Abstract

We introduce a Hoare logic for higher-order functional languages with control operators such as callcc. The key idea is to build the assertion language and proof rules on the basis of types that generalise the standard types for control operators (for ’jumping-to’) with dual types (for ’being-jumped-to’). This enables the assertion language to capture precisely the intensional and extensional effects of jumps by internalising rely/guarantee reasoning, leading to simple proof rules for call-by-value PCF with callcc and/or name-abstraction. All new operators come with powerful associated axioms. We show that the logic allows specification and reasoning about non-trivial examples of using callcc. The logic matches exactly with the operational semantics of the target language (observational completeness), is relatively complete in Cook’s sense and allows efficient generation of characteristic formulae.

Citations