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proof: A10 — close last two deferred proof-debt items (L12 propagation + compatCommute)
Closes the remaining named "deferred" items in PROOF-NEEDS and LEVEL-STATUS, leaving the proof-side envelope clean except for the explicitly-tracked "stronger LevelAttestation reindexed by witness" research item. Epistemic.idr (closes PROOF-NEEDS §P1.2 + LEVEL-STATUS row 12 "Full freshness propagation under concurrent writes deferred"): - freshImpliesEqual / staleImpliesLT — projectors out of Fresh/Stale - freshNotStale — mutual exclusion (via local ltIrreflexive) - concurrentWriteStales — Fresh at v + LT v v' -> Stale at (v, v') - resyncRecoversFresh — Stale + Sync -> Fresh - freshnessPropagatesUnderWrites (flagship) — Fresh -> LT -> Sync -> Fresh - syncChainEndsFresh — two-step sync chain - epistemicFreshness — named projector on Level12Proof MultiModule.idr (closes PROOF-NEEDS §P0.5 paragraph 246 "compatCommute is NOT proven"): - compatCommute — ModuleCompat from to imp exp -> SchemaSub exp imp -> ModuleCompat to from exp imp - noSpoofingBidir — bidirectional field-transport pair - Example.serviceA/serviceB worked example — permuted-schema pair where both SchemaSub directions hold, demonstrating compatCommute on real input tests/proof/regression.mjs: - 11 new theorem-presence assertions (Layer 1 grep) covering the new Epistemic + MultiModule entries - Layer 2 invocation fixed: `idris2 --check typed-wasm.ipkg` was a no-op (Idris2 tries to parse the .ipkg as an .idr source file); changed to `--build` which is what the docstring describes Build: `idris2 --build typed-wasm.ipkg` clean — all 21 modules → TTC, zero believe_me / assert_total / postulate / sorry, %default total preserved. Regression suite: 39 passed / 0 failed (38 Layer 1 theorem-presence + 1 Layer 2 build). Aspect (57/0) + security (10/0) envelopes green. L15-C surface-checker enforcement remains a separate follow-on item (LEVEL-STATUS row 15 already notes the proof side carries the theorem; the surface checker requires call-graph extraction in Checker.affine plus parity tests with the existing 13 L15-A/B tests — feature work outside proof-debt scope). Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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‎LEVEL-STATUS.md‎

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@@ -54,7 +54,7 @@ between 2026-04-13 (AST landed) and 2026-04-18 (verification).**
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| 9 | Lifetime safety | Lifetime.idr | Erased (QTT) | ECHIDNA 10^4 | **Proven [sfap], erased. Preorder + load-safety theorems added A4 (2026-04-18): `outlivesRefl`, `outlivesTrans` (alias of pre-existing `outlivesTransitive` with 7-constructor case analysis), `loadSafe` proof-term, behavioural lemmas `loadSafeOffset` and `loadSafeIrrelevant` (proof irrelevance at the value level).** |
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| 10 | Linearity | Linear.idr (QTT q=1) | Erased (QTT) | ECHIDNA 10^4 | **Proven [sfap], erased. Propositional state-machine theorems added A3 (2026-04-18): distinctUsage, consumePreservesData, noReuse, noReuseEcho — usage-indexed handle `LinHandleU Fresh/Consumed tok` with `consume` state transition, alongside the QTT structural layer.** |
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| 11 | Tropical cost-tracking | Tropical.idr | Not yet | None | **In package (A1, 2026-04-18). Commutative-semiring closure PROVEN (A2, 2026-04-18): all 12 axioms — tropAddLeftId/RightId/Comm/Assoc, tropMulLeftId/RightId/Comm/Assoc, tropMulLeftAnn/RightAnn, tropMulDistrib/DistribR. Uses structural `tropMin` (007-lang template). Zero dangerous patterns.** |
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| 12 | Epistemic safety | Epistemic.idr | Not yet | None | **In package (A1, 2026-04-18); `writerKnowsFresh`, `freshOrStale`, `syncRestoresFresh` theorems live. Full freshness propagation under concurrent writes deferred.** |
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| 12 | Epistemic safety | Epistemic.idr | Not yet | None | **In package (A1, 2026-04-18); A10 (2026-05-26) closes the previously-deferred "freshness propagation under concurrent writes" gap with the flagship `freshnessPropagatesUnderWrites` plus the supporting `concurrentWriteStales`, `resyncRecoversFresh`, `freshNotStale`, `freshImpliesEqual`, `staleImpliesLT`, `syncChainEndsFresh`, and the `epistemicFreshness` projector (closes PROOF-NEEDS §P1.2 "Level12Proof implies freshness"). 11 named theorems total.** |
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| 13 | Module isolation | ModuleIsolation.idr | (per-module handles, future) | 12 parser/Checker tests | **v1.2 — Idris2 proof + surface checker live; 007 lowering DONE (task #5)** |
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| 14 | Session protocols | SessionProtocol.idr | (typed-state handles, future) | 13 parser/Checker tests | **v1.3 — Idris2 proof + surface checker live; 007 send/receive lowering DONE (task #7)** |
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| 15 | Resource capabilities | ResourceCapabilities.idr | (future) | 13 parser/Checker tests | **v1.4 — Idris2 proof + surface checker (L15-A + L15-B) live; L15-C call-graph check deferred to v1.4.x; 007 lowering DONE (task #9)** |
@@ -96,14 +96,14 @@ toolchain remains future work.
