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VCPUOpsRefine.md

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ProofHigh

Require Import Coqlib.
Require Import Errors.
Require Import AST.
Require Import Integers.
Require Import Floats.
Require Import Op.
Require Import Events.
Require Import Globalenvs.
Require Import Smallstep.
Require Import Values.
Require Import Memory.
Require Import Maps.
Require Import ZSet.
Require Import ListLemma2.
Require Import CommonTactic.
Require Import AuxLemma.
Require Import AuxStateDataType.
Require Import RealParams.
Require Import RefinementTactic.
Require Import PrimSemantics.
Require Import LayerCalculusLemma.
Require Import TacticsForTesting.
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 RData.
Require Import Constants.
Require Import VCPUOpsAux.Layer.
Require Import VCPUOps.Layer.
Require Import HypsecCommLib.
Require Import VCPUOps.Spec.

Local Open Scope Z_scope.
Local Opaque Z.add Z.mul Z.div Z.shiftl Z.shiftr Z.land Z.lor.

Section VCPUOpsProofHigh.

  Local Open Scope string_scope.
  Local Open Scope Z_scope.

  Context `{real_params: RealParams}.

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

  Notation HDATAOps := (cdata (cdata_ops := VCPUOps_ops) HDATA).
  Notation LDATAOps := (cdata (cdata_ops := VCPUOpsAux_ops) HDATA).

  Section WITHMEM.

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

    Record relate_RData (f:meminj) (hadt: HDATA) (ladt: LDATA) :=
      mkrelate_RData {
          id_rel: hadt = ladt
        }.

    Inductive match_RData: stencil -> HDATA -> mem -> meminj -> Prop :=
    | MATCH_RDATA: forall habd m f s, match_RData s habd m f.

    Local Hint Resolve MATCH_RDATA.

    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 := nil
      }.

    Global Instance rel_prf: CompatRel HDATAOps LDATAOps.
    Proof.
      constructor; intros; simpl; trivial.
      constructor; inv H; trivial.
    Qed.

    Section FreshPrim.

      Lemma save_shadow_kvm_regs_spec_exists:
        forall habd habd' labd  f
               (Hspec: save_shadow_kvm_regs_spec  habd = Some habd')
               (Hrel: relate_RData f habd labd),
          exists labd', save_shadow_kvm_regs_spec  labd = Some labd' /\ relate_RData f habd' labd'.
        Proof.
          intros. inv Hrel; subst.
          eexists; split. eassumption.
          constructor; reflexivity.
        Qed.

      Lemma restore_shadow_kvm_regs_spec_exists:
        forall habd habd' labd  f
               (Hspec: restore_shadow_kvm_regs_spec  habd = Some habd')
               (Hrel: relate_RData f habd labd),
          exists labd', restore_shadow_kvm_regs_spec  labd = Some labd' /\ relate_RData f habd' labd'.
        Proof.
          intros. inv Hrel; subst.
          eexists; split. eassumption.
          constructor; reflexivity.
        Qed.

    End FreshPrim.

  End WITHMEM.

End VCPUOpsProofHigh.