Перевод из одной системы счисления в другую

(define (correct-number? s b)
  (define (iter xs b)
    (if (null? xs) (null? xs) (f (cond
                                ((<= (char->integer (car xs)) (char->integer #\9))
                                     (- (char->integer (car xs)) (char->integer #\0)))
                                ((<= (char->integer (car xs)) (char->integer #\Z))
                                     (+ (- (char->integer (car xs)) (char->integer #\A)) 10))
                                ((<= (char->integer (car xs)) (char->integer #\z))
                                     (+ (- (char->integer (car xs)) (char->integer #\a)) 10)))
  (cdr xs) b)))
  (define (f x xs b)
    (if (< x b) (iter xs b) (< x b)))
(iter (string->list s) b))



(define (certain->decimal s b)
  (define (f1 n b k)
    (if (= n 1)
        k
        (f1 (- n 1) b (* k b))))
  (define (iter xs b k it)
    (if (null? xs)
        it
        (f (cond
             ((<= (char->integer (car xs)) (char->integer #\9)) (- (char->integer (car xs)) (char->integer #\0)))
             ((<= (char->integer (car xs)) (char->integer #\Z)) (+ (- (char->integer (car xs)) (char->integer #\A)) 10))
             ((<= (char->integer (car xs)) (char->integer #\z)) (+ (- (char->integer (car xs)) (char->integer #\a)) 10)))
           (cdr xs) b k it)))
  (define (f x xs b k it)
    (if (< x b)
        (iter xs b (quotient k b) (+ it (* x k)))
        'number-conversion-error))
  (iter (string->list s) b (f1 (string-length s) b 1) 0))



(define (decimal->certain d b)
  (define (f d b k)
    (if (< d b)
        k
        (f (quotient d b) b (* k b))))
  (define (iter xs d b k)
    (if (zero? k)
        (if (null? xs)
            "0"
            (list->string xs))
        (iter (append xs (list (cond
                                ((<= (quotient d k) 9) (integer->char (+ (quotient d k) (char->integer #\0))))
                                ((<= (quotient d k) 35) (integer->char (+ (- (quotient d k) 10) (char->integer #\a)))))))
           (remainder d k) b (quotient k b))))
  (if (< b 37)
      (iter '() d b (f d b 1))))