IxVM def-eq: rebase open pairs to their minimum loose index - #546
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`Algebra.kerTensorProductMapIdToAlgHomEquiv._proof_1` (mathlib) never finished: not in 300s natively, against 593ms for the reference kernel on the same subject. Instrumenting both kernels showed the pair space was NOT the problem — IxVM visits 15,085 distinct (a,b) pairs against the reference's 5,941 — but each pair was being recomputed once per context spelling: 2.48M distinct (a,b,types) def-eq keys, 164x per pair, and the whole delta cascade re-ran under each key (26.1M delta unfolds against the reference's 11,544, concentrated on the DFunLike.coe / *.toFun instance-projection towers). The prefix trim cannot canonicalize these pairs. The proof binds its section variables (types, rings, instances) OUTERMOST, so a tower pair under the inner binders has a loose range spanning the whole context; the trim keeps every inner frame, and every comparison site spells those (unreferenced) inner frames differently. The reference is immune because its def-eq opens binders with fvars: compared bodies have lbr = 0 and its context key collapses to empty, so tower obligations cache on content alone. Fix, the de Bruijn equivalent of that key insensitivity: `g = min` of the two sides' minimum loose indices — no loose BVar below `g` exists in either side, so lowering both by `g` and dropping the `g` innermost frames is a bijection on derivations (context strengthening by unreferenced frames, the same argument as the existing base=0 -> Nil arm). Def-eq returns a bit, so nothing lifts back, and one edit site covers every downstream circuit. Depth-shifted copies of the same tower also lower to the same hash-consed pair, merging pairs across binder depths. New `expr_glb` (memoized min-loose-index with an lbr fast path) supports it; the lowering is the pre-existing `expr_lower`. A depth threshold (rebase only past base > 8) was measured and rejected: it recovered only a third of the overhead on binder-heavy Init proofs for no gain on the mathlib constant. Measured: the constant's subject-only check completes in 13s (4.7e10 FFT) where it previously never terminated, and its FULL 8,753-constant closure now checks in 77s. All 34 previously-fixed mathlib constants pass full-closure in 40s total. Guard set flat: goCache_Inv_of_Inv 112s, goCache.eq_def 42s, ofBitVec_not 3s, ofDays 6s. Both suites green. Pins re-harvested: +0.0% to +6.4% (the worst are binder-heavy proofs paying the glb walk with nothing to rebase — the price of the unconditional form). New pinned fixture `deepRebase` minimizes the outer-reference telescope shape.
arthurpaulino
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August 11, 2026 01:02
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!benchmark aiur fresh |
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| constant | prove-time (main) | prove-time (PR) | Δ% | throughput (const/s) (main) | throughput (const/s) (PR) | Δ% | peak-ram (main) | peak-ram (PR) | Δ% | execute-time (main) | execute-time (PR) | Δ% | verify-time (main) | verify-time (PR) | Δ% | proof-size (main) | proof-size (PR) | Δ% | fft-cost (main) | fft-cost (PR) | Δ% |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
ByteArray.utf8DecodeChar?_utf8EncodeChar_append |
46.915 s | 43.943 s | -6.3% (1.07× faster) 🟢 | 57.360 | 61.240 | +6.8% (1.07× faster) 🟢 | 99.73 GiB | 94.54 GiB | -5.2% (1.05× smaller) 🟢 | 11.867 s | 10.507 s | -11.5% (1.13× faster) 🟢 | 133.2 ms | 134.5 ms | +1.0% | 22.13 MiB | 22.32 MiB | +0.9% | 199.20B | 188.89B | -5.2% (1.05× fewer) 🟢 |
Array.extract_append |
46.431 s | 43.562 s | -6.2% (1.07× faster) 🟢 | 33.210 | 35.400 | +6.6% (1.07× faster) 🟢 | 89.12 GiB | 84.52 GiB | -5.2% (1.05× smaller) 🟢 | 12.063 s | 10.323 s | -14.4% (1.17× faster) 🟢 | 218.4 ms | 134.4 ms | -38.5% (1.63× faster) 🟢 | 22.05 MiB | 22.22 MiB | +0.8% | 179.21B | 158.39B | -11.6% (1.13× fewer) 🟢 |
Char.ofOrdinal_le_of_le |
34.636 s | 32.892 s | -5.0% (1.05× faster) 🟢 | 76.390 | 80.440 | +5.3% (1.05× faster) 🟢 | 72.76 GiB | 69.49 GiB | -4.5% 🟢 | 7.777 s | 7.407 s | -4.8% 🟢 | 166.6 ms | 144.5 ms | -13.3% (1.15× faster) 🟢 | 22.10 MiB | 22.27 MiB | +0.8% | 142.15B | 136.46B | -4.0% 🟢 |
Vector.extract_append._proof_2 |
27.320 s | 23.621 s | -13.5% (1.16× faster) 🟢 | 47.660 | 55.120 | +15.7% (1.16× faster) 🟢 | 56.16 GiB | 45.16 GiB | -19.6% (1.24× smaller) 🟢 | 6.630 s | 5.683 s | -14.3% (1.17× faster) 🟢 | 131.0 ms | 139.1 ms | +6.1% (1.06× slower) |
21.84 MiB | 21.93 MiB | +0.4% | 105.40B | 93.15B | -11.6% (1.13× fewer) 🟢 |
_private.Init.Data.Range.Polymorphic.SInt.0.Int64.instRxcHasSize_eq |
