(* Open Source License *)
(* Copyright (c) 2020 Nomadic Labs. <contact@nomadic-labs.com> *)

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(* copy of this software and associated documentation files (the "Software"), *)
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Require Import String.
Require Import NArith.
Require Import ZArith.
Require List.
Require Import Coq.micromega.Lia.

Require Import Michocoq.macros.
Import syntax.
Import comparable.
Require Import semantics.
Require Import util.
Import error.

Require dexter_definition.
Require dexter_spec.
Require dexter_verification.

Module Dexter_verification_main (C : ContractContext).

  Module Ep_verif := dexter_verification.Dexter_verification C.
  Import Ep_verif.
  Import Ep_verif.Spec.semantics.


  Lemma main_correct
        (env : @proto_env (Some (dexter_definition.parameter_ty, None)))
        (p : data dexter_definition.parameter_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 *)
    500 <= fuel ->
    eval env Def.main2 fuel ((p, sto), tt) = Return ((ret_ops, ret_sto), tt) <->
    Spec.main env p sto ret_ops ret_sto.
  Proof.
    (* Case distinction on parameter p, and then apply lemmas from
    section entrypoints. *)

    unfold ">=".
    intros Hfuel.
    rewrite return_precond.
    rewrite eval_precond_correct.

    destruct p as
        [ [ [ | ] | [ | ]] |
          [ [ | ] | [ | ]] ];
      do 4 (more_fuel; simpl).

    - apply ep_approve_correct; lia.
    - apply ep_addLiquidity_correct; lia.
    - apply ep_removeLiquidity_correct; lia.
    - destruct d as [ | ]; do 1 (more_fuel; simpl).
       + apply ep_xtzToToken_correct; lia.
       + apply ep_tokenToXtz_correct; lia.
    - apply ep_tokenToToken_correct; lia.
    - destruct d as [ | ]; do 1 (more_fuel; simpl).
      + apply ep_updateTokenPool_correct; lia.
      + apply ep_updateTokenPoolInternal_correct; lia.
    - apply ep_setBaker_correct; lia.
    - destruct d as [ | ];  do 1 (more_fuel; simpl).
      + apply ep_setManager_correct; lia.
      + apply ep_default_correct; lia.
  Qed.
End Dexter_verification_main.