#lang racket

; transform an infix expression tree E into an quoted s-expression that
; when eval'd evaulates to the value of the expression tree E.  For example
; (exp-translate '( (1 + x) * (3 + (4 / 5)) )) is 
;      '(* (+ 1 x) (+ 3 (/ 4 5)))


(define (exp-translate ex)
  (cond
    ; atoms are themselves
    [ (not (list? ex)) ex ]  
    ; single element lists are the value of their first element, so 
    ; drill down
    [ (null? (rest ex)) (exp-translate (first ex)) ] 
    
    ; binary expressions just need to be rewritten in prefix form
    [ else (list (second ex) 
                 (exp-translate (first ex)) 
                 (exp-translate (third ex))) ]
    ))


(define (etest E) 
  (let [ (T (exp-translate E) ) ]
    (fprintf (current-output-port)
           ;"~a => ~s evals to "
           "(exp-translate ~v) is ~v\n"
           E T)
           
    ;(displayln (eval T))
    ))

(define (testseq) 
  
   ;(etest '1)
   ;(etest '(1))
   (etest '(1 + 2))
   (etest '(3 * 4))
   (etest '( (1 + 2) * (3 + 4) ))
   ; these next one should fail unless x is defined 
   (define x 42)
   (etest 'x)
   (etest '(1 + x))
   )
  
(testseq)