Require Import Coqlib.
Require Import Maps.
Require Import ASTExtra.
Require Import Integers.
Require Import Floats.
Require Import Values.
Require Import Memory.
Require Import Events.
Require Import Stacklayout.
Require Import Globalenvs.
Require Import AsmX.
Require Import Smallstep.
Require Import AuxStateDataType.
Require Import Constant.
Require Import GlobIdent.
Require Import FlatMemory.
Require Import CommonTactic.
Require Import AuxLemma.
Require Import RealParams.
Require Import PrimSemantics.
Require Import LAsm.
Require Import LoadStoreSem2.
Require Import XOmega.
Require Import ObservationImpl.

Require Import liblayers.logic.PTreeModules.
Require Import liblayers.logic.LayerLogicImpl.
Require Import liblayers.compat.CompatLayers.
Require Import liblayers.compat.CompatGenSem.

Require Import CalRealPTPool.
Require Import CalRealPT.
Require Import CalRealIDPDE.
Require Import CalRealInitPTE.
Require Import CalRealSMSPool.

Require Import INVLemmaContainer.
Require Import INVLemmaMemory.

Require Import AbstractDataType.

Require Export ObjCPU.
Require Export ObjFlatMem.
Require Export ObjContainer.
Require Export ObjVMM.
Require Export ObjLMM.
Require Export ObjShareMem.

Section WITHMEM.

  Local Open Scope Z_scope.

  Context `{real_params: RealParams}.

  Record high_level_invariant (abd: RData) :=
    mkInvariant {
        valid_nps: pg abd = true → kern_low ≤ nps abd ≤ maxpage;
        valid_AT_kern: pg abd = true → LAT_kern (LAT abd) (nps abd);
        valid_AT_usr: pg abd = true → LAT_usr (LAT abd) (nps abd);
        valid_kern: ipt abd = false → pg abd = true;
        valid_iptt: ipt abd = true → ikern abd = true;
        valid_iptf: ikern abd = false → ipt abd = false;
        valid_ihost: ihost abd = false → pg abd = true ∧ ikern abd = true;
        valid_container: Container_valid (AC abd);
        valid_pperm_ppage: Lconsistent_ppage (LAT abd) (pperm abd) (nps abd);
        init_pperm: pg abd = false → (pperm abd) = ZMap.init PGUndef;
        valid_PMap: pg abd = true →
                    (∀ i, 0≤ i < num_proc →
                               PMap_valid (ZMap.get i (ptpool abd)));
        
        valid_PT_kern: pg abd = true → ipt abd = true → (PT abd) = 0;
        valid_PMap_kern: pg abd = true → PMap_kern (ZMap.get 0 (ptpool abd));
        valid_PT: pg abd = true → 0≤ PT abd < num_proc;
        valid_dirty: dirty_ppage (pperm abd) (HP abd);

        valid_idpde: pg abd = true → IDPDE_init (idpde abd);
        valid_pperm_pmap: consistent_pmap (ptpool abd) (pperm abd) (LAT abd) (nps abd);
        valid_pmap_domain: consistent_pmap_domain (ptpool abd) (pperm abd) (LAT abd) (nps abd);
        valid_lat_domain: consistent_lat_domain (ptpool abd) (LAT abd) (nps abd);

        valid_root: pg abd = true → cused (ZMap.get 0 (AC abd)) = true
      }.

  Global Instance mshareintro_data_ops : CompatDataOps RData :=
    {
      empty_data := init_adt;
      high_level_invariant := high_level_invariant;
      low_level_invariant := low_level_invariant;
      kernel_mode adt := ikern adt = true ∧ ihost adt = true;
      observe := ObservationImpl.observe
    }.

  Section Property_Abstract_Data.

