Program Logics for Sequential Higher-Order Control

Abstract. We introduce a Hoare logic for call-by-value higher-order functional languages with control operators such as callcc. The key idea is to build the assertion language and proof rules around an explicit logical representation of jumps and their dual 'places-to-jump-to'. This enables the assertion language to capture precisely the intensional and extensional effects of jumping by internalising rely/guarantee reasoning, leading to simple proof rules for higher-order functions with callcc. We show that the logic can reason easily about non-trivial uses of 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.

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