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 LoadStoreSem1.
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 INVLemmaMemory.

Require Import AbstractDataType.

Require Export ObjCPU.
Require Export ObjMM.
Require Export ObjFlatMem.
Require Export ObjPMM.

Section WITHMEM.

  Local Open Scope Z_scope.

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

  Record high_level_invariant (abd: RData) :=
    mkInvariant {
        valid_nps: init abd= true → kern_low ≤ nps abd ≤ maxpage;
        valid_kern: ikern abd = false → pg abd = true ∧ init abd = true;
        valid_AT_kern: init abd = true → AT_kern (AT abd) (nps abd);
        valid_AT_usr: init abd = true → AT_usr (AT abd) (nps abd);
        valid_CR3: pg abd= true → CR3_valid (CR3 abd);
        valid_ihost: ihost abd = false → pg abd = true ∧ init abd = true ∧ ikern abd = true
      }.

  Global Instance malop_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.
    Qed.

    Global Instance malop_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.

  Section INV.

    Global Instance setPG_inv: PreservesInvariants setPG0_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant; auto.
    Qed.

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

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

    Global Instance set_at_u_inv: PreservesInvariants set_at_u_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant; auto.
      - intros; eapply AT_kern_norm; eauto.
      - intros; eapply AT_usr_norm; eauto.
    Qed.

    Global Instance set_at_c_inv: PreservesInvariants set_at_c_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant; auto.
      - intros; eapply AT_kern_norm; eauto.
      - intros; eapply AT_usr_norm; eauto.
    Qed.

    Global Instance mem_init_inv: PreservesInvariants mem_init_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant.
      - apply real_nps_range.
      - apply real_at_kern_valid.
      - apply real_at_usr_valid.
    Qed.

    Global Instance setCR3_inv: SetCR3Invariants setCR30_spec.
    Proof.
      constructor; intros; functional inversion H.
      - inv H0; constructor; trivial.
      - inv H0; constructor; auto.
      - assumption.
    Qed.

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

    Global Instance trapout_inv: PrimInvariants trapout0_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 fstore_inv: PreservesInvariants fstore'_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant; auto.
    Qed.

    Global Instance flatmem_copy_inv: PreservesInvariants flatmem_copy'_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant; eauto.
    Qed.

  End INV.

  Definition exec_loadex {F V} := exec_loadex1 (F := F) (V := V).

  Definition exec_storeex {F V} := exec_storeex1 (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; constructor; auto.
    - functional inversion H1; constructor; auto.
  Qed.

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

  Definition malop_fresh: compatlayer (cdata RData) :=
    mem_init ↦ gensem mem_init_spec.

  Definition malop_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
          ⊕ set_pg ↦ gensem setPG0_spec
          ⊕ clear_cr2 ↦ gensem clearCR2_spec
          ⊕ set_cr3 ↦ setCR3_compatsem setCR30_spec
          ⊕ get_nps ↦ gensem get_nps_spec
          ⊕ is_norm ↦ gensem is_at_norm_spec
          ⊕ at_get ↦ gensem get_at_u_spec
          ⊕ at_get_c ↦ gensem get_at_c_spec
          ⊕ at_set ↦ gensem set_at_u_spec
          ⊕ at_set_c ↦ gensem set_at_c_spec
          ⊕ trap_in ↦ primcall_general_compatsem trapin_spec
          ⊕ trap_out ↦ primcall_general_compatsem trapout0_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 malop : compatlayer (cdata RData) := malop_fresh ⊕ malop_passthrough.


End WITHMEM.

Section WITHPARAM.

  Context `{real_params: RealParams}.

  Local Open Scope Z_scope.

  Section Impl.

  Function pfree_spec (i: Z) (adt: RData): option RData :=
    match (ikern adt, ihost adt, init adt) with
      | (true, true, true) ⇒
        if zle_lt 0 i maxpage then
          match ZMap.get i (AT adt) with
            | ATValid true ATNorm 0 ⇒
              Some adt {AT: ZMap.set i (ATValid false ATNorm 0) (AT adt)}
            | _ ⇒ None
          end
        else None
      | _ ⇒ None
    end.

  Function palloc_spec (adt: RData): option (RData × Z) :=
    match (ikern adt, init adt, ihost adt) with
      | (true, true, true) ⇒
          match first_free (AT adt) (nps adt) with
            | inleft (exist i _) ⇒
              Some (adt {AT: ZMap.set i (ATValid true ATNorm 0) (AT adt)}, i)
            | _ ⇒ Some (adt, 0)
          end
      | _ ⇒ None
    end.

  End Impl.

End WITHPARAM.