    Lemma empty_data_high_level_invariant:
      high_level_invariant init_adt.
    Proof.
      constructor; simpl; intros; auto; try inv H.
      - apply empty_container_valid.
      - eapply Lconsistent_ppage_init.
      - eapply dirty_ppage_init.
      - eapply consistent_pmap_init.
      - eapply consistent_pmap_domain_init.
      - eapply consistent_lat_domain_init.
    Qed.

    Global Instance mshareintro_data_prf : CompatData RData.
    Proof.
      constructor.
      - apply low_level_invariant_incr.
      - apply empty_data_low_level_invariant.
      - apply empty_data_high_level_invariant.
    Qed.

  End Property_Abstract_Data.

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

  Section INV.

    Global Instance flatmem_copy_inv: PreservesInvariants flatmem_copy_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant;
      try eapply dirty_ppage_gss_copy; eauto.
    Qed.

    Section ALLOC.

      Lemma alloc_high_level_inv:
        ∀ d d' i n,
          alloc_spec i d = Some (d', n) →
          high_level_invariant d →
          high_level_invariant d'.
      Proof.
        intros. functional inversion H; subst; eauto.
        inv H0. constructor; simpl; eauto.
        - intros; eapply LAT_kern_norm; eauto. eapply _x.
        - intros; eapply LAT_usr_norm; eauto.
        - eapply alloc_container_valid'; eauto.
        - eapply Lconsistent_ppage_norm_alloc; eauto.
        - intros; congruence.
        - eapply dirty_ppage_gso_alloc; eauto.
        - eapply consistent_pmap_gso_at_false; eauto. apply _x.
        - eapply consistent_pmap_domain_gso_at_false; eauto. apply _x.
        - eapply consistent_lat_domain_gss_nil; eauto.
        - zmap_solve.
      Qed.

      Lemma alloc_low_level_inv:
        ∀ d d' n n' i,
          alloc_spec i d = Some (d', n) →
          low_level_invariant n' d →
          low_level_invariant n' d'.
      Proof.
        intros. functional inversion H; subst; eauto.
        inv H0. constructor; eauto.
      Qed.

      Lemma alloc_kernel_mode:
        ∀ d d' i n,
          alloc_spec i d = Some (d', n) →
          kernel_mode d →
          kernel_mode d'.
      Proof.
        intros. functional inversion H; subst; eauto.
      Qed.

      Global Instance alloc_inv: PreservesInvariants alloc_spec.
      Proof.
        preserves_invariants_simpl'.
        - eapply alloc_low_level_inv; eassumption.
        - eapply alloc_high_level_inv; eassumption.
        - eapply alloc_kernel_mode; eassumption.
      Qed.

    End ALLOC.

    Global Instance pfree_inv: PreservesInvariants pfree_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant; eauto 2.
      - intros; eapply LAT_kern_norm; eauto.
      - intros; eapply LAT_usr_norm; eauto.
      - eapply Lconsistent_ppage_norm_undef; eauto.
      - eapply dirty_ppage_gso_undef; eauto.
      - eapply consistent_pmap_gso_pperm_alloc; eauto.
      - eapply consistent_pmap_domain_gso_at_0; eauto.
      - eapply consistent_lat_domain_gss_nil; eauto.
    Qed.

    Global Instance trapin_inv: PrimInvariants trapin_spec.
    Proof.
      PrimInvariants_simpl H H0.
    Qed.

    Global Instance trapout_inv: PrimInvariants trapout_spec.
    Proof.
      PrimInvariants_simpl H H0.
    Qed.

    Global Instance hostin_inv: PrimInvariants hostin_spec.
    Proof.
      PrimInvariants_simpl H H0.
    Qed.

    Global Instance hostout_inv: PrimInvariants hostout_spec.
    Proof.
      PrimInvariants_simpl H H0.
    Qed.

    Global Instance ptin_inv: PrimInvariants ptin_spec.
    Proof.
      PrimInvariants_simpl H H0.
    Qed.

    Global Instance ptout_inv: PrimInvariants ptout_spec.
    Proof.
      PrimInvariants_simpl H H0.
    Qed.

