Towards a Unified Theory of Operational and Axiomatic Semantics

Abstract

This paper presents a nine-rule {\em language-independent} proof system that takes an operational semantics as axioms and derives program reachability properties, including ones corresponding to Hoare triples. This eliminates the need for language-specific Hoare-style proof rules to verify programs, and, implicitly, the tedious step of proving such proof rules sound for each language separately. The key proof rule is {\em Circularity}, which is coinductive 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 verifier.