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Kripke Models over Recursively Defined Metric Worlds : Steps and Domains

We show that models of higher-order store phenomena naturally can be given as Kripke models over worlds that are recursively defined in a category of metric spaces. It leads to a unification of methods based on classical domain theory and on step-indexed operational models. We show that our metric approach covers a wide range of stepindexed models, by demonstrating how it can be specialized to Hobor et. al.’s recent indirection theory, and by developing a new step-indexed model of separation logic for higherorder store.