(defun  inf-to-pre  (ae)
  (cond  ((atom ae)  ae)
         (T  (inf-aux  ae nil nil))))

(defun  inf-aux  (ae  operators operands)
  (inf-iter  (cdr  ae)
             operators
             (cons  (inf-to-pre  (car ae))  operands)))

(defun  inf-iter  (ae  operators operands)
  (cond  ((and  (null  ae)  (null  operators))
          (car  operands))
         ((and  (not  (null  ae))
                (or   (null operators)
                      (> (weight  (car  ae))
                         (weight  (car  operators)))))
          (inf-aux  (cdr  ae)
                    (cons  (car  ae)  operators)
                    operands))
         (T  (inf-iter  ae
                        (cdr  operators)
                        (cons  (list  (opcode  (car  operators))
                                      (cadr  operands)
                                      (car  operands))
                               (cddr  operands))))))

(defun  weight  (operator)
  (cond  ((equal  operator '=)  0)
         ((equal  operator '+)  1) 
         ((equal  operator '-)  1) 
         ((equal  operator '*)  2) 
         ((equal  operator '/)  2) 
         ((equal  operator '\\) 2) 
         ((equal  operator '^)  3)
         (T  (print  `(,operator not an operator)) 4)))
 
(defun  opcode  (operator)
  (cond  ((equal  operator '=)  'setq)
         ((equal  operator '+)  '+)
         ((equal  operator '-)  '-)
         ((equal  operator '*)  '*)
         ((equal  operator '/)  '/)
         ((equal  operator '\\) 'rem)
         ((equal  operator '^)  'expt)
         (T  (print  `(,operator not an operator)) operator)))