(datatype Math
  (Num i64)
  (Var String)
  (Add Math Math)
  (Mul Math Math))

;; expr1 = 2 * (x + 3)
(let expr1 (Mul (Num 2) (Add (Var "x") (Num 3))))
;; expr2 = 6 + 2 * x
(let expr2 (Add (Num 6) (Mul (Num 2) (Var "x"))))


;; (rule ((= __root (Add a b)))
;;       ((union __root (Add b a)))
(rewrite (Add a b)
         (Add b a))
(rewrite (Mul a (Add b c))
         (Add (Mul a b) (Mul a c)))
(rewrite (Add (Num a) (Num b))
         (Num (+ a b)))
(rewrite (Mul (Num a) (Num b))
         (Num (* a b)))

(run 10)
(check (= expr1 expr2))