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/Main.lean

@@ -0,0 +1,40 @@
+/-
+Port of `Main.agda`. Prints the constant- and sign-analysis results for the
+test program (Agda: `putStrLn (output-Const ++ "\n" ++ output-Sign)`).
+-/
+import Spa.Analysis.Sign
+import Spa.Analysis.Constant
+
+namespace Spa
+
+/-- Agda: `testCode`. -/
+def testCode : Stmt :=
+  .andThen (.basic (.assign "zero" (.num 0)))
+    (.andThen (.basic (.assign "pos" (.add (.var "zero") (.num 1))))
+      (.andThen (.basic (.assign "neg" (.sub (.var "zero") (.num 1))))
+        (.basic (.assign "unknown" (.add (.var "pos") (.var "neg"))))))
+
+/-- Agda: `testCodeCond₁`. -/
+def testCodeCond₁ : Stmt :=
+  .andThen (.basic (.assign "var" (.num 1)))
+    (.ifElse (.var "var")
+      (.basic (.assign "var" (.add (.var "var") (.num 1))))
+      (.andThen (.basic (.assign "var" (.sub (.var "var") (.num 1))))
+        (.basic (.assign "var" (.num 1)))))
+
+/-- Agda: `testCodeCond₂`. -/
+def testCodeCond₂ : Stmt :=
+  .andThen (.basic (.assign "var" (.num 1)))
+    (.ifElse (.var "var")
+      (.basic (.assign "x" (.num 1)))
+      (.basic .noop))
+
+/-- Agda: `testProgram`. -/
+def testProgram : Program := ⟨testCode⟩
+
+end Spa
+
+/-- Agda: `main`. -/
+def main : IO Unit :=
+  IO.println (Spa.ConstAnalysis.output Spa.testProgram ++ "\n" ++
+              Spa.SignAnalysis.output Spa.testProgram)