ABI Layer 3: compositionality of inductive invariants (conjunction is inductive)#39
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…emantics Add a flagship machine-checked semantic proof raising the Tlaiser Idris2 ABI to Layer 2. Models a two-process lock-based mutual-exclusion state machine (the canonical PlusCal example) with an Init predicate, a nondeterministic Step relation, and an inductive Reachable closure. Headline theorem (safetySound): mutual exclusion (Safe) holds on every reachable state. The engine is invInductive (TLA+ INV1): a strengthened, genuinely inductive invariant Inv that couples "process is Critical" to "process holds the lock" holds initially (initEstablishes) and is preserved by every transition (stepPreserves), hence holds on all reachable states; Safe is derived from Inv (invImpliesSafe). Includes a sound+complete Dec (decSafe), a Result-valued certifier with soundness (certifyReachableSound), a positive control (a real reachable Critical state, proven Safe) and negative controls (the (Critical,Critical) state has no Safe proof and is unreachable). The "both critical" bad case has no constructor, so a deliberately false safety witness is rejected by idris2 (non-vacuity verified). Builds clean (idris2 0.7.0, zero warnings). Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01A6PSzJWpRxtzGDjUCEh7Mx
…inductive)
Add Tlaiser.ABI.Invariants, a deeper, distinct machine-checked theorem built
over the SAME Layer-2 state-machine model (St/Init/Step/Reachable/Inv in
Tlaiser.ABI.Semantics; no datatypes redefined).
Layer-2 proved INV1 for one hand-crafted invariant. Layer-3 proves the
meta-theorem that licenses modular invariant construction in TLA+/TLAPS:
andInductive : IsInductive p -> IsInductive q -> IsInductive (And p q)
"the conjunction of two inductive invariants is itself inductive."
Contents:
- IsInductive p: the two INV1 premises (established by Init, preserved by Step)
packaged as a first-class value so inductiveness can be combined.
- inductiveOnReachable: generic INV1 (any inductive p holds on all reachable
states), proved once polymorphically.
- andInductive: the headline composition theorem.
- HolderCrit: a SECOND, independent concrete invariant ("the lock holder is
Critical"), proved inductive from scratch (holderInit + holderStep over the
existing Step relation), packaged as holderIsInductive.
- combinedIsInductive / combinedOnReachable: Inv and HolderCrit composed via
andInductive, yielding the conjunction on every reachable state with no new
induction.
- decHolderCrit: sound + complete Dec for the second invariant; certifyHolder
reuses the Result ABI; certifyHolderReachableSound ties it together.
- Controls: positive (inhabited reachable witness of the conjunction +
decided Ok), negative (Not (HolderCrit (Idle,Idle,HeldBy0))), and a
distinctness/non-vacuity control (HolderCrit holds but Inv fails on
(Critical,Critical,Free) — proving the two predicates are genuinely
different).
Clean build, zero warnings; adversarial false statements rejected. No
believe_me/postulate/assert_total/idris_crash. %default total throughout.
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 compositionality of inductive invariants — the conjunction of two inductive invariants is itself inductive, so independently-verified safety properties compose. Distinct from and deeper than the Layer-2 single-invariant soundness theorem.
New module
Tlaiser.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