feat: make Bool.xor a standalone definition#13995
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Previously `Bool.xor` was an `abbrev` for `bne`. Make it a semireducible def with its own simp lemma set (early lemmas in SimpLemmas, the rest in Bool). Move the `^^` notation and definition to Prelude, and fix the `or` recommended_spelling target. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Use the `xor_*` lemmas (`xor_false`, `xor_left_inj`, `xor_assoc`, …) where proofs previously relied on `xor` being defeq to `bne`. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
xor is now opaque; dedicated grind propagators will replace the unfold. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Make `Bool.xor` `@[inline]` and define it with a direct `match`, trim its docstring, and drop the now-redundant re-exports. Round out the xor/bne simp normal forms: `@[simp]` on `xor_eq_false_iff` and new `eq_not_self_*`/`eq_not_*_self` lemmas, with matching `bool_simp` coverage. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Add `propagateBoolXorUp`/`propagateBoolXorDown` so `grind` reasons about `Bool.xor` directly on the Bool equivalence graph, rather than relying on it being unfolded to `bne`. Propagates truth values from either argument, and the `a ≡ b ⟹ false` / `a ≠ b ⟹ true` equivalence facts in both directions, with supporting lemmas in `Init.Grind.Lemmas`. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
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Opening this as a draft for visibility alongside RFC #13994. I'd like to hold it for review until the RFC has had feedback, since the design decision — in particular the change to the |
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This PR makes
Bool.xora standalone definition instead of a reducible abbreviation forbne, so thatsimpandgrindtreat exclusive-or as an operation in its own right rather than unfolding it away. It adds dedicatedxorsimplemmas andgrindpropagators, giving predictable xor-shaped normal forms and lettinggrindclose goals involving^^that previously needed manual rewriting throughbne.Bool.xoris now defined by a branchingmatchon its first argument, with the definition and^^notation living inInit.PreludeandInit.Notation. Thexorlemmas inInit.Data.Boolare restated directly in terms ofxorrather than asbnewrappers; newsimpnormal-form lemmas andStd.Commutative,Std.Associative, andStd.LawfulIdentityinstances are added; andgrindpropagators forBool.xorare registered, with supporting lemmas inInit.Grind.Lemmas. TheBitVecbitblasting andStd.SatAIG code is adapted to the new normal forms.This implements RFC #13994.
AI disclosure: the
grindpropagators (propagateBoolXorUp/propagateBoolXorDowninLean.Meta.Tactic.Grind.Propagate) and their supporting lemmas inInit.Grind.Lemmaswere authored by Claude (Claude Code) and reviewed by me; theBool.xordefinition change and thesimplemma set are my own work.