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ABI Layer 5: end-to-end soundness capstone certificate (#38)
* abi: prove OneForOne restart invariant (Layer 2 semantic proof) Add Otpiser.ABI.Semantics: a faithful Idris2 model of a one-for-one OTP supervisor (children keyed by id, each Running/Failed) and a restart step, with machine-checked proofs of the headline fault-tolerance invariant: - restartPreservesChildSet: restarting any child leaves the ordered set of supervised child ids unchanged (real propositional equality). - restartLeavesOthersUntouched: every sibling whose id differs from the target survives the restart byte-for-byte identical (Elem soundness). - restartHeadRuns / RestartedRunning: the targeted child is set Running. Positive controls exhibit concrete witnesses over a 3-worker supervisor; the negative control (negativeSiblingNotReset) refutes, by machine, the OneForAll-style claim that a failed sibling is reset — establishing the property is non-vacuous. No believe_me / postulate / assert_total. Registered in otpiser-abi.ipkg; ABI builds clean with zero warnings. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01A6PSzJWpRxtzGDjUCEh7Mx * abi: add Layer-3 rest-for-one invariants (idempotence + prefix-untouched) Add Otpiser.ABI.Invariants, a second machine-checked theorem distinct from and deeper than the Layer-2 one-for-one flagship. Reuses the Semantics model (Child/ChildStatus/Supervisor) and reasons about the rest_for_one transition: T1 IDEMPOTENCE (algebraic law): restForOne target . restForOne target = restForOne target -- a genuine fixpoint, proven via a triggered-branch lemma; not a restatement of "siblings untouched". T2 child-id-set preservation across the rest-for-one transition. T3 prefix-untouched: children strictly before the target survive identically (the directional core of rest-for-one), via a BeforeTarget certificate. T4 sound+complete Dec (decIsTargetHead) + certifier. Five positive controls (concrete witnesses incl. Refl-checked transition shape and idempotence) and three negative/non-vacuity controls (Not-Elem refutation, decision refutation, not-the-identity). No believe_me/postulate/assert_total; %default total; SPDX MPL-2.0. Registered last in otpiser-abi.ipkg. Clean build (0 warnings); adversarial false-equality check rejected. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01A6PSzJWpRxtzGDjUCEh7Mx * Add Layer 4 FfiSeam proof sealing the ABI<->FFI seam Prove the FFI result-code/enum encoding is sound: distinct ABI outcomes never collide on the C wire (injectivity) and the wire integer faithfully round-trips back to the ABI value (lossless decode). - intToResult decoder + resultRoundTrip (Refl per constructor) - resultToIntInjective derived from the round-trip (justInjective + cong) - same treatment for SupervisorStrategy (reuses Types.strategyRoundTrip) and ChildRestartType (new decoder + round-trip) - positive controls (concrete decodes = Refl) and negative/non-vacuity controls (distinct codes have distinct wire ints, machine-checked) Genuine total proofs: no believe_me/postulate/assert_total/etc. %default total; zero build warnings. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01A6PSzJWpRxtzGDjUCEh7Mx * Add Layer-5 capstone: end-to-end ABI soundness certificate Assemble the existing per-layer proofs into one inhabited value `abiContractDischarged : ABISound`, tying manifest semantics -> ABI proofs (flagship one-for-one + rest-for-one idempotence) -> FFI seam injectivity into a single end-to-end soundness statement. Fields reuse only already-exported witnesses/theorems: - Layer 2 (Semantics): positiveTargetRunning, positiveSiblingUntouched - Layer 3 (Invariants): restForOneIdempotent - Layer 4 (FfiSeam): resultToIntInjective The value typechecks iff every prior layer is sound. An adversarial false certificate (bogus sibling witness) is rejected by the type checker, confirming non-vacuity. No believe_me/postulate/assert_total. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01A6PSzJWpRxtzGDjUCEh7Mx --------- Signed-off-by: Jonathan D.A. Jewell <6759885+hyperpolymath@users.noreply.github.com> Co-authored-by: Claude <noreply@anthropic.com>
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‎src/interface/abi/Otpiser/ABI/Capstone.idr‎

