#lang racket

(provide full-parse)

; + - * / ^ ( ) [0-9]

; 5+3*x
(define (full-parse str)
  (define (get-general expr operator next-operation)
    (define (char->wanted c)
      ((if (char-numeric? c)
         string->number string->symbol)
       (string c)))

    ; used to add a completed part of the operation to the list of operations
    ; 5 is one of those in the addition iteration
    ; 3 and x are in the product iteration
    (define (add-operation-to-list operation seq)
      ;(display (list operator "|" operation "|" seq))
      ;(newline)
      (cons (if (= (length operation) 1) 
              (char->wanted (car operation))
              (next-operation operation))
            seq))

    (define (contains value seq)
      (memq value seq))

    (define (inner current-term other-terms remaining-expression)
      (cond
        [(null? remaining-expression)
         (reverse (add-operation-to-list current-term other-terms))]
        [(eqv? (car remaining-expression) operator)
         (inner '() (add-operation-to-list current-term other-terms) (cdr remaining-expression))]
        [else
          (inner (cons (car remaining-expression) current-term) other-terms (cdr remaining-expression))]))

    (if (not (contains operator expr))
      (next-operation expr)
      (cons (char->wanted operator) (inner '() '() expr))))

  (define (create-trace expr ops)
    (lambda (expr) 
      (get-general expr (car ops) 
                   (if (null? (cdr ops))
                     (lambda (x) x)
                     (create-trace expr (cdr ops))))))

  (let ((expr (string->list str)))
    ((create-trace expr '(#\+ #\- #\* #\/)) expr)))