Conclusion

Interface Traversable and its main function traverse are incredibly powerful forms of abstraction - even more so, because both Applicative and Traversable are closed under composition. If you are interested in additional use cases, the publication, which introduced Traversable to Haskell, is a highly recommended read: The Essence of the Iterator Pattern

The base library provides an extended version of the state monad in module Control.Monad.State. We will look at this in more detail when we talk about monad transformers. Please note also, that IO itself is implemented as a simple state monad over an abstract, primitive state type: %World.

Here's a short summary of what we learned in this chapter:

• Function traverse is used to run effectful computations over container types without affecting their size or shape.
• We can use IORef as mutable references in stateful computations running in IO.
• For referentially transparent computations with "mutable" state, the State monad is extremely useful.
• Applicative functors are closed under composition, so we can run several effectful computations in a single traversal.
• Traversables are also closed under composition, so we can use traverse to operate on a nesting of containers.

For now, this concludes our introduction of the Prelude's higher-kinded interfaces, which started with the introduction of Functor, Applicative, and Monad, before moving on to Foldable, and - last but definitely not least - Traversable. There's one still missing - Alternative - but this will have to wait a bit longer, because we need to first make our brains smoke with some more type-level wizardry.