350.rkt

;; The first three lines of this file were inserted by DrRacket. They record metadata
;; about the language level of this file in a form that our tools can easily process.
#reader(lib "htdp-intermediate-lambda-reader.ss" "lang")((modname 350ex) (read-case-sensitive #t) (teachpacks ()) (htdp-settings #(#t constructor repeating-decimal #f #t none #f () #f)))
#|
+-----------------------------------------------------------------------------+
| Exercise 350.                                                               |
| -------------                                                               |
| What is unusual about the definition of this program with respect to the    |
| design recipe?                                                              |
+-----------------------------------------------------------------------------+
|#

; An S-expr is one of: 
; – Atom
; – SL
 
; An SL is one of: 
; – '()
; – (cons S-expr SL)
          

; An Atom is one of: 
; – Number
; – String
; – Symbol 


;; -----------------------------------------------------------------------------

; S-expr -> BSL-expr
(define (parse s)
  (cond
    [(atom? s) (parse-atom s)]
    [else (parse-sl s)]))
 
; SL -> BSL-expr 
(define (parse-sl s)
  (local ((define L (length s)))
    (cond
      [(< L 3) (error WRONG)]
      [(and (= L 3) (symbol? (first s)))
       (cond
         [(symbol=? (first s) '+)
          (make-add (parse (second s)) (parse (third s)))]
         [(symbol=? (first s) '*)
          (make-mul (parse (second s)) (parse (third s)))]
         [else (error WRONG)])]
      [else (error WRONG)])))
 
; Atom -> BSL-expr 
(define (parse-atom s)
  (cond
    [(number? s) s]
    [(string? s) (error WRONG)]
    [(symbol? s) (error WRONG)]))

;; -----------------------------------------------------------------------------

; the template for SL calls for empty? and cons? predicate, this is not
; followed in parse-sl (which decides based on <, =, and > the length of the
; expression)