ABI Layer 3: McCarthy store/select array-update laws (write-then-read, read-other)#43
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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
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Summary
Layer 3 (second, deeper invariant): proves the McCarthy store/select array laws over the Layer-2 SafeArray/Vect/Fin model — write-then-read (
read i (write i v a) = v) and read-other (a write atileaves indexj≠iunchanged). Distinct from and deeper than the Layer-2 in-bounds totality property.New module
Idrisiser.ABI.Invariants(imports the Layer-2Semanticsmodel). Positive + non-vacuity controls.Testing
Idris2 0.7.0
--build→ exit 0, zero warnings. Adversarial rejection confirmed.build/removed. Nobelieve_me/postulate/sorry.🤖 Generated with Claude Code
https://claude.ai/code/session_01A6PSzJWpRxtzGDjUCEh7Mx
Generated by Claude Code