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

(* Permission is hereby granted, free of charge, to any person obtaining a *)
(* copy of this software and associated documentation files (the "Software"), *)
(* to deal in the Software without restriction, including without limitation *)
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(* Software is furnished to do so, subject to the following conditions: *)

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(* in all copies or substantial portions of 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_setBaker_correct
      (env : @proto_env dexter_definition.self_type)
      (p : data dexter_definition.parameter_ep_setBaker_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_setBaker
                 (fun x => x = (ret_ops, ret_sto, tt))
                 (p, (sto, tt)) <->
    Spec.ep_setBaker env p sto ret_ops ret_sto.
Proof.
  intros Hfuel.
  auto_fuel.
  destruct_sto sto
               tokenPool xtzPool lqtTotal selfIsUpdatingTokenPool freezeBaker manager tokenAddress lqtAddress.
  destruct p as (param_baker, param_freeze_baker).
  repeat apply and_both_0.
  - apply bool_false_not.
  - rewrite lt_is_leb.
    rewrite Bool.negb_false_iff.
    apply comparison_to_int_tez_compare_le_zero.
  - unfold_spec. unfold dexter_definition.Storage.sto_manager.
    rewrite Bool.negb_false_iff.
    rewrite (eqb_eq address). easy.
  - unfold dexter_definition.Storage.sto_freezeBaker.
    apply bool_false_not.
  - unfold dexter_definition.Storage.sto_set_freezeBaker.
    split.
    + intros. injection H; intros; subst; auto.
    + intros. destruct H. subst. auto.
Qed.