(use-syntax (ice-9 syncase))

(define (operator? x)
  (and (member x '(#\+ #\- #\/ #\*)) #t))

(define (separator? x)
  (and (member x '(#\space #\tab #\newline)) #t))

(define (digit? x)
  (and (<= 48 (char->integer x))
       (>= 57 (char->integer x))))

(define-syntax ++
  (syntax-rules ()
    ((_ i) (+ i 1))))

(define-syntax while
  (syntax-rules ()
    ((while a expr ...)
     (let loop ()
       (if a (begin expr ... (loop)))))))

(define (check-integer string)
  (let loop ((i 0))
    (cond ((= i (string-length string)))
          ((or (and (= i 0) (> (string-length string) 1) (operator? (string-ref string i)))
               (digit? (string-ref string i)))
           (loop (++ i)))
          (else #f))))

(define (scan-integer string)
  (cond ((check-integer string) string)
        (else #f)))

(define (scan-many-integers string)
  (let loop ((i 0)
             (start 0)
             (res '()))
    (cond ((= i (string-length string)) (make-numbers (reverse (cons (substring string start i) res))))
          ((separator? (string-ref string i)) (loop (++ i) (++ i) (if (not (= i start))
                                                                   (cons (substring string start i) res)
                                                                   res)))
          ((or (and (= i start) (operator? (string-ref string i)))
               (digit? (string-ref string i)))
           (loop (++ i) start res))
          (else #f))))

(define (empty? xs)
  (member (car xs) '("+" "-" "/" "*")))

(define (make-numbers xs)
  (cond ((null? xs) '())
        ((empty? xs) #f)
        (else (if (not (equal? (car xs) ""))
                  (cons (string->number (car xs)) (make-numbers (cdr xs)))
                  (make-numbers (cdr xs))))))