Require Import Coqlib.
Require Import Errors.
Require Import AST.
Require Import Integers.
Require Import Floats.
Require Import Op.
Require Import Asm.
Require Import Events.
Require Import Globalenvs.
Require Import Smallstep.
Require Import Values.
Require Import Memory.
Require Import Maps.
Require Import CommonTactic.
Require Import AuxLemma.
Require Import FlatMemory.
Require Import AuxStateDataType.
Require Import Constant.
Require Import GlobIdent.
Require Import RealParams.
Require Import LoadStoreSem1.
Require Import AsmImplLemma.
Require Import GenSem.
Require Import RefinementTactic.
Require Import PrimSemantics.
Require Import XOmega.

Require Import liblayers.logic.PTreeModules.
Require Import liblayers.logic.LayerLogicImpl.
Require Import liblayers.compcertx.Stencil.
Require Import liblayers.compcertx.MakeProgram.
Require Import liblayers.compat.CompatLayers.
Require Import liblayers.compat.CompatGenSem.
Require Import compcert.cfrontend.Ctypes.
Require Import LayerCalculusLemma.
Require Import AbstractDataType.

Require Import DSerialIntro.
Require Import DAbsConsoleBuffIntro.
Require Import SerialIntroGenSpec.
Require Import DeviceStateDataType.

Section Refinement.

  Local Open Scope string_scope.
  Local Open Scope error_monad_scope.
  Local Open Scope Z_scope.

  Context `{real_params: RealParams}.
  Context `{oracle_prop: MultiOracleProp}.

  Notation HDATA := RData.
  Notation LDATA := RData.

  Notation HDATAOps := (cdata (cdata_ops := dserialintro_data_ops) HDATA).
  Notation LDATAOps := (cdata (cdata_ops := dabsconsolebuffintro_data_ops) LDATA).

  Section WITHMEM.

    Context `{Hstencil: Stencil}.
    Context `{Hmem: Mem.MemoryModelX}.
    Context `{Hmwd: UseMemWithData mem}.

    Section REFINEMENT_REL.

        Inductive match_serial_exists: stencil → Z → mem → meminj → Prop :=
        | MATCH_SERIAL_EXISTS:
            ∀ v m b f s,
              Mem.load Mint32 m b 0 = Some (Vint v)
              → Mem.valid_access m Mint32 b 0 Writable
              → find_symbol s serial_exists_LOC = Some b
              → match_serial_exists s (Int.unsigned v) m f.

        Inductive match_RData: stencil → HDATA → mem → meminj → Prop :=
        | MATCH_RDATA:
            ∀ hadt m f s,
              match_serial_exists s (serial_exists (drv_serial hadt)) m f
              → match_RData s hadt m f.

        Record relate_RData (f: meminj) (hadt: HDATA) (ladt: LDATA) :=
          mkrelate_RData {
              flatmem_re: FlatMem.flatmem_inj (HP hadt) (HP ladt);
              vmxinfo_re: vmxinfo hadt = vmxinfo ladt;
              CR3_re: CR3 hadt = CR3 ladt;
              ikern_re: ikern hadt = ikern ladt;
              MM_re: MM hadt = MM ladt;
              MMSize_re: MMSize hadt = MMSize ladt;
              pg_re: pg hadt = pg ladt;
              ihost_re: ihost hadt = ihost ladt;
              AC_re: AC hadt = AC ladt;
              ti_fst_re: (fst (ti hadt)) = (fst (ti ladt));
              ti_snd_re: val_inject f (snd (ti hadt)) (snd (ti ladt));
              AT_re: AT hadt = AT ladt;
              nps_re: nps hadt = nps ladt;
              init_re: init hadt = init ladt;

              buffer_re: buffer hadt = buffer ladt;

              com1_re: com1 hadt = com1 ladt;
              console_re: console hadt = console ladt;
              console_concrete_re: console_concrete hadt = console_concrete ladt;
              ioapic_re: ioapic ladt = ioapic hadt;
              lapic_re: lapic ladt = lapic hadt;
              intr_flag_re: intr_flag ladt = intr_flag hadt;
              saved_intr_flags_re: saved_intr_flags ladt = saved_intr_flags hadt;
              curr_intr_num_re: curr_intr_num ladt = curr_intr_num hadt;
              in_intr_re: in_intr hadt = in_intr ladt;
              tf_re: tfs_inj f (tf hadt) (tf ladt);

              CPU_ID_re: CPU_ID hadt = CPU_ID ladt;
              cid_re: cid hadt = cid ladt;
              multi_oracle_re: multi_oracle hadt = multi_oracle ladt;
              multi_log_re: multi_log hadt = multi_log ladt;
              lock_re: lock hadt = lock ladt
            }.

        Global Instance rel_ops: CompatRelOps HDATAOps LDATAOps :=
          {
            relate_AbData s f d1 d2 := relate_RData f d1 d2;
            match_AbData s d1 m f := match_RData s d1 m f;
            new_glbl := serial_exists_LOC :: nil
          }.

    End REFINEMENT_REL.

