ABI Layer 3: reversible operations form a group (modulo denotational equivalence)#32
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Add Oblibeniser.ABI.Semantics, a machine-checked proof of oblibeniser's
headline domain property: operations are reversible.
Models a faithful family of structurally-invertible operations (FlipAll,
XorMask, Rev, Nop, Seq) over a bit-register state (List Bool), and proves
the round-trip law as a real propositional equality:
reversible : (op : Op) -> (s : State) -> unapply op (apply op s) = s
Also proved: the dual direction (apply . unapply = id, so each op is a
genuine bijection), closure under sequencing, and an unforgeable
IsReversible certificate tied to the ABI Result code. Positive controls
exhibit inhabited witnesses; negative controls machine-refute the bad
case (a wrong inverse). No believe_me / postulate / assert — Integer was
deliberately avoided since its primitive ops do not reduce symbolically;
the bit-register model gives honest, reduction-friendly involutions.
Adversarial check: a deliberately false round-trip (= [True] instead of
[False]) is rejected by idris2, confirming non-vacuity.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01A6PSzJWpRxtzGDjUCEh7Mx
Add Oblibeniser.ABI.Invariants, a second, deeper machine-checked theorem over the SAME Layer-2 model (Op/State/apply/invert/unapply). Where Layer 2 proves the per-element round-trip laws, Layer 3 proves the whole collection is a GROUP under Seq, quotiented by denotational equivalence Equiv: - Equiv is an equivalence relation and a congruence for Seq; - Seq is associative; Nop is a two-sided unit; - every op has a two-sided inverse (reusing reversible / reversibleDual); - inverses are UNIQUE (cancellation theorem); - invert is an involution and anti-homomorphism up to Equiv. Includes a sound+complete decision procedure decAgreeOn for agreement on a finite probe set, an unforgeable IsGroupInverse certificate tied to the ABI Result codes with a soundness lemma, positive controls (concrete witnesses + inhabited certificate), and negative/non-vacuity controls (Not-equivalences machine-checked, decision returns No). No believe_me/postulate/assert_total; %default total; builds with zero warnings; adversarial false proof rejected. 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 3 (second, deeper invariant): proves the reversible operations form a group under sequencing, modulo denotational equivalence —
Equivis an equivalence relation and aSeq-congruence,Seqis associative,Nopis a two-sided unit, every op has a two-sided inverse (reusing the Layer-2 round-trip laws), inverses are unique, andinvertis an involution / anti-homomorphism. Distinct from and deeper than the Layer-2 round-trip law.New module
Oblibeniser.ABI.Invariants(imports the Layer-2Semanticsmodel). Sound+completeDec, 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