    Global Instance fstore_inv: PreservesInvariants fstore_spec.
    Proof.
      split; intros; inv_generic_sem H; inv H0; functional inversion H2.
      - functional inversion H. split; trivial.
      - functional inversion H.
        split; subst; simpl;
        try (eapply dirty_ppage_store_unmaped; try reflexivity; try eassumption); trivial.
      - functional inversion H0.
        split; simpl; try assumption.
    Qed.

    Global Instance setPT_inv: PreservesInvariants setPT_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant; eauto 2.
    Qed.

    Global Instance pmap_init_inv: PreservesInvariants pmap_init_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant.
      - apply real_nps_range.
      - apply real_lat_kern_valid.
      - apply real_lat_usr_valid.
      - apply real_container_valid.
      - rewrite init_pperm0; try assumption.
        apply Lreal_pperm_valid.
      - eapply real_pt_PMap_valid; eauto.
      - apply real_pt_PMap_kern.
      - omega.
      - assumption.
      - apply real_idpde_init.
      - apply real_pt_consistent_pmap.
      - apply real_pt_consistent_pmap_domain.
      - apply Lreal_at_consistent_lat_domain.
    Qed.

    Global Instance clearCR2_inv: PreservesInvariants clearCR2_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant; auto.
    Qed.

    Section PTINSERT.

      Section PTINSERT_PTE.

        Lemma ptInsertPTE_high_level_inv:
          ∀ d d' n vadr padr p,
            ptInsertPTE0_spec n vadr padr p d = Some d' →
            high_level_invariant d →
            high_level_invariant d'.
        Proof.
          intros. functional inversion H; subst; eauto.
          inv H0; constructor_gso_simpl_tac; intros.
          - eapply LAT_kern_norm; eauto.
          - eapply LAT_usr_norm; eauto.
          - eapply Lconsistent_ppage_norm; eassumption.
          - eapply PMap_valid_gso_valid; eauto.
          - functional inversion H2. functional inversion H1.
            eapply PMap_kern_gso; eauto.
          - functional inversion H2. functional inversion H0.
            eapply consistent_pmap_ptp_same; try eassumption.
            eapply consistent_pmap_gso_pperm_alloc'; eassumption.
          - functional inversion H2.
            eapply consistent_pmap_domain_append; eauto.
            destruct (ZMap.get pti pdt); try contradiction;
            red; intros (v0 & p0 & He); contra_inv.
          - eapply consistent_lat_domain_gss_append; eauto.
            subst pti; destruct (ZMap.get (PTX vadr) pdt); try contradiction;
            red; intros (v0 & p0 & He); contra_inv.
        Qed.

        Lemma ptInsertPTE_low_level_inv:
          ∀ d d' n vadr padr p n',
            ptInsertPTE0_spec n vadr padr p d = Some d' →
            low_level_invariant n' d →
            low_level_invariant n' d'.
        Proof.
          intros. functional inversion H; subst; eauto.
          inv H0. constructor; eauto.
        Qed.

        Lemma ptInsertPTE_kernel_mode:
          ∀ d d' n vadr padr p,
            ptInsertPTE0_spec n vadr padr p d = Some d' →
            kernel_mode d →
            kernel_mode d'.
        Proof.
          intros. functional inversion H; subst; eauto.
        Qed.

      End PTINSERT_PTE.

      Section PTALLOCPDE.

