Prolog implementations provide destructive operations and mutation, but here above this is done with unification only. Arguably, you could say that unification performs mutation (but only once).
Better than that, you can "mutate" if you're not invalidating information about the variable. Oz (not incidentally, developed by Prolog people) lets you add constraints to a variable as long as they don't contradict the previous ones. Binding to a specific value is just a very strong constraint. Re-binding to the same value is okay.
This is less strict than pure functional programming, but still feels declarative and makes concurrent programming easy: no piece of code that looked previously at your variable will have its assumptions about it broken.
Arguably we could argue that everything flips 1's to 0's and back under the hood, though. Instantiation of a new lexical environment with fresh bindings mutates something in the machine.
