fix(coq/cno): drop cno_decidable axiom (Rice's theorem territory)#36
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Owner-ruled drop. Universal decidability of is_CNO over arbitrary programs asks for a constructive decision procedure over an unbounded state space (Memory, Registers, IOState all unbounded; is_CNO's universally-quantified clauses range over all states). This is essentially the Rice's theorem situation: deciding a non-trivial semantic property of an arbitrary program is undecidable. Net axiom count in proofs/coq/common/CNO.v: 3 -> 2 with this commit. Refs hyperpolymath/standards#124, scoping doc standards#157 (Stage 3). Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
This was referenced May 20, 2026
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Salvaged from #25 — the only commit on that branch with content not already on
mainin some form.What
Drops
Axiom cno_decidable : forall p, {is_CNO p} + {~ is_CNO p}fromproofs/coq/common/CNO.v(owner ruling, Stage 3 of standards#157).Replaces the axiom line with a doc comment explaining why: universal decidability of `is_CNO` over arbitrary programs asks for a constructive decision procedure over an unbounded state space (`Memory : nat -> nat`, unbounded registers, unbounded I/O traces), and `is_CNO`'s universally-quantified clauses range over all of them — Rice's-theorem territory, not constructively achievable.
Verification
coqc -R common CNO common/CNO.v— builds clean locally on Coq 8.18.0.grep -rn cno_decidable proofs/— only the new doc-comment reference remains; no theorem in the corpus depended on it.Provenance
Cherry-pick of
8b78d27from #25. The other commit on #25 (89deef7, eval_respects_state_eq via existential reformulation) is not salvaged here becausemainalready discharges those two axioms a different way (#2699ec572, deletion + downstream refactor) — the existential approach is competing, not additive.Closes #25 once merged; #33 and #35 closed as superseded separately.
Refs standards#124, standards#157.
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Co-Authored-By: Claude Opus 4.7 (1M context) noreply@anthropic.com