A semantic foundation for hidden state

We present the first complete soundness proof of the antiframe rule, a recently proposed proof rule for capturing information hiding in the presence of higher-order store. Our proof involves solving a non-trivial recursive domain equation, and it helps identify some of the key ingredients for soundness

Nested Hoare Triples and Frame Rules for Higher-order Store

Separation logic is a Hoare-style logic for reasoning about programs with heap-allocated mutable data structures. As a step toward extending separation logic to high-level languages with ML-style general (higher-order) storage, we investigate the compatibility 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 of certain frame rules is in fact unsound. A particular combination of rules can be shown consistent by means of a Kripke model where worlds live in a recursively defined ultrametric space. The resulting logic allows us to elegantly prove programs involving stored code. In particular, using recursively defined assertions, it leads to natural specifications and proofs of invariants required for dealing with recursion through the store.Comment: 42 page

A simple model of separation logic for higher-order store

Separation logic is a Hoare-style logic for reasoning about pointer-manipulating programs. Its core ideas have recently been extended from low-level to richer, high-level languages. In this paper we develop a new semantics of the logic for a programming language where code can be stored (i.e., with higher-order store). The main improvement on previous work is the simplicity of the model. As a consequence, several restrictions imposed by the semantics are removed, leading to a considerably more natural assertion language with a powerful specification logic