; find x[i] = i in an array

(define x (vector -3 -1 0 3 5 7))
(define y (vector -3 -1 0 2 5 7))

(define (f x)
  (let loop ((i 0))
    (cond ((= i (vector-length x)) -1) ; not present
          ((= i (vector-ref x i)) i) ; found solution
          (else (loop (+ i 1)))))) ; try next element

(display (f x)) (newline)
(display (f y)) (newline)

(define (f x)
  (let loop ((lo 0) (hi (- (vector-length x) 1)))
    (if (< hi lo) -1 ; not present
      (let ((mid (quotient (+ lo hi) 2)))
        (cond ((< (vector-ref x mid) mid)
                (loop (+ mid 1) hi))
              ((< mid (vector-ref x mid))
                (loop lo (- mid 1)))
              (else mid)))))) ; found solution

(display (f x)) (newline)
(display (f y)) (newline)

3
-1
3
-1