functions in demand semantics

What should the demand semantics interpretation of be?

Intuitively, it should agree with the “type” of demand semantics. So I would expect something like So far, so good. But then, how do we interpret a function?

There seems to be no sensible answer. A -abstraction induces no immediate demands on the environment in which it is created–indeed, it is a value–which suggests that we should return an empty demand. But that cannot be the whole story, because applying a function does, in general, induce demands on the captured environment.