Library mcertikos.mm.ALOpGen

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*            The CertiKOS Certified Kit Operating System              *
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This file provide the contextual refinement proof between MALInit layer and MALOp 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 LoadStoreSem1.
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 LayerCalculusLemma.

Require Import AbstractDataType.
Require Import MALOp.
Require Import MALInit.
Require Import ALOpGenSpec.

Notation 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}.

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

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

  Section WITHMEM.

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

Definition the refinement relation: relate_RData + match_RData

    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));
          AT_re: AT hadt = AT ladt;
          nps_re: nps hadt = nps ladt;
          init_re: init hadt = init 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
        }.

    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.
      Qed.

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

    End Rel_Property.

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

    Section OneStep_Forward_Relation.

      Section FRESH_PRIM.

        Lemma mem_init_kern_mode:
          ∀ i d d´,
            mem_init_spec i d = Some d´
            → kernel_mode d.
        Proof.
          unfold mem_init_spec. simpl; intros.
          subdestruct. auto.
        Qed.

        Lemma mem_init_spec_ref:
          compatsim (crel HDATA LDATA) (gensem mem_init_spec) mem_init_spec_low.
        Proof.
          compatsim_simpl (@match_AbData).
          exploit mem_init_exist; eauto 1.
          intros [labd´ [HP HM]].
          refine_split; try econstructor; eauto.
          - eapply mem_init_kern_mode; eauto.
          - constructor.
        Qed.

      End FRESH_PRIM.

      Section PASSTHROUGH_RPIM.

        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) malop_passthrough malinit.
        Proof.
          sim_oplus.
          - apply fload´_sim.
          - apply fstore´_sim.
          - apply flatmem_copy´_sim.
          - apply vmxinfo_get_sim.
          - apply setPG0_sim.
          - apply setCR30_sim.
          - apply get_nps_sim.
          - apply is_at_norm_sim.
          - apply get_at_u_sim.
          - apply get_at_c_sim.
          - apply set_at_u_sim.
          - apply set_at_c_sim.
          - apply container_get_parent_sim.
          - apply container_get_quota_sim.
          - apply container_get_usage_sim.
          - apply container_can_consume_sim.
          - apply container_split_sim.
          - apply container_alloc_sim.
          - apply cli_sim.
          - apply sti_sim.
          - apply cons_buf_read_sim.
          - apply serial_putc_sim.
          - apply serial_intr_disable_sim.
          - apply serial_intr_enable_sim.
          - apply trapin_sim.
          - apply trapout0_sim.
          - apply hostin_sim.
          - apply hostout_sim.
          - apply trap_info_get_sim.
          - apply trap_info_ret_sim.
          - layer_sim_simpl.
            + eapply load_correct1.
            + eapply store_correct1.
        Qed.

      End PASSTHROUGH_RPIM.

    End OneStep_Forward_Relation.

  End WITHMEM.

End Refinement.