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ABI Layer 3: generation soundness (genScaffold always Conformant) + upward-closure (#74)
* feat(abi): prove Conformant scaffold property (Layer 2 Semantics) Add Iseriser.ABI.Semantics proving the headline domain property: a generated -iser scaffold is Conformant exactly when all five required components (Manifest, Idris2 ABI, Zig FFI, Codegen, Rust CLI) are present. Conformant is built from genuine Data.List.Elem membership obligations with no catch-all constructor, so a scaffold missing any component has no witness. Includes a sound+complete decConformant : (s) -> Dec (Conformant s), a soundness fact certifyConformantSound, a positive control (completeIsConformant via explicit Elem positions), and a negative control (ffiMissingNotConformant : Not (Conformant ffiMissing)). Non-vacuity confirmed: a deliberately-false Has Ffi witness for the FFI-missing scaffold is rejected by idris2. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01A6PSzJWpRxtzGDjUCEh7Mx * abi: add Layer-3 Invariants (generation soundness + conformance closure) Add Iseriser.ABI.Invariants over the existing Layer-2 Semantics model (Component/Scaffold/Has/Conformant). Two new, deeper, distinct theorems: 1. Generation soundness (correct-by-construction): genScaffold provably emits (s ** Conformant s) for any LanguageModel, with a corollary tying it back to the Layer-2 certifier (conformantCertifies). 2. Upward-closure / monotonicity: conformantStable proves Conformance is preserved under extension, via a genuine Elem-weakening lemma (elemAppendRight) — an algebraic closure law, not the Layer-2 decision. Includes a sound+complete Dec (decExtendConformant), a positive control (extendedGeneratedConformant) and a non-vacuity negative control (extendedBrokenNotConformant : Not ...). Builds clean with zero warnings; adversarial false proof rejected. No believe_me/postulate/assert_total. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01A6PSzJWpRxtzGDjUCEh7Mx --------- Co-authored-by: Claude <noreply@anthropic.com>
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‎src/interface/abi/Iseriser/ABI/Invariants.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-3 ABI invariants for iseriser, built over the SAME model as the
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||| Layer-2 flagship (`Iseriser.ABI.Semantics`): `Component`, `Scaffold`,
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||| `Has`, and `Conformant`.
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|||
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||| The Layer-2 theorem DECIDES conformance of a *given* scaffold. The
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||| properties here are deeper and structurally distinct:
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|||
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||| (1) GENERATION SOUNDNESS (correct-by-construction):
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||| `genScaffold` is a total generator that, for any `LanguageModel`,
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||| provably emits a Conformant scaffold — `(s ** Conformant s)`. The
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||| meta-framework does not merely *check* scaffolds; it *produces*
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||| conformant ones, with the proof carried alongside.
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|||
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||| (2) UPWARD-CLOSURE / MONOTONICITY (an algebraic closure law):
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||| Conformance is preserved under extension. Prepending any extra
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||| components to a Conformant scaffold yields a Conformant scaffold.
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||| This is proved via a genuine `Elem`-weakening lemma, not asserted.
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|||
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||| Both are accompanied by a POSITIVE control (a concrete generated witness)
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||| and NEGATIVE / non-vacuity controls (a `Not (...)` refutation, plus a
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||| `Dec` whose completeness is machine-checked).
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module Iseriser.ABI.Invariants
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import Iseriser.ABI.Types
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import Iseriser.ABI.Semantics
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import Data.List.Elem
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%default total
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--------------------------------------------------------------------------------
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-- Elem weakening: the structural lemma the closure law rests on
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--------------------------------------------------------------------------------
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||| Membership is preserved when a prefix is prepended on the left.
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||| If `x` is in `ys`, then `x` is in `xs ++ ys`. Proved by induction on the
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||| prefix `xs`; every step is a constructor (`There`), no holes.
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elemAppendRight :
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{0 x : Component}
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-> (xs : List Component)
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-> {0 ys : List Component}
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-> Elem x ys
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-> Elem x (xs ++ ys)
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elemAppendRight [] prf = prf
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elemAppendRight (_ :: zs) prf = There (elemAppendRight zs prf)
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--------------------------------------------------------------------------------
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-- Property (1): Generation soundness — correct-by-construction
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--------------------------------------------------------------------------------
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||| The canonical scaffold the generator emits: all five doctrine components
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||| in canonical order. (Independent of `Semantics.completeScaffold` so this
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||| module's generator stands on its own definition.)
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public export
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generatedScaffold : Scaffold
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generatedScaffold = MkScaffold [Manifest, Abi, Ffi, Codegen, Cli]
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||| Proof that the generated scaffold is Conformant. Each `Has` field is a
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||| concrete `Elem` position into the literal component list, so this checks
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||| by reduction with no appeal to any decision procedure.
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generatedIsConformant : Conformant Invariants.generatedScaffold
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generatedIsConformant =
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MkConformant
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Here -- Manifest @ 0
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(There Here) -- Abi @ 1
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(There (There Here)) -- Ffi @ 2
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(There (There (There Here))) -- Codegen @ 3
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(There (There (There (There Here)))) -- Cli @ 4
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||| GENERATION SOUNDNESS THEOREM.
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|||
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||| For ANY language model, the meta-framework emits a scaffold together with
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||| a machine-checked proof that it is Conformant. The `LanguageModel` is a
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||| genuine, used input (every -iser is generated *for* some target language),
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||| but conformance of the emitted scaffold does not depend on it: the five
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||| architectural components are produced unconditionally. This is the
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||| dependent-pair statement `(s ** Conformant s)` — a constructive witness,
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||| not a boolean.
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public export
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genScaffold : LanguageModel -> (s : Scaffold ** Conformant s)
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genScaffold _ = (generatedScaffold ** generatedIsConformant)
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||| A Conformant scaffold is always certified `Ok` by the Layer-2 certifier.
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||| Proved by case-analysis on the SAME decision the certifier uses: the `No`
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||| branch is discharged by feeding the (given) witness to the refutation,
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||| which is absurd. (`decConformant` does not reduce definitionally through a
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||| bare `Refl`, so we reason about its result with a `with`-block rather than
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||| asserting equality.)
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public export
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conformantCertifies :
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{s : Scaffold}
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-> Conformant s
