Library mcertikos.devdrivers.ConsoleBuffIntroGenLink

Require Import LinkTemplate.
Require Import DConsoleBuffIntro.
Require Import ConsoleBuffIntroGen.
Require Import ConsoleBuffIntroGenLinkSource.
Require Import MQTicketLock.
Require Import MQTicketLockCSource.
Require Import MQTicketLockCode.
Require Import AST.

Section WITHCOMPCERTIKOS.
  Context `{compcertikos_prf: CompCertiKOS} `{real_params_prf: RealParams}.
  Context `{oracle_prop: MultiOracleProp}.

  Lemma init_correct:
    init_correct_type DConsoleBuffIntro_module mqticketlock dconsolebuffintro.
  Proof.
    init_correct.
    specialize (Globalenvs.Genv.init_mem_characterization _ _ Hbvi Hm); eauto.
    unfold Globalenvs.Genv.perm_globvar. simpl. intros (Hperm & _ & init).
    specialize (init eq_refl); destruct init as (init0 & init4 & _).

    econstructor.
    instantiate (1:= b).
    split.
    intros.
    assert(Mem.valid_access m2 Mint32 b (ofs × 4) Writable).
    {
      split.
      unfold Mem.range_perm; intros; apply Hperm.
      simpl in H1.
      change (Z.max 2056 0) with 2056.
      omega.
      eexists; reflexivity.
    }
    assert (readable : Mem.valid_access m2 Mint32 b (ofs × 4) Readable).
    { eapply Mem.valid_access_implies; eauto; constructor. }

    exploit Mem.valid_access_load; eauto.
    intros [ v load ].
    ∃ v; split; [| split ]; eauto.
    simpl.
    rewrite Maps.ZMap.gi.
    econstructor.
    split.

    ∃ (Vint Integers.Int.zero).
    change (Z.max 2048 0) with 2048 in init0.
    change (512 × 4) with 2048.
    split.
    assumption.
    split.
    assert(Mem.valid_access m2 Mint32 b 2048 Writable).
    {
      split.
      unfold Mem.range_perm; intros; apply Hperm.
      simpl in H0.
      omega.
      ∃ 512.
      reflexivity.
    }
    assert (readable : Mem.valid_access m2 Mint32 b 2048 Readable).
    { eapply Mem.valid_access_implies; eauto; constructor. }
    exploit Mem.valid_access_load; eauto.
    simpl.
    econstructor.
    reflexivity.
    omega.

    ∃ (Vint Integers.Int.zero).
    change (Z.max 2052 0) with 2052 in init0.
    change ((512 + 1) × 4) with 2052.
    split.
    assumption.
    split.
    assert(Mem.valid_access m2 Mint32 b 2052 Writable).
    {
      split.
      unfold Mem.range_perm; intros; apply Hperm.
      simpl in H0.
      omega.
      ∃ 513.
      reflexivity.
    }
    assert (readable : Mem.valid_access m2 Mint32 b 2052 Readable).
    { eapply Mem.valid_access_implies; eauto; constructor. }
    exploit Mem.valid_access_load; eauto.
    simpl.
    econstructor.
    reflexivity.
    omega.

    assumption.
  Qed.

  Lemma link_correct_aux:
    link_correct_aux_type DConsoleBuffIntro_module mqticketlock dconsolebuffintro.
  Proof.
    link_correct_aux.
    - link_cfunction
        cons_buf_init_concrete_spec_ref
        MQTICKETLOCKCODE.cons_buf_init_correct.
    - link_cfunction
        cons_buf_write_concrete_spec_ref
        MQTICKETLOCKCODE.cons_buf_write_correct.
    - link_cfunction
        cons_buf_read_concrete_spec_ref
        MQTICKETLOCKCODE.cons_buf_read_correct.
    - link_cfunction
        cons_buf_wpos_concrete_spec_ref
        MQTICKETLOCKCODE.cons_buf_wpos_correct.
    - apply passthrough_correct.
  Qed.

  Theorem cl_backward_simulation:
    cl_backward_simulation_type DConsoleBuffIntro_module mqticketlock dconsolebuffintro.
  Proof.
    cl_backward_simulation init_correct link_correct_aux.
  Qed.

  Theorem make_program_exists:
    make_program_exist_type DConsoleBuffIntro_module mqticketlock dconsolebuffintro.
  Proof.
    make_program_exists link_correct_aux.
  Qed.
End WITHCOMPCERTIKOS.