(define-type WAE
   [num (n number?)]
   [add (lhs WAE?) (rhs WAE?)]
   [sub (lhs WAE?) (rhs WAE?)]
   [with (name symbol?) (named-expr WAE?) (body WAE?)]
   [id (name symbol?)])

;; subst : WAE symbol WAE → WAE
(define (subst expr sub-id val)
   (type-case WAE expr
      [num (n) expr]
      [add (l r) (add (subst l sub-id val)
                        (subst r sub-id val))]
      [sub (l r) (sub (subst l sub-id val)
                       (subst r sub-id val))]
      [with (bound-id named-expr bound-body)
             (if (symbol=? bound-id sub-id)
                 (with bound-id
                       (subst named-expr sub-id val)
                       bound-body)
                 (with bound-id
                       (subst named-expr sub-id val)
                       (subst bound-body sub-id val)))]
      [id (v) (if (symbol=? v sub-id) val expr)]))

;; calc : WAE → number
;(define (calc expr)
;   (type-case WAE expr
;      [num (n) n]
;      [add (l r) (+ (calc l) (calc r))]
;      [sub (l r) (- (calc l) (calc r))]
;      [with (bound-id named-expr bound-body)
;             (calc (subst bound-body
;                           bound-id
;                           (num (calc named-expr))))]
;      [id (v) (error ’calc ”free identifier”)]))

(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)))])]))

(parse (read))