For example, let's say that one of the things you want to compute is the number of friends of the current user. This value is used all over the codebase, but it only makes sense in the context of the current request (because every request has a different idea of "the current user"). So this is a memoized value, even though in the language it looks like a top-level expression.

Memoization only stores results during a request. It starts empty at the beginning of the request and is discarded at the end, and it is not shared with any other requests. It's just a map that's passed around (inside the monad) during a request.