Switch Reaching analysis to use Finset for more efficiency

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

lean/Spa/Analysis/Reaching.lean

@@ -1,6 +1,5 @@
 import Spa.Analysis.Forward
-import Spa.Lattice.Bool
-import Spa.Lattice.Tuple
+import Spa.Lattice.Finset
 import Spa.Language.Tagged.Graphs
 import Spa.Showable
 
@@ -8,15 +7,13 @@ namespace Spa
 
 open Forward
 
-instance : Showable Bool := ⟨fun b => if b then "true" else "false"⟩
-
-instance {n : ℕ} {β : Type*} [Showable β] : Showable (Fin n → β) :=
-  ⟨fun f =>
+instance {n : ℕ} : Showable (Finset (Fin n)) :=
+  ⟨fun s =>
     "{" ++ (List.finRange n).foldr
-        (fun i rest => show' i ++ " ↦ " ++ show' (f i) ++ ", " ++ rest) ""
+        (fun i rest => if i ∈ s then show' i ++ ", " ++ rest else rest) ""
         ++ "}"⟩
 
-abbrev DefSet (prog : Program) : Type := prog.NodeId → Bool
+abbrev DefSet (prog : Program) : Type := Finset prog.NodeId
 
 namespace ReachingAnalysis
 
@@ -24,7 +21,7 @@ variable (prog : Program)
 
 def genSet (s : prog.State) {bs : BasicStmt} (h : prog.code s = some bs) :
     DefSet prog :=
-  Function.update (⊥ : DefSet prog) (prog.nodeIdOfNonempty s h) true
+  {prog.nodeIdOfNonempty s h}
 
 def eval (s : prog.State) :
     (bs : BasicStmt) → prog.code s = some bs →
@@ -65,15 +62,15 @@ instance stateInterp : StateInterp (DefSet prog) prog where
   St := fun _ => Run prog
   init := Run.nil
   interp vs _ run := ∀ (x : String) (assigners : DefSet prog), (x, assigners) ∈ vs →
-    ∀ (n : prog.NodeId), LastAssign prog x run n → assigners n = true
+    ∀ (n : prog.NodeId), LastAssign prog x run n → n ∈ assigners
   interp_sup := by
     intro vs₁ vs₂ ρ run h x assigners hmem n hla
     obtain ⟨a₁, a₂, rfl, h₁, h₂⟩ := FiniteMap.mem_sup hmem
-    aesop
+    aesop (add simp Finset.mem_union)
   interp_inf := by
     intro vs₁ vs₂ ρ run h x assigners hmem n hla
     obtain ⟨a₁, a₂, rfl, h₁, h₂⟩ := FiniteMap.mem_inf hmem
-    aesop
+    aesop (add simp Finset.mem_inter)
 
 instance validStateEvaluator : ValidStateEvaluator (DefSet prog) prog where
   step := by intro s _ _ bs hcode _ rest; exact Run.cons s bs hcode rest
@@ -88,7 +85,7 @@ instance validStateEvaluator : ValidStateEvaluator (DefSet prog) prog where
       by_cases hx : k = x
       · subst hx
         have hd := FiniteMap.generalizedUpdate_mem_eq (List.mem_singleton.mpr rfl) hmem2
-        aesop (add simp genSet)
+        aesop (add simp [genSet, Finset.mem_singleton])
       · have hmem' := FiniteMap.generalizedUpdate_not_mem_backward
           (fun hc => hx (List.mem_singleton.mp hc)) hmem2
         aesop