mtl is Not a Monad Transformer Library

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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”.

The Patterns

MonadError

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 IO and 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 throwError and catchError.

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 Either or IO.

MonadState

A 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 String state.

State…for free!

Again, we can actually imbue any Monad m with some very rudimentary, “dumb” stateful interface, using a type called StateT. A StateT s m behaves just like our monad m (be it IO, Reader, ST, 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. MonadState doesn’t exist for StateT. 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…really, MonadState has nothing to do with StateT fundamentally, any more than Monad has to do with Maybe fundamentally. And MonadState 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

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.

MonadIO

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.

That’s what 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.

Aside

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…liftIO from 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! (MonadState + MonadIO, maybe?)

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!

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