#reader(lib "htdp-intermediate-reader.ss" "lang")((modname main) (read-case-sensitive #t) (teachpacks ()) (htdp-settings #(#t constructor repeating-decimal #f #t none #f () #f)))

; A MaybeTree is one of
; - (make-tree [Number MaybeTree MaybeTree])
(define-struct tree [n left right])
; - 'end

(define sprout (make-tree 0 'end 'end))
(define seedling (make-tree 5 sprout (make-tree 6 'end 'end)))
(define sapling (make-tree 10 (make-tree 6 sprout 'end) (make-tree 12 'end 'end)))
(define good-tree (make-tree 50 sapling (make-tree 100 'end 'end)))
(define broke-tree (make-tree 5 good-tree good-tree))

; Tree -> Bool
; Determines whether a Tree is a binary search tree.
(define (bst? t)
  (local [; Tree Number -> Bool
          ; Recursively checks left and right.
          (define (recurse t)
            (or (and (symbol? t) (symbol=? t 'end))
                (and (acc-right (tree-right t) (tree-n t))
                     (acc-left (tree-left t) (tree-n t)))))

          ; Tree Number -> Bool
          ; Accumulates the current number to check left.
          (define (acc-left t n)
            (or (and (symbol? t) (symbol=? t 'end))
                (and (< (tree-n t) n) (recurse t))))

          ; Tree Number -> Bool
          ; Accumulates the current number to check right.
          (define (acc-right t n)
            (or (and (symbol? t) (symbol=? t 'end))
                (and (> (tree-n t) n) (recurse t))))]
    (recurse t)))

(check-expect (bst? sprout) #t)
(check-expect (bst? sapling) #t)
(check-expect (bst? good-tree) #t)
(check-expect (bst? broke-tree) #f)