Hm so it is a state machine, but (my hope is that) all state transitions are simple and direct (and observable!) outcomes of user action. If the transitions get at all complex or unobservable, I'll probably call it a failed experiment.
It might also end up being the case that users keep types "visible" at all times, only turning them off in certain situations. I can also imagine a flag to "only hide inferred types that are primitives" or something similar.