Library mcertikos.proc.UCtxtIntroGenDef


This file provide the contextual refinement proof between PIPC layer and PUCtxtIntro layer
Require Export Coqlib.
Require Export Errors.
Require Export AST.
Require Export Integers.
Require Export Floats.
Require Export Op.
Require Export Asm.
Require Export Events.
Require Export Globalenvs.
Require Export Smallstep.
Require Export Values.
Require Export Memory.
Require Export Maps.
Require Export CommonTactic.
Require Export AuxLemma.
Require Export FlatMemory.
Require Export AuxStateDataType.
Require Export Constant.
Require Export GlobIdent.
Require Export RealParams.
Require Export LoadStoreSem2.
Require Export AsmImplLemma.
Require Export GenSem.
Require Export RefinementTactic.
Require Export PrimSemantics.
Require Export XOmega.

Require Export liblayers.logic.PTreeModules.
Require Export liblayers.logic.LayerLogicImpl.
Require Export liblayers.compcertx.Stencil.
Require Export liblayers.compcertx.MakeProgram.
Require Export liblayers.compat.CompatLayers.
Require Export liblayers.compat.CompatGenSem.
Require Export compcert.cfrontend.Ctypes.
Require Export LAsmModuleSemAux.
Require Export LayerCalculusLemma.
Require Export AbstractDataType.

Require Export PUCtxtIntro.
Require Export PQThread.

Require Import GlobalOracleProp.

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

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

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

Definition of the refinement relation

Section Refinement.

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

  Section WITHMEM.

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

Definition the refinement relation: relate_RData + match_RData

    Section REFINEMENT_REL.

Relation between the kernel context pool and the underline memory
      Inductive match_UCtxt: stencil → UContextPool → mem → meminj → Prop :=
      | MATCH_UCTXT:
          ∀ uctxt m b s f,
            (∀ i n,
               0≤ i < num_proc
               → 0≤ n < UCTXT_SIZE
               → (∃ v,
                     Mem.load Mint32 m b (i × UCTXT_SIZE × 4 + n × 4) = Some v ∧
                     Mem.valid_access m Mint32 b (i × UCTXT_SIZE × 4 + n × 4) Writable ∧
                     
                     True ∧
                     val_inject f (Val.load_result Mint32 (ZMap.get n (ZMap.get i uctxt))) v))
            → find_symbol s UCTX_LOC = Some b
            → match_UCtxt s uctxt m f.

Relation between the new raw data at the higher layer with the mememory at lower layer
        Inductive match_RData: stencil → HDATA → mem → meminj → Prop :=
        | MATCH_RDATA:
            ∀ hadt m s f,
              match_UCtxt s (uctxt hadt) m f
              → match_RData s hadt m f.

Relation between raw data at two layers
        Record relate_RData (f: meminj) (hadt: HDATA) (ladt: LDATA) :=
          mkrelate_RData {
              flatmem_re: FlatMem.flatmem_inj (HP hadt) (HP ladt);
              vmxinfo_re: vmxinfo hadt = vmxinfo ladt;
              CR3_re: CR3 hadt = CR3 ladt;
              ikern_re: ikern hadt = ikern ladt;
              pg_re: pg hadt = pg ladt;
              ihost_re: ihost hadt = ihost ladt;
              AC_re: AC hadt = AC ladt;
              ti_fst_re: (fst (ti hadt)) = (fst (ti ladt));
              ti_snd_re: val_inject f (snd (ti hadt)) (snd (ti ladt));
              LAT_re: LAT hadt = LAT ladt;
              nps_re: nps hadt = nps ladt;
              init_re: init hadt = init ladt;

              pperm_re: pperm hadt = pperm ladt;
              PT_re: PT hadt = PT ladt;
              ptp_re: ptpool hadt = ptpool ladt;
              idpde_re: idpde hadt = idpde ladt;
              ipt_re: ipt hadt = ipt ladt;
              smspool_re: smspool hadt = smspool ladt;

              CPU_ID_re: CPU_ID hadt = CPU_ID ladt;
              cid_re: cid hadt = cid ladt;
              multi_oracle_re: multi_oracle hadt = multi_oracle ladt;
              multi_log_re: multi_log hadt = multi_log ladt;
              lock_re: lock hadt = lock ladt;

              com1_re: com1 hadt = com1 ladt;
              console_re: console hadt = console ladt;
              console_concrete_re: console_concrete hadt = console_concrete ladt;
              ioapic_re: ioapic ladt = ioapic hadt;
              lapic_re: lapic ladt = lapic hadt;
              intr_flag_re: intr_flag ladt = intr_flag hadt;
              curr_intr_num_re: curr_intr_num ladt = curr_intr_num hadt;
              in_intr_re: in_intr ladt = in_intr hadt;
              drv_serial_re: drv_serial hadt = drv_serial ladt;

              kctxt_re: kctxt_inj f num_proc (kctxt hadt) (kctxt ladt);

              
              syncchpool_re: syncchpool hadt = syncchpool ladt

              
              
 
              
              

              
            }.

        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 := UCTX_LOC :: nil
          }.

    End REFINEMENT_REL.

Properties of relations

    Section Rel_Property.

