(define factorial
  (lambda (n)
    (do ((i 1 (+ i 1))
         (fact 1 (* fact i)))
      ((> i n) fact))))

(define sum-of-digits
  (lambda (n)
    (do ((n n (quotient n 10))
         (result 0 (+ result (remainder n 10))))
      ((zero? n) result))))

;; return a vector of the same length as the input vector v
;; but having values equal to 1/2 of corresponding element in v
;; e.g.  #(2 4 6) => #(1 2 3)
(define half
  (lambda (v)
     (do ((w (make-vector (vector-length v)))
          (i 0 (+ i 1)))
         ((= i (vector-length v)) w)
         (vector-set! w i (/ (vector-ref v i) 2)))))

;; return a vector containing the reverse of the input vector by Colin Smith
(define reverse
  (lambda (v)
    (let ((w (make-vector (vector-length v)))
          (length (vector-length v)))
      (do ((i (- length 1) (- i 1)))
        ((negative? i) w)
        (vector-set! w (- length (+ i 1)) (vector-ref v i))))))