; damm algorithm
; http://en.wikipedia.org/wiki/Damm_algorithm

(define (digits n . args)
  (let ((b (if (null? args) 10 (car args))))
    (let loop ((n n) (d '()))
      (if (zero? n) d
          (loop (quotient n b)
                (cons (modulo n b) d))))))

(define damm '#(
  #(0 3 1 7 5 9 8 6 4 2)
  #(7 0 9 2 1 5 4 8 6 3)
  #(4 2 0 6 8 7 1 3 5 9)
  #(1 7 5 0 9 8 3 4 2 6)
  #(6 1 2 3 0 4 5 9 7 8)
  #(3 6 7 4 2 0 9 5 8 1)
  #(5 8 6 9 7 2 0 1 3 4)
  #(8 9 4 5 3 6 2 0 1 7)
  #(9 4 3 8 6 1 7 2 0 9)
  #(2 5 8 1 4 3 6 7 9 0)))

(define (check num)
  (let loop ((d 0) (ds (digits num)))
    (if (null? ds) (+ (* num 10) d)
      (loop (vector-ref (vector-ref damm d) (car ds)) (cdr ds)))))

(define (valid? num)
  (let loop ((d 0) (ds (digits num)))
    (if (null? ds) (zero? d)
      (loop (vector-ref (vector-ref damm d) (car ds)) (cdr ds)))))

(display (check 572)) (newline)
(display (valid? 5724)) (newline)

5724
#t