        Lemma ptAllocPDE_high_level_inv:
          ∀ d d' n vadr v,
            ptAllocPDE0_spec n vadr d = Some (d', v) →
            high_level_invariant d →
            high_level_invariant d'.
        Proof.
          intros. functional inversion H; subst; eauto.
          inv H0; constructor_gso_simpl_tac; intros.
          - eapply LAT_kern_norm; eauto. eapply _x.
          - eapply LAT_usr_norm; eauto.
          - eapply alloc_container_valid'; eauto.
          - apply Lconsistent_ppage_norm_hide; try assumption.
          - congruence.
          - eapply PMap_valid_gso_pde_unp; eauto.
            eapply real_init_PTE_defined.
          - functional inversion H3.
            eapply PMap_kern_gso; eauto.
          - eapply dirty_ppage_gss; eauto.
          - eapply consistent_pmap_ptp_gss; eauto; apply _x.
          - eapply consistent_pmap_domain_gso_at_false; eauto; try apply _x.
            eapply consistent_pmap_domain_ptp_unp; eauto.
            apply real_init_PTE_unp.
          - apply consistent_lat_domain_gss_nil; eauto.
            apply consistent_lat_domain_gso_p; eauto.
          - zmap_solve.
        Qed.

        Lemma ptAllocPDE_low_level_inv:
          ∀ d d' n vadr v n',
            ptAllocPDE0_spec n vadr d = Some (d', v) →
            low_level_invariant n' d →
            low_level_invariant n' d'.
        Proof.
          intros. functional inversion H; try congruence; subst; eauto.
          inv H0. constructor; eauto.
        Qed.

        Lemma ptAllocPDE_kernel_mode:
          ∀ d d' n vadr v,
            ptAllocPDE0_spec n vadr d = Some (d', v) →
            kernel_mode d →
            kernel_mode d'.
        Proof.
          intros. functional inversion H; try congruence; subst; eauto.
        Qed.

      End PTALLOCPDE.

      Lemma ptInsert_high_level_inv:
        ∀ d d' n vadr padr p v,
          ptInsert0_spec n vadr padr p d = Some (d', v) →
          high_level_invariant d →
          high_level_invariant d'.
      Proof.
        intros. functional inversion H; subst; eauto.
        - eapply ptInsertPTE_high_level_inv; eassumption.
        - eapply ptAllocPDE_high_level_inv; eassumption.
        - eapply ptInsertPTE_high_level_inv; try eassumption.
          eapply ptAllocPDE_high_level_inv; eassumption.
      Qed.

      Lemma ptInsert_low_level_inv:
        ∀ d d' n vadr padr p n' v,
          ptInsert0_spec n vadr padr p d = Some (d', v) →
          low_level_invariant n' d →
          low_level_invariant n' d'.
      Proof.
        intros. functional inversion H; subst; eauto.
        - eapply ptInsertPTE_low_level_inv; eassumption.
        - eapply ptAllocPDE_low_level_inv; eassumption.
        - eapply ptInsertPTE_low_level_inv; try eassumption.
          eapply ptAllocPDE_low_level_inv; eassumption.
      Qed.

      Lemma ptInsert_kernel_mode:
        ∀ d d' n vadr padr p v,
          ptInsert0_spec n vadr padr p d = Some (d', v) →
          kernel_mode d →
          kernel_mode d'.
      Proof.
        intros. functional inversion H; subst; eauto.
        - eapply ptInsertPTE_kernel_mode; eassumption.
        - eapply ptAllocPDE_kernel_mode; eassumption.
        - eapply ptInsertPTE_kernel_mode; try eassumption.
          eapply ptAllocPDE_kernel_mode; eassumption.
      Qed.

    End PTINSERT.

    Section PTRESV.

      Lemma ptResv_high_level_inv:
        ∀ d d' n vadr p v,
          ptResv_spec n vadr p d = Some (d', v) →
          high_level_invariant d →
          high_level_invariant d'.
      Proof.
        intros. functional inversion H; subst; eauto.
        eapply ptInsert_high_level_inv; try eassumption.
        eapply alloc_high_level_inv; eassumption.
      Qed.

      Lemma ptResv_low_level_inv:
        ∀ d d' n vadr p n' v,
          ptResv_spec n vadr p d = Some (d', v) →
          low_level_invariant n' d →
          low_level_invariant n' d'.
      Proof.
        intros. functional inversion H; subst; eauto.
        eapply ptInsert_low_level_inv; try eassumption.
        eapply alloc_low_level_inv; eassumption.
      Qed.

