chore: ICERM notation demo

doc/examples/ICERM2022/notation.lean

@@ -0,0 +1,49 @@
+import Lean
+
+def f (x y : Nat) := x * y + 1
+
+infixl:65 " *' " => f
+
+#check 2 *' 3
+
+notation "unitTest " x => Prod.mk x ()
+
+#check unitTest 42
+
+notation "parenthesisTest " x => Nat.sub (x)
+#check parenthesisTest 12
+
+def Set (α : Type u) := α → Prop
+def setOf {α : Type} (p : α → Prop) : Set α := p
+notation "{ " x " | " p " }" => setOf (fun x => p)
+
+#check { x | x ≤ 1 }
+
+notation "cdotTest " "(" x ", " y ")" => Prod.map (· + 1) (1 + ·) (x, y)
+
+#check cdotTest (13, 12)
+
+notation "tupleFunctionTest " "(" x ", " y ")"=> Prod.map (Nat.add 1) (Nat.add 2) (x, y)
+
+#check tupleFunctionTest (15, 12)
+
+notation "diag " x => Prod.mk x x
+
+#check diag 12
+
+open Lean Meta PrettyPrinter Delaborator SubExpr in
+@[delab app.Prod.mk] def delabDoubleRhsTest : Delab := do
+   let e ← getExpr
+   let #[_, _, x, y] := e.getAppArgs | failure
+   guard (← isDefEq x y) 
+   let stx ← withAppArg delab
+   `(diag $stx)     
+
+#check diag 3
+#check (3, 3)
+#check (3, 4)
+#check (2+1, 3)
+#check (true, true)
+
+
+