nth list element

Write a recursive function that accepts a list l and a number n and returns the nth element of l (0th element is leftmost).

 $ cat nle.rkt 
 #lang racket 
  
 (define (nth-list-element-generic f) 
  
  ; Return a function accepting a list l and a whole number n 
  ; that calls (f l n) to return the nth element of l (0th 
  ; element is leftmost) if n is in the range [0..(length l)); 
  ; otherwise the function throws an exception. 
  
   (lambda (l n) 
     (if (and (<= 0 n) (< n (length l))) 
       (f l n) 
       (error (format 
         "the element index ~a is out of the range [0..~a)" 
         n (length l)))))) 
  
  
 (define nth-list-element-recursive 
  
   (nth-list-element-generic   
     (lambda (l n) 
       (let loop ((l l) (n n)) 
         (if (zero? n) 
           (car l) 
           (loop (cdr l) (- n 1))))))) 
  
  
 (define nth-list-element-iterative 
  
   (nth-list-element-generic 
     (lambda (l n) 
       (do ((l l (cdr l)) (n n (- n 1))) ((zero? n) (car l)) 
         (void))))) 
  
  
 (require rackunit "utl.rkt") 
  
 (define (test-it f n) 
  
   (let 
  
     ((l (vector->list (iota-vector n))) 
      (ce (lambda (l n) 
            (check-exn exn:fail? (lambda () (f l n)))))) 
  
     (do ((i 0 (+ i 1))) ((= i n) (void)) 
       (check-eq? (f l i) i)) 
      
     (ce '() 0) 
     (ce l -1) 
     (ce l n))) 
  
 (test-it nth-list-element-recursive 10) 
 (test-it nth-list-element-iterative 10) 
  
 $ racket nle.rkt 
  
 $