      Lemma ptResv_kernel_mode:
        ∀ d d' n vadr p v,
          ptResv_spec n vadr p d = Some (d', v) →
          kernel_mode d →
          kernel_mode d'.
      Proof.
        intros. functional inversion H; subst; eauto.
        eapply ptInsert_kernel_mode; try eassumption.
        eapply alloc_kernel_mode; eassumption.
      Qed.

      Global Instance ptResv_inv: PreservesInvariants ptResv_spec.
      Proof.
        preserves_invariants_simpl'.
        - eapply ptResv_low_level_inv; eassumption.
        - eapply ptResv_high_level_inv; eassumption.
        - eapply ptResv_kernel_mode; eassumption.
      Qed.

    End PTRESV.

    Section PTRESV2.

      Lemma ptResv2_high_level_inv:
        ∀ d d' n vadr p n' vadr' p' v,
          ptResv2_spec n vadr p n' vadr' p' d = Some (d', v) →
          high_level_invariant d →
          high_level_invariant d'.
      Proof.
        intros; functional inversion H; subst; eauto;
        eapply ptInsert_high_level_inv; try eassumption.
        - eapply alloc_high_level_inv; eassumption.
        - eapply ptInsert_high_level_inv; try eassumption.
          eapply alloc_high_level_inv; eassumption.
      Qed.

      Lemma ptResv2_low_level_inv:
        ∀ d d' n vadr p n' vadr' p' l v,
          ptResv2_spec n vadr p n' vadr' p' d = Some (d', v) →
          low_level_invariant l d →
          low_level_invariant l d'.
      Proof.
        intros; functional inversion H; subst; eauto;
        eapply ptInsert_low_level_inv; try eassumption.
        - eapply alloc_low_level_inv; eassumption.
        - eapply ptInsert_low_level_inv; try eassumption.
          eapply alloc_low_level_inv; eassumption.
      Qed.

      Lemma ptResv2_kernel_mode:
        ∀ d d' n vadr p n' vadr' p' v,
          ptResv2_spec n vadr p n' vadr' p' d = Some (d', v) →
          kernel_mode d →
          kernel_mode d'.
      Proof.
        intros; functional inversion H; subst; eauto;
        eapply ptInsert_kernel_mode; try eassumption.
        - eapply alloc_kernel_mode; eassumption.
        - eapply ptInsert_kernel_mode; try eassumption.
          eapply alloc_kernel_mode; eassumption.
      Qed.

      Global Instance ptResv2_inv: PreservesInvariants ptResv2_spec.
      Proof.
        preserves_invariants_simpl'.
        - eapply ptResv2_low_level_inv; eassumption.
        - eapply ptResv2_high_level_inv; eassumption.
        - eapply ptResv2_kernel_mode; eassumption.
      Qed.

    End PTRESV2.

    Global Instance pt_new_inv: PreservesInvariants pt_new_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant; eauto 2;
       rename i into id, i0 into q, z into i.
      - exploit split_container_valid; eauto.
        eapply container_split_some; eauto.
        auto.
      - unfold update_cusage, update_cchildren; zmap_solve.
    Qed.

    Global Instance set_shared_mem_state_inv:
      PreservesInvariants set_shared_mem_state_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant; eauto 2.
    Qed.

    Global Instance set_shared_mem_seen_inv:
      PreservesInvariants set_shared_mem_seen_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant; eauto 2.
    Qed.

    Global Instance set_shared_mem_loc_inv:
      PreservesInvariants set_shared_mem_loc_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant; eauto 2.
    Qed.

    Global Instance clear_shared_mem_inv:
      PreservesInvariants clear_shared_mem_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant; eauto 2.
    Qed.