    Section Rel_Property.

      Lemma inject_match_correct:
        ∀ s d1 m2 f m2´ j,
          match_RData s d1 m2 f →
          Mem.inject j m2 m2´ →
          inject_incr (Mem.flat_inj (genv_next s)) j →
          match_RData s d1 m2´ (compose_meminj f j).
      Proof.
        inversion 1; subst; intros.
        inv H0.
        assert (HFB0: j b = Some (b, 0)).
        {
          eapply stencil_find_symbol_inject´; eauto.
        }
        econstructor; eauto; intros.
        rewrite <- H3.
        econstructor; eauto; intros.
        specialize (Mem.load_inject _ _ _ _ _ _ _ _ _ H1 H4 HFB0).
        repeat rewrite Z.add_0_r.
        intros [v1´[HLD1´ HV1´]].
        inv HV1´. assumption.
        specialize(Mem.valid_access_inject _ _ _ _ _ _ _ _ _ HFB0 H1 H5).
        rewrite Z.add_0_r; trivial.
      Qed.

      Lemma store_match_correct:
        ∀ s abd m0 m0´ f b2 v v´ chunk,
          match_RData s abd m0 f →
          (∀ i b,
             In i new_glbl →
             find_symbol s i = Some b → b ≠ b2) →
          Mem.store chunk m0 b2 v v´ = Some m0´ →
          match_RData s abd m0´ f.
      Proof.
        intros. inv H. inv H2.
        econstructor; eauto.
        rewrite <- H.
        econstructor; eauto.
        eapply H0 in H6; simpl; eauto.
        repeat rewrite (Mem.load_store_other _ _ _ _ _ _ H1); auto.
        eapply Mem.store_valid_access_1; eauto.
      Qed.

      Lemma storebytes_match_correct:
        ∀ s abd m0 m0´ f b2 v v´,
          match_RData s abd m0 f →
          (∀ i b,
             In i new_glbl →
             find_symbol s i = Some b → b ≠ b2) →
          Mem.storebytes m0 b2 v v´ = Some m0´ →
          match_RData s abd m0´ f.
      Proof.
        intros. inv H. inv H2.
        econstructor; eauto.
        rewrite <- H.
        econstructor; eauto.
        eapply H0 in H6; simpl; eauto.
        repeat rewrite (Mem.load_storebytes_other _ _ _ _ _ H1); eauto.
        eapply Mem.storebytes_valid_access_1; eauto.
      Qed.

      Lemma free_match_correct:
        ∀ s abd m0 m0´ f ofs sz b2,
          match_RData s abd m0 f→
          (∀ i b,
             In i new_glbl →
             find_symbol s i = Some b → b ≠ b2) →
          Mem.free m0 b2 ofs sz = Some m0´ →
          match_RData s abd m0´ f.
      Proof.
        intros; inv H; inv H2.
        econstructor; eauto.
        rewrite <- H.
        econstructor; eauto.
        eapply H0 in H6; simpl; eauto.
        repeat rewrite (Mem.load_free _ _ _ _ _ H1); auto.
        eapply H0 in H6; simpl; eauto.
        eapply Mem.valid_access_free_1; eauto.
      Qed.

      Lemma alloc_match_correct:
        ∀ s abd m´0 m´1 f f´ ofs sz b0 b´1,
          match_RData s abd m´0 f→
          Mem.alloc m´0 ofs sz = (m´1, b´1) →
          f´ b0 = Some (b´1, 0%Z) →
          (∀ b : block, b ≠ b0 → f´ b = f b) →
          inject_incr f f´ →
          (∀ i b,
             In i new_glbl →
             find_symbol s i = Some b → b ≠ b0) →
          match_RData s abd m´1 f´.
      Proof.
        intros. rename H1 into HF1, H2 into HB. inv H; inv H1.
        econstructor; eauto.
        rewrite <- H.
        econstructor; eauto;
        try (apply (Mem.load_alloc_other _ _ _ _ _ H0));
        try (eapply Mem.valid_access_alloc_other); eauto.
      Qed.

      Lemma relate_incr:
        ∀ abd abd´ f f´,
          relate_RData f abd abd´
          → inject_incr f f´
          → relate_RData f´ abd abd´.
      Proof.
        inversion 1; subst; intros; inv H; constructor; eauto.
        eapply tfs_inj_incr; eauto.
      Qed.

      Global Instance rel_prf: CompatRel HDATAOps LDATAOps.
      Proof.
        constructor.
        - apply inject_match_correct.
        - apply store_match_correct.
        - apply alloc_match_correct.
        - apply free_match_correct.
        - apply storebytes_match_correct.
        - intros. eapply relate_incr; eauto.
      Qed.

    End Rel_Property.

    Section OneStep_Forward_Relation.

      Ltac pattern2_refinement_simpl:=
        pattern2_refinement_simpl´ (@relate_AbData).

      Section FRESH_PRIM.

