(** This module gives lists with internal binders. *)

type ('a, 'b) t =
  | BNil
  | BCons of 'a * ('a, 'b) t
  | BNew of ('b -> ('a, 'b) t)

let (^::) x l = BCons (x, l)

let rec (^@) l1 l2 = match l1 with
  | BNil -> l2
  | BCons (x, l1') -> BCons (x, l1' ^@ l2)
  | BNew f -> BNew (fun x -> f x ^@ l2)

let (?^) f = BNew f

let b_rev l =
  let rec rev_acc acc = function
    | BNil -> acc
    | BCons (x, l) -> rev_acc (BCons (x, acc)) l
    | BNew f -> BNew (fun x -> rev_acc acc (f x)) in
  rev_acc BNil l