Formal Proof Verification
How it works
A proof expressed in the assistant's formal language (e.g. Lean tactics) is reduced to a sequence of axiom and inference-rule applications. A small, trusted kernel checks every step; if any is incorrect, the whole proof is rejected. In a loop with AI: the model generates/completes the proof, the verifier returns success or an error, and the outcome serves as a repair signal or a training reward. Correctness rests on trusting the (very small) kernel and the axioms.
Problem solved
LLM reasoning can be persuasive yet wrong (hallucinations). Formal verification provides an objective, machine-checkable criterion of proof correctness, giving AI a reliable ground-truth signal.
Key mechanisms
Strengths & limitations
Components
A small, trusted kernel checking every proof step.
A formal proof representation (e.g. Lean tactics) reduced to rules.
Official
A corpus of verified definitions and theorems (e.g. mathlib).
Official
Implementation
Verification is only as trustworthy as the kernel and chosen axioms.
Complex proofs can be computationally expensive to check.
Evolution
One of the key proof assistants is created.
Microsoft Research starts Lean; later the mathlib library.
Lean verification as a ground-truth signal for AI reasoning (IMO medal level).