(define-struct dir (name contents))

; Clearly don't need to recur on the natural number.
;(define (g a-dir n)
;  ...(dir-name a-dir)...
;  ...(f (dir-contents a-dir) n)...)

; dir-files-at-depth : dir nat -> lof
(define (dir-files-at-depth a-dir n)
  (lofd-files-at-depth (dir-contents a-dir) n))


;(define (f a-lofd n)
;  (cond [(and (empty? a-lofd)
;	      (zero? n))
;	 ...]
;	[(and (empty? a-lofd)
;	      (positive? n))
;	 ...(f a-lofd (sub1 n))...]
;	[(and (cons? a-lofd) (symbol? (first a-lofd))
;	      (zero? n))
;	 ...(first a-lofd)...
;	 ...(f (rest a-lofd) n)...]
;	[(and (cons? a-lofd) (symbol? (first a-lofd))
;	      (positive? n))
;	 ...(first a-lofd)...
;	 ...(f (rest a-lofd) n)...]
;	 ...(f a-lofd (sub1 n))...]
;	 ...(f (rest a-lofd) (sub1 n))...]
;	[(and (cons? a-lofd) (dir? (first a-lofd))
;	      (zero? n))
;	 ...(g (first a-lofd))...
;	 ...(f (rest a-lofd) n)...]
;	[(and (cons? a-lofd) (dir? (first a-lofd))
;	      (positive? n))
;	 ...(g (first a-lofd))...
;	 ...(f (rest a-lofd) n)...]
;	 ...(f a-lofd (sub1 n))...]
;	 ...(f (rest a-lofd) (sub1 n))...]))



; lofd-files-at-depth : lofd nat -> lof
; The first two cases of the template have been combined.
(define (lofd-files-at-depth a-lofd n)
  (cond [(empty? lofd)
	 empty]
	[(and (cons? lofd) (symbol? (first lofd))
	      (zero? n))
	 (cons (first lofd)
	       (lofd-files-at-depth (rest lofd) n)))]
	[(and (cons? lofd) (symbol? (first lofd))
	      (positive? n))
	 (lofd-files-at-depth (rest lofd) n)]
	[(and (cons? lofd) (dir? (first lofd))
	      (zero? n))
	 (lofd-files-at-depth (rest lofd) n)]
	[(and (cons? lofd) (dir? (first lofd))
	      (positive? n))
	 (append (dir-files-at-depth (first lofd) (sub1 n))
		 (lofd-files-at-depth (rest lofd) n))]))