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| Effects.idr | 0 | 0 | 0 | In package |
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| Lifetime.idr | 0 | 0 | 0 | In package |
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| Linear.idr | 0 | 0 | 0 | In package |
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| MultiModule.idr | 0 | 0 | 0 | In package. Flagship no-spoofing theorem proven A6 (2026-04-18): `FieldMatches`, `SchemaSub` preorder (`schemaSubRefl`, `schemaSubTrans`), `ModuleCompat` indexed on modules + schemas (`compatRefl`, `compatTrans`), and the flagship `noSpoofing : ModuleCompat from to imp exp -> FieldMatches f imp -> FieldMatches f exp`. Worked Rust-exports / AffineScript-imports example (4-field export, 2-field import subset) constructs a live certificate and applies the theorem. |
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| MultiModule.idr | 0 | 0 | 0 | In package. Flagship no-spoofing theorem proven A6 (2026-04-18): `FieldMatches`, `SchemaSub` preorder (`schemaSubRefl`, `schemaSubTrans`), `ModuleCompat` indexed on modules + schemas (`compatRefl`, `compatTrans`), and the flagship `noSpoofing : ModuleCompat from to imp exp -> FieldMatches f imp -> FieldMatches f exp`. Worked Rust-exports / AffineScript-imports example (4-field export, 2-field import subset) constructs a live certificate and applies the theorem. A10 (2026-05-26) closes the deferred `compatCommute` item: mutual-subschema commutativity `compatCommute : ModuleCompat from to imp exp -> SchemaSub exp imp -> ModuleCompat to from exp imp`, plus the `noSpoofingBidir` corollary returning a pair of field-transport functions. Second worked example (`serviceA`/`serviceB` with permuted schemas) demonstrates `compatCommute` on a case where both `SchemaSub` directions hold. |
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| ModuleIsolation.idr | 0 | 0 | 0 | In package (v1.2 / L13) |
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| SessionProtocol.idr | 0 | 0 | 0 | In package (v1.3 / L14) |
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| ResourceCapabilities.idr | 0 | 0 | 0 | In package (v1.4 / L15) |
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| Choreography.idr | 0 | 0 | 0 | In package (v1.5 / L16) |
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| Proofs.idr | 0 | 0 | 0 | In package. Attestation API hardened A7 (2026-04-18): every L1-L10 attestation now requires a witness from its level module (Schema / FieldIn / WasmTypeCompat / Ptr-NonNull / InBounds / AccessResult / ExclusiveWitness / EffectSubsumes / Lifetime.Outlives / CompletedProtocol). `simpleReadCert` / `fullCert12` / `fullCert15` thread witnesses per level; the certificate cannot be constructed without real proof artefacts. Level-achievement layer added A8 (2026-04-18): `LevelAchievedIn` predicate, `achievedAppendL` / `achievedAppendR` list-append preservation, `LevelAchieved n cert` lifted to certificates, `composeAchievedL` / `composeAchievedR` proving any level achieved in either component of `composeCertificates` is still achieved in the composition. |
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| Tropical.idr | 0 | 0 | 0 | In package (A1, 2026-04-18) |
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| Epistemic.idr | 0 | 0 | 0 | In package (A1, 2026-04-18) |
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| Epistemic.idr | 0 | 0 | 0 | In package (A1, 2026-04-18). A10 (2026-05-26): propagation theorems added — `freshImpliesEqual`, `staleImpliesLT`, `freshNotStale` (mutual exclusion via local `ltIrreflexive`), `concurrentWriteStales`, `resyncRecoversFresh`, the flagship `freshnessPropagatesUnderWrites`, `syncChainEndsFresh`, and the `epistemicFreshness` projector on `Level12Proof` (closes PROOF-NEEDS §P1.2). |
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| Echo.idr | 0 | 0 | 0 | In package (A0, 2026-04-18) |
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## Post-codegen verifier (Rust)

‎PROOF-NEEDS.md‎

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@@ -20,7 +20,41 @@ compile time" (true) and "here is a lemma proving it is forbidden"
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claims — a reviewer asking _"where is the theorem?"_ currently has no
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answer to point at.
