All-Path Reachability Logic

TL;DR

This paper introduces a language-independent proof system for verifying reachability properties in non-deterministic programs, ensuring correctness across all execution paths, and has been mechanized in Coq and integrated into the K framework.

Contribution

It presents a novel, language-agnostic proof system for all-path reachability, with formal soundness and completeness, applicable to concurrent and non-deterministic languages.

Findings

Proof system is sound and relatively complete

Mechanized in Coq for formal verification

Implemented in the K framework for semantics-based verification

Abstract

This paper presents a language-independent proof system for reachability properties of programs written in non-deterministic (e.g., concurrent) languages, referred to as all-path reachability logic. It derives partial-correctness properties with all-path semantics (a state satisfying a given precondition reaches states satisfying a given postcondition on all terminating execution paths). The proof system takes as axioms any unconditional operational semantics, and is sound (partially correct) and (relatively) complete, independent of the object language. The soundness has also been mechanized in Coq. This approach is implemented in a tool for semantics-based verification as part of the K framework (http://kframework.org)