STM and alter in clojure

Question

I am working through the Programming Clojure book. While explaining alter and the STM, they say that if, during an alter, Clojure detects a change to the ref from outside the transaction, it will re-run the transaction with the new value. If that is the case, I would imagine the update function you pass in needs to be pure, but that isn't indicated in the docs (and it is in other similar situations).

So is my assumption correct? If not, how does the STM re-apply the function? If it is correct, is it the case that you can't rely on the docs to tell you when you can have side effects, and when you can't?