How to implement a dictionary as a function in OCaml?

I am learning Jason Hickey's Introduction to Objective Caml.

Here is an exercise I don't have any clue

First of all, what does it mean to implement a dictionary as a function? How can I image that?

Do we need any array or something like that? Apparently, we can't have array in this exercise, because array hasn't been introduced yet in Chapter 3. But How do I do it without some storage?

So I don't know how to do it, I wish some hints and guides.