;; compare Program 7.28, pg. 227
;; In the following I have put leaf? inside the definition of deep-recur,
;; since if clients use deep-recur, they will not need leaf?.

(define deep-recur
  ; TYPE: (-> (T (-> (S T) T) (-> (T T) T)) (-> ((tree S)) T))
  (lambda (seed item-proc list-proc)
    ; ENSURES: (result '()) = seed,
    ;          (result (cons x t)) = (item-proc x (result t)),
    ;          (result (cons t1 t2)) = (list-proc (result t1) (result t2))
    ;  where x:a and t1,t2:tree of a
    (letrec
      ((helper  ; TYPE: (-> ((tree S)) T)
         (lambda (ls)
           (if (null? ls)
               seed
               (let ((a (car ls)))
                 (if (leaf? a)
                     (item-proc a (helper (cdr ls)))
                     (list-proc (helper a) (helper (cdr ls)))))
	       )))
       (leaf? ; TYPE: (-> (datum) boolean)
	(lambda (x)
	  ; ENSURES: result is true iff x is a leaf of a tree
	  (not (or (pair? x) (null? x))))
	))
      helper)))