fix(proofs): repair bit-rotted WokeLang.v (Coq) + meticulous audit + CI gate#82
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The Coq formalization `docs/proofs/verification/WokeLang.v` claimed type safety
but did NOT compile under Coq 8.18 — the same "verified but unchecked" hazard
the Lean file had, because no CI ever ran the prover.
Rot fix:
- `value_eq_dec` used `decide equality; ... apply list_eq_dec; assumption`, but
the recursive IH for the nested `list value` is no longer in scope under 8.18
("No such assumption"). Fixed with an explicit fixpoint
(`fix IH 1; ...; apply list_eq_dec; exact IH`). This was the ONLY rot; the
rest of the file (incl. the large preservation proof) then compiled.
Meticulous soundness check (Print Assumptions): NO Admitted/admit/Axiom; the
headline theorems (progress, preservation, type_safety) depend only on
`ClassicalDedekindReals.sig_forall_dec` + `functional_extensionality`, both
pulled in unavoidably by modelling floats as `R` — exactly as the header claims.
Also fixed a real latent bug + added the missing gate:
- `cap_subsumes` catch-all was `TODO: false`, so subsumption was not even
reflexive. Fixed to fall back to decidable equality (`capability_eq_dec`,
kept Opaque) and proved `cap_subsumes_refl` (axiom-free). `cap_subsumes_trans`
documented as a follow-up (needs explicit per-kind analysis).
- `.github/workflows/coq-proofs.yml` — installs Coq 8.18 (pinned ubuntu-24.04)
and runs `coqc WokeLang.v` on every push, so it cannot silently rot again.
- AUDIT.md gains a full Coq section (rot, axioms, coverage vs Lean — Coq is
AHEAD on arrays/well-founded progress, BEHIND on binops — and the
brute-force-preservation quality follow-up). .gitignore for Coq artifacts.
https://claude.ai/code/session_013wg3Mtq2QFhYi4XVw1Z6z7
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Summary
The Coq formalization
docs/proofs/verification/WokeLang.vclaimed type safety but did not compile under Coq 8.18 — the same "verified-but-never-checked" hazard the Lean file had, because no CI ever ran the prover. This sorts out the rot, audits the file meticulously, fixes a latent bug, and adds the missing gate.The rot (fixed)
Exactly one breakage:
value_eq_decuseddecide equality; … apply list_eq_dec; assumption, but the recursive IH for the nestedlist valueis no longer in scope under 8.18 ("No such assumption"). Fixed with an explicit fixpoint (fix IH 1; …; apply list_eq_dec; exact IH). Everything else — including the largepreservationproof — then compiled clean.Meticulous soundness check
Print Assumptionsonprogress/preservation/type_safety: noAdmitted/admit/Axiom; they depend only onClassicalDedekindReals.sig_forall_dec+functional_extensionality, both pulled in unavoidably by modelling floats as real numbers (R) — exactly as the file header claims.cap_subsumes_reflis even axiom-free ("Closed under the global context").Latent bug fixed
cap_subsumes's catch-all wasTODO: false, so subsumption wasn't even reflexive (cap_subsumes CapProcess CapProcess = false). Fixed to fall back to decidable equality (capability_eq_dec, keptOpaque), and provedcap_subsumes_refl.cap_subsumes_transis documented as a follow-up (needs explicit per-kind analysis; the 6×6×6 automation is brittle).Durability + audit
.github/workflows/coq-proofs.yml— installs Coq 8.18 (pinnedubuntu-24.04, since the file is version-sensitive) and runscoqc WokeLang.von every push. Can't silently rot again.AUDIT.mdgains a full Coq section: rot, axiom honesty, and coverage vs the Lean file — Coq is ahead on arrays (fullT_Array+ array stepping + well-foundedprogressonexpr_size, the exact Tier-1 item still open in Lean) and behind on binops (onlyadd/eq/and). Also flags the brute-forcepreservation("Nuclear option") as a clean-rewrite follow-up..gitignorefor Coq build artifacts.Verification
https://claude.ai/code/session_013wg3Mtq2QFhYi4XVw1Z6z7
Generated by Claude Code