(defn diff [expr var]
  (cond
    (symbol? expr) (if (= expr var) 1 0)
    (number? expr) 0
    (match expr
      [op & args] (case op
        '+ ['+ ;(map |(diff $ var) args)]
        '* (let [[a b] args]
             ['+ ['* (diff a var) b]
                        ['* a (diff b var)]])
        (errorf "unknown op: %v" op)))))

(defn simplify [expr]
  (cond
    (symbol? expr) expr
    (number? expr) expr
    (match expr [op & args]
      (do
        (def args (map simplify args))
        (case op
          '+ (do
               (def terms (filter |(not= $ 0) args))
               (if (= (length terms) 1) (first terms) ['+ ;terms]))
          '* (cond
               (find |(= $ 0) args) 0
               (find |(= $ 1) args) (first (filter |(not= $ 1) args))
               ['* ;args]) # otherwise leave unchanged
          [op ;args])))))


(pp (simplify (diff '(+ (* x x) 3) 'x)))
(pp (simplify (diff '(+ x 3) 'x)))