As in some other branches of mathematics, it is customary to assume also that the stack states are only those whose existence can be proved from the axioms in a finite number of steps. In the abstract stack example above, this rule means that every stack is a finite sequence of values, that becomes the empty stack (Λ) after a finite number of pops. By themselves, the axioms above do not exclude the existence of infinite stacks (that can be poped forever, each time yielding a different state) or circular stacks (that return to the same state after a finite number of pops).