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(*  OCaml code from the book ``Learn Programming with OCaml''       *)
(*  See https://usr.lmf.cnrs.fr/lpo/                                *)
(*                                                                  *)
(*  Sylvain Conchon and Jean-Christophe Filliâtre                   *)
(*  Copyright 2025 Université Paris-Saclay and CNRS                 *)
(*                                                                  *)
(*  Openly licensed via CC BY SA 4.0                                *)
(*  See https://creativecommons.org/licenses/by-sa/4.0/deed.en      *)
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(* Program 74 on page 330
   A zipper structure on a binary tree *)

  type 'a tree = E | N of 'a tree * 'a * 'a tree

  type 'a path =
    | Top
    | Left of 'a path * 'a * 'a tree
    | Right of 'a tree * 'a * 'a path

  type 'a zipper = { path: 'a path; tree: 'a tree }

  let of_tree t = { path = Top; tree = t }

  let down_left z = match z.tree with
    | E -> invalid_arg "down_left"
    | N (l, x, r) -> { path = Left (z.path, x, r); tree = l }

  let down_right z = match z.tree with
    | E -> invalid_arg "down_right"
    | N (l, x, r) -> { path = Right (l, x, z.path); tree = r }

  let up z = match z.path with
    | Top ->
        invalid_arg "up"
    | Left (p, x, r) ->
        { path = p; tree = N (z.tree, x, r) }
    | Right (l, x, p) ->
        { path = p; tree = N (l, x, z.tree) }

  let rec to_tree z =
    if z.path = Top then z.tree else to_tree (up z)

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