Nested Hoare Triples and Frame Rules for Higher-Order Store

Separation logic is a Hoare-style logic for reasoning about programs withheap-allocated mutable data structures. As a step toward extending separation logic tohigh-level languages with ML-style general (higher-order) storage, we investigate the com-patibility of nested Hoare triples with several variations of higher-order frame rules.The interaction of nested triples and frame rules can be subtle, and the inclusion ofcertain frame rules is in fact unsound. A particular combination of rules can be shownconsistent by means of a Kripke model where worlds live in a recursively defined ultrametricspace. The resulting logic allows us to elegantly prove programs involving stored code. Inparticular, using recursively defined assertions, it leads to natural specifications and proofsof invariants required for dealing with recursion through the store.