        Lemma get_serial_exists_spec_ref:
          compatsim (crel HDATA LDATA) (gensem get_serial_exists_spec) get_serial_exists_spec_low.
        Proof.
          compatsim_simpl (@match_AbData). inv H.
          assert(HOS: kernel_mode d2).
          {
            simpl; inv match_related.
            functional inversion H2; repeat split; trivial; congruence.
          }
          assert (HP: v = z).
          {
            functional inversion H2; subst. rewrite H in H0.
            inv H0.
            rewrite <- Int.repr_unsigned.
            rewrite <- Int.repr_unsigned with v.
            rewrite <- H9.
            reflexivity.
          }
          refine_split; eauto; econstructor; eauto.
        Qed.

        Lemma set_serial_exists_spec_ref:
          compatsim (crel HDATA LDATA) (gensem set_serial_exists_spec) set_serial_exists_spec_low.
        Proof.
          compatsim_simpl (@match_AbData).
          assert (Hkern: kernel_mode d2).
          {
            inv match_related. functional inversion H1; subst;
            repeat split; try congruence; eauto.
          }
          inv H.
          specialize (Mem.valid_access_store _ _ _ _ (Vint Int.one) H3); intros [m´ HST].
          specialize (Mem.valid_access_store _ _ _ _ (Vint Int.zero) H3); intros [m´2 HST2].
          functional inversion H1; subst.
          {
            refine_split.
            - econstructor; eauto.
              omega.
              instantiate (2:= m´).
              instantiate (1:= d2).
              simpl; lift_trivial. subrewrite´.
            - constructor.
            - split; eauto; pattern2_refinement_simpl.
              econstructor; simpl; eauto.
              change 1 with (Int.unsigned Int.one).
              econstructor; eauto; intros.
              eapply Mem.load_store_same in HST; eauto.
              eapply Mem.store_valid_access_1; eauto.
            - apply inject_incr_refl.
          }
          {
            refine_split.
            - eapply set_serial_exists_spec_low_intro_0; eauto.
              omega.
              instantiate (2:= m´2).
              instantiate (1:= d2).
              simpl; lift_trivial. subrewrite´.
            - constructor.
            - split; eauto; pattern2_refinement_simpl.
              econstructor; simpl; eauto.
              change 0 with (Int.unsigned Int.zero).
              econstructor; eauto; intros.
              eapply Mem.load_store_same in HST2; eauto.
              eapply Mem.store_valid_access_1; eauto.
            - apply inject_incr_refl.
          }
        Qed.

      End FRESH_PRIM.

      Section PASSTHROUGH_PRIM.

        Global Instance: (LoadStoreProp (hflatmem_store:= flatmem_store´) (lflatmem_store:= flatmem_store´)).
        Proof.
          accessor_prop_tac.
          - eapply flatmem_store´_exists; eauto.
        Qed.

        Lemma passthrough_correct:
          simRR HDATAOps LDATAOps (crel HDATA LDATA) dserial_intro_passthrough dabsconsolebuffintro.
        Proof.
          sim_oplus.
          - apply fload´_sim.
          - apply fstore´_sim.
          - apply page_copy´_sim.
          - apply page_copy_back´_sim.

          - apply vmxinfo_get_sim.
          - apply setPG_sim.
          - apply setCR3_sim.
          - apply get_size_sim.
          - apply is_mm_usable_sim.
          - apply get_mm_s_sim.
          - apply get_mm_l_sim.
          - apply get_CPU_ID_sim.
          - apply get_curid_sim.
          - apply set_curid_sim.
          - apply set_curid_init_sim.
          - apply (release_lock_sim (valid_arg_imply:= Shared2ID0_imply)).
          -
            eapply acquire_lock_sim0; eauto.
            intros. inv H; trivial; try inv H0.
          - apply ticket_lock_init0_sim.
          - apply serial_irq_check_sim.
          - apply iret_sim.
          - apply cli_sim.
          - apply sti_sim.
          - apply serial_irq_current_sim.
          - apply ic_intr_sim.
          - apply save_context_sim.
          - apply restore_context_sim.
          - apply local_irq_save_sim.
          - apply local_irq_restore_sim.
          - apply serial_in_sim.
          - apply serial_out_sim.
          - apply serial_hw_intr_sim.
          - apply ioapic_read_sim.
          - apply ioapic_write_sim.
          - apply lapic_read_sim.
          - apply lapic_write_sim.
          - apply cons_buf_init_sim.
          - apply cons_buf_write_sim.
          - apply cons_buf_read_sim.
          - layer_sim_simpl; compatsim_simpl (@match_AbData); intros.
            exploit cons_buf_wpos_exist; eauto 1.
            match_external_states_simpl.
            rewrite H0.
            econstructor.
          - apply trapin_sim.
          - apply trapout´_sim.
          - apply hostin_sim.
          - apply hostout´_sim.
          - apply proc_create_postinit_sim.
          - apply trap_info_get_sim.
          - apply trap_info_ret_sim.
          - layer_sim_simpl.
            + eapply load_correct1.
            + eapply store_correct1.
        Qed.

      End PASSTHROUGH_PRIM.

    End OneStep_Forward_Relation.

  End WITHMEM.

End Refinement.