(define (make-tree entry left right)
  (list entry left right))

(define (entry tree) (car tree))

(define (left tree) (cadr tree))

(define (right tree) (caddr tree))

(define (parse expr)
  (parse-helper expr '() '()))

(define (parse-helper expr operators operands)
  (cond ((null? expr)
         (if (null? operators)
             (car operands)
             (handle-op '() operators operands)))
        ((number? (car expr))
         (parse-helper (cdr expr)
                       operators
                       (cons (make-tree (car expr) '() '()) operands)))
        ((list? (car expr))
         <???>
         (else (if (or (null? operators)
                       (> (precedence (car expr))
                          (precedence (car operators))))
                   <???>
                   <???> ))))
  
  ; form a subtree with the first operator and the first two operands and continue parsing
  (define (handle-op expr operators operands)
    (parse-helper expr
                  (cdr operators)
                  (cons (make-tree (car operators)
                                   (cadr operands)
                                   (car operands))
                        (cddr operands))))
  
  (define (precedence oper)
    (if (member oper '(+ -)) 1 2))
  
  (define (compute tree)
    <???>)
  
  (define (function-named-by oper)
    (cond ((equal? oper '+) +)
          ((equal? oper '-) -)
          ((equal? oper '*) *)
          ((equal? oper '/) /)
          (else (error "no such operator as" oper))))