#lang plai

(define-type AE
  [num (n number?)]
  [add (lhs AE?) (rhs AE?)]
  [sub (lhs AE?) (rhs AE?)])

(define (parse sexp)
  (cond
    [(number? sexp) (num sexp)]
    [(list? sexp)
     (case (first sexp)
       [(+) (add (parse (second sexp))
                 (parse (third sexp)))]
       [(-) (sub (parse (second sexp))
                 (parse (third sexp)))])]))

(define (calc an-ae)
  (type-case AE an-ae
             [num (n) n]
             [add (l r) (+ (calc l) (calc r))]
             [sub (l r) (- (calc l) (calc r))]))