[jimminy]

It's not really uncomfortably close to determinism, it is baseline deterministic which is necessary for the verification. The powerful part of idempotence is that it's deterministic + a verified assurance "as if we run it only once."

Deterministic (but not idempotent): send_message(id=1, body) without verifying the state of id, could result in the message being received multiple times.

Idempotent: send_message(id=1, body) would verify that the id token hadn't been consumed, before acting, thus only allowing the message to be sent one time.

[Twisol]

In your second example, if you run `send_message(id=1, body)` once and then run `send_message(id=1, body)` again, it behaves differently the second time than the first time, despite receiving the same input. So `send_message` is idempotent, but its behavior is not determined by its inputs (i.e. it is not pure).

If you imagine the hidden state that `send_message` reads and writes to be part of the input, then when you run it the second time, its inputs have changed. So it wouldn't be correct to say you're running it multiple times "on the same input".

These details are not obvious from the given definition, and that's why I say it's uncomfortably close to purity. Idempotence is very much not about purity (though you can have both), and that's why I like the author's goal-oriented explanation better: it makes the role of state very explicit.

[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.