[josephg]

Even looking through a state lens, I think the commutativity requirement makes sense to think about.

For example, one of the simplest state CRDTs is the MAX function. The commutativity rule requires that if we merge some set of states A, B, C, ... in any order, we get the same result. This requires the MAX function to be commutative - ie, MAX(a, b) == MAX(b, a). (And also MAX(a, b, c) == MAX(c, a, b), and so on.)

This must hold for the CRDT to converge & be correct.

I thought the C stood for commutativity for the longest time after learning CRDTs. I admitted that to Martin Kleppmann the first time I met him. He thought for a solid minute, then laughed and said "yeah, I think that works too!"