      Lemma inject_match_correct:
        ∀ s d1 m2 f m2´ j,
          match_RData s d1 m2 f →
          Mem.inject j m2 m2´ →
          inject_incr (Mem.flat_inj (genv_next s)) j →
          match_RData s d1 m2´ (compose_meminj f j).
      Proof.
        inversion 1; subst; intros.
        inv H0.
        assert (HFB0: j b = Some (b, 0)).
        {
          eapply stencil_find_symbol_inject´; eauto.
        }
        econstructor; eauto; intros.
        econstructor; eauto; intros.
        specialize (H3 _ _ H0 H5).
        destruct H3 as [v1[HL1[HV1 [_ HM]]]].
        specialize (Mem.load_inject _ _ _ _ _ _ _ _ _ H1 HL1 HFB0).
        repeat rewrite Z.add_0_r.
        intros [v1´[HLD1´ HV1´]].
        refine_split´; eauto.
        specialize(Mem.valid_access_inject _ _ _ _ _ _ _ _ _ HFB0 H1 HV1).
        rewrite Z.add_0_r; trivial.
        eapply val_inject_compose; eauto.
      Qed.

      Lemma store_match_correct:
        ∀ s abd m0 m0´ f b2 v v´ chunk,
          match_RData s abd m0 f →
          (∀ i b,
             In i new_glbl →
             find_symbol s i = Some b → b ≠ b2) →
          Mem.store chunk m0 b2 v v´ = Some m0´ →
          match_RData s abd m0´ f.
      Proof.
        intros. inv H. inv H2.
        econstructor; eauto.
        econstructor; eauto.
        intros. specialize (H _ _ H2 H4).
        destruct H as [v1[HL1[HV1[_ HM]]]].
        eapply H0 in H3; simpl; eauto.
        repeat rewrite (Mem.load_store_other _ _ _ _ _ _ H1); auto.
        refine_split´; eauto;
        eapply Mem.store_valid_access_1; eauto.
      Qed.

      Lemma storebytes_match_correct:
        ∀ s abd m0 m0´ f b2 v v´,
          match_RData s abd m0 f →
          (∀ i b,
             In i new_glbl →
             find_symbol s i = Some b → b ≠ b2) →
          Mem.storebytes m0 b2 v v´ = Some m0´ →
          match_RData s abd m0´ f.
      Proof.
        intros. inv H. inv H2.
        econstructor; eauto.
        econstructor; eauto.
        intros. specialize (H _ _ H2 H4).
        destruct H as [v1[HL1[HV1[_ HM]]]].
        eapply H0 in H3; simpl; eauto.
        repeat rewrite (Mem.load_storebytes_other _ _ _ _ _ H1); eauto.
        refine_split´; eauto;
        eapply Mem.storebytes_valid_access_1; eauto.
      Qed.

      Lemma free_match_correct:
        ∀ s abd m0 m0´ f ofs sz b2,
          match_RData s abd m0 f→
          (∀ i b,
             In i new_glbl →
             find_symbol s i = Some b → b ≠ b2) →
          Mem.free m0 b2 ofs sz = Some m0´ →
          match_RData s abd m0´ f.
      Proof.
        intros; inv H; inv H2.
        econstructor; eauto.
        econstructor; eauto.
        intros. specialize (H _ _ H2 H4).
        destruct H as [v1[HL1[HV1[_ HM]]]].
        eapply H0 in H3; simpl; eauto.
        repeat rewrite (Mem.load_free _ _ _ _ _ H1); auto.
        refine_split´; eauto;
        eapply Mem.valid_access_free_1; eauto.
      Qed.

      Lemma alloc_match_correct:
        ∀ s abd m´0 m´1 f f´ ofs sz b0 b´1,
          match_RData s abd m´0 f→
          Mem.alloc m´0 ofs sz = (m´1, b´1) →
          f´ b0 = Some (b´1, 0%Z) →
          (∀ b : block, b ≠ b0 → f´ b = f b) →
          inject_incr f f´ →
          (∀ i b,
             In i new_glbl →
             find_symbol s i = Some b → b ≠ b0) →
          match_RData s abd m´1 f´.
      Proof.
        intros. rename H1 into HF1, H2 into HB. inv H; inv H1.
        econstructor; eauto.
        econstructor; eauto.
        intros. specialize (H _ _ H1 H5).
        destruct H as [v1[HL1[HV1[_ HM]]]].
        refine_split´; eauto;
        try (apply (Mem.load_alloc_other _ _ _ _ _ H0));
        try (eapply Mem.valid_access_alloc_other); eauto.
      Qed.

Prove that after taking one step, the refinement relation still holds
      Lemma relate_incr:
        ∀ abd abd´ f f´,
          relate_RData f abd abd´
          → inject_incr f f´
          → relate_RData f´ abd abd´.
      Proof.
        inversion 1; subst; intros; inv H; constructor; eauto.
        - eapply kctxt_inj_incr; eauto.
      Qed.

      Global Instance rel_prf: CompatRel HDATAOps LDATAOps.
      Proof.
        constructor.
        - apply inject_match_correct.
        - apply store_match_correct.
        - apply alloc_match_correct.
        - apply free_match_correct.
        - apply storebytes_match_correct.
        - intros. eapply relate_incr; eauto.
      Qed.

    End Rel_Property.

  End WITHMEM.

End Refinement.