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hyperpolymath merged 1 commit into from
Jun 20, 2026
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docs(L10): point reversibility note at the landed echo-types bridge #56

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24 changes: 21 additions & 3 deletions docs/echo-residue-integration.adoc
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Expand Up @@ -248,12 +248,30 @@ The replay uses a *per-variable delta*: `reversible as <name>` captures the
before-image of only the fields its body mutates (a static scan of the body),
and `reverse <name>` writes just those back — so unrelated state, including
intervening `set`s by other handlers, survives the reversal. The proof-side
bridge lemma against echo-types remains the natural next step.
bridge lemma against echo-types has now landed — see the next section.

== Cross-repo bridge (echo-types)

`Type::Echo<T>` corresponds to echo-types' `Echo f y`, and 007's CNO layer
(`proofs/agda/CNO.agda`) already bridges to `echo-types/EchoCNOBridge`. A
direct Agda bridge from the 007 reversibility model to echo-types'
`EchoTotalCompletion` / `EchoLinear` is the natural place to discharge the
phase-2 proof obligations against the upstream library of record.
`EchoTotalCompletion` / `EchoLinear` discharges the phase-2 proof obligations
against the upstream library of record. It has *landed* as
`echo-types/proofs/agda/EchoReversibilityBridge.agda` (`--safe --without-K`,
zero postulates):

* `ReversibleCompletion` re-states the interface this model needs — arm a
residue (`hold`), take-it-for-reverse (`takeForReverse`), and the once-only
correctness that replay recovers the input (`reverse-recovers`);
* `echo-reversible` proves `Echo f` satisfies it (its `takeForReverse` is
`reverseLinear`'s witness extraction, the `Just`-branch of this model's
`takeForReverse : … → Maybe`);
* `reversibility-via-totality : Σ B (Echo f) ↔ A` is the slogan iso
("irreversible f + residue = reversible representation");
* `capability-can-be-dropped` / `no-recovery-once-dropped` pin the phase-2
"affine capability, linear consumption" discipline via `EchoLinear.weaken`
/ `no-section-weaken`.

Honest scope: this is the type-level totality + recovery + linear→affine
no-section content. 007's linear `(1 e : Echo f y)` quantity is not re-proved
in Agda — the full quantity-semantics port is the documented next slice.
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