The regular-language semantics of second-order idealized ALGOL

We explain how recent developments in game semantics can be applied to reasoning about equivalence of terms in a non-trivial fragment of Idealized Algol (IA) by expressing sets of complete plays as regular languages. Being derived directly from the fully abstract game semantics for IA, our model inherits its good theoretical properties; in fact, for second-order IA taken as a stand-alone language the regular language model is fully abstract. The method is algorithmic and formal, which makes it suitable for automation. We show how reasoning is carried out using a meta-language of extended regular expressions, a language for which equivalence is decidable.