#lang racket
(require racket/trace)
(require "chez-init.rkt")

;; (define zero (lambda () '()))
;; (define iszero? null?)
;; (define successor (lambda (n) (cons 42 n)))
;; (define predecessor cdr)

(define zero (lambda () 0))
(define iszero? zero?)
(define successor (lambda (n) (+ 1 n)))
(define predecessor (lambda (n) (- n 1)))

;(define-datatype number number?
;  'nyi)


(define one (successor (zero)))
(define two (successor (successor (zero))))

;;; Code below is implementation independent
(define plus
  (lambda (x y)
    (if (iszero? x)
        y
        (successor (plus (predecessor x) y)))))

(define-datatype bintree bintree?
  [null-node]
  [leaf-node
   (datum number?)]
  [interior-node
   (datum number?)
   (left-tree bintree?)
   (right-tree bintree?)])

(define sum
  (lambda (t)
    (cases bintree t
      [null-node () 0]
      [leaf-node (datum) datum]
      [interior-node (datum pig cow) (+ datum (sum pig)(sum cow))])))

(define t1 (leaf-node 3))
(define t2 (leaf-node 4))
(define t3 (interior-node 5 t1 t2))
(define t4 (interior-node 6 t3 (leaf-node 7)))

;; bintree with null nodes.

;; (define-datatype bintree bintree?
;;   [leaf-node
;;    (datum number?)]
;;   [null-node]
;;   [interior-node
;;    (datum number?)
;;    (left-tree bintree?)
;;    (right-tree bintree?)])

;; (define sum
;;   (lambda (tree)
;;     (cases bintree tree
;;       [null-node () 0]
;;       [leaf-node (datum) datum]
;;       [interior-node (datum left
;;                             right)
;;                      (+ datum (sum left) (sum
;;                                           right))])))
;;(trace sum)

;; (define-datatype bintree bintree?
;;   [leaf-node
;;    (datum foo?)]
;;   [interior-node
;;    (datum number?)
;;    (left-tree bintree?)
;;    (right-tree bintree?)])
;;
;; (define foo?
;;   (lambda (x)
;;     (or (number? x)(null? x))))
;;
;; (define sum
;;   (lambda (tree)
;;     (cases bintree tree
;;       [leaf-node (datum) (if (null? datum)
;;                              0
;;                              datum)]
;;       [interior-node (datum left right)
;;                      (+ datum (sum left) (sum
;;   right))])))
;;(trace sum)