Definition

Formal verification uses mathematical proof systems (e.g., Lean 4) to machine-check software correctness and mathematical theorems. Unlike testing, it provides exhaustive logical guarantees when proofs compile successfully.

Key Points

  • Lean 4: Dominant proof assistant for AI-for-math research in 2026
  • Autoformalization: Converting natural language specs into formal proof obligations — bottleneck AI models like leanstral address
  • 2026-07-10: openai GPT-5.6 Sol Ultra candidate proof of cycle-double-cover-conjecture — natural-language PDF without Lean check; community verification pending (2026-07-12-openai-cdc-proof-dev-community)
  • 2026-07-02: leanstral 1.5 saturates miniF2F, SOTA on PutnamBench/FATE benchmarks; finds real bugs in OSS code
  • Bridges academic formal methods and practical software engineering

Sources