We can think of a list of some type as a wrapper around that type. For example, a list of strings contains strings [citation needed].

```
list_of_strings = ["Adam", "Bobby", "Caroline"]
```

If we have a `length`

function that converts strings into integers:

```
def length(some_string):
return len(some_string)
length("Adam") == 4 # str -> int
length("Bobby") == 5 # str -> int
length("Caroline") == 8 # str -> int
```

Then we can trivially get from a *list* of strings to a *list* of integers, just by using the same `length`

function and the `map`

operation:

```
>>> map(length, ["Adam", "Bobby", "Caroline"])
[4, 5, 8]
```

**The map function is a powerful pattern that allows us to operate on wrapped types, just by defining how to operate on their elements.** And anything that can be mapped over like that, are called

The map function has the following signature:

`(a -> b) -> f a -> f b`

That is, it takes a function that transforms type `a`

to type `b`

, and gives us a function that transforms `f a`

to `f b`

, where `f a`

is a functor that wraps the type `a`

.

It's important to point out that `f`

aren't limited to lists - sets and trees can be mapped over in a similar manner.

It doesn't even have to be collections either. Consider the `Option a`

type, which represents a "container" that may contain some value of type `a`

, or nothing. It is a common pattern to say, I have this thing that may be some value, or it might be null. If I have an actual value, then do `a -> b`

; otherwise, just give me null. Either way, I want an Option of type `b`

.

That operation kinda looks like

`Option a -> (a -> b) -> Option b`

Which after some rearranging, looks a lot like the definition of `map`

above! Indeed, Option types can be thought of as functors as well.

In summary, a functor is a "wrapper" of one type, that can be transformed into a "wrapper" of a different type, just by applying a function on its elements. Simple as that.