claude-bot
fbcb0c3383
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
41 lines
1.8 KiB
Python
41 lines
1.8 KiB
Python
import unittest
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from textbook.check_proofs import ALLOWED_AXIOMS, AXIOM_LINE, check_proof
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class CheckProofsTests(unittest.TestCase):
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"""Only the Lean-free logic is unit-tested here; actually compiling a proof needs
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Lean and Mathlib, which is what running check_proofs.py on a real machine does."""
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def test_missing_proof_fails_without_invoking_lean(self):
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result = check_proof('t', 'True', '')
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self.assertFalse(result.ok)
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self.assertIn('no proof recorded', result.diagnostics)
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def test_sorry_is_rejected_without_invoking_lean(self):
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for escape in ('sorry', 'admit', 'native_decide'):
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result = check_proof('t', 'True', f'intro h\n{escape}')
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self.assertFalse(result.ok, escape)
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self.assertIn(escape, result.diagnostics)
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def test_proof_mentioning_sorry_only_as_substring_is_not_rejected_for_that(self):
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# 'sorryAx' contains 'sorry' but \b...\b must not match a longer identifier,
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# otherwise a legitimate name would be banned by accident.
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from textbook.check_proofs import BANNED
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self.assertIsNone(BANNED.search('exact notsorryreally'))
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self.assertIsNotNone(BANNED.search('exact sorry'))
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def test_axiom_line_parsing_separates_standard_from_ours(self):
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line = "'goodman_1_6_1' depends on axioms: [propext, Classical.choice, Quot.sound]"
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used = {a.strip() for a in AXIOM_LINE.search(line).group(1).split(',')}
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self.assertEqual(used - ALLOWED_AXIOMS, set())
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def test_axiom_line_parsing_flags_a_book_asserted_axiom(self):
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line = "'x' depends on axioms: [propext, goodman_1_6_7, sorryAx]"
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used = {a.strip() for a in AXIOM_LINE.search(line).group(1).split(',')}
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self.assertEqual(used - ALLOWED_AXIOMS, {'goodman_1_6_7', 'sorryAx'})
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if __name__ == '__main__':
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unittest.main()
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