# Applicative and Traversable Functors

**An example from the standard library

One of the most useful functions when working with `scala.concurrent.Future`

is `Future.traverse`

, presented below
in a simplified form.

```
import scala.concurrent.{ExecutionContext, Future}
def traverseFuture[A, B](as: List[A])(f: A => Future[B])(implicit ec: ExecutionContext): Future[List[B]] =
Future.traverse(as)(f)
```

`traverseFuture`

takes a `List[A]`

and for each `A`

in the list applies the function `f`

to it, gathering results
as it goes along. `f`

is often referred to as an *effectful* function, where the `Future`

effect is running the computation
concurrently, presumably on another thread. This effect is apparent in the result of the function, which has
gathered results inside `Future`

.

But what if the effect we wanted wasn't `Future`

? What if instead of concurrency for our effect we wanted validation
(`Option`

, `Either`

, `Validated`

) or `State`

? It turns out we can abstract out the commonalities between all these
data types and write a generic `traverse`

function once and for all. We can even go further and abstract over data
types that can be traversed over such as `List`

, `Vector`

, and `Option`

.

In this series we will build up the machinery needed to generalize the standard library's `Future.traverse`

into
its fully abstract and most reusable form.

If you'd like to read the published literature on these ideas, some good starting points are "Applicative Programming with Effects" by McBride and Patterson, and "The Essence of the Iterator Pattern" by Gibbons and Oliveira.