refactor(bz): migrate HexBerlekampZassenhaus to the module system - #8597
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Migrate the executable Berlekamp-Zassenhaus library onto the Lean 4 module system (module / public import / public section), the prerequisite for splitting the 19k-line Basic.lean monolith. Works around two lean4 module-system reduction bugs found in the process: - Array.instDecidableEqImpl is not @[expose], so decide/rfl over Array equality does not reduce in the kernel under the module system for nonempty arrays. Worked around with import all Init.Data.Array.DecidableEq (keeping the efficient Array instance); upstream fix in leanprover/lean4#14270. - Array.back? does not reduce under the module system; reimplement DensePoly.leadingCoeff as coeffs.getD (size - 1) 0 (equal, reducible). Adds public meta imports for the #guards, the backward.{proofsInPublic, privateInPublic} options, @[expose] on the executable defs exported defeq proofs reduce through, and de-privatises the leaked GcdLaws Rat instance. No runtime performance regression (only leadingCoeff's compiled body changes, equal-or-faster; DecidableEq unchanged). See progress/20260704T000000Z_bz-module-migration-phase1a.md. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
This was referenced Jul 4, 2026
kim-em
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July 4, 2026 11:56
…vers The DensePoly.leadingCoeff reimplementation (coeffs.getD (size-1) 0 instead of coeffs.back?.getD 0) broke the monic-witness proofs in the bench exe and emit-fixture drivers, which the module-migration commit missed because a plain `lake build` does not build the bench/conformance sub-projects (CI does). Rewrite the `change ...back?.getD 0 = 1` proofs to close the getD form via Array.getElem_push. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
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…tem (#8600) Migrate the Mathlib-side Berlekamp-Zassenhaus correspondence library (the 13 files under `HexBerlekampZassenhausMathlib/` plus the umbrella) onto the Lean 4 module system, the Phase-1b follow-up to #8597 and the prerequisite for the Phase-2 split of the 22k-line `Basic.lean`. Per file: `module`, `public import`, `public section`, and the `backward.{proofsInPublic,privateInPublic}` crutch where private decls are referenced in public. The bridge proves correctness by unfolding executable and Mathlib-side defs, so it needs a large `@[expose]` pass (89 defs, driven outward from each "not an exposed body" / "not unfolded because not exposed" error until green) spanning the executable `HexBerlekampZassenhaus`/`HexHensel` layers, the `HexBerlekampMathlib`/`HexPolyZMathlib` bridges, and the library's own defs. The `irreducible_cert` tactic and its tests need their elaboration-time helpers marked `meta` (`public meta import` for the reifier), and the certificate kernel replay reduces `checkIrreducibleCertLinear` and its Berlekamp pow-chain plus `Array`/`DensePoly` `==` through `import all` of the executable checker modules and `Init.Data.Array.DecidableEq`. Two proof-text repairs in the `monicModPImage`-zero branch adapt to module reduction (a `simp` that started leaving a spurious `SemigroupWithZero` metavariable, and a `dvd_zero` on `toMathlibPolynomial 0`); no theorem statements change. See progress/20260704T141029Z_bz-mathlib-module-migration-phase1b.md. Co-authored-by: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
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This PR migrates the executable
HexBerlekampZassenhauslibrary onto the Lean 4 module system (module/public import/public section), the prerequisite for splitting its 19k-lineBasic.leanmonolith into dependency-ordered leaves.The migration surfaced two genuine lean4 module-system reduction bugs, both diagnosed to root and worked around locally (each with a
-- revert once upstream landscomment):Array.instDecidableEqImplis not@[expose], sodecide/rfloverArrayequality does not reduce in the kernel under the module system for two nonempty arrays (Array.instDecidableEqinlines the empty cases but delegates the nonempty case to the opaque impl). Worked around withimport all Init.Data.Array.DecidableEq, keeping the efficientArrayinstance rather than switching to a slowerList-based one. Upstream fix: fix: expose Array equality for kernel reduction leanprover/lean4#14270.Array.back?does not reduce under the module system, soDensePoly.leadingCoeffis reimplemented ascoeffs.getD (size - 1) 0instead ofcoeffs.back?.getD 0(definitionally equal, kernel-reducible, and it avoids anOptionallocation).The remaining changes are the standard migration mechanics:
public meta imports so the 117#guardcompile-time checks evaluate, thebackward.{proofsInPublic,privateInPublic}options for private-in-public references,@[expose]on the executable defs that exporteddecide/rfl/unfoldproofs reduce through (including the shallowfactor 0constant-branch closure), de-privatising the leakedGcdLaws Ratinstance, and exposingSquareFreeRat. TheleadingCoeffreimplementation rippled into about a dozenleadingCoeff = coeff (size - 1)re-proofs across HexPoly/HexHensel/HexBerlekamp/HexPolyFp/HexPolyZ/HexPolyMathlib/HexBerlekampZassenhausMathlib, all rewritten to thesimp [leadingCoeff, coeff, size]form.There is no runtime performance regression: the only change to compiled code is
leadingCoeff(equal or marginally faster), and theDecidableEqinstance is unchanged. Fulllake build(4088 jobs) is green,check_dag.pypasses, and nosorry/axiomis introduced.🤖 Prepared with Claude Code