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mrwulf
a6b6e86865
Phase B - montgomery_reduce (Proofs/ScalarMontSpec.lean + Proofs/ScalarReduceSpec.lean): - mont_key: LFACTOR*L0 + 1 = 214835089243030*2^52 (the -1 inverse identity, norm_num) - mont_cancel: (s + ((s*LFACTOR) % 2^52)*L0) % 2^52 = 0 via Nat.ModEq - every part1 shift is an EXACT division, nothing discarded - part1_spec / part2_spec: per-round helpers (carry*2^52 = sum + p*L0; exact split) - mont_head_telescope (E0-E4) and mont_tail_telescope (E5-E8): linear_combination certificates with weights 2^52k; mont_bound: X' < 2*ell from Z < 2^260*ell - montgomery_reduce_spec: post `scDenote r * 2^260 = Z` in ZMod ell + 52-bit bounds. METHOD-4 split at the round-4/5 boundary: the 74-step monolith is elaboration-pathological; each half compiles in ~25s/3GB. - The single death-spiral line: an omega for the nonce-sum bound with ~110 hypotheses in context never returns; extracted to nonce_sum_bound (5 hypotheses, instant). Bisected with fail-probes; documented in control-repo FAILURES.md. Phase C - mul (Proofs/ScalarFullMulSpec.lean): - RR_limbs/RR_scVal/RR_lt; RR_denote: RR = 2^520 - K*ell kernel-checked, so ⟦RR⟧ = R^2; R_isUnit: 2^260 unit of ZMod ell (coprime oddness witness) - mul_spec: mul_internal -> montgomery_reduce -> mul_internal(*, RR) -> montgomery_reduce composed; column values folded by `ring`; R cancelled via IsUnit.mul_right_cancel. Hypothesis scVal a * scVal b < 2^260*ell (honest Montgomery bound; canonical inputs satisfy it). Aggregate (Proofs/ScalarMain.lean): scalar_add/sub/mul_correct on ScBnd interfaces + canonical_mul_bound + scalarImplementation bundling all three. sub_val_spec/add_val_spec posts strengthened with result-limb 52-bit bounds (the montgomery tail feeds sub's output back into mul_internal). check-scalar.sh: 9 proof files, 10 kernel audits (was 6), all exactly [propext, Classical.choice, Quot.sound]. Button pressed fresh: green.
44 lines
2.5 KiB
Bash
Executable file
44 lines
2.5 KiB
Bash
Executable file
#!/usr/bin/env bash
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# Scalar-layer check (Scalar52 arithmetic mod ℓ). Compiles the gen model + the
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# proven foundation. add/sub (Range-loop reductions) and the Montgomery mul
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# path are in progress — see README. Guarded compiles throughout.
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set -uo pipefail
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source ~/aeneas-toolchain/env.sh
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HERE="$(cd "$(dirname "$0")" && pwd)"
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AENEAS_LEAN="$AENEAS_HOME/backends/lean"
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GEN=(CurveScalar/TypesExternal CurveScalar/Types CurveScalar/FunsExternal CurveScalar/Funs)
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PROOFS=(ScalarDenote ScalarLoop ScalarSubSpec ScalarAddSpec ScalarMulSpec ScalarMontSpec ScalarReduceSpec ScalarFullMulSpec ScalarMain)
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echo "=== stub/axiom audit ==="
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grep -rnE '^(private |protected |noncomputable )*axiom ' "$HERE"/Proofs/Scalar*.lean 2>/dev/null && { echo "axiom under Proofs/"; exit 1; }
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echo " clean"
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echo "=== compile (guarded) ==="
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cd "$AENEAS_LEAN"
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lake env bash -c "
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set -uo pipefail
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cd '$HERE/gen' && export LEAN_PATH=\"\$LEAN_PATH:\$PWD:$HERE\"
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for m in ${GEN[*]}; do echo \" · gen \$m\"; LEAN_TIMEOUT=300 LEAN_MEM_MB=6144 '$HERE/lean-guard' \"\$m.lean\" || exit 1; done
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cd '$HERE'
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for m in ${PROOFS[*]}; do echo \" · proof \$m\"; LEAN_TIMEOUT=300 LEAN_MEM_MB=4096 '$HERE/lean-guard' \"Proofs/\$m.lean\" || exit 1; done
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" || { echo FAIL; exit 1; }
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echo "=== Phase 3: axiom audit (kernel-level) ==="
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cd "$AENEAS_LEAN"
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lake env bash -c "
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set -uo pipefail
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export LEAN_PATH=\"\$LEAN_PATH:$HERE/gen:$HERE\"
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cd '$HERE'
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AUD=\$(mktemp '$HERE/.audit-scalar-XXXX.lean')
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{ echo 'import Proofs.ScalarMain'; echo '#print axioms ScalarProofs.L_val'
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echo '#print axioms ScalarProofs.sub_loop_spec'
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echo '#print axioms ScalarProofs.cond_add_l_one_spec'; echo '#print axioms ScalarProofs.sub_val_spec'; echo '#print axioms ScalarProofs.add_val_spec'; echo '#print axioms ScalarProofs.mul_internal_spec'
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echo '#print axioms ScalarProofs.part1_spec'; echo '#print axioms ScalarProofs.montgomery_reduce_spec'; echo '#print axioms ScalarProofs.mul_spec'; echo '#print axioms ScalarProofs.scalarImplementation'; } > \"\$AUD\"
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OUT=\$(LEAN_TIMEOUT=120 LEAN_MEM_MB=4096 '$HERE/lean-guard' \"\$AUD\" 2>&1)
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echo \"\$OUT\"
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rm -f \"\$AUD\" \"\${AUD%.lean}.olean\"
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N=\$(echo \"\$OUT\" | grep -cF \"depends on axioms: [propext, Classical.choice, Quot.sound]\" || true)
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[ \"\$N\" -eq 10 ] || { echo \"AXIOM AUDIT FAILED: \$N/10 clean\"; exit 1; }
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" || { echo FAIL; exit 1; }
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echo " L_val axiom-clean"
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echo ""
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echo "SCALAR LAYER COMPLETE: add, sub, mul (Montgomery reduction, double round through RR) proven mod ℓ; aggregate certificate scalarImplementation kernel-audited."
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