Require Export Coqlib.
Require Export Errors.
Require Export AST.
Require Export Integers.
Require Export Floats.
Require Export Op.
Require Export Asm.
Require Export Events.
Require Export Globalenvs.
Require Export Smallstep.
Require Export Values.
Require Export Memory.
Require Export Maps.
Require Export CommonTactic.
Require Export AuxLemma.
Require Export FlatMemory.
Require Export AuxStateDataType.
Require Export Constant.
Require Export GlobIdent.
Require Export RealParams.
Require Export LoadStoreSem3.
Require Export AsmImplLemma.
Require Export GenSem.
Require Export RefinementTactic.
Require Export PrimSemantics.
Require Export XOmega.

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

Require Export VVMXIntro.

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

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

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

Section Refinement.

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



  Section WITHMEM.

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

    Section REFINEMENT_REL.

      Inductive match_VMX: stencil → Z → VMX → mem → meminj → Prop :=
      | MATCH_VMX:
          ∀ vvmx m b s f vmid,
            (∀ i,
               0≤ i < VMX_Size´ →
               (∃ v,
                  Mem.load Mint32 m b (VMX_Size´ × 4 × vmid + i × 4) = Some v ∧
                  Mem.valid_access m Mint32 b (VMX_Size´ × 4 × vmid + i × 4) Writable ∧
                  val_inject f (Val.load_result Mint32 (ZMap.get i vvmx)) v)) →
            find_symbol s VMX_LOC = Some b →
            match_VMX s vmid vvmx m f.

        Inductive match_RData: stencil → HDATA → mem → meminj → Prop :=
        | MATCH_RDATA:
            ∀ hadt m s f,
              match_VMX s (CPU_ID hadt) (ZMap.get (CPU_ID hadt) (vmx 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;
              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));
              LAT_re: LAT hadt = LAT ladt;
              nps_re: nps hadt = nps ladt;
              init_re: init hadt = init ladt;

              pperm_re: pperm hadt = pperm ladt;
              PT_re: PT hadt = PT ladt;
              ptp_re: ptpool hadt = ptpool ladt;
              idpde_re: idpde hadt = idpde ladt;
              ipt_re: ipt hadt = ipt ladt;
              smspool_re: smspool hadt = smspool 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;

              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;
              curr_intr_num_re: curr_intr_num ladt = curr_intr_num hadt;
              in_intr_re: in_intr ladt = in_intr hadt;
              drv_serial_re: drv_serial hadt = drv_serial ladt;

              kctxt_re: kctxt_inj f num_proc (kctxt hadt) (kctxt ladt);
              uctxt_re: uctxt_inj f (uctxt hadt) (uctxt ladt);
              
              syncchpool_re: syncchpool hadt = syncchpool ladt;

              ept_re: ept hadt = ept ladt;
              vmcs_re: VMCSPool_inj f (vmcs hadt) (vmcs 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 := VMX_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.
        econstructor; eauto; intros.
        specialize (H3 _ H0).
        destruct H3 as [v1[HL1[HV1 HM]]].
        specialize (Mem.load_inject _ _ _ _ _ _ _ _ _ H1 HL1 HFB0).
        repeat rewrite Z.add_0_r.
        intros [v1´[HLD1´ HV1´]].
        refine_split´; eauto.
        specialize(Mem.valid_access_inject _ _ _ _ _ _ _ _ _ HFB0 H1 HV1).
        rewrite Z.add_0_r; trivial.
        eapply val_inject_compose; eauto.
      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.
        econstructor; eauto.
        intros. specialize (H _ H2).
        destruct H as [v1[HL1[HV1 HM]]].
        eapply H0 in H3; simpl; eauto.
        repeat rewrite (Mem.load_store_other _ _ _ _ _ _ H1); auto.
        refine_split´; eauto;
        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.
        econstructor; eauto.
        intros. specialize (H _ H2).
        destruct H as [v1[HL1[HV1 HM]]].
        eapply H0 in H3; simpl; eauto.
        repeat rewrite (Mem.load_storebytes_other _ _ _ _ _ H1); eauto.
        refine_split´; 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.
        econstructor; eauto.
        intros. specialize (H _ H2).
        destruct H as [v1[HL1[HV1 HM]]].
        eapply H0 in H3; simpl; eauto.
        repeat rewrite (Mem.load_free _ _ _ _ _ H1); auto.
        refine_split´; 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.
        econstructor; eauto.
        intros. specialize (H _ H1).
        destruct H as [v1[HL1[HV1 HM]]].
        refine_split´; 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 kctxt_inj_incr; eauto.
        - eapply uctxt_inj_incr; eauto.
        - unfold VMCSPool_inj.
          intros.
          eapply VMCS_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.

  End WITHMEM.

End Refinement.