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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
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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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