AI · 8 min read · May 2, 2026
Formal Proofs Verify Machine Governance in AI Systems
McCann's mechanized theory establishes mathematical foundations for controlling intelligent systems through coinductive safety predicates and verified interpreter specifications.
McCann proves five theorems about structural governance for intelligent systems, with three mechanized in Coq and two on paper, plus a verified runtime specification.
- — Coinductive Safety Predicate (gov_safe) captures governance safety for infinite program behaviors using boolean permission flags.
- — Governance Invariance Theorem shows governance properties hold uniformly across meta-recursive levels by definitional equality.
- — Four atomic primitives (code, reason, memory, call) are expressively complete for any discrete intelligent system.
- — Alternating Normal Form decomposes machines into canonical alternating code and effect layers with confluent rewriting.
- — Necessity Theorem proves the reason primitive is mathematically required for semantic judgment problems via Rice's theorem reduction.
- — Verified Interpreter Specification formalizes BEAM runtime trust and capability logic, tested against 70,000+ generated sequences with zero disagreements.
- — Mechanization spans 12,000 lines across 36 Coq modules with 454 theorems and zero admitted lemmas.
Frequently asked
- The Coinductive Safety Predicate (gov_safe) is a mathematical property that captures whether an intelligent system's behavior remains governed across infinite execution. It uses a boolean permission flag that is provably false for ungoverned input/output and true for governed interpretations. This matters because it provides a formal, machine-checkable definition of governance that holds for systems that run indefinitely, not just finite programs.