```(***********************************************************************)
(*                                                                     *)
(*  OCaml library from the book ``Apprendre à programmer avec OCaml''  *)
(*                                                                     *)
(*  Sylvain Conchon and Jean-Christophe Filliâtre                      *)
(*  Université Paris Sud                                               *)
(*                                                                     *)
(*  file is distributed under the terms of the GNU Library General     *)
(*  Public License, with the same special exception on linking as the  *)
(*  OCaml library. See http://caml.inria.fr/ocaml/license.fr.html      *)
(*                                                                     *)
(***********************************************************************)

(* Programme 36 page 209
Équilibrage d'un AVL *)

let balance l v r =
let hl = height l in
let hr = height r in
if hl > hr + 1 then begin
match l with
| Node (ll, lv, lr, _) when height ll >= height lr ->
node ll lv (node lr v r)
| Node (ll, lv, Node (lrl, lrv, lrr, _),_)->
node (node ll lv lrl) lrv (node lrr v r)
| _ ->
assert false
end else if hr > hl + 1 then begin
match r with
| Node (rl, rv, rr, _) when height rr >= height rl ->
node (node l v rl) rv rr
| Node (Node(rll, rlv, rlr, _), rv, rr, _) ->
node (node l v rll) rlv (node rlr rv rr)
| _ ->
assert false
end else
node l v r
```

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