One-Path Reachability Logic

This paper introduces (one-path) reachability logic, a
language-independent proof system for program verification, which
takes an operational semantics as axioms and derives reachability
rules, which generalize Hoare triples. This system improves on
previous work by allowing operational semantics given with conditional
rewrite rules, which are known to support all major styles of
operational semantics. In particular, Kahn’s big-step and Plotkin’s
small-step semantic styles are now supported. The reachability logic
proof system is shown sound (i.e., partially correct) and (relatively)
complete. Reachability logic thus eliminates the need to independently
define an axiomatic and an operational semantics for each language,
and the non-negligible effort to prove the former sound and complete
w.r.t. the latter. The soundness result has also been formalized in
Coq, allowing reachability logic derivations to serve as formal proof
certificates that rely only on the operational semantics.