Logical reasoning for higher-order functions with local state

Abstract

We introduce an extension of Hoare logic for call-by-value higherorder functions with ML-like local reference generation. Local references may be generated dynamically and exported outside their scope, may store higherorder functions and may be used to construct complex mutable data structures. This primitive is captured logically using a predicate asserting reachability of a reference name from a possibly higher-order datum and quantifiers over hidden references. The logic enjoys three completeness properties: relative completeness, a logical characterisation of the contextual congruence and derivability of characteristic formulae. The axioms for reachability and local invariants play a fundamental role in reasoning about non-trivial programs combining higher-order procedures and dynamically generated references. © Springer-Verlag Berlin Heidelberg 2007.