Lean migration: Phase 7 (Sign + Constant analyses, executable)

- Spa.Showable: port of Showable.agda (quoted strings, map format) for
  output parity
- Spa.Analysis.Utils: eval_combine₂
- Spa.Lattice.AboveBelow.le_cases: order of the flat lattice by cases
- Spa.Analysis.Sign / Spa.Analysis.Constant: the four monotonicity
  POSTULATES from the Agda files are now proved theorems (via le_cases);
  interpretations, evaluator validity, analyze_correct per analysis
- Main + lake exe spa: runs both analyses on the Agda test program;
  constant analysis folds unknown=0, sign analysis gives unknown=⊤

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

lean/Spa/Showable.lean

@@ -0,0 +1,47 @@
+/-
+Port of `Showable.agda` (plus the `Showable` instances that lived on
+`Lattice/Map.agda` and `Lattice/AboveBelow.agda`).
+
+Lean has `ToString`, but its `String` instance does not quote (the Agda one
+does), so to reproduce the Agda output exactly we port the class as-is.
+-/
+import Spa.Lattice.FiniteMap
+import Spa.Lattice.AboveBelow
+
+namespace Spa
+
+/-- Agda: `Showable` (`show` is a Lean keyword, hence `show'`). -/
+class Showable (α : Type*) where
+  show' : α → String
+
+export Showable (show')
+
+instance : Showable String := ⟨fun s => "\"" ++ s ++ "\""⟩
+
+instance : Showable ℕ := ⟨toString⟩
+
+instance : Showable ℤ := ⟨toString⟩
+
+instance {n : ℕ} : Showable (Fin n) := ⟨fun i => toString i.val⟩
+
+instance {α β : Type*} [Showable α] [Showable β] : Showable (α × β) :=
+  ⟨fun p => "(" ++ show' p.1 ++ ", " ++ show' p.2 ++ ")"⟩
+
+instance : Showable PUnit := ⟨fun _ => "()"⟩
+
+/-- Agda: the `Showable` instance of `Lattice/AboveBelow.agda`. -/
+instance {α : Type*} [Showable α] : Showable (AboveBelow α) :=
+  ⟨fun
+    | .bot => "⊥"
+    | .top => "⊤"
+    | .mk x => show' x⟩
+
+/-- Agda: the `Showable` instance of `Lattice/Map.agda` (inherited by
+`FiniteMap`). -/
+instance {α β : Type*} {ks : List α} [Showable α] [Showable β] :
+    Showable (FiniteMap α β ks) :=
+  ⟨fun fm =>
+    "{" ++ fm.val.foldr (fun p rest => show' p.1 ++ " ↦ " ++ show' p.2 ++ ", " ++ rest) ""
+        ++ "}"⟩
+
+end Spa