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Prove that analysis results apply to all states, not just the final one

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Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
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Danila Fedorin
2026-06-28 14:24:46 -05:00
parent 319fa272ac
commit 778e974dfb
5 changed files with 94 additions and 11 deletions
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7
lean/Spa/Analysis/Sign.lean
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@@ -213,6 +213,13 @@ theorem analyze_correct {ρ : Env} (hrun : EvalStmt [] prog.rootStmt ρ) :
⟦ variablesAt prog.finalState (result SignLattice prog) ⟧ ρ () :=
Forward.analyze_correct SignLattice prog hrun
theorem analyze_correct_at {ρf : Env} (hrun : EvalStmt [] prog.rootStmt ρf)
{s : prog.State} {ρin ρout : Env} {stin stout : PUnit}
(hr : Reaches (L := SignLattice) (prog.trace hrun) PUnit.unit s ρin ρout stin stout) :
⟦ joinForKey s (result SignLattice prog) ⟧ ρin stin
∧ ⟦ variablesAt s (result SignLattice prog) ⟧ ρout stout :=
Forward.analyze_correct_at SignLattice prog hrun hr
end SignAnalysis
end Spa