lean-verify

---

name: lean-verify summary: Verifier-backed Lean proof repair using autocontext and Pi. description: Use when running the experimental Lean formal-proof harness, validating machine-checked proof candidates, benchmarking playbook transfer, or invoking the pi-autocontext-lean-verify package. Triggers: Lean proof repair, formal proof, theorem proving, verifier-backed proof, autocontext formal, proof playbook, pre-repair hints.

Formal Proof Harness

Use this skill for the external Lean proof-repair experiment harness. The package wraps support/formal-proof-lean-pilot and exposes the autocontext_lean_verify Pi tool.

Core rule

Lean is the correctness oracle. Never count prose, mathematical-looking text, or an LLM's claim of success as a theorem proof. A proof succeeds only when the fixed Lean theorem template compiles with the candidate proof body.

Guardrails

The harness rejects or avoids:

• sorry
• admit
• new axioms
• unsafe
• theorem weakening
• changing theorem statements
• new imports / proof-by-importing-answer
• candidates that are not proof bodies for the {{PROOF}} placeholder

Recommended workflow

Run, benchmark, and attribution actions default to short temp result paths under the system temp directory (pi-autocontext-lean-verify/...) (or $AUTOCONTEXT_LEAN_VERIFY_RESULTS_ROOT) so npm-loaded packages avoid Pi session path-length failures.

Use challenge_v6_frontier and challenge_v7_frontier for the first packaged verifier-only frontier suites. v7 is the first packaged suite where seeded autocontext is intentionally unstable while unseeded/direct solve none. Version 0.1.10 packages challenge_v8_diagnostics, challenge_v9_composition_gradient, challenge_v10_stats_reification, challenge_v11_metric_composition, and challenge_v12_simultaneous_metrics. Version 0.1.11 packages challenge_v13_decomposition_order and challenge_v14_metric_order_permutations; version 0.1.12 packages challenge_v15_proof_shape_hints. Version 0.1.13 packages challenge_v16_compact_reassembly_hints and challenge_v17_proof_plan_hints; version 0.1.14 packages challenge_v18_prompt_only_skeleton_hints, challenge_v19_bare_skeleton_names, and challenge_v20_description_only_skeleton to test whether detailed descriptions, bare labels, or both can live only in seeded playbook context without theorem-level True hypotheses. Version 0.1.15 packages challenge_v21_neutral_anchor_skeleton and the process-group timeout/short-run-root hardening used before v22 code-like anchor probes. Version 0.1.16 packages challenge_v22_code_like_anchor_skeleton, challenge_v23_exact_labels_without_plan_prefix, challenge_v24_plan_prefix_generic_labels, and challenge_v25_step_prefix_exact_labels; v22-v25 collectively show that snake_case anchors, exact roots without the original prefix, generic prefix labels, and alternate-prefixed exact roots do not reproduce v18 stability. Version 0.1.16 also carries a second timeout hardening patch that bounds post-kill waits and force-closes leaked subprocess pipes. Version 0.1.17 updates the explicit autocontext runtime pin to autocontext==0.5.1 to inherit the upstream Pi CLI timeout/process cleanup hardening.

1. Run setup or preflight first:

{
  "action": "setup"
}

or:

{
  "action": "preflight"
}

setup runs preflight and a minimal Lean smoke proof.

2. For the current strongest repair-only mode, use a named fixture group:

{
  "action": "run",
  "mode": "pre_repair_hint",
  "fixtureGroup": "broader"
}

This maps to the validated harness flags:

--no-pregenerate
--structured-alternate-retry
--structured-hint-candidates
--pre-repair-hint-candidates
--max-attempts 2
--rounds 2
--timeout 60

3. For expanded negative controls, prefer maxAttempts=3:

{
  "action": "run",
  "mode": "pre_repair_hint",
  "fixtureGroup": "negative_controls",
  "maxAttempts": 3,
  "rounds": 2,
  "timeoutSeconds": 60
}

4. To reproduce the proof-transfer benchmark, compare seeded autocontext/Pi against direct Pi repair-loop on no-expected-proof challenge fixtures:

{
  "action": "benchmark",
  "fixtureGroup": "challenge_v3_generalization",
  "maxAttempts": 2,
  "rounds": 2,
  "timeoutSeconds": 120
}

This mode uses --no-pregenerate and --structured-alternate-retry; synthetic hint candidates are disabled.

