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ABI Layer 4: prove the FFI result-code seam is injective + faithful (#44)
## Summary Layer 4 (seal the ABI↔FFI seam): proves the FFI result-code encoding (`resultToInt`) is a **sound, lossless wire encoding** — decoder `intToResult` with `resultRoundTrip`, from which `resultToIntInjective` is derived. Distinct ABI outcomes never collide on the C wire. Complements the structural `abi-ffi-gate.py`. New module `*.ABI.FfiSeam` (imports `Types`). Positive + non-vacuity controls. ## Testing Idris2 0.7.0 `--build` → exit 0, zero warnings. Adversarial rejection confirmed. `build/` removed. No `believe_me`/`postulate`/`sorry`. 🤖 Generated with [Claude Code](https://claude.com/claude-code) https://claude.ai/code/session_01A6PSzJWpRxtzGDjUCEh7Mx --- _Generated by [Claude Code](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/Julianiser/ABI/FfiSeam.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 4: ABI <-> FFI seam soundness proofs for Julianiser.
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|||
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||| The structural gate (scripts/abi-ffi-gate.py) checks that the Idris2 `Result`
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||| enum and the Zig FFI enum agree by name+value. THIS module is the proof-side
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||| guarantee that the wire encoding is itself SOUND:
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|||
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||| (a) `resultToIntInjective` — distinct ABI `Result` outcomes never collide
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||| on the wire (the encoding is unambiguous).
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||| (b) `intToResult` + `resultRoundTrip` — the C integer faithfully and
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||| losslessly round-trips back to the originating ABI `Result`.
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|||
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||| Injectivity (a) is DERIVED from the round-trip (b) via `cong` + `justInj`,
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||| which is the cleanest argument: if two results encode to the same int, then
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||| decoding that int yields the same `Just`, hence the results are equal.
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|||
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||| Julianiser has exactly one FFI enum encoder (`Result`/`resultToInt`); there
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||| is no `ProofStatus`/`statusToInt` or other encoder to mirror, so clause (c)
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||| of the seam obligation is vacuous here.
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|||
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||| Genuine proof only: no `believe_me`, `idris_crash`, `assert_total`,
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||| `postulate`, `sorry`. Decidable primitive Bits32 equality discharges the
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||| negative (non-vacuity) control.
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module Julianiser.ABI.FfiSeam
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import Julianiser.ABI.Types
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%default total
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--------------------------------------------------------------------------------
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-- Local lemma
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--------------------------------------------------------------------------------
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||| `Just` is injective. Proved by pattern matching on the single inhabitant
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||| of the equality (the `Just x = Just y` shape forces `x = y`).
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private
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justInj : {0 x, y : a} -> Just x = Just y -> x = y
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justInj Refl = Refl
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--------------------------------------------------------------------------------
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-- Decoder: the inverse of resultToInt
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--------------------------------------------------------------------------------
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||| Decode a C integer result code back to the ABI `Result`. Built with nested
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||| boolean `if`/`==` on concrete Bits32 literals so the round-trip equalities
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||| reduce definitionally to `Refl`. Unknown codes decode to `Nothing`.
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public export
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intToResult : Bits32 -> Maybe Result
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intToResult x =
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if x == 0 then Just Ok
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else if x == 1 then Just Error
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else if x == 2 then Just InvalidParam
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else if x == 3 then Just OutOfMemory
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else if x == 4 then Just NullPointer
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else if x == 5 then Just ParseError
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else if x == 6 then Just CodegenError
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else Nothing
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--------------------------------------------------------------------------------
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-- (b) Faithful / lossless round-trip
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--------------------------------------------------------------------------------
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||| The wire encoding is lossless: decoding the encoding of any `Result`
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||| recovers exactly that `Result`. Each clause reduces through the boolean
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||| `==` comparisons on concrete literals.
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export
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resultRoundTrip : (r : Result) -> intToResult (resultToInt r) = Just r
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resultRoundTrip Ok = Refl
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resultRoundTrip Error = Refl
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resultRoundTrip InvalidParam = Refl
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resultRoundTrip OutOfMemory = Refl
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resultRoundTrip NullPointer = Refl
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resultRoundTrip ParseError = Refl
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resultRoundTrip CodegenError = Refl
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--------------------------------------------------------------------------------
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-- (a) Injectivity, DERIVED from the round-trip
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--------------------------------------------------------------------------------
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||| The encoding is unambiguous: distinct `Result` values never map to the same
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||| C integer. Derived from the round-trip — if `resultToInt a = resultToInt b`,
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||| then applying `intToResult` to both sides (via `cong`) gives
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||| `Just a = Just b` (using both round-trips), and `justInj` yields
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||| `a = b`. No case analysis on the 49-cell matrix is needed.
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export
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resultToIntInjective : (a, b : Result) ->
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resultToInt a = resultToInt b -> a = b
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resultToIntInjective a b prf =
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justInj $
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rewrite sym (resultRoundTrip a) in
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rewrite sym (resultRoundTrip b) in
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cong intToResult prf
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--------------------------------------------------------------------------------
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-- Positive controls (concrete decodes machine-checked = Refl)
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--------------------------------------------------------------------------------
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||| Positive control: code 0 decodes to Ok.
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export
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decodeZeroIsOk : intToResult 0 = Just Ok
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decodeZeroIsOk = Refl
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||| Positive control: code 6 decodes to CodegenError (the largest code).
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export
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decodeSixIsCodegenError : intToResult 6 = Just CodegenError
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decodeSixIsCodegenError = Refl
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||| Positive control: an out-of-range code decodes to Nothing.
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export
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decodeSevenIsNothing : intToResult 7 = Nothing
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decodeSevenIsNothing = Refl
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--------------------------------------------------------------------------------
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-- Negative / non-vacuity control (machine-checked)
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--------------------------------------------------------------------------------
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||| Non-vacuity: two DISTINCT result codes have DISTINCT wire integers. If this
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||| were not machine-checkable the injectivity theorem above would be vacuously
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||| true. Discharged by Idris's coverage checker on distinct primitive Bits32
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||| literals (0 vs 1).
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export
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okIntNotErrorInt : Not (resultToInt Ok = resultToInt Error)
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okIntNotErrorInt = \case Refl impossible
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||| A second distinct-pair witness across non-adjacent codes (0 vs 6).
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export
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okIntNotCodegenInt : Not (resultToInt Ok = resultToInt CodegenError)
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okIntNotCodegenInt = \case Refl impossible

‎src/interface/abi/julianiser-abi.ipkg‎

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@@ -11,3 +11,4 @@ modules = Julianiser.ABI.Types
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, Julianiser.ABI.Proofs
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, Julianiser.ABI.Semantics
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, Julianiser.ABI.Invariants
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, Julianiser.ABI.FfiSeam

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