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 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 INVLemmaContainer.
Require Import INVLemmaMemory.

Require Import AbstractDataType.

Require Import INVLemmaQLock.
Require Import INVLemmaInterrupt.
Require Import INVLemmaDriver.
Require Import DeviceStateDataType.
Require Import FutureTactic.

Require Export MPTInit.

Section WITHMEM.

  Local Open Scope Z_scope.

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

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

  Section INV.

    Global Instance pt_new_inv: PreservesInvariants pt_new_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant; auto.
      - exploit split_container_valid; eauto.
    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_latc_valid.
      - apply AC_init_container_valid.
      - rewrite init_pperm; [|try assumption].
        apply real_pperm_log_valid.
      - eapply real_pt_PMap_valid; eauto.
      - apply real_pt_PMap_kern.
      - omega.
      - assumption.
      - apply real_idpde_init.
      - apply real_pt_weak_consistent_pmap.
      - apply real_pt_consistent_pmap_domain.
      - apply Lreal_at_consistent_lat_domain.
      - eapply LATCTable_log_real; eauto.
      - assumption.
      - eapply real_valid_hlock_pool1; eauto.
      - assumption.
      - eapply real_valid_AT_log_pool_H; eauto.
    Qed.

    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; clear H.
        - eapply palloc_high_level_inv; eassumption.
        - eapply ptInsert_high_level_inv; try eassumption.
          eapply palloc_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 palloc_low_level_inv; eassumption.
        eapply ptInsert_low_level_inv; try eassumption.
        eapply palloc_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 palloc_kernel_mode; eassumption.
        eapply ptInsert_kernel_mode; try eassumption.
        eapply palloc_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; clear H.
        - eapply palloc_high_level_inv; eassumption.
        - eapply ptInsert_high_level_inv; try eassumption.
          eapply palloc_high_level_inv; eassumption.
        - eapply ptInsert_high_level_inv; try eassumption.
          eapply ptInsert_high_level_inv; try eassumption.
          eapply palloc_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 palloc_low_level_inv; eassumption.
        - eapply ptInsert_low_level_inv; try eassumption.
          eapply palloc_low_level_inv; eassumption.
        - eapply ptInsert_low_level_inv; try eassumption.
          eapply ptInsert_low_level_inv; try eassumption.
          eapply palloc_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 palloc_kernel_mode; eassumption.
        - eapply ptInsert_kernel_mode; try eassumption.
          eapply palloc_kernel_mode; eassumption.
        - eapply ptInsert_kernel_mode; try eassumption.
          eapply ptInsert_kernel_mode; try eassumption.
          eapply palloc_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.

  End INV.

  Definition mptnew_fresh : compatlayer (cdata RData) :=
    pt_resv ↦ gensem ptResv_spec
            ⊕ pt_resv2 ↦ gensem ptResv2_spec
            ⊕ pt_new ↦ gensem pt_new_spec
            
            ⊕ pmap_init ↦ gensem pmap_init_spec.

  Definition mptnew_passthrough : compatlayer (cdata RData) :=
    fload ↦ gensem fload_spec
          ⊕ fstore ↦ gensem fstore_spec
          
          ⊕ page_copy ↦ gensem page_copy_spec
          ⊕ page_copy_back ↦ gensem page_copy_back_spec

          ⊕ vmxinfo_get ↦ gensem vmxinfo_get_spec
          ⊕ palloc ↦ gensem palloc_spec
          
          ⊕ set_pt ↦ gensem setPT_spec
          ⊕ pt_read ↦ gensem ptRead_spec
          ⊕ pt_read_pde ↦ gensem ptReadPDE_spec
          
          ⊕ pt_rmv ↦ gensem ptRmv0_spec
          ⊕ pt_in ↦ primcall_general_compatsem´ ptin_spec (prim_ident:= pt_in)
          ⊕ pt_out ↦ primcall_general_compatsem´ ptout_spec (prim_ident:= pt_out)
          ⊕ 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

          ⊕ get_CPU_ID ↦ gensem get_CPU_ID_spec
          ⊕ get_curid ↦ gensem get_curid_spec
          ⊕ set_curid ↦ gensem set_curid_spec
          ⊕ set_curid_init ↦ gensem set_curid_init_spec
          ⊕ release_lock ↦ primcall_release_lock_compatsem release_lock release_lock_spec1
          ⊕ acquire_lock ↦ primcall_acquire_lock_compatsem acquire_lock_spec1
          

          ⊕ cli ↦ gensem cli_spec
          ⊕ sti ↦ gensem sti_spec
          ⊕ serial_intr_disable ↦ gensem serial_intr_disable_spec
          ⊕ serial_intr_enable ↦ gensem serial_intr_enable_spec
          ⊕ serial_putc ↦ gensem serial_putc_spec
          ⊕ cons_buf_read ↦ gensem cons_buf_read_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
          ⊕ proc_create_postinit ↦ gensem proc_create_postinit_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 _ _ _ _ _ _ _ _ _ _ _ _ _ _ Hmwd);
                           exec_store := (@exec_storeex _ _ _ _ _ _ _ _ _ _ _ _ _ _ Hmwd) |}.

  Definition mptnew : compatlayer (cdata RData) := mptnew_fresh ⊕ mptnew_passthrough.

End WITHMEM.