A simple data structure helping us ask questions of the following sort: "does all this data have the same BLANK and if so what is it?"

For example:

doTheseHaveTheSameLength :: [String] -> String
doTheseHaveTheSameLength l = case foldMap (Somebody . length) of
  Somebody n -> "They all have length " <> show n
  Nobody     -> "The lengths differ"
  Anybody    -> "You didn't give me any strings"

This can of course be done with `Maybe (Maybe x)` instead, but doing so runs the risk of getting confused: which is Nothing and which is `Just Nothing`?

Unfortunately, there are two Applicative instances.

One is easy to motivate intrinsically. If we think of Anybody as an empty list, Somebody as a singleton list, and Nobody as a multi-element list, and think of the applicative instance on as corresponding to the cartesian product, then we get an Applicative instance with

Anybody <*> Anybody = Anybody
Anybody <*> Nobody = Nobody

This however cannot possibly correspond to a Monad instance (if the first argument of >>= is Anybody, there's no way of inspecting the second). We thus choose another, which does.