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Towards a Unified Theory of Operational and Axiomatic Semantics

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Executive Summary

This paper presents a nine-rule language-independent proof system that takes an operational semantics as axioms and derives program properties, including ones corresponding to Hoare triples. This eliminates the need for language-specific Hoare-style proof rules in order to verify programs, and, implicitly, the tedious step of proving such proof rules sound for each language separately. The key proof rule is Circularity, which is co-inductive in nature and allows for reasoning about constructs with repetitive behaviors (e.g., loops). The generic proof system is shown sound and has been implemented in the MatchC program verifier.

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