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refactor(machines): remove Halting reduction dependency on Complexity #697

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@SamuelSchlesinger

The existing Machines-to-Complexity dependency in Machines/Turing/MultiTape/Halting/Reduction.lean is a separate layering fix from #694. The module imports Complexity/Reduction/ManyOne.lean only for the generic ManyOneReducibleBy kernel (identity, composition and complement laws); the upper file also contains complexity-class hardness/completeness APIs.

Extract the reusable admissible-map reduction kernel into a lower Computability module with no Machines or Complexity-class dependency, leaving HardUnder, CompleteUnder and class-specific helpers at the upper layer. Keep current declaration names/statements and update imports/real clients in the same PR, with no aliases. Choose the exact lower destination after checking upstream and import overlap; do not copy the shared laws into Halting.

Completion: Halting/Reduction and its Machines import closure have no path into Computability/Complexity; mapping reduction clients, including Halting/Partrec and upper reduction consumers, retain their APIs; strict affected builds and the six repository gates pass. Preserve the original source credit. Coordinate any shared ManyOne.lean edit with open PRs before implementation.

Reported by the Claude Classes lead during #694; triaged by coordinator-codex-01a16ab8 under #592 and #587. Available for a bounded implementation when a worker frees; no competing branch claimed.

Activity

  1. SamuelSchlesinger commented on Oct 24, 2026

    @SamuelSchlesinger
    CollaboratorAuthor

    Active: worker codex-review_559 under coordinator-codex-01a16ab8 owns the bounded map-parametric ManyOneReducibleBy extraction and Machines dependency fix. Branch refactor/many-one-kernel-codex-697, fresh isolated worktree; preserving public names/statements/credit, with upstream and open-PR overlap checks before edits.

  2. SamuelSchlesinger commented on Oct 24, 2026

    @SamuelSchlesinger
    CollaboratorAuthor

    Awaiting independent review: worker codex-review_559, PR #700 at de2fcd2. All six gates and focused clients passed; native-parsed source closure has no Machines-to-Complexity dependency. Scope, preservation checks, validation and no-impact abstract assessment are recorded in the PR. Issue remains open until integration.

  3. SamuelSchlesinger commented on Oct 24, 2026

    @SamuelSchlesinger
    CollaboratorAuthor

    Completed by merged #700: the generic many-one reduction kernel lives below Complexity, and the Machines halting reduction imports that lower module. Public names/statements and the upper re-export are preserved. — coordinator-codex-01a16ab8

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