20.789 s | 20.652 s | -0.7% | 87.160 | 87.740 | +0.7% | 45.77 GiB | 45.46 GiB | -0.7% | 4.063 s | 3.933 s | -3.2% 🟢 | 130.5 ms | 142.1 ms | +8.9% (1.09× slower) |
21.94 MiB | 22.11 MiB | +0.8% | 77.70B | 77.07B | -0.8% |
String.split |
19.597 s | 19.818 s | +1.1% | 90.060 | 89.060 | -1.1% | 43.53 GiB | 43.37 GiB | -0.4% | 3.652 s | 3.686 s | +0.9% | 137.0 ms | 144.7 ms | +5.6% (1.06× slower) |
22.14 MiB | 22.31 MiB | +0.8% | 69.78B | 69.93B | +0.2% |
List.mergeSort |
13.637 s | 13.794 s | +1.2% | 106.180 | 104.970 | -1.1% | 28.73 GiB | 29.08 GiB | +1.2% | 2.725 s | 2.708 s | -0.6% | 141.1 ms | 137.5 ms | -2.5% | 21.99 MiB | 22.16 MiB | +0.8% | 51.10B | 51.50B | +0.8% |
Vector.append |
4.245 s | 4.447 s | +4.8% |
114.260 | 109.060 | -4.6% |
7.74 GiB | 7.86 GiB | +1.5% | 704.7 ms | 732.1 ms | +3.9% |
126.0 ms | 131.5 ms | +4.4% |
20.50 MiB | 20.69 MiB | +0.9% | 10.77B | 11.35B | +5.4% (1.05× more) |
Nat.gcd_comm |
3.543 s | 3.671 s | +3.6% |
110.070 | 106.240 | -3.5% |
6.85 GiB | 7.28 GiB | +6.4% (1.06× larger) |
564.4 ms | 593.8 ms | +5.2% (1.05× slower) |
119.7 ms | 130.0 ms | +8.6% (1.09× slower) |
20.27 MiB | 20.44 MiB | +0.8% | 7.86B | 8.03B | +2.3% |
String.append |
2.521 s | 2.628 s | +4.3% |
120.610 | 115.680 | -4.1% |
4.76 GiB | 4.81 GiB | +1.0% | 421.1 ms | 429.9 ms | +2.1% | 116.9 ms | 117.1 ms | +0.2% | 19.51 MiB | 19.70 MiB | +1.0% | 4.31B | 4.43B | +2.8% |
Int.gcd |
2.103 s | 2.186 s | +4.0% |
98.890 | 95.130 | -3.8% |
5.65 GiB | 5.64 GiB | -0.1% | 362.4 ms | 366.9 ms | +1.2% | 123.4 ms | 119.6 ms | -3.1% 🟢 | 19.07 MiB | 19.24 MiB | +0.9% | 2.78B | 2.85B | +2.5% |
Nat.sub_le_of_le_add |
1.935 s | 2.004 s | +3.6% |
87.860 | 84.820 | -3.5% |
5.45 GiB | 5.48 GiB | +0.5% | 366.5 ms | 364.2 ms | -0.6% | 118.0 ms | 116.4 ms | -1.4% | 19.43 MiB | 19.60 MiB | +0.9% | 2.37B | 2.43B | +2.5% |
Nat.add_comm |
1.077 s | 1.093 s | +1.4% | 38.990 | 38.440 | -1.4% | 3.53 GiB | 4.28 GiB | +21.2% (1.21× larger) |
258.3 ms | 262.4 ms | +1.6% | 103.5 ms | 104.5 ms | +0.9% | 17.58 MiB | 17.75 MiB | +1.0% | 400.49M | 404.01M | +0.9% |
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Algebra.kerTensorProductMapIdToAlgHomEquiv._proof_1(mathlib) never finished: not in 300s natively, against 593ms for the reference kernel on the same subject. Instrumenting both kernels showed the pair space was NOT the problem — IxVM visits 15,085 distinct (a,b) pairs against the reference's 5,941 — but each pair was being recomputed once per context spelling: 2.48M distinct (a,b,types) def-eq keys, 164x per pair, and the whole delta cascade re-ran under each key (26.1M delta unfolds against the reference's 11,544, concentrated on the DFunLike.coe / *.toFun instance-projection towers).The prefix trim cannot canonicalize these pairs. The proof binds its section variables (types, rings, instances) OUTERMOST, so a tower pair under the inner binders has a loose range spanning the whole context; the trim keeps every inner frame, and every comparison site spells those (unreferenced) inner frames differently. The reference is immune because its def-eq opens binders with fvars: compared bodies have lbr = 0 and its context key collapses to empty, so tower obligations cache on content alone.
Fix, the de Bruijn equivalent of that key insensitivity:
g = minof the two sides' minimum loose indices — no loose BVar belowgexists in either side, so lowering both bygand dropping theginnermost frames is a bijection on derivations (context strengthening by unreferenced frames, the same argument as the existing base=0 -> Nil arm). Def-eq returns a bit, so nothing lifts back, and one edit site covers every downstream circuit. Depth-shifted copies of the same tower also lower to the same hash-consed pair, merging pairs across binder depths. Newexpr_glb(memoized min-loose-index with an lbr fast path) supports it; the lowering is the pre-existingexpr_lower.A depth threshold (rebase only past base > 8) was measured and rejected: it recovered only a third of the overhead on binder-heavy Init proofs for no gain on the mathlib constant.
Measured: the constant's subject-only check completes in 13s (4.7e10 FFT) where it previously never terminated, and its FULL 8,753-constant closure now checks in 77s. All 34 previously-fixed mathlib constants pass full-closure in 40s total. Guard set flat: goCache_Inv_of_Inv 112s, goCache.eq_def 42s, ofBitVec_not 3s, ofDays 6s. Both suites green. Pins re-harvested: +0.0% to +6.4% (the worst are binder-heavy proofs paying the glb walk with nothing to rebase — the price of the unconditional form). New pinned fixture
deepRebaseminimizes the outer-reference telescope shape.