functor

One of the first cool things you encounter in functional programming is map.

Say you have a function length :: String -> Int which gives the length of a string:

> length "hello"
5

(in real haskell, thats not actually the type of length but its close enough for now)

Now you can apply that to a list of strings, like this:

> map length ["hello","goodbye"]
[5,7]

For most of I've thought of this as meaning "apply the function length to each element of the list ["hello", "goodbye"].

But theres a slightly different interpretation thats a bit more "functional" feeling, that I've come across recently.

Consider only applying the first argument to map (you can do that in haskell...):

map length

Whats the type of this expression? It is [String] -> [Int]. So what its done is converted a function from string to int, into a new function from lists-of-strings to lists-of-ints.
And now we have that function that converts a list of strings to lists of ints, we can apply it to a list of strings:

> (map length) ["hello","goodbye"]
[5,7]

So the different reading that I see now is "lift this function to work on lists", first, followed by application to a list.

The same new intuition applies to functors in general and fmap, and its from thinking more about category theory that this view of things starts to appeal to me.