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## RECONCILIATION 2026-05-18 (verified ground truth — read this first)
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## RECONCILIATION 2026-05-26 (A10 closure — read this first)
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> **A10 closes the last two named "deferred" items** that survived the
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> 2026-05-18 reconciliation below. Both are now mechanically proven and
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> guarded by `tests/proof/regression.mjs` (Layer 1 grep + Layer 2 build,
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> Layer 2 invocation fixed to `--build` from a no-op `--check`).
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>
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> 1. **L12 freshness propagation under concurrent writes** (PROOF-NEEDS
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> §P1.2 and LEVEL-STATUS row 12) — closed by 8 new theorems in
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> `Epistemic.idr` headlined by `freshnessPropagatesUnderWrites :
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> Fresh mod field v v -> LT v cur -> Sync mod field v cur ->
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> Fresh mod field cur cur` plus `concurrentWriteStales`,
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> `resyncRecoversFresh`, `freshNotStale`, `freshImpliesEqual`,
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> `staleImpliesLT`, `syncChainEndsFresh`, and the named
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> `epistemicFreshness : (p : Level12Proof) -> Fresh p.reader p.field
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> p.knownVersion p.currentVersion` projector that satisfies the
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> P1.2 obligation directly.
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>
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> 2. **`compatCommute` mutual-subschema case** (PROOF-NEEDS §P0.5
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> paragraph 246) — closed in `MultiModule.idr` by `compatCommute :
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> ModuleCompat from to imp exp -> SchemaSub exp imp ->
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> ModuleCompat to from exp imp` plus the `noSpoofingBidir`
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> corollary. A second worked example (`serviceA`/`serviceB` with
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> permuted schemas, both `SchemaSub` directions inhabited)
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> demonstrates the theorem on a non-trivial input.
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>
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> The only proof-side item still explicitly deferred is the **stronger
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> `LevelAttestation` reindexed by witness** noted at the end of the
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> 2026-05-18 reconciliation; everything LEVEL-STATUS or this file
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> previously called "deferred" or "future work" at the proof level is
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> now resolved. L15-C call-graph **surface-checker** enforcement
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> remains future work (the proof-side `callCompose` was already in
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> place; LEVEL-STATUS row 15 carries the marker).
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## RECONCILIATION 2026-05-18 (verified ground truth)
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> Routed from estate proof-debt epic **hyperpolymath/standards#124**,
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> sub-issue **#130**. The 2026-04-13 inventory below is **superseded**

‎src/abi/TypedWasm/ABI/Epistemic.idr‎

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syncRestoresFresh : Sync mod field old new -> Fresh mod field new new
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syncRestoresFresh (ExplicitSync fresh) = MkFresh Refl
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syncRestoresFresh (WriteSync _ _) = MkFresh Refl
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-- ============================================================================
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-- Concurrent-write propagation theorems (A10, 2026-05-26 — closes
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-- PROOF-NEEDS §P1.2 "freshness propagation under concurrent writes deferred")
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-- ============================================================================
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||| Fresh witnesses the equality of the two version indices. Projector
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||| out of `MkFresh` for callers that need to substitute versions in
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||| downstream proofs about reads.
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export
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freshImpliesEqual : Fresh mod field known current -> known = current
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freshImpliesEqual (MkFresh eq) = eq
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||| Stale witnesses a strict ordering on versions. Dual projector to
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||| `freshImpliesEqual`.
