The guard checker in Rocq Prover treats a parameter of a nested mutual fixpoint as uniform without examining calls between the different bodies of that fixpoint. find_uniform_parameters in kernel/inductive.ml inspects only self-recursive calls, so when no body calls itself the function concludes that every parameter is uniform. A parameter that grows through a cross-call from one body to another therefore keeps the subterm specification it inherited from the enclosing fixpoint, and a recursive call guarded by that specification is accepted although the argument is not structurally smaller. A non-terminating definition is admitted as structurally decreasing, which yields a term whose value equals its own successor and so a proof of False, from which any proposition follows. The proof requires no axioms, plugins or unsafe flags and Print Assumptions reports it as closed under the global context. Introduced in Coq 8.20 and fixed in Rocq 9.2.0.

Affected: rocq-prover rocq

1. Summary ========== A soundness bug in the Rocq (formerly Coq) kernel's guard checker allows construction of a checked proof of False — and by extension, any proposition, including 0 = 1 — without axioms, tactics, plugins, or unsafe flags. Print Assumptions reports the proof as closed under the global context. The guard checker treats all parameters of a nested mutual fixpoint as uniform without examining cross-calls between the fixpoint's bodies. A parameter that grows through a cross-call retains an incorrect subterm specification, and a recursive call on a non-structurally-decreasing argument is accepted. This admits a non-terminating definition from which False follows. 2. Context ========== Rocq (formerly Coq) is the reference implementation of the Calculus of Inductive Constructions and one of the most widely deployed proof assistants. Its kernel is the trusted core that checks every proof before acceptance. A soundness bug in the guard checker — the component that enforces termination of recursive definitions — undermines the guarantees of any system built on Rocq-checked proofs. Formally verified systems certified under Common Criteria (ISO 15408) or DO-178C (airborne software) derive their assurance from the correctness of the proof checker. A kernel-level bypass invalidates that assurance chain. 3. Impact ========= - Formally verified compilers (CompCert) - Verified OS kernels (CertiKOS) - Separation logic frameworks (Iris) - Mathematical libraries (MathComp) - P…

The guard checker in Rocq Prover treats a parameter of a nested mutual fixpoint as uniform without examining calls between the different bodies of that fixpoint. find_uniform_parameters in kernel/inductive.ml inspects only self-recursive calls, so when no body calls itself the function concludes that every parameter is uniform. A parameter that grows through a cross-call from one body to another therefore keeps the subterm specification it inherited from the enclosing fixpoint, and a recursive call guarded by that specification is accepted although the argument is not structurally smaller. A non-terminating definition is admitted as structurally decreasing, which yields a term whose value equals its own successor and so a proof of False, from which any proposition follows. The proof requires no axioms, plugins or unsafe flags and Print Assumptions reports it as closed under the global context. Introduced in Coq 8.20 and fixed in Rocq 9.2.0.