(define-structure (tree-empty))
(define-structure (tree-branch value l r))

(define emptytree (make-tree-empty))
(define exampletree
    (make-tree-branch
        30
        (make-tree-branch
            20
            (make-tree-branch
                10
                emptytree
                emptytree)
            emptytree)
        (make-tree-branch
            15
            (make-tree-branch
                40
                emptytree
                (make-tree-branch
                    14
                    emptytree
                    emptytree))
            (make-tree-branch
                70
                (make-tree-branch
                    8
                    emptytree
                    emptytree)
                emptytree))))

(define-structure (path-none))
(define-structure (path-empty))
(define-structure (path-some value rest))

(define nopath (make-path-none))
(define emptypath (make-path-empty))

; given: a value, a binary tree, a path so far to get to this tree
; returns: false if the value is not in the tree
;          the path to the value if the value is in the tree
(define depth-first-search
   (lambda (value tree path)
       (cond ((tree-empty? tree)
              nopath)
             ((eq? value (tree-branch-value tree))
              (make-path-some (tree-branch-value tree) path))
             (else ((lambda (path-l)
                        (if (path-none? path-l)
                            (depth-first-search
                                 value
                                 (tree-branch-r tree)
                                 (make-path-some (tree-branch-value tree)
                                                 path))
                            path-l))
                    (depth-first-search
                         value
                         (tree-branch-l tree)
                         (make-path-some (tree-branch-value tree) path)))))))

(depth-first-search 14 exampletree emptypath)