balance = 0 balance += 100 balance -= 50
You can't swap the order of addition and subtraction, because that would mean withdrawing from an empty account, and afaik you can't do that. Is there something I'm missing?
It is entirely up to the bank whether or not it will be allowed to complete, but regardless the response from the bank the end result of the operations will be correct, but it may be different (it will be different if the bank will reject an operation in one order, but accept all of them when presented in a different order).
You are right that they are therefore technically not strictly commutative in the sense the outcome may differ in edge cases.
But the point is that what will not happen, is that you will get incorrect results. E.g. money won't "disappear" or "appear" spontaneously.
Most commonly things like this are done by somehow reifying the operation as data and attaching some information to determine ordering. One way would be to attach a timestamp to bank transactions. By itself, that would be enough to ensure bank transactions commute (but without bounds on clock synchronization, wouldn't guarantee that you see those operations in the order you issue them). You could also require a single consistent read to an account to get a state version number and attach an incremented version of that in your transaction. Ties in both cases could be resolved by account id of the person initiating the transaction.