(* 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.
Opaque int64bv.sign.
Opaque int64bv.to_Z.
Opaque negb.
Opaque ediv_Z.
Opaque Z.add.
Opaque Z.sub.
Opaque Z.mul.
Opaque N.add.
Opaque N.sub.

  Lemma ep_updateTokenPool_correct
        (env : @proto_env dexter_definition.self_type)
        (p : data dexter_definition.parameter_ep_updateTokenPool_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_seq_precond fuel env Def.ep_updateTokenPool
                 (fun x => x = (ret_ops, ret_sto, tt))
                 (p, (sto, tt)) <->
    Spec.ep_updateTokenPool env p sto ret_ops ret_sto.
  Proof.
    intros Hfuel.
    auto_fuel.
    destruct_sto sto
                 tokenPool xtzPool lqtTotal selfIsUpdatingTokenPool freezeBaker manager tokenAddress lqtAddress.
    unfold Spec.ep_updateTokenPool.
    unfold dexter_definition.Storage.sto_selfIsUpdatingTokenPool.
    unfold Spec.fa12.is_ep_getBalance. unfold Spec.fa12.ep_getBalance_annot.
    unfold Spec.env_self_address'. unfold dexter_definition.Storage.sto_tokenAddress.
    unfold dexter_definition.Storage.sto_set_selfIsUpdatingTokenPool.

    unfold Spec.fa12.getBalance.
    unfold Spec.env_self_address_ep_default.
    unfold Spec.fa12.ep_getBalance_ty.
    unfold dexter_definition.parameter_ep_default_ty.
    destruct p.
    rewrite Bool.negb_false_iff. rewrite (eqb_eq address).
    rewrite lt_is_leb.
    rewrite Bool.negb_false_iff. rewrite ex_and_comm.
    rewrite comparison_to_int_tez_compare_le_zero.
    intuition.
    - destruct H2.
      exists x. destruct H1. destruct H2. injection H3. intros.
      intuition; subst;  try reflexivity; try assumption.
    - destruct H. destruct H. destruct H0. destruct H0. destruct H1.
      assumption.
    -  destruct H. destruct H. destruct H0; assumption.
    - destruct H. destruct H. destruct H0. destruct H1.
      destruct H2. destruct H3.
      exists x.
      subst. intuition; subst; try reflexivity; try assumption; auto.
      intuition.
      apply Bool.eq_bool_prop_intro.
      destruct selfIsUpdatingTokenPool; try easy.
  Qed.