feat: prove confluence for βη-reduction#456
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chenson2018 merged 39 commits intoleanprover:mainfrom Mar 26, 2026
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It's great to see that the definitions I added about strongly commuting relations are getting some use! Just some style notes, very similar to the previous PRs.
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| /-- Full βη-reduction. -/ | ||
| @[reduction_sys "βηᶠ"] | ||
| abbrev FullBetaEta : Term Var → Term Var → Prop := FullBeta ⊔ FullEta |
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I know in a previous PR I mentioned proving Xi r₁ ⊔ Xi r₂ = Xi (r₁ ⊔ r₂), but is this actually true generally? If so this could be written maybe slightly nicer as Xi (Beta ⊔ Eta), but I got stuck on an abstraction case.
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I agree that Xi (Beta ⊔ Eta) is more elegant, but the abstraction case requires some heavy renaming lemmas. To keep this PR focused, I think sticking with FullBeta ⊔ FullEta is best for now. I'd be happy to tackle that refactor in a future PR! Let me know if everything else looks good to merge.
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Sound good to me, I've sent to the merge queue. Great to see this complete! Please let me know if there's other work you're considering.
….lean Co-authored-by: Chris Henson <46805207+chenson2018@users.noreply.github.com>
….lean Co-authored-by: Chris Henson <46805207+chenson2018@users.noreply.github.com>
….lean Co-authored-by: Chris Henson <46805207+chenson2018@users.noreply.github.com>
….lean Co-authored-by: Chris Henson <46805207+chenson2018@users.noreply.github.com>
…aEtaConfluence.lean Co-authored-by: Chris Henson <46805207+chenson2018@users.noreply.github.com>
…aEtaConfluence.lean Co-authored-by: Chris Henson <46805207+chenson2018@users.noreply.github.com>
…aEtaConfluence.lean Co-authored-by: Chris Henson <46805207+chenson2018@users.noreply.github.com>
…aEtaConfluence.lean Co-authored-by: Chris Henson <46805207+chenson2018@users.noreply.github.com>
…aEtaConfluence.lean Co-authored-by: Chris Henson <46805207+chenson2018@users.noreply.github.com>
….lean Co-authored-by: Chris Henson <46805207+chenson2018@users.noreply.github.com>
….lean Co-authored-by: Chris Henson <46805207+chenson2018@users.noreply.github.com>
….lean Co-authored-by: Chris Henson <46805207+chenson2018@users.noreply.github.com>
….lean Co-authored-by: Chris Henson <46805207+chenson2018@users.noreply.github.com>
….lean Co-authored-by: Chris Henson <46805207+chenson2018@users.noreply.github.com>
….lean Co-authored-by: Chris Henson <46805207+chenson2018@users.noreply.github.com>
…tion (leanprover#329) This PR reaches a major milestone by proving that omega-regular languages are closed under complementation, using W. Thomas's presentation of R. Büchi's original proof. Most of the groundwork has been laid in previous PRs and the only nontrivial theorem proved in this PR is `buchiFamily_cover` in BuchiCongruence.lean, which uses the Ramsey theorem for infinite graphs.
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Mar 26, 2026
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Depends on leanprover#455. Adds $\eta$-reduction properties and proves confluence for $\beta \eta$-reduction. --------- Co-authored-by: Chris Henson <chrishenson.net@gmail.com> Co-authored-by: Chris Henson <46805207+chenson2018@users.noreply.github.com> Co-authored-by: Ching-Tsun Chou <chingtsun.chou@gmail.com>
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Depends on leanprover#455. Adds $\eta$-reduction properties and proves confluence for $\beta \eta$-reduction. --------- Co-authored-by: Chris Henson <chrishenson.net@gmail.com> Co-authored-by: Chris Henson <46805207+chenson2018@users.noreply.github.com> Co-authored-by: Ching-Tsun Chou <chingtsun.chou@gmail.com>
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Depends on #455. Adds$\eta$ -reduction properties and proves confluence for $\beta \eta$ -reduction.