```(**************************************************************************)
(*                                                                        *)
(*  Copyright (C) Jean-Christophe Filliatre                               *)
(*                                                                        *)
(*  This software is free software; you can redistribute it and/or        *)
(*  modify it under the terms of the GNU Library General Public           *)
(*  described in file LICENSE.                                            *)
(*                                                                        *)
(*  This software is distributed in the hope that it will be useful,      *)
(*  but WITHOUT ANY WARRANTY; without even the implied warranty of        *)
(*  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.                  *)
(*                                                                        *)
(**************************************************************************)

(* Persistent arrays implemented using Backer's trick.

A persistent array is a usual array (node Array) or a change into
another persistent array (node Diff). Invariant: any persistent array is a
(possibly empty) linked list of Diff nodes ending on an Array node.

As soon as we try to access a Diff, we reverse the linked list to move
the Array node to the position we are accessing; this is achieved with
the reroot function.
*)

type 'a t = 'a data ref
and 'a data =
| Array of 'a array
| Diff of int * 'a * 'a t

let create n v = ref (Array (Array.create n v))
let make = create

let init n f = ref (Array (Array.init n f))

(* reroot t ensures that t becomes an Array node *)
let rec reroot t = match !t with
| Array _ -> ()
| Diff (i, v, t') ->
reroot t';
begin match !t' with
| Array a as n ->
let v' = a.(i) in
a.(i) <- v;
t := n;
t' := Diff (i, v', t)
| Diff _ -> assert false
end

(* we rewrite it using CPS to avoid a possible stack overflow *)
let rec rerootk t k = match !t with
| Array _ -> k ()
| Diff (i, v, t') ->
rerootk t' (fun () -> begin match !t' with
| Array a as n ->
let v' = a.(i) in
a.(i) <- v;
t := n;
t' := Diff (i, v', t)
| Diff _ -> assert false end; k())

let reroot t = rerootk t (fun () -> ())

let rec get t i = match !t with
| Array a ->
a.(i)
| Diff _ ->
reroot t;
begin match !t with Array a -> a.(i) | Diff _ -> assert false end

let set t i v =
reroot t;
match !t with
| Array a as n ->
let old = a.(i) in
if old == v then
t
else begin
a.(i) <- v;
let res = ref n in
t := Diff (i, old, res);
res
end
| Diff _ ->
assert false

(* wrappers to apply an impure function from Array to a persistent array *)
let impure f t =
reroot t;
match !t with Array a -> f a | Diff _ -> assert false

let length t = impure Array.length t

let to_list t = impure Array.to_list t

let iter f t = impure (Array.iter f) t
let iteri f t = impure (Array.iteri f) t

let fold_left f acc t = impure (Array.fold_left f acc) t
let fold_right f t acc = impure (fun a -> Array.fold_right f a acc) t

```

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