proof(ir): switch support — full loop-free splice simulation (lane 2.2) - #2295
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…ee fragment (lane 2.2) Extend SpliceSim with switch (cases/default sub-fragments and LoopFree bridges), prove the find? commutation with the key-preserving case splice, membership bound domination, and spliced_cons_switch (selected case via find?, default, and no-default branches, each propagating through the list step). The main induction gains structurally-static companion recursions over case lists and defaults (execIRStmts_splicedCases/_splicedDflt), avoiding membership-based termination measures. The end-to-end guardedUnit theorems inherit the widened fragment unchanged.
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This was referenced Aug 12, 2026
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Removes the
switchexclusion from #2291's fragment:SpliceSimnow coversswitch(cases + default), with thefind?-vs-splice commutation, bound domination by membership,spliced_cons_switch, and structurally-static companion recursions (execIRStmts_splicedCases/_splicedDflt) in the main mutual induction. The end-to-endguardedUnittheorems (#2294) inherit the widened fragment with no change — the guarded correspondence now covers every loop-free compiled body with modeled exits.Validation: full
lake buildOK,make checkall passed, no sorry/admit/new axiom.Note
Medium Risk
Changes are proof-only but extend a critical IR correctness chain (non-reentrant guard /
guardedUnit); errors would be in formal reasoning, not runtime code.Overview
Extends the lock-release splice simulation fragment so
switch(case arms and default) is no longer excluded:SpliceSimnow mirrorsLoopFreewithSpliceSimCases/SpliceSimDflt, andSpliceSim.loopFreeproves the fragment still implies loop-freedom.Adds the switch cons-step machinery for
execIRStmts_spliced:find?_spliceCases(branch lookup commutes with splicing),spliced_case_bound_le(fuel bounds for spliced arms),spliced_cons_switch, and mutual companion lemmasexecIRStmts_splicedCases/execIRStmts_splicedDfltwith explicittermination_by/decreasing_byon the main induction.Registers the new lemmas in
PrintAxioms.leanand allowlistsspliced_cons_switchincheck_proof_length.py(theorem count 6239 → 6247).Reviewed by Cursor Bugbot for commit 6474250. Bugbot is set up for automated code reviews on this repo. Configure here.