#lang racket
(require "chez-init.rkt")
(require racket/trace)

;<expression>::= <identifier>
;            ::= <number>
;            ::= (if <expression> <expression> <expression>)
;            ::= (lambda (<identifier>+) <expression>)
;            ::= (<expression> <expression>+)

(define-datatype expression expression?
  [var-exp
   (id symbol?)]
  [num-exp
   (val number?)]
  [if-exp
   (condition expression?)
   (if-true expression?)
   (if-false expression?)]
  [lambda-exp
   (ids (listof symbol?))
   (body expression?)]
  [app-exp
   (da-exp (listof expression?))])

(define parse-exp
  (lambda (input)
    (cond [(symbol? input) [var-exp input]]
          [(number? input) [num-exp input]]
          [(pair? input)
           (cond [(eq? (car input) 'lambda)
                  [lambda-exp (cadr input) (parse-exp (caddr input))]]
                 [(eq? (car input) 'if)
                  [if-exp (parse-exp (cadr input))
                          (parse-exp (caddr input))
                          (parse-exp (cadddr input))]]
                 [else [app-exp (map parse-exp input)]])]
          [else 'error])))

(define unparse-exp
 (lambda (parse-tree)
   (cases expression parse-tree
     [var-exp (id) id]
     [num-exp (val) val]
     [if-exp (condition if-true if-false)
             (list 'if (unparse-exp condition) (unparse-exp if-true) (unparse-exp if-false))]
     [lambda-exp (ids body) (list 'lambda ids (unparse-exp body))]
     [app-exp (da-exp)
              (map unparse-exp da-exp)])))