Functional Idempotence

Idempotence is often defined as:

f(f(x)) = f(x)

But this way makes more sense to me:

f: (S, A) => (S, B)

f(s0, x) = (s1, y1)
f(s1, x) = (s1, y2)

In this talk, we walk through how I like to think about it.