s c h e m a t i c s : c o o k b o o k

; binary-search : vector-of-numbers number -> (union #f integer)
;   return the index of x in the sorted vector v if x is in v,
;   otherwise return #f
(define (binary-search v x)
  (define (get i)   (vector-ref v i))
  (let loop ([low  0]
             [high (vector-length v)])
    (let ([mid (quotient (+ low high) 2)])
      (cond
        [(>= low high)   #f]
        [(= (get mid) x) mid]
        [(< (get mid) x) (loop (+ mid 1) high)]
        [else            (loop low       mid)]))))

(define v (vector 1 3 5 7 9 11))

(map (lambda (x)
       (binary-search v x))
     (list 0 1 2 3 4 5 6 7 8 9 10 11 12))

; => (#f 0 #f 1 #f 2 #f 3 #f 4 #f 5 #f)