Have LatticeInterpretation extend Interp

LatticeInterpretation now extends Interp L (Value → Prop), so each analysis
defines only its LatticeInterpretation instance and gets the ⟦⟧ notation for
free. Drops the standalone per-analysis Interp instances (signInterp and the
anonymous constInterp). The Interp class is kept for other uses.

The interp*_mk_disjoint bootstrap lemmas now state on the raw interp function
since they feed the instance and run before any Interp instance exists; the
trivial sup/inf wrappers are inlined into the instance.

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

lean/Spa/Analysis/Constant.lean

@@ -42,27 +42,17 @@ def interpConst : ConstLattice → Value → Prop
   | .top, _ => True
   | .mk z, v => v = .int z
 
-instance : Interp ConstLattice (Value → Prop) := ⟨interpConst⟩
-
 theorem interpConst_mk_disjoint {z₁ z₂ : ℤ} (hne : z₁ ≠ z₂) {v : Value} :
-    ¬(⟦(.mk z₁ : ConstLattice)⟧ v ∧ ⟦(.mk z₂ : ConstLattice)⟧ v) := by
+    ¬(interpConst (.mk z₁) v ∧ interpConst (.mk z₂) v) := by
   rintro ⟨h₁, h₂⟩
   rw [h₁] at h₂
   injection h₂ with hz
   exact hne hz
 
-theorem interpConst_sup {s₁ s₂ : ConstLattice} (v : Value)
-    (h : ⟦s₁⟧ v ∨ ⟦s₂⟧ v) : ⟦s₁ ⊔ s₂⟧ v :=
-  AboveBelow.interp_sup_of (fun _ h => h) (fun _ => trivial) v h
-
-theorem interpConst_inf {s₁ s₂ : ConstLattice} (v : Value)
-    (h : ⟦s₁⟧ v ∧ ⟦s₂⟧ v) : ⟦s₁ ⊓ s₂⟧ v :=
-  AboveBelow.interp_inf_of (fun hne _ => interpConst_mk_disjoint hne) v h
-
 instance constInterpretation : LatticeInterpretation ConstLattice where
   interp := interpConst
-  interp_sup := fun {l₁ l₂} v h => interpConst_sup (s₁ := l₁) (s₂ := l₂) v h
-  interp_inf := fun {l₁ l₂} v h => interpConst_inf (s₁ := l₁) (s₂ := l₂) v h
+  interp_sup := fun v h => AboveBelow.interp_sup_of (fun _ h => h) (fun _ => trivial) v h
+  interp_inf := fun v h => AboveBelow.interp_inf_of (fun hne _ => interpConst_mk_disjoint hne) v h
 
 variable (prog : Program)