add short-circuiting error behavior to any Monad we wanted. But remember,
ExceptT is not the “point” of
MonadError. It’s just one way to generate instances for free given a Monad. The real power of
MonadError is in the ability to write generically over many Monads with some sort of “error” behavior, like
MonadState s m is a Monad
m where, during in the context of
m, you have access to a global state of type
s that you can modify.
You can “get” it with
get :: m s. You can modify it with
modify :: (s -> s) -> m (). You can replace it with
put :: s -> m ().
There are a lot of types that can offer this type of interface. You might have, for example, a type where “getting” the state comes from reading an
IORef, and “putting” it comes from writing to the
IORef. Or maybe the state can come from a a query to a database…where
get queries a database in IO, and
put writes to the database.
MonadState, as a typeclass, gives you the ability to write generically over all Monads with state. You can now write generically over those database state things…or those IORef state things…or those web query things…or anything that cares to implement the interface!
MonadState says, “the functions and actions I write can work for all Monads offering state I can modify!” An action of type
MonadState String m => m Double can create a
Double from any monad offering some sort of
Again, we can actually imbue any Monad
m with some very rudimentary, “dumb” stateful interface, using a type called
StateT s m behaves just like our monad
m (be it
STM…), except now we have access to a rudimentary state getting-and-putting mechanism on a state of type
s, using a form of function composition. The implementation of the
StateT handles it under the hood.
Obviously, being able to add a rudimentary stateful interface on top of any Monad is pretty useful. Very useful, in fact!
But remember, this isn’t the point of
MonadState doesn’t exist for
StateT is just a way to generate a free instance of
MonadState if you just want to add rudimentary statefulness to an existing Monad. But there are many instances of
MonadState has nothing to do with
StateT fundamentally, any more than
Monad has to do with
Maybe fundamentally. And
StateT don’t even come from the same library!
mtl offers a generic interface for working with all monads offering a statey API.
MonadReader is more or less the same thing…it offers a generic interface to work on monads that have access to some sort of global, unchanging “environment”. An example might be a Monad where you could work with command line arguments, or environment variables, assuming they are read once and fixed when things start up. You could access the command line arguments with
ask, and use them in your program.
This one is actaully from transformers, but it gives a nice picture. Any
MonadIO m is a
Monad that allows you to embed and sequence in any arbitrary IO action. This is pretty useful! In the persistent database library, for example — the main “database access type monad” can sequence actions that access databases and arbitrary IO actions, as well. A lot of resource managers and DSL’s offer the ability to sequence IO in the middle of all the other actions.
MonadIO is for — it allows you to write functions and say, “hey, my function is generic over all things that can embed IO…anything that can embed IO can sequence my function/type”. The generic “embedding” action is
liftIO :: MonadIO m => IO a -> m a.
You know…ideally, all of these typeclasses would have laws, so we could make conclusions and apply equational reasoning to generically written functions.
Some of the laws are simple…
MonadIO should be a monad morphism. But the rest of them don’t really have any well-established laws. This is a bit of a shame, because we’d really like to be able to apply reasoning to generic functions.
People have suggested
MonadState have laws similar to how view/set/over interact in the lens laws. But as of now, most of we have in terms of our capability of analyzing generic programs is rough heuristins/feelings about what “should” be right.
A bit un-ideal, but…in practice, this ends up working not-so-badly :)
Not a Monad Transformer Library
So, let’s work together to dispel the myth that mtl is a monad transformer library. It really has nothing to do with monad transformers at all…any more than
Control.Monad is an “IO module”, or
Control.Monoid is a “list module”. Transformers don’t even come from the mtl library!
Together, we can overcome this myth. We can show people that we can live in a world where we can combine effects, work generically in Monads with multiple types of effects by writing functions generic over many different mtl typeclasses at once! (
We don’t have to reach for Monad transformers to work with combined effects. We can write our own combined effects monads and just write the instances…or we can write generically and not even care about what Monad we actually use in the end. We don’t have to teach people to be afraid of monad transformers as if they were the only way to get things done, and mtl is tied to them like a ball and chain.
mtl is not a Monad transformer library. How liberating!