Kripke Models over Recursively Defined Metric Worlds: Steps and Domains

We show that models of higher-order store phenomenanaturally can be given as Kripke models over worlds thatare recursively defined in a category of metric spaces. Itleads to a unification of methods based on classical do-main theory and on step-indexed operational models. Weshow that our metric approach covers a wide range of step-indexed models, by demonstrating how it can be specializedto Hobor et. al.’s recent indirection theory, and by develop-ing a new step-indexed model of separation logic for higher-order store.