The expressive theory of stacks (Q580954)

The usual theory of stacks is not expressive in the sense of Cook; that is, loop invariants needed to prove programs that use stacks cannot be stated in the logic. We first prove this assertion, then suggest ways of augmenting theories with new operators so as to achieve expressiveness. The main technique is to regard data types as function spaces. The technique is applied to stacks as well as to other data types.