[jimminy]

Yeah, my example was bad. I was more trying to point out that determinism of the intrinsic action is a pre-condition to the idempotency, in order to make and verify the assurance required.

You could easily split the deterministic action, and comparison/verification against existing state into two different Pure functions. Being able to perform the verification separately is valuable for addressing the "at most once", "at least once", and "exactly once" assurance described in another comment in this the thread.

I was casually opening my scope up to the outer state, in the example, to express the "assurance" portion of the definition. But you're correct, it's an erroneous example that doesn't pass the more rigorous definition of Pure Determinism, when applied the local scope of the function.