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fix(coq/cno): drop cno_decidable axiom (Rice's theorem territory) #36

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Merged
hyperpolymath merged 1 commit into from
May 20, 2026
Merged

fix(coq/cno): drop cno_decidable axiom (Rice's theorem territory) #36

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16 changes: 14 additions & 2 deletions proofs/coq/common/CNO.v
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Expand Up @@ -572,9 +572,21 @@ Qed.
(** ** Decidability *)

(** Question: Is CNO verification decidable? *)
(** This is a major research question *)

Axiom cno_decidable : forall p, {is_CNO p} + {~ is_CNO p}.
(** Universal decidability of [is_CNO] over arbitrary programs was
previously asserted as an [Axiom] [cno_decidable]. That axiom has
been dropped (owner ruling, Stage 3 of standards#157): the
universal form 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. This is
essentially the Rice's-theorem situation: deciding a non-trivial
semantic property of an arbitrary program is undecidable, so the
universal-decidability claim is not constructively achievable in
Coq and any client that wants decidability must work in a
restricted syntactic fragment of [Program] (which the current
development does not formalise). No theorem in this file depended
on it. *)

(** ** Complexity *)

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