nth bst value

Write a function that accepts a binary search tree and a non-negative integer n and returns the nth value in the tree.

 $ cat ntv.rkt 
 #lang racket 
  
 (require "bst.rkt") 
  
 (define (nth-value root n) 
  
   ; If the given binary search tree defines a sequence of at least n 
   ; values, return true and the nth value in the sequence (0th value 
   ; is the smallest), otherwise return false and an undefined value. 
  
   (define (dive root values-to-go) 
     (if (root 'is-empty?) 
       (values values-to-go #f) 
       (let-values 
         (((values-left value) (dive (root 'left-child) values-to-go))) 
         (cond 
           ((= values-left 0) 
             (values values-left value)) 
           ((= values-left 1) 
             (values 0 (root 'value))) 
           (#t 
             (dive (root 'right-child) (- values-left 1))))))) 
  
   (if (< n 0) 
     (values #f #f) 
     (let-values (((values-left value) (dive root (+ n 1)))) 
       (values (= values-left 0) value)))) 
  
  
 (require rackunit "utl.rkt" srfi/1) 
  
 (let ((n 6)) 
   (call-with-list-permutations (iota n) 
     (lambda (p) 
       (let ((t (fold (lambda (v t) (t 'add v)) (binary-search-tree) p))) 
         (do ((i 0 (+ i 1))) ((>= i n) #t) 
           (let-values (((found value) (nth-value t i))) 
             (check-eq? found #t) 
             (check-eq? value i))))))) 
              
 $ mzscheme ntv.rkt 
  
 $