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mrwulf
00647814b8
FIDELITY (the deliverable): fidelity/lean_defs.py transliterates the Lean MTH/Path/Root/ConsRec (post-refactor decidable-if base) to Python; fidelity/run_fidelity.py differential-tests them vs the DEPLOYED pacta verifiers over test_paper_verifiers.py's exact case generation. Result: MTH==merkle_root (256), Path==inclusion_proof (32,896), verifier agreement over 164,479 inclusion + 164,224 consistency cases (incl. honest consistency). Pinned counts match the paper. Wired as check.sh Phase 4 (gated on pacta presence, SKIP_FIDELITY to skip). HONEST CORRECTION: three cone pins added in S5.3-S6 were WRONG (take_all and consRec_base_true_eq are [propext]; consRec_base_false_eq is [propext, Classical.choice, Quot.sound]) — I had guessed [propext, Quot.sound]. check.sh's Phase 3 audit was therefore EXITING 1 since S5.3, but I reported 'green' from tailing cert lines instead of checking the exit code / ALL GREEN. Pins now corrected to the observed cones; the button now genuinely exits 0 with ALL GREEN + FIDELITY GREEN. No THEOREM was ever wrong (kernel-checked); the failure was the audit harness rejecting mis-pinned cones — working as designed, caught late by my process gap. Process fixed: verify exit code + ALL GREEN, never tail. 35 certs green (verified by exit 0). LTL untouched. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
106 lines
3.5 KiB
Python
106 lines
3.5 KiB
Python
"""Line-faithful Python transliteration of the LEAN definitions in
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Proofs/Basic.lean and Proofs/Completeness.lean (commit-current forms,
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including the decidable-if ConsRec base and the recursive kbelow).
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Each function quotes its Lean source. The fidelity harness
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(run_fidelity.py) differential-tests these against the DEPLOYED pacta
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verifiers; any transliteration drift is caught by the exhaustive run,
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any Lean-vs-deployed drift is the finding the harness exists for.
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"""
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import hashlib
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def sha256(b: bytes) -> bytes:
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return hashlib.sha256(b).digest()
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def hleaf(d: bytes) -> bytes:
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# Lean: hleaf d = sha256 (0x00 :: d)
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return sha256(b"\x00" + d)
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def hnode(x: bytes, y: bytes) -> bytes:
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# Lean: hnode x y = sha256 (0x01 :: (x.val ++ y.val))
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return sha256(b"\x01" + x + y)
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def kbelow(n: int) -> int:
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# Lean: if n ≤ 2 then 1 else 2 * kbelow ((n + 1) / 2)
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if n <= 2:
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return 1
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return 2 * kbelow((n + 1) // 2)
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def MTH(D: list) -> bytes:
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# Lean: if length = 0 then sha256 [] ; if length = 1 then hleaf (headD [])
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# else hnode (MTH (take k)) (MTH (drop k)), k = kbelow length
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if len(D) == 0:
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return sha256(b"")
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if len(D) == 1:
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return hleaf(D[0])
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k = kbelow(len(D))
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return hnode(MTH(D[:k]), MTH(D[k:]))
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def Path(m: int, D: list) -> list:
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# Lean: if length ≤ 1 then [] else (m<k: Path m take ++ [MTH drop]
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# | else: Path (m-k) drop ++ [MTH take])
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if len(D) <= 1:
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return []
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k = kbelow(len(D))
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if m < k:
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return Path(m, D[:k]) + [MTH(D[k:])]
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return Path(m - k, D[k:]) + [MTH(D[:k])]
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def Root(v: bytes, m: int, n: int, P: list):
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# Lean: n=1: (if P = [] then some v else none); n=0: none;
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# P.getLast? none: none; m<k: (Root v m k P').map (hnode · s)
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# else (Root v (m-k) (n-k) P').map (hnode s ·)
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if n == 1:
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return v if P == [] else None
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if n == 0:
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return None
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if P == []:
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return None
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s = P[-1]
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k = kbelow(n)
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if m < k:
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x = Root(v, m, k, P[:-1])
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return None if x is None else hnode(x, s)
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x = Root(v, m - k, n - k, P[:-1])
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return None if x is None else hnode(s, x)
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def ConsRec(n0: int, n: int, C: list, b: bool, r: bytes):
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# Lean (post-refactor, machine-verified equivalent to the original):
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# n0=n: b: (if C = [] then some (r,r) else none)
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# ¬b: (if C.length = 1 then some (getLastD, getLastD) else none)
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# n0>n ∨ n0=0 ∨ n≤1: none ; getLast? none: none
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# n0≤k: sub.map (fun (x,y) => (x, hnode y s))
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# else: sub(false).map (fun (x,y) => (hnode s x, hnode s y))
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if n0 == n:
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if b:
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return (r, r) if C == [] else None
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return (C[-1], C[-1]) if len(C) == 1 else None
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if n0 > n or n0 == 0 or n <= 1:
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return None
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if C == []:
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return None
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s = C[-1]
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k = kbelow(n)
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if n0 <= k:
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sub = ConsRec(n0, k, C[:-1], b, r)
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return None if sub is None else (sub[0], hnode(sub[1], s))
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sub = ConsRec(n0 - k, n - k, C[:-1], False, r)
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return None if sub is None else (hnode(s, sub[0]), hnode(s, sub[1]))
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def accept_incl(d: bytes, m: int, n: int, P: list, root: bytes) -> bool:
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# Lean acceptance: m < n ∧ Root (hleaf d) m n P = some root
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return m < n and Root(hleaf(d), m, n, P) == root
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def accept_cons(n0: int, n1: int, r0: bytes, r1: bytes, C: list) -> bool:
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# Lean acceptCons: n0 = 0 ∨ ConsRec n0 n1 C true r0 = some (r0, r1)
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return n0 == 0 or ConsRec(n0, n1, C, True, r0) == (r0, r1)
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