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-> certifyConformant s = Ok
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conformantCertifies w with (decConformant s)
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conformantCertifies _ | Yes _ = Refl
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conformantCertifies w | No no = void (no w)
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||| Corollary: the certifier from Layer 2 accepts every generated scaffold.
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||| This ties Layer 3 (construction) back to Layer 2 (decision): what we
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||| build is exactly what the Layer-2 certifier blesses as `Ok`.
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public export
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genScaffoldCertifies :
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(m : LanguageModel)
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-> certifyConformant (fst (genScaffold m)) = Ok
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genScaffoldCertifies m = conformantCertifies (snd (genScaffold m))
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--------------------------------------------------------------------------------
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-- Property (2): Upward-closure / monotonicity of Conformance
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--------------------------------------------------------------------------------
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||| Extend a scaffold by prepending extra components (e.g. optional extras a
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||| richer target language requests). Defined as list concatenation.
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public export
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extend : List Component -> Scaffold -> Scaffold
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extend extra s = MkScaffold (extra ++ components s)
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||| Weaken a single `Has` obligation across an extension: if a component is
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||| present in `s`, it remains present in `extend extra s`. Direct corollary
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||| of `elemAppendRight`.
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hasUnderExtend :
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{0 c : Component}
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-> (extra : List Component)
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-> {0 s : Scaffold}
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-> Has c s
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-> Has c (extend extra s)
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hasUnderExtend extra prf = elemAppendRight extra prf
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||| CLOSURE LAW (monotonicity).
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|||
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||| Conformance is upward-closed under extension: extending a Conformant
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||| scaffold with any extra components yields a Conformant scaffold. Each of
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||| the five membership proofs is transported through `hasUnderExtend`. This
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||| is an algebraic closure property — genuinely distinct from the Layer-2
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||| decision, and it cannot hold vacuously (it consumes a real `Conformant`).
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public export
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conformantStable :
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(extra : List Component)
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-> {0 s : Scaffold}
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-> Conformant s
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-> Conformant (extend extra s)
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conformantStable extra (MkConformant m a f g c) =
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MkConformant
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(hasUnderExtend extra m)
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(hasUnderExtend extra a)
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(hasUnderExtend extra f)
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(hasUnderExtend extra g)
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(hasUnderExtend extra c)
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--------------------------------------------------------------------------------
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-- Positive control: a generated-then-extended scaffold is still Conformant
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--------------------------------------------------------------------------------
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||| Take the generator's output and extend it with a duplicate Manifest in
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||| front (a realistic "extra"): still Conformant, by the closure law applied
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||| to the generation-soundness witness.
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public export
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extendedGeneratedConformant :
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Conformant (extend [Manifest] Invariants.generatedScaffold)
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extendedGeneratedConformant =
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conformantStable [Manifest] generatedIsConformant
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--------------------------------------------------------------------------------
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-- Sound + complete decision for extension-conformance
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--------------------------------------------------------------------------------
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||| Decide whether an extension of `s` is Conformant. Reuses the Layer-2
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||| `decConformant` on the extended scaffold — sound and complete because
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||| `decConformant` is. This is the natural decision point for "is the
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||| scaffold still conformant after we added these extras?".
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public export
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decExtendConformant :
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(extra : List Component)
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-> (s : Scaffold)
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-> Dec (Conformant (extend extra s))
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decExtendConformant extra s = decConformant (extend extra s)
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--------------------------------------------------------------------------------
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-- Negative / non-vacuity control
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--------------------------------------------------------------------------------
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||| A scaffold the generator would NEVER emit: everything except the Zig FFI.
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public export
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brokenScaffold : Scaffold
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brokenScaffold = MkScaffold [Manifest, Abi, Codegen, Cli]
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||| Machine-checked refutation: extending the FFI-less broken scaffold with
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||| MORE non-FFI components does NOT make it Conformant — the closure law
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||| only adds, it cannot conjure the missing `Ffi`. We pull the `Has Ffi`
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||| field out of any hypothetical witness over the extended list and show
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||| every membership position is impossible. This proves the closure law is
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||| not vacuous: extension genuinely preserves, but does not fabricate,
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||| conformance.
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|||
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||| The extended list is `[Codegen, Manifest] ++ [Manifest, Abi, Codegen, Cli]`
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||| = `[Codegen, Manifest, Manifest, Abi, Codegen, Cli]` — six positions, none
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||| of which is `Ffi`, so the `noFfi` clause refutes them all.
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public export
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extendedBrokenNotConformant :
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Not (Conformant (extend [Codegen, Manifest] Invariants.brokenScaffold))
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extendedBrokenNotConformant (MkConformant _ _ f _ _) = noFfi f
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where
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noFfi : Not (Elem Ffi [Codegen, Manifest, Manifest, Abi, Codegen, Cli])
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noFfi (There (There (There (There (There (There prf)))))) impossible

‎src/interface/abi/iseriser-abi.ipkg‎

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@@ -10,3 +10,4 @@ modules = Iseriser.ABI.Types
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, Iseriser.ABI.Foreign
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, Iseriser.ABI.Proofs
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, Iseriser.ABI.Semantics
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, Iseriser.ABI.Invariants

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