; Funciones de listas
; (member a l) retorna la sublista que contiene a o #f
(define (member a l)
   (if (null? l)
        #f
        (if (equal? a (car l))
            l
            (member a (cdr l)) )))

; (append l1 l2) concatena listas
(define (append l1 l2)
   (if (null? l1)
        l2
        (cons (car l1) (append (cdr l1) l2)) ))

; (reverse l) invierte lista
(define (reverse l)
   (if (null? l)
        '()
        (append (reverse (cdr l)) (cons (car l) '())) ))

; Evaluador de expresion de arbol
; expresiones binarias como '(+ (* 1 2) 3)

(define (evtree expr)
    (if (null? expr)
        (error "Bad Expr ~S" expr)
        (cond
          ((number? expr)
            expr )
          ((symbol? (car expr))
            ((eval (car expr)) (evtree (cadr expr)) (evtree (caddr expr))) )
          (else
            (error "Bad Expr ~S" expr) ))))

; Evaluador de prefijo
; expresiones como '(+ * 1 2 3)

(define (evpref expr)
  (define (recpref)
    (let ((aux 0))
        (if (null? expr)
            (error "Bad Expr")
            (cond
              ((number? (car expr))
                (set! aux (car expr))
                (set! expr (cdr expr))
                aux )

              ((symbol? (car expr))
                (set! aux (car expr))
                (set! expr (cdr expr))
                ((eval aux) (recpref) (recpref)) )

              (else
                (error "Bad Expr") )))))

  (recpref) )

  
;; Imprime en infijo expresiones de prefijo

(define (dtree expr)
    (if (null? expr)
        (error "Bad Expr ~S" expr)
        (cond
          ((number? expr)
            (display expr) )
          ((symbol? (car expr))
            (display "(")
            (dlist (car expr) (cdr expr))
            (display ")") )
          (else
            (error "Bad Expr ~S" expr) ))))

(define (dlist op largs)
   (dtree (car largs))
   (if (pair? (cdr largs))
     (begin
           (display op)
           (dlist op (cdr largs)) )))  

;; Imprime en infijo expresiones de prefijo
;; Sin parentesis superfluos
        
(define (dptree expr)
   (define (dptreein expr op)
    (if (null? expr)
        (error "Bad Expr ~S" expr)
        (cond
          ((number? expr)
            (display expr) )
          ((symbol? (car expr))
            (if (not (eq? (car expr) op))
                (display "(") )
            (dplist (car expr) (cdr expr))
            (if (not (eq? (car expr) op))
                (display ")") ))
          (else
            (error "Bad Expr ~S" expr) ))))

   (define (dplist op largs)
      (dptreein (car largs) op)
      (if (pair? (cdr largs))
        (begin
             (display op)
             (dplist op (cdr largs)) )))


   (dptreein expr ())
   (newline) )