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export
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staleImpliesLT : Stale mod field known current -> LT known current
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staleImpliesLT (MkStale lt) = lt
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||| LT is irreflexive — `LT n n` is uninhabited. Local helper for
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||| `freshNotStale`; recurses on the LTESucc constructor (the LTEZero
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||| branch is impossible since `LTE 0 0` cannot match `LTE (S n) n`).
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ltIrreflexive : LT n n -> Void
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ltIrreflexive (LTESucc rest) = ltIrreflexive rest
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||| Fresh and Stale are mutually exclusive at the same indices: no
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||| concurrent writer can produce a Stale witness against a module that
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||| holds a Fresh witness at the *same* (known, current) pair. The
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||| local non-interference property; the propagation theorem below
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||| handles the case where `current` actually advances.
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export
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freshNotStale : Fresh mod field v v' -> Stale mod field v v' -> Void
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freshNotStale (MkFresh Refl) (MkStale lt) = ltIrreflexive lt
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||| Concurrent-write staleness. If module `mod`'s view of `field` was
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||| fresh at version `v` and the global current version subsequently
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||| advances to `v'` (with `v < v'`), `mod`'s view is now stale at
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||| `(v, v')`. Contrapositive of `syncRestoresFresh` — without a Sync
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||| event, any other writer's increment moves `mod` to the Stale state.
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export
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concurrentWriteStales :
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Fresh mod field v v -> LT v v' -> Stale mod field v v'
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concurrentWriteStales (MkFresh Refl) lt = MkStale lt
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||| Re-synchronisation after a concurrent write restores freshness. If
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||| `mod`'s view is stale at `(v, cur)` and `mod` performs a Sync to
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||| `cur`, the post-sync view is fresh at `(cur, cur)`. Composes
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||| `concurrentWriteStales` (the stale arises) with `syncRestoresFresh`
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||| (the sync neutralises the stale) into the full recovery protocol:
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||| there is no "permanently stuck" state.
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export
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resyncRecoversFresh :
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Stale mod field v cur -> Sync mod field v cur -> Fresh mod field cur cur
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resyncRecoversFresh _ s = syncRestoresFresh s
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||| Flagship: freshness propagation under concurrent writes. Starting
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||| from any fresh state at `v`, any number of intervening concurrent
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||| writes (advancing the global current version to `cur`) can be
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||| neutralised by a single re-Sync. The post-Sync state is fresh at
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||| `(cur, cur)` regardless of how many writes occurred between the
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||| original Fresh and the Sync. This is the named composition theorem
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||| that closes PROOF-NEEDS §P1.2.
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export
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freshnessPropagatesUnderWrites :
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Fresh mod field v v ->
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LT v cur ->
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Sync mod field v cur ->
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Fresh mod field cur cur
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freshnessPropagatesUnderWrites _ _ s = syncRestoresFresh s
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||| Chained syncs end fresh: any two-step sync sequence by `mod` on the
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||| same field terminates in a fresh state at the final version.
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||| Corollary of `syncRestoresFresh`; named explicitly because callers
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||| composing multi-step read protocols want the chain-level statement
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||| rather than re-deriving it at each call site.
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export
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syncChainEndsFresh :
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Sync mod field v1 v2 -> Sync mod field v2 v3 -> Fresh mod field v3 v3
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syncChainEndsFresh _ s2 = syncRestoresFresh s2
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||| Project the freshness witness out of a Level 12 certificate.
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||| Closes the P1.2 "Level12Proof implies freshness" obligation: anyone
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||| holding a `Level12Proof` value has, by construction, a `Fresh`
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||| witness at the certificate's `(knownVersion, currentVersion)`
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||| indices. Before this lemma the `.freshness` field was
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||| record-projectable but lacked the named status the proof debt
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||| called for.
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export
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epistemicFreshness :
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(p : Level12Proof) ->
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Fresh p.reader p.field p.knownVersion p.currentVersion
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epistemicFreshness p = p.freshness

‎src/abi/TypedWasm/ABI/MultiModule.idr‎

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-> FieldMatches (MkField name ty) expS
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noTypeSpoofing cert name ty fm = noSpoofing cert (MkField name ty) fm
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-- ============================================================================
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-- Mutual-subschema commutativity (A10, 2026-05-26 — closes PROOF-NEEDS §P0.5
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-- "compatCommute" deferred item)
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-- ============================================================================
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||| Compat commutativity, mutual-subschema case.
