Add proof of reaching definition analysis

This requires a few pieces:

* Make node tags use `Fin n` intead of natural numbers. This makes
  it possible to build a finite lattice over AST nodes, and also
  ensure automatic, total indexing from CFG nodes into the AST that
  created them. For this, use the elaborator to derive the ordering
  statements etc. where possible.
* Adjust the forward framework to enable proofs that don't just state
  correctness on the environment, but also on an arbitrary additional
  state accumulated from traversing the trace.
* State the reaching definition analysis's correctness in terms
  of this new framework.

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

lean/Spa/Analysis/Forward/Evaluation.lean

@@ -7,8 +7,9 @@ namespace Forward
 variable (L : Type) [Lattice L] (prog : Program)
 
 class StmtEvaluator where
-  eval : prog.State → BasicStmt → VariableValues L prog → VariableValues L prog
-  eval_mono : ∀ s bs, Monotone (eval s bs)
+  eval : (s : prog.State) → (bs : BasicStmt) → prog.code s = some bs →
+    VariableValues L prog → VariableValues L prog
+  eval_mono : ∀ s bs h, Monotone (eval s bs h)
 
 class ExprEvaluator where
   eval : Expr → VariableValues L prog → L
@@ -17,13 +18,13 @@ class ExprEvaluator where
 class ValidExprEvaluator [ExprEvaluator L prog] [I : LatticeInterpretation L] :
     Prop where
   valid : ∀ {vs : VariableValues L prog} {ρ : Env} {e : Expr} {v : Value},
-    EvalExpr ρ e v → ⟦ vs ⟧ ρ → I.interp (ExprEvaluator.eval e vs) v
+    EvalExpr ρ e v → ⟦ vs ⟧ ρ () → I.interp (ExprEvaluator.eval e vs) v
 
 class ValidStmtEvaluator [E : StmtEvaluator L prog] [LatticeInterpretation L] :
     Prop where
   valid : ∀ {s : prog.State} {vs : VariableValues L prog} {ρ₁ ρ₂ : Env}
-    {bs : BasicStmt},
-    EvalBasicStmt ρ₁ bs ρ₂ → ⟦ vs ⟧ ρ₁ → ⟦ E.eval s bs vs ⟧ ρ₂
+    {bs : BasicStmt} (hcode : prog.code s = some bs),
+    EvalBasicStmt ρ₁ bs ρ₂ → ⟦ vs ⟧ ρ₁ () → ⟦ E.eval s bs hcode vs ⟧ ρ₂ ()
 
 end Forward