(define-datatype AE AE?
  [num (n number?)]
  [binop (op procedure?)
         (lhs AE?)
         (rhs AE?)])

;; calc : AE -> number
;; to define a calculator for AEs
(define (calc an-ae)
  (cases AE an-ae
    [num (n) n]
    [binop (op l r) (op (calc l) (calc r))]))

(calc (num 3)) "should equal" 3
(calc (binop + (num 3) (num 4))) "should equal" 7
(calc (binop + (binop + (num 3) (num 4)) (num 7))) "should equal" 14
(calc (binop * (binop - (num 1) (num 3)) (binop / (num 4) (num 2)))) "should equal" -4