5. For seeded/unseeded/direct attribution on v5 fixtures:

{
  "action": "attribution",
  "fixtureGroup": "challenge_v5_attribution",
  "maxAttempts": 2,
  "rounds": 2,
  "timeoutSeconds": 120
}

6. Summarize a run with:

{
  "action": "summarize",
  "runRoot": "results/<run>"
}

Fixture groups

• smoke: one quick theorem, add_zero_right.
• broader: seven broader fixtures covering Nat distribution, Bool/List recursion, list helpers, tree helpers, and reverse/append.
• heldout: seven original held-out transfer fixtures.
• combined: broader + heldout (14 fixtures).
• negative_controls: six fixtures where generic Nat/List hint candidates should fail Lean before fallback: distribution, multiplication associativity/commutativity, addition cancellation, and filter length bound.
• challenge_v2_no_helper: three no-expected-proof fixtures requiring local helper lemma discovery.
• challenge_v3_generalization: four no-expected-proof theorem-generalization fixtures requiring accumulator and multi-helper proof plans.
• challenge_transfer: all v2/v3 challenge fixtures (7 fixtures).
• challenge_v4_count: four no-expected-proof count/list/tree fixtures.
• challenge_v5_attribution: four no-expected-proof simultaneous-invariant and multi-helper composition fixtures.
• challenge_v5_tree_tally: one hard tree/tally mirror fixture.
• challenge_v6_frontier: four frontier fixtures covering multi-accumulator reverse invariants, nested tree partition stats, successor-map reverse count/sum, and mutual tree stats.
• challenge_v7_frontier: four frontier-plus fixtures combining partition/tree mirror composition with stats accumulator normalization.
• challenge_v8_diagnostics: four diagnostic fixtures isolating the v7 partition-heavy accumulator frontier into smaller components.
• challenge_v9_composition_gradient: six composition-gradient fixtures splitting keep/drop partition-through-mirror into scalar and paired length/sum obligations.
• challenge_v10_stats_reification: six statsAcc-reification fixtures isolating tuple normalization, metric extensionality, count metrics, and stats equality from metric hypotheses.
• challenge_v11_metric_composition: six metric-composition fixtures combining keep/drop metric bundles with statsAcc extensionality boundaries.
• challenge_v12_simultaneous_metrics: seven simultaneous-metric fixtures splitting keep/drop count-only, length-only, sum-only, pair, and triple metric bundles.
• challenge_v13_decomposition_order: six decomposition/order fixtures isolating v12 triple-bundle ordering, append/filter sub-lemmas, tree-only metrics, and conjunction reassembly.
• challenge_v14_metric_order_permutations: six metric-order permutation fixtures covering all count/length/sum orderings in the full simultaneous keep/drop triple bundle.
• challenge_v15_proof_shape_hints: four proof-shape hint fixtures exposing metric-bundle, side-bundle, append/filter, and final reassembly hypotheses.
• challenge_v16_compact_reassembly_hints: four compact reassembly-hint fixtures replacing the large v15 higher-order hypothesis with generic/named packers.
• challenge_v17_proof_plan_hints: four harmless True proof-plan skeleton hint fixtures naming induction, case split, simp, and Nat add normalization steps.
• challenge_v18_prompt_only_skeleton_hints: two v16 theorem-shape fixtures where detailed proof-plan skeleton names are present only in seeded playbook context.
• challenge_v19_bare_skeleton_names: ablation over the clean v18 fixtures using only bare skeleton-name bullets in the seeded playbook.
• challenge_v20_description_only_skeleton: ablation over the clean v18 fixtures using compact skeleton descriptions without plan_... labels in the seeded playbook.
• challenge_v21_neutral_anchor_skeleton: ablation over the clean v18 fixtures using neutral step anchors plus compact skeleton descriptions without plan_... labels in the seeded playbook.
• challenge_v22_code_like_anchor_skeleton: ablation over the clean v18 fixtures using compact descriptions plus code-like snake_case step anchors without the earlier detailed-plan prefix.
• challenge_v23_exact_labels_without_plan_prefix: ablation over the clean v18 fixtures using v18's exact detailed labels with only the prefix removed.
• challenge_v24_plan_prefix_generic_labels: ablation over the clean v18 fixtures using compact descriptions plus shorter generic plan_ labels.
• challenge_v25_step_prefix_exact_labels: ablation over the clean v18 fixtures using compact descriptions plus step_ prefixed exact v18 label roots.
• challenge_extended_transfer: all v2/v3/v4/v5/v6/v7/v8/v9/v10/v11/v12/v13/v14/v15/v16/v17/v18 challenge fixtures (78 fixtures).

Modes

• seeded_pregenerate: allow Pi/autocontext to pregenerate from the verified playbook, then Lean-check.
• pre_repair_hint: no pregeneration; try Lean-checked strategy candidates before primary Pi repair.
• post_repair_hint: no pregeneration; run primary Pi repair, then Lean-checked hints before alternate Pi fallback.
• structured_retry: no pregeneration; structured alternate Pi retry without hint candidates.

Interpretation guidance

• Challenge fixtures intentionally omit expected_proof.lean; success must come from the generated proof body passing Lean.
• Use action="attribution" when comparing seeded, unseeded isolated, and direct Pi repair-loop outcomes.
• Treat pre_repair_hint as a hybrid experiment mode, not pure LLM proof generation.
• Lean-rejected hint candidates are good safety evidence when fallback recovers.
• Compare methods using proof success, Pi calls, Lean verifier attempts, repair edits, and token edit distance.
• Keep artifacts indexed with results/index.json and results/EXPERIMENTS.md.

Packaging status

This package is npm-distributed as pi-autocontext-lean-verify. Current patch releases use GitHub trusted publishing with npm provenance. The package remains experimental: report proof-transfer results as verifier-backed evidence, not as a claim that autocontext is a standalone theorem prover.