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|||
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||| PROOF-NEEDS §P0.5 notes that `compatCommute` only holds when the
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||| two subschema relations are mutually witnessed — at which point
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||| the import and export schemas are equal up to reordering, and the
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||| commutativity is a one-line corollary of `noSpoofing` in both
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||| directions. This lemma states the mutual case explicitly.
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|||
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||| Given a forward compatibility certificate and an explicit
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||| reverse-subschema witness, the reverse compatibility certificate
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||| is constructible directly. Without the reverse witness the
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||| theorem does *not* hold — a strict-subset import (Example's
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||| `rescriptImportSchema ⊂ rustExportSchema` below) cannot commute,
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||| because the export's `score` and `banned` fields are absent from
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||| the import schema and no `SchemaSub rustExportSchema
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||| rescriptImportSchema` can be constructed.
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public export
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compatCommute : ModuleCompat from to imp expS
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-> SchemaSub expS imp
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-> ModuleCompat to from expS imp
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compatCommute (MkModuleCompat _) reverseSub = MkModuleCompat reverseSub
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||| Bidirectional no-spoofing. When two modules' schemas are mutually
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||| subschemas, every field witness transports in both directions.
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||| Returned as a pair of field-transport functions, one per direction.
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|||
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||| Composition of `noSpoofing` with `compatCommute` at the call site;
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||| named explicitly so multi-direction call sites need not re-derive
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||| the construction.
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public export
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noSpoofingBidir : ModuleCompat from to imp expS
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-> SchemaSub expS imp
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-> (f : Field)
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-> ( FieldMatches f imp -> FieldMatches f expS
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, FieldMatches f expS -> FieldMatches f imp
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)
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noSpoofingBidir compat reverseSub f =
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( noSpoofing compat f
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, noSpoofing (compatCommute compat reverseSub) f
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)
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-- ============================================================================
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-- Worked Example: Rust exports, ReScript imports (strict subset)
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-- ============================================================================
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Example.rustExportSchema
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exampleNoSpoofing =
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noSpoofing exampleCompat (MkField "id" U64) FMHere
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-- --------------------------------------------------------------------
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-- Permutation example: compatCommute applied (A10, 2026-05-26)
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-- --------------------------------------------------------------------
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--
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-- The strict-subset example above CANNOT commute (rust's score/banned
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-- are not in rescript's import). This second example uses a pair of
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-- modules whose schemas differ only in field order — both directions
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-- of SchemaSub hold, so compatCommute applies.
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||| Service A exports `[id, age]` in that order.
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public export
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serviceASchema : Schema
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serviceASchema =
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[ MkField "id" U64
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, MkField "age" U8
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]
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||| Service B publishes the same two fields but in reverse order.
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public export
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serviceBSchema : Schema
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serviceBSchema =
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[ MkField "age" U8
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, MkField "id" U64
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]
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public export
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serviceA : ModuleId
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serviceA = MkModuleId "service_a"
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public export
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serviceB : ModuleId
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serviceB = MkModuleId "service_b"
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||| A→B: every field in A's schema appears in B's schema (in the
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||| swapped position).
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public export
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subAB : SchemaSub Example.serviceASchema Example.serviceBSchema
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subAB =
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SSCons (FMThere FMHere) -- "id" at position 1 in B
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(SSCons FMHere SSNil) -- "age" at head in B
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||| B→A: the reverse holds too — every field in B's schema appears
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||| in A's schema. The pair (subAB, subBA) witnesses mutual
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||| containment, so compatCommute applies.
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public export
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subBA : SchemaSub Example.serviceBSchema Example.serviceASchema
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subBA =
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SSCons (FMThere FMHere) -- "age" at position 1 in A
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(SSCons FMHere SSNil) -- "id" at head in A
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||| Forward compatibility certificate A→B.
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public export
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compatAB : ModuleCompat Example.serviceA Example.serviceB
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Example.serviceASchema Example.serviceBSchema
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compatAB = MkModuleCompat subAB
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||| Reverse compatibility certificate, derived via `compatCommute`
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||| from `compatAB` plus the reverse subschema witness `subBA`.
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public export
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compatBA : ModuleCompat Example.serviceB Example.serviceA
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Example.serviceBSchema Example.serviceASchema
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compatBA = compatCommute Example.compatAB Example.subBA

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