(* 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"), *)
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Require Import Michocoq.macros.
Import syntax.
Import comparable.
Require Import NArith.
Require Import semantics.
Require Import util.
Import error.
Require List.

Require Import Coq.micromega.Lia.

Require dexter_definition.
Require dexter_spec.

Module Dexter_verification (C : ContractContext).

  Module Def := dexter_definition.Dexter_definition C.
  Module Spec := dexter_spec.Dexter_spec C.

  Module semantics := Semantics C. Import semantics.

  Section entrypoints.
    Variable (env : @proto_env dexter_definition.self_info).

    Lemma ep_addLiquidity_correct
          (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 p sto ret_ops ret_sto.
    Proof.
      (* TODO: add proof *)
    Admitted.


    Lemma ep_approve_correct
          (p : data dexter_definition.parameter_ep_approve_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_approve
                   (fun x => x = (ret_ops, ret_sto, tt))
                   (p, (sto, tt)) <->
      Spec.ep_approve p sto ret_ops ret_sto.
    Proof.
      (* TODO: add proof *)
    Admitted.



    Lemma ep_default_correct
          (p : data dexter_definition.parameter_ep_default_ty)
          (sto : data dexter_definition.storage_ty)
          (ret_ops : Datatypes.list (data operation))
          (ret_sto : data dexter_definition.storage_ty)
          (fuel : Datatypes.nat) :
      400 <= fuel ->
      eval_precond fuel env Def.ep_default
                   (fun x => x = (ret_ops, ret_sto, tt))
                   (p, (sto, tt)) <->
      Spec.ep_default p sto ret_ops ret_sto.
    Proof.
      intro Hfuel.
      do 5 more_fuel; simpl.
      unfold Spec.ep_default.
      intuition congruence.
    Qed.

    Lemma ep_removeLiquidity_correct
          (p : data dexter_definition.parameter_ep_removeLiquidity_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_removeLiquidity
                   (fun x => x = (ret_ops, ret_sto, tt))
                   (p, (sto, tt)) <->
      Spec.ep_removeLiquidity p sto ret_ops ret_sto.
    Proof.
      (* TODO: add proof *)
    Admitted.

    Lemma ep_setBaker_correct
          (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_precond fuel env Def.ep_setBaker
                   (fun x => x = (ret_ops, ret_sto, tt))
                   (p, (sto, tt)) <->
      Spec.ep_setBaker p sto ret_ops ret_sto.
    Proof.
      (* TODO: add proof *)
    Admitted.

    Lemma ep_updateTokenPool_correct
          (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_precond fuel env Def.ep_updateTokenPool
                   (fun x => x = (ret_ops, ret_sto, tt))
                   (p, (sto, tt)) <->
      Spec.ep_updateTokenPool p sto ret_ops ret_sto.
    Proof.
      (* TODO: add proof *)
    Admitted.


    Lemma ep_tokenToXtz_correct
          (p : data dexter_definition.parameter_ep_tokenToXtz_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_tokenToXtz
                   (fun x => x = (ret_ops, ret_sto, tt))
                   (p, (sto, tt)) <->
      Spec.ep_tokenToXtz p sto ret_ops ret_sto.
    Proof.
      (* TODO: add proof *)
    Admitted.

    Lemma ep_xtzToToken_correct
          (p : data dexter_definition.parameter_ep_xtzToToken_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_xtzToToken
                   (fun x => x = (ret_ops, ret_sto, tt))
                   (p, (sto, tt)) <->
      Spec.ep_xtzToToken p sto ret_ops ret_sto.
    Proof.
      (* TODO: add proof *)
    Admitted.
  End entrypoints.

  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.main fuel ((p, sto), tt) = Return ((ret_ops, ret_sto), tt) <->
    Spec.main 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
        [ [ [ | ] | [ | ]] |
          [ [ | ] | [ | ]] ];
      simpl Spec.main;
      unfold Def.main;
      do 7 more_fuel; simpl.

    - apply ep_approve_correct; lia.
    - apply ep_addLiquidity_correct; lia.
    - apply ep_removeLiquidity_correct; lia.
    - apply ep_xtzToToken_correct; lia.
    - apply ep_tokenToXtz_correct; lia.
    - apply ep_updateTokenPool_correct; lia.
    - apply ep_setBaker_correct; lia.
    - apply ep_default_correct; lia.
  Qed.
End Dexter_verification.