(************************************************************************)
(*         *      The Rocq Prover / The Rocq Development Team           *)
(*  v      *         Copyright INRIA, CNRS and contributors             *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(*   \VV/  **************************************************************)
(*    //   *    This file is distributed under the terms of the         *)
(*         *     GNU Lesser General Public License Version 2.1          *)
(*         *     (see LICENSE file for the text of the license)         *)
(************************************************************************)
(** * Memoization *)
(** Successive outputs of a given function [f] are stored in a stream in order to avoid duplicated computations. *)
Section MemoFunction.
Variable A: Type.
Variable f: nat -> A.
CoFixpoint memo_make (n:nat) : Stream A := Cons (f n) (memo_make (S n)).
Definition memo_list := memo_make 0.
Fixpoint memo_get (n:nat) (l:Stream A) : A :=
match n with
| O => hd l
| S n1 => memo_get n1 (tl l)
end.

(* Specifications: *)
Theorem memo_get_correct: forall n, memo_get n memo_list = f n.
Variable g: A -> A.