Library mcertikos.proc.KContextNewGen


This file provide the contextual refinement proof between PKContext layer and PKCtxtNew layer
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 GenSem.
Require Import RefinementTactic.
Require Import PrimSemantics.
Require Import XOmega.

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 AbstractDataType.
Require Import LayerCalculusLemma.

Require Import PKContextNew.

Require Import KContextNewGenSpec.

Definition of the refinement relation

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}.

    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)

        }.

    Inductive match_RData: stencil → HDATA → mem → meminj → Prop :=
    | MATCH_RDATA: ∀ 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
      }.

Properties of relations

    Section Rel_Property.

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.

    End Rel_Property.

    Global Instance rel_prf: CompatRel HDATAOps LDATAOps.
    Proof.
      constructor; intros; simpl; trivial.
      eapply relate_incr; eauto.
    Qed.

Proofs the one-step forward simulations for the low level specifications

    Section OneStep_Forward_Relation.

The low level specifications exist

      Section Exists.

        Lemma kctxt_new_exist:
          ∀ s habd habd´ labd b b´ ofs´ id q n f,
            ObjThread.kctxt_new_spec habd b b´ ofs´ id q = Some (habd´, n)
            → relate_RData f habd labd
            → high_level_invariant habd
            → find_symbol s STACK_LOC = Some b
            → (∃ id, find_symbol s id = Some b´)
            → inject_incr (Mem.flat_inj (genv_next s)) f
            → ∃ labd´, kctxt_new_spec labd b b´ ofs´ id q = Some (labd´, n)
                             ∧ relate_RData f habd´ labd´
                             ∧ kernel_mode labd.
        Proof.
          unfold ObjThread.kctxt_new_spec, kctxt_new_spec,
          kctxt_ra_spec, kctxt_sp_spec, pt_new_spec.
          intros until f; intros HP HR; inv HR. simpl.
          intros HH Hsys Hsys´ Hincr.
          revert HP. subrewrite´. intros HQ.
          subdestruct. inv HQ; simpl.
          rewrite zle_lt_true; [simpl| omega].
          rewrite zeq_false; [ |omega].
          subrewrite´; simpl.
          subrewrite´; simpl.
          repeat rewrite ZMap.gss; rewrite ZMap.set2.
          refine_split´; eauto 2.
          econstructor; eauto 2; simpl.
          unfold kctxt_inj in *; kctxt_inj_simpl.
          × destruct Hsys´ as [id´ Hsys´].
            eapply stencil_find_symbol_inject´; eauto.
          × rewrite Int.add_zero; trivial.
          × eapply stencil_find_symbol_inject´; eauto.
          × rewrite Int.add_zero; trivial.
          × eapply kctxt_re0; eauto. omega.
        Qed.

      End Exists.

      Section FRESH_PRIM.

        Lemma kctxt_new_spec_ref:
          compatsim (crel HDATA LDATA) (dnew_compatsem ObjThread.kctxt_new_spec)
                    kctxt_new_spec_low.
        Proof.
          compatsim_simpl (@match_AbData).
          exploit kctxt_new_exist; eauto 1.
          intros (labd´ & HP & HM & Hkern).
          destruct H8 as [fun_id Hsymbol].
          exploit (stencil_find_symbol_inject´ s ι fun_id b´); eauto.
          intros HFB.
          refine_split; try econstructor; eauto. constructor.
        Qed.

      End FRESH_PRIM.

      Section PASSTHROUGH_PRIM.

        Global Instance: (LoadStoreProp (hflatmem_store:= flatmem_store) (lflatmem_store:= flatmem_store)).
        Proof.
          accessor_prop_tac.
          - eapply flatmem_store_exists; eauto.
        Qed.

        Lemma passthrough_correct:
          sim (crel HDATA LDATA) pkcontextnew_passthrough pkcontext.
        Proof.
          sim_oplus.
          - apply fload_sim.
          - apply fstore_sim.
          - apply page_copy_sim.
          - apply page_copy_back_sim.
          - apply vmxinfo_get_sim.
          - apply palloc_sim.
          - apply setPT_sim.
          - apply ptRead_sim.
          - apply ptResv_sim.
          - apply sharedmem_init_sim.
          - apply shared_mem_status_sim.
          - apply offer_shared_mem_sim.
          - apply ptin_sim.
          - apply ptout_sim.
          - apply container_get_nchildren_sim.
          - apply container_get_quota_sim.
          - apply container_get_usage_sim.
          - apply container_can_consume_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; trivial.

          - 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.
          - apply kctxt_switch_sim.
          - layer_sim_simpl.
            + eapply load_correct2.
            + eapply store_correct2.
        Qed.

      End PASSTHROUGH_PRIM.

    End OneStep_Forward_Relation.

  End WITHMEM.

End Refinement.