ABI Layer 5: end-to-end soundness capstone certificate#42
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Flagship semantic proof: negation involution + De Morgan laws, plus a decidable `Designated` (classical-truth) proposition with sound+complete Dec, certifier soundness, conjunction preservation, and positive + negative controls (negation is provably not the identity; U/F are provably not designated). Verified with idris2 0.7.0 (build clean, zero warnings) + adversarial false-proof rejection. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01A6PSzJWpRxtzGDjUCEh7Mx
…er the Kleene order Adds Betlangiser.ABI.Invariants, a second, deeper machine-checked theorem built over the existing Semantics model (Trit/and3/or3), distinct from the Layer-2 doubleNeg/De Morgan laws: - and3Comm, and3Assoc (full 27-case), and3Idem — the semilattice laws; - Leq3, the Kleene information order F <= U <= T, with reflexivity, transitivity, and a sound+complete decision procedure decLeq3; - and3LowerL/R + and3Greatest proving and3 is the meet (GLB) for Leq3; - positive controls (inhabited witnesses) and negative/non-vacuity controls (tNotLeqU, andUUNotTop, topNotBelowMeetTF). No believe_me/postulate/assert/sorry. %default total. Adversarially verified: a false `Leq3 T U` is rejected by the type checker. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01A6PSzJWpRxtzGDjUCEh7Mx
Seals the ABI<->FFI seam with a proof-side soundness guarantee that complements the structural abi-ffi-gate.py check: - intToResult decoder + resultRoundTrip: the C integer faithfully and losslessly round-trips back to the ABI Result value. - resultToIntInjective: distinct ABI outcomes never collide on the wire, derived cleanly from the round-trip via a local justInj (Just-injective). - Same round-trip + injectivity for the TernaryBool FFI enum encoder (ternaryToInt / intToTernary). - Positive controls (concrete decode = Refl) and machine-checked negative / non-vacuity controls (distinct codes => distinct ints). Genuine total proof: no believe_me, idris_crash, assert_total, postulate, or sorry. Builds clean with zero warnings; a false seam claim (resultToInt Ok = resultToInt Error) is rejected by the type checker. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01A6PSzJWpRxtzGDjUCEh7Mx
Assemble the existing Layer-2 (Semantics.andTTDesignated), Layer-3 (Invariants.meetTU_belowU), and Layer-4 (FfiSeam.resultToIntInjective) proofs into one inhabited certificate value, abiContractDischarged : ABISound. Genuine composition only; a deliberately-false meet field is rejected by the typechecker (adversarial control). Build is clean with zero 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 Kleene logic), the deeper invariant (L3 meet-semilattice 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