#lang racket

; a binary numeric tree is a
; leaf vertex - which is a single element list containing a number
; internal vertes - which is a 2-element list, each element being
;   a binary numeric tree.

; constructors are not needed since we just use list operations, and
; we are being lazy.
(define (MakeLeaf v) (list v))
(define (Join t0 t1) (list t0 t1))

; fetch Left and Right subtrees
(define Left (lambda (tree) (first tree)))
(define Right (lambda (tree) (second tree)))
(define Value (lambda (tree) (first tree)))

; is the tree a leaf?
(define AtBase? (lambda (tree) (null? (rest tree))))
; if so, you can fetch the leaf value
(define BaseCase (lambda (tree) (first tree)))
; if not, you can add together the two subtrees
(define Combine (lambda (tree l r) (+ l r)))

(define val (lambda (tree)
              (if (AtBase? tree) (BaseCase tree)
                  (Combine tree (val (Left tree)) (val (Right tree))) )))

(define val-cc (lambda (tree cc)
   (if (AtBase? tree) (cc (BaseCase tree))
       (val-cc (Left tree) 
               (lambda (lval) (val-cc (Right tree)
                 (lambda (rval) (cc (Combine tree lval rval)))))))
))

(define t '( (1) ( (2)  (3) )))
(val t)
(val-cc t (lambda (x) x))