fbcb0c3383e98a3204d457cd2ce8d3fae4e92c11
2 Commits
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 claude-bot
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fbcb0c3383 |
Record and gate proofs, so "proven" means Lean verified it
The index had no proof field and every entry was an axiom, so the database asserted its premises rather than proving them. Adds the proof half, with the verification gate that makes the status trustworthy. - Database records now carry `proof` and `proof_checked`, and the search index exposes the proof, with status one of proved / proof_pending / asserted. build_database.py emits a real `theorem` only when a proof has been verified (by check_proofs.py, or by a lean-bench run via --results); a recorded but unverified proof stays an `axiom` and is reported as proof_pending, so the library never claims more than Lean has confirmed. A test pins that gating in both directions. - textbook/check_proofs.py verifies proofs by compiling `theorem ... := by <proof>`. Stricter than check_statements.py in three ways: it rejects sorry/admit/native_decide outright, and it reads `#print axioms` to reject any proof depending on more than Lean's own three axioms (propext, Classical.choice, Quot.sound) -- which in particular catches a proof leaning on one of this database's own book-asserted axioms, since that is not an independent proof. With --update it writes proof_checked back, promoting entries on the next build. - Ten candidate proofs recorded, all currently proof_checked=false pending a Lean run: goodman-1-6-1 (the eight algebraic identities are `ring`, plus a short argument for the nonzero conjunct), the four parts of Proposition 1.6.2 (Int.mul_eq_one_iff_eq_one_or_neg_one, associated_of_dvd_dvd with Int.associated_iff, dvd_trans, dvd_add with mul_left), 1-6-4 (Nat.exists_prime_and_dvd), 1-6-15 (Int.gcd_eq_one_iff_coprime, where IsCoprime unfolds to exactly the target existential), 1-6-17 (IsCoprime.mul_dvd via Nat.isCoprime_iff_coprime), 1-6-19 (Int.Prime.dvd_mul') and 1-6-20 (Prime.dvd_prod_iff). These are citations of existing Mathlib results, which is the realistic way to populate a textbook premise library -- the remaining 11 (1-6-6, -7, -9, -10, -11, -13, -18, -21, -23, -24, -26) are the ones needing actual work and carry no proof yet. Written without Lean available here, so expect a real failure rate on first compile -- run check_proofs.py --update and send back the FAILED ids with diagnostics, same loop as the statement fixes. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_017vbLFFJiHSZqGZHEkjvG5x |
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claude-bot
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69c5b788b9 |
Generate the citable premise database, and goal-driven retrieval over it
The database was the missing half: extraction and assembly existed, but nothing turned the book's main-content statements into something an agent could actually cite mid-proof, and nothing searched it. Two new scripts. textbook/build_database.py takes the main-content statements and emits both halves of a usable premise library: - an importable Lean file where every entry is a named declaration, so a proof can cite goodman_1_6_20 by name; - a JSONL search index carrying each entry's name, statement, mentioned identifiers and status. An entry is emitted as an `axiom` (asserted from the textbook) until a real lean-bench run proves it; passing --results upgrades those entries to real theorems carrying the exact verified proof. This mirrors how the book itself works -- its exercises are posed assuming its body results, the same way using Mathlib does not mean re-proving Mathlib. The cost is explicit: anything proven through an axiom inherits it, so a garbled extraction asserted as an axiom makes downstream proofs worthless. Guards: --require-checked refuses entries that have not passed check_statements.py (all 21 section 1.6 entries have, and are now marked accordingly), and the verifier's existing #print axioms check surfaces what a finished proof rests on. textbook/search_database.py is the retrieval step the proof loop calls at each line: given the current goal, it ranks premises by identifier and symbol overlap, weighting rare identifiers far above common ones (IsGCDOfList matching means much more than Int matching), preferring a proven premise over an asserted one, and formats the top few for the prompt. Verified against three real goals: the exactly-applicable premise tops each ranking by a wide margin (11.4 vs 1.6 for the gcd goal, 5.1 vs 3.7 for the prime-divides-product goal). It is a ranking heuristic, not a decision procedure -- only Lean can say whether a premise applies. Replacing score_premise() is the whole job of swapping in embeddings. Also: renamed library_candidates/ to database/ to match what it is; generated lib/Goodman/Chapter01Section06.lean (21 premises, 0 proven, 21 asserted) and database/goodman-1.6.index.jsonl; noted a latent bug in the older build_library.py, which attaches each entry's non-import prelude per-theorem and so would emit a shared `def` twice in one file -- build_database.py hoists and dedupes, and has a test pinning that. 13 new tests, all green (33 total, the one failure remains the pre-existing unrelated lean_agent import error in test_dataset.py). Still not done, and worth being clear about: nothing has been proven yet. The bench targets have not been elaboration-checked, no lean-bench run has happened over either file, and the goal-directed loop that would consume this retrieval does not exist -- lean-bench's solve() is still single-shot. Separately, lean-bench cannot currently run at all in this checkout, because lean_bench/cli.py imports lean_agent at module load and lean-agent is not installed. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_017vbLFFJiHSZqGZHEkjvG5x |