ABI Layer 5: end-to-end soundness capstone certificate#45
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Raise the Idrisiser Idris2 ABI to Layer 2 with a genuine, machine-checked semantic proof of the repo's headline domain property (proven-correct wrappers via dependent types). Module Idrisiser.ABI.Semantics models a length-indexed SafeArray (Vect n a) with a total accessor safeIndex : SafeArray n a -> Fin n -> a, and proves: - InBounds i n is inhabited exactly when i < n (carries an LT i n proof); the out-of-range case has no constructor. - Uninhabited (InBounds i 0): no index exists into an empty array, so out-of-range access is unrepresentable. - decInBounds : sound + complete Dec (InBounds i n), backed by isLT. - finToNatNatToFinLT / safeIndexUsesExactSlot: the proven index round-trips exactly to the requested raw position (no off-by-one, no runtime failure). - certifyBounded + certifyBoundedSound: certifier into the ABI Totality witness, returning Total only when genuinely in bounds. - Positive control (idx2InBounds reads "gamma") and negative controls (Not (InBounds 5 3), Not (InBounds i 0)), all machine-checked. No believe_me / postulate / assert; the headline property is non-vacuous (a deliberately-false InBounds 5 3 witness is rejected by idris2 0.7.0). Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01A6PSzJWpRxtzGDjUCEh7Mx
Add a second, deeper machine-checked theorem over the SAME Layer-2 model
(SafeArray/Vect/Fin), raising the Idris2 ABI to Layer 3.
New module Idrisiser.ABI.Invariants proves McCarthy's store/select array
axioms — distinct from Layer-2 in-bounds totality:
- safeReadAfterWriteSame: read i after write v@i = v (write-then-read)
- safeReadAfterWriteOther: write@j leaves slot i/=j unchanged (read-other)
- predictReadOverWrite + safeReadOverWriteCorrect: sound decEq-driven
decision procedure with correctness proof in both branches
Vect-level lemmas (indexReplaceAtSame, indexReplaceAtOther) proved by hand
via induction, not delegated to a library lemma. Defines safeWrite as the
formal dual of safeIndex. Positive controls (write-then-read, other-slot
preserved, prediction agrees) plus a negative/non-vacuity control
(writeReallyChangedSlot: the write genuinely changed the slot). %default
total, no believe_me/postulate/assert. Clean build, zero 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 Idrisiser.ABI.FfiSeam proving the resultToInt encoding is sound: - resultRoundTrip: total decoder intToResult faithfully recovers every Result (lossless C-integer encoding). - resultToIntInjective: distinct ABI outcomes never collide on the wire, derived cleanly from the round-trip via cong + Just-injectivity. - positive controls (concrete decodes = Refl) and a machine-checked non-vacuity control (Ok and Error map to distinct wire integers). Genuine proof: no believe_me/postulate/assert_total/idris_crash. %default total, zero warnings. Registered in idrisiser-abi.ipkg. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01A6PSzJWpRxtzGDjUCEh7Mx
Assemble the existing per-layer ABI proofs into one inhabited end-to-end certificate in Idrisiser.ABI.Capstone: - record ABISound with one field per discharged layer: * flagshipControl : InBounds 2 3 (Layer 2 flagship positive control) * layer3Invariant : write-then-read law instance (Layer 3 invariant) * ffiSeamInjective : resultToInt injectivity (Layer 4 FFI seam) - abiContractDischarged : ABISound built ONLY from the real exported witnesses (Semantics.idx2InBounds, writeThenReadDelta, resultToIntInjective). If any prior layer were unsound this value would not typecheck. Non-vacuity: a bogus certificate (Layer-3 field claiming the old value "beta" instead of "delta") is rejected by the type checker. Genuine composition only: no believe_me/postulate/assert/%hint. %default total, SPDX header, zero build warnings. 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>
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Summary
Layer 5 (the capstone, completing the 5-layer proof track): a new
*.ABI.Capstonemodule importing every prior layer and assembling a single inhabitedABISoundcertificate (abiContractDischarged) from the real exported witnesses of the flagship property (L2 bounded array access), the deeper invariant (L3 store/select laws), and the FFI-seam injectivity (L4). One end-to-end soundness statement.Genuine composition only — reuses real exported names.
Testing
Idris2 0.7.0
--build→ exit 0, zero warnings. Adversarial: a bogus-field certificate was rejected.build/removed. Nobelieve_me/postulate/sorry.🤖 Generated with Claude Code
https://claude.ai/code/session_01A6PSzJWpRxtzGDjUCEh7Mx
Generated by Claude Code