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 LoadStoreSem2.
Require Import AsmImplLemma.
Require Import LAsm.
Require Import RefinementTactic.
Require Import PrimSemantics.

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 PTKernGenSpec.
Require Import LayerCalculusLemma.

Require Import MPTKern.
Require Import AbstractDataType.

Require Import PTOpGen.
Require Import PTCommGen.

Require Import AbstractDataType.

Section Refinement.

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

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

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

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

  Section WITHMEM.

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

    Section OneStep_Forward_Relation.

      Section Exists.

        Lemma pt_init_kern_exist:
          ∀ habd habd´ labd i f,
            pt_init_kern_spec i habd = ret habd´
            → relate_RData f habd labd
            → ∃ labd´, pt_init_kern_spec i labd = Some labd´ ∧ relate_RData f habd´ labd´
                             ∧ kernel_mode labd.
        Proof.
          unfold pt_init_kern_spec. intros until f; exist_simpl.
        Qed.

        Lemma ptInsertPTE_exist:
          ∀ habd habd´ labd n v pa pe f,
            ptInsertPTE_spec n v pa pe habd = Some habd´
            → relate_RData f habd labd
            → ∃ labd´, ptInsertPTE_spec n v pa pe labd = Some labd´
                             ∧ relate_RData f habd´ labd´
                             ∧ kernel_mode labd.
        Proof.
          unfold ptInsertPTE_spec; intros until f. exist_simpl.
        Qed.

        Lemma ptInsert_exist:
          ∀ habd habd´ labd i n v pa pe s f,
            ptInsert_spec n v pa pe habd = Some (habd´, i)
            → relate_AbData s f habd labd
            → ∃ labd´, ptInsert_spec n v pa pe labd = Some (labd´, i)
                             ∧ relate_AbData s f habd´ labd´
                             ∧ kernel_mode labd.
        Proof.
          unfold ptInsert_spec; intros. pose proof H0 as HR. inv H0. revert H.
          subrewrite. subdestruct.
          - inv HQ. exploit ptInsertPTE_exist; eauto. intros (labd´ & HP & HR´ & Hk).
            rewrite HP. refine_split´; trivial.
          - inv HQ. exploit ptAllocPDE_exist; eauto. intros (labd´ & HP & HR´ & Hk).
            rewrite HP. subst; simpl. refine_split´; trivial.
          - inv HQ. exploit ptAllocPDE_exist; eauto. intros (labd´ & HP & HR´ & Hk).
            rewrite HP. destruct (zeq i 0); contra_inv.
            exploit ptInsertPTE_exist; eauto.
            intros (labd´´ & HP´ & HR´´ & Hk´).
            rewrite HP´. refine_split´; trivial.
        Qed.

        Lemma ptRmv_exist:
          ∀ n v habd habd´ labd i f,
            ptRmv_spec n v habd = Some (habd´, i)
            → relate_RData f habd labd
            → ∃ labd´, ptRmv_spec n v labd = Some (labd´, i)
                             ∧ relate_RData f habd´ labd´
                             ∧ kernel_mode labd.
        Proof.
          unfold ptRmv_spec; intros until f. exist_simpl.
        Qed.

      End Exists.

      Section FRESH_PRIM.

        Lemma pt_init_kern_spec_ref:
          compatsim (crel HDATA LDATA) (gensem pt_init_kern_spec) pt_init_kern_spec_low.
        Proof.
          compatsim_simpl (@match_AbData).
          exploit pt_init_kern_exist; eauto 1.
          intros [labd´ [HP [HM Hkern]]].
          refine_split; try econstructor; eauto. constructor.
        Qed.

        Lemma ptInsert_spec_ref:
          compatsim (crel HDATA LDATA) (gensem ptInsert_spec) ptInsert_spec_low.
        Proof.
          compatsim_simpl (@match_AbData).
          exploit ptInsert_exist; eauto 1.
          intros [labd´ [HP [HM Hkern]]].
          refine_split; try econstructor; eauto. constructor.
        Qed.

        Lemma ptRmv_spec_ref:
          compatsim (crel HDATA LDATA) (gensem ptRmv_spec) ptRmv_spec_low.
        Proof.
          compatsim_simpl (@match_AbData).
          exploit ptRmv_exist; eauto 1.
          intros [labd´ [HP [HM Hkern]]].
          refine_split; try econstructor; eauto. constructor.
        Qed.

      End FRESH_PRIM.

      Section PASSTHROUGH_RPIM.

        Lemma passthrough_correct:
          sim (crel HDATA LDATA) mptkern_passthrough mptcommon.
        Proof.
          sim_oplus.
          - apply fload_sim.
          - apply fstore_sim.
          - apply page_copy_sim.
          - apply page_copy_back_sim.
          - apply vmxinfo_get_sim.
          - apply setPG1_sim.
          - apply get_at_c_sim.
          - apply set_at_c0_sim.
          - apply lpalloc_sim.
          - apply setPT´_sim.
          - apply ptRead_sim.
          - apply ptReadPDE_sim.
          - apply ptin´_sim.
          - apply ptout_sim.
          - apply container_get_parent_sim.
          - apply container_get_nchildren_sim.
          - apply container_get_quota_sim.
          - apply container_get_usage_sim.
          - apply container_can_consume_sim.
          - apply container_split_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:= Shared2ID1_imply)).
          - eapply acquire_lock_sim1; eauto.
            intros. inv H.
          - apply cli_sim.
          - apply sti_sim.
          - apply serial_intr_disable_sim.
          - apply serial_intr_enable_sim.
          - apply serial_putc_sim.
          - apply cons_buf_read_sim.
          - 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_correct2.
            + eapply store_correct2.
        Qed.

      End PASSTHROUGH_RPIM.

    End OneStep_Forward_Relation.

  End WITHMEM.

End Refinement.