    Global Instance device_output_inv: PreservesInvariants device_output_spec.
    Proof.
      preserves_invariants_simpl'' low_level_invariant high_level_invariant; eauto.
    Qed.

  End INV.

  Definition exec_loadex {F V} := exec_loadex2 (F := F) (V := V).

  Definition exec_storeex {F V} := exec_storeex2 (flatmem_store:= flatmem_store) (F := F) (V := V).

  Global Instance flatmem_store_inv: FlatmemStoreInvariant (flatmem_store:= flatmem_store).
  Proof.
    split; inversion 1; intros.
    - functional inversion H0. split; trivial.
    - functional inversion H1.
      split; simpl; try (eapply dirty_ppage_store_unmaped'; try reflexivity; try eassumption); trivial.
  Qed.

  Global Instance trapinfo_set_inv: TrapinfoSetInvariant.
  Proof.
    split; inversion 1; intros; constructor; auto.
  Qed.

  Definition mshareintro_fresh : compatlayer (cdata RData) :=
    clear_shared_mem ↦ gensem clear_shared_mem_spec
                     ⊕ get_shared_mem_state ↦ gensem get_shared_mem_state_spec
                     ⊕ get_shared_mem_seen ↦ gensem get_shared_mem_seen_spec
                     ⊕ get_shared_mem_loc ↦ gensem get_shared_mem_loc_spec
                     ⊕ set_shared_mem_state ↦ gensem set_shared_mem_state_spec
                     ⊕ set_shared_mem_seen ↦ gensem set_shared_mem_seen_spec
                     ⊕ set_shared_mem_loc ↦ gensem set_shared_mem_loc_spec.

  Definition mshareintro_passthrough : compatlayer (cdata RData) :=
    fload ↦ gensem fload_spec
          ⊕ fstore ↦ gensem fstore_spec
          ⊕ flatmem_copy ↦ gensem flatmem_copy_spec
          ⊕ vmxinfo_get ↦ gensem vmxinfo_get_spec
          ⊕ device_output ↦ gensem device_output_spec
          ⊕ pfree ↦ gensem pfree_spec
          ⊕ set_pt ↦ gensem setPT_spec
          ⊕ pt_read ↦ gensem ptRead_spec
          ⊕ pt_resv ↦ gensem ptResv_spec
          ⊕ pt_resv2 ↦ gensem ptResv2_spec
          ⊕ pt_new ↦ gensem pt_new_spec
          
          ⊕ pmap_init ↦ gensem pmap_init_spec

          ⊕ pt_in ↦ primcall_general_compatsem' ptin_spec (prim_ident:= pt_in)
          ⊕ pt_out ↦ primcall_general_compatsem' ptout_spec (prim_ident:= pt_out)
          ⊕ clear_cr2 ↦ gensem clearCR2_spec
          ⊕ container_get_nchildren ↦ gensem container_get_nchildren_spec
          ⊕ container_get_quota ↦ gensem container_get_quota_spec
          ⊕ container_get_usage ↦ gensem container_get_usage_spec
          ⊕ container_can_consume ↦ gensem container_can_consume_spec
          ⊕ container_alloc ↦ gensem alloc_spec
          ⊕ trap_in ↦ primcall_general_compatsem trapin_spec
          ⊕ trap_out ↦ primcall_general_compatsem trapout_spec
          ⊕ host_in ↦ primcall_general_compatsem hostin_spec
          ⊕ host_out ↦ primcall_general_compatsem hostout_spec
          ⊕ trap_get ↦ primcall_trap_info_get_compatsem trap_info_get_spec
          ⊕ trap_set ↦ primcall_trap_info_ret_compatsem trap_info_ret_spec
          ⊕ accessors ↦ {| exec_load := @exec_loadex; exec_store := @exec_storeex |}.

  Definition mshareintro : compatlayer (cdata RData) := mshareintro_fresh ⊕ mshareintro_passthrough.

End WITHMEM.