(* Open Source License *)
(* Copyright (c) 2019 Nomadic Labs. <contact@nomadic-labs.com> *)

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(* copy of this software and associated documentation files (the "Software"), *)
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(* Coq *)
Require Import String.
Require Import Michocoq.macros.
Import syntax.
Import comparable.
Require Import NArith.
Require Import ZArith.
Require Import Coq.Setoids.Setoid.
Require Import Coq.micromega.Lia.
From Coq Require Import Program.Tactics.

(* Mi-Cho-Coq *)
Require Import semantics.
Require Import util.
Import error.
Require List.

(* Dexter *)
Require dexter_definition.
Require dexter_spec.
Require Import dexter_util.
Require Import dexter_spec_util.

Module Spec := dexter_spec.

Module Def := dexter_definition.

Import Def.Storage.

Import Tactics.

Require Import contract_semantics.


(* It's better not to unfold compare in this proof,
 * this makes it easier to use util.eqb_eq.
 *)
Opaque N.mul.
Opaque N.add.
Opaque Z.modulo.
Opaque compare.

Lemma ep_addLiquidity_correct
        (env : @proto_env dexter_definition.self_type)
        (p : data dexter_definition.parameter_ep_addLiquidity_ty)
        (sto : data dexter_definition.storage_ty)
        (ret_ops : Datatypes.list (data operation))
        (ret_sto : data dexter_definition.storage_ty)
        (fuel : Datatypes.nat) :
    (* TODO: fuel may have to be adapted to suit the entrypoint *)
    400 <= fuel ->

    eval_precond fuel env Def.ep_addLiquidity
                 (fun x => x = (ret_ops, ret_sto, tt))
                 (p, (sto, tt)) <->
    Spec.ep_addLiquidity env p sto ret_ops ret_sto.
  Proof.
    intros Hfuel.
    destruct_sto sto tokenPool xtzPool lqtTotal selfIsUpdatingTokenPool freezeBaker manager tokenAddress lqtAddress.
    destruct p as (owner, (min_lqt_minted, (max_tokens_deposited, deadline))).

  (*
   * unfold Spec.ep_addLiquidity.
   * unfold Spec.ep_addLiquidity_header.
   * 
   * 
   * (*
   *  * re-order conjuncts to match spec.
   *  *)
   * repeat rewrite and_assoc.
   * repeat apply and_both_0_inv.
   * 
   * simpl (Spec.Storage.sto_lqtTotal _).
   * destruct lq_total; simpl;
   *   repeat fold_eval_precond;
   *   rewrite fold_eval_seq_precond_aux.
   * 
   * - rewrite ep_addLiquidity_no_lqt_correct; [| lia].
   * 
   *   unfold Spec.ep_addLiquidity_no_lqt.
   *   ex_and_comm_intro c.
   *   ex_and_comm_intro x.
   *   intuition.
   * - rewrite ep_addLiquidity_some_lqt_correct; [| lia].
   * 
   *   unfold Spec.ep_addLiquidity_some_lqt.
   *   ex_and_comm_intro c.
   *   ex_and_comm_intro x.
   *   intuition.
   * - rewrite <- comparison_to_int_compare_gt_lt.
   *   apply comparison_to_int_tez_compare_lt_zero.
   * - apply comparison_to_int_compare_nat_lt.
   * - apply comparison_to_int_compare_nat_lt.
   * - apply check_deadline_correct.
   * - apply bool_false_not.
   * - rewrite eqb_eq.
   *   reflexivity.
   * - rewrite eqb_eq.
   *   reflexivity.
   *)
Admitted.