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-- SPDX-License-Identifier: MPL-2.0
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-- Copyright (c) 2026 Jonathan D.A. Jewell (hyperpolymath) <j.d.a.jewell@open.ac.uk>
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--
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||| Layer 5 — the CAPSTONE: a single end-to-end ABI soundness certificate.
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|||
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||| Every prior proof layer of the Otpiser ABI is discharged independently:
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|||
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||| * Layer 2 (`Otpiser.ABI.Semantics`) — the FLAGSHIP one-for-one restart
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||| property: restarting a single failed child sets exactly that child to
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||| Running and leaves siblings byte-for-byte untouched, with the child-id
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||| set preserved.
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||| * Layer 3 (`Otpiser.ABI.Invariants`) — a DEEPER, distinct invariant: the
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||| `rest_for_one` transition is IDEMPOTENT (an algebraic fixpoint law) and
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||| freezes the untriggered prefix.
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||| * Layer 4 (`Otpiser.ABI.FfiSeam`) — the FFI SEAM is sound: the C-wire
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||| result-code encoder is INJECTIVE, so distinct ABI outcomes never collide.
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|||
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||| This module ties them into ONE inhabited value. `abiContractDischarged`
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||| assembles, in a single record, the actual exported witnesses of each layer:
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||| the manifest's domain semantics (flagship + deeper invariant) and the
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||| FFI-seam soundness that carries those outcomes across the language boundary.
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||| If ANY prior layer were unsound — a false positive control, a broken
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||| idempotence law, or a colliding wire encoder — this value would FAIL to
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||| typecheck. Its mere existence is the end-to-end soundness statement:
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|||
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||| manifest -> ABI proofs (flagship + invariant) -> FFI seam
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|||
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||| is discharged together, as one contract.
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|||
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||| Strict genuine composition: every field is built ONLY from already-exported
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||| witnesses/theorems of the layers above. No believe_me / idris_crash /
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||| assert_total / postulate / sorry / %hint hacks anywhere.
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module Otpiser.ABI.Capstone
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import Otpiser.ABI.Types
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import Otpiser.ABI.Semantics
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import Otpiser.ABI.Invariants
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import Otpiser.ABI.FfiSeam
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import Data.List.Elem
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%default total
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--------------------------------------------------------------------------------
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-- The capstone certificate type
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--------------------------------------------------------------------------------
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||| `ABISound` is inhabited exactly when the full Otpiser ABI contract holds.
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||| Each field is a key proven fact from a distinct prior layer; the record
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||| therefore witnesses that all layers are simultaneously sound.
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public export
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record ABISound where
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constructor MkABISound
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||| LAYER 2 (flagship, positive control): under a one-for-one restart of the
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||| failed child "db", the targeted child is now Running in the result list.
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||| Reuses `Otpiser.ABI.Semantics.positiveTargetRunning`.
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flagshipTargetRunning :
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Elem (MkChild "db" Running)
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(restartIn "db"
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[MkChild "db" Failed, MkChild "cache" Running, MkChild "api" Running])
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||| LAYER 2 (flagship, sibling independence): the sibling "cache" survives the
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||| one-for-one restart of "db" identical and untouched.
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||| Reuses `Otpiser.ABI.Semantics.positiveSiblingUntouched`.
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flagshipSiblingUntouched :
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Elem (MkChild "cache" Running)
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(restartIn "db"
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[MkChild "db" Failed, MkChild "cache" Running, MkChild "api" Running])
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||| LAYER 3 (deeper invariant): the rest-for-one transition is IDEMPOTENT on
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||| any supervisor — the algebraic fixpoint law.
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||| Reuses `Otpiser.ABI.Invariants.restForOneIdempotent`.
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restForOneIsIdempotent :
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(target : String) -> (sup : Supervisor) ->
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restForOne target (restForOne target sup) = restForOne target sup
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||| LAYER 4 (FFI seam): the C-wire result-code encoder is INJECTIVE, so
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||| distinct ABI outcomes never collide on the boundary.
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||| Reuses `Otpiser.ABI.FfiSeam.resultToIntInjective`.
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ffiSeamInjective :
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(a, b : Result) -> resultToInt a = resultToInt b -> a = b
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--------------------------------------------------------------------------------
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-- The capstone value: every prior proof, assembled into one certificate
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--------------------------------------------------------------------------------
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||| THE CAPSTONE. A single inhabited value of `ABISound`, constructed entirely
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||| from the existing exported witnesses/theorems of Layers 2, 3 and 4. This is
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||| the end-to-end discharge of the Otpiser ABI contract: manifest semantics
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||| (flagship one-for-one + deeper rest-for-one idempotence) carried soundly
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||| across the FFI seam. It typechecks iff every component layer is sound.
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public export
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abiContractDischarged : ABISound
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abiContractDischarged = MkABISound
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positiveTargetRunning -- Layer 2 flagship: targeted child Running
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positiveSiblingUntouched -- Layer 2 flagship: sibling untouched
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restForOneIdempotent -- Layer 3 deeper invariant: idempotence law
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resultToIntInjective -- Layer 4 FFI seam: wire-encoder injectivity

‎src/interface/abi/otpiser-abi.ipkg‎

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, Otpiser.ABI.Semantics
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, Otpiser.ABI.Invariants
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, Otpiser.ABI.FfiSeam
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, Otpiser.ABI.Capstone

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