***********************************************************************
*                                                                     *
*            The CertiKOS Certified Kit Operating System              *
*                                                                     *
*                   The FLINT Group, Yale University                  *
*                                                                     *
*  Copyright The FLINT Group, Yale University.  All rights reserved.  *
*  This file is distributed under the terms of the Yale University    *
*  Non-Commercial License Agreement.                                  *
*                                                                     *
*********************************************************************** 

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 LayerCalculusLemma.
Require Import AbstractDataType.

Require Import PQueueIntro.
Require Import PQueueInit.
Require Import QueueInitGenSpec.

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 := pqueueinit_data_ops) HDATA).
  Notation LDATAOps := (cdata (cdata_ops := pthreadinit_data_ops) LDATA).

  Section WITHMEM.

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

    Record relate_RData (f: meminj) (hadt: LDATA) (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;

          pb_re: pb hadt = pb ladt;
          kctxt_re: kctxt_inj f num_proc (kctxt hadt) (kctxt ladt);
          tcb_re: tcb hadt = tcb ladt;
          tdq_re: tdq hadt = tdq 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
      }.

    Section Rel_Property.

      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; intros; simpl; trivial.
        eapply relate_incr; eauto.
      Qed.

    End Rel_Property.

    Section OneStep_Forward_Relation.

      Section Exists.

        Lemma tdqueue_init_exist:
          ∀ habd habd´ labd i f,
            tdqueue_init_spec i habd = ret habd´
            → relate_RData f habd labd
            → ∃ labd´, PQueueIntro.tdqueue_init_spec i labd = Some labd´
                             ∧ relate_RData f habd´ labd´
                             ∧ kernel_mode labd.
        Proof.
          unfold tdqueue_init_spec, PQueueIntro.tdqueue_init_spec, thread_init_spec.
          intros until f. exist_simpl.
        Qed.

        Lemma queue_rmv_exist:
          ∀ habd habd´ labd n i f,
            queue_rmv_spec n i habd = ret habd´
            → relate_RData f habd labd
            → ∃ labd´, queue_rmv_spec n i labd = Some labd´
                             ∧ relate_RData f habd´ labd´
                             ∧ kernel_mode labd.
        Proof.
          unfold queue_rmv_spec. intros until f. exist_simpl.
        Qed.

        Lemma enqueue_exist:
          ∀ habd habd´ labd n i f,
            enqueue_spec n i habd = ret habd´
            → relate_RData f habd labd
            → high_level_invariant habd
            → ∃ labd´, PQueueIntro.enqueue_spec n i labd = Some labd´
                             ∧ relate_RData f habd´ labd´
                             ∧ kernel_mode labd.
        Proof.
          unfold enqueue_spec, PQueueIntro.enqueue_spec.
          intros until f.
          intros HP HR HINV. pose proof HR as HR´. inv HR; revert HP.
          specialize (valid_TDQ _ HINV).
          unfold TDQCorrect_range; unfold Queue_arg. simpl.
          subrewrite´; intros HTDQ HQ. subdestruct; inv HQ.
          - refine_split´; eauto. inv HR´.
            econstructor; eauto 1.
          - specialize (HTDQ refl_equal _ a).
            destruct HTDQ as [head0[tail0[HTDQ[_ HTail]]]].
            inv HTDQ. rewrite H0 in Hdestruct5. inv Hdestruct5.
            rewrite zle_lt_true; [|omega].
            refine_split´; eauto. inv HR´.
            econstructor; eauto.
        Qed.

        Lemma dequeue_exist:
          ∀ habd habd´ labd n i f,
            dequeue_spec n habd = ret (habd´, i)
            → relate_RData f habd labd
            → high_level_invariant habd
            → ∃ labd´, PQueueIntro.dequeue_spec n labd = Some (labd´, i)
                             ∧ relate_RData f habd´ labd´
                             ∧ kernel_mode labd.
        Proof.
          unfold dequeue_spec, PQueueIntro.dequeue_spec. intros until f.
          intros HP HR HINV. pose proof HR as HR´. inv HR; revert HP.
          specialize (valid_TDQ _ HINV).
          unfold TDQCorrect_range. unfold Queue_arg.
          subrewrite´; intros HTDQ HQ. subdestruct; inv HQ.
          - refine_split´; eauto.
          - specialize (HTDQ refl_equal _ a).
            destruct HTDQ as [head0[tail0[HTDQ[Head HTail]]]].
            inv HTDQ. rewrite H0 in Hdestruct4. inv Hdestruct4.
            rewrite zle_lt_true; [|omega].
            refine_split´; eauto.
            econstructor; eauto.
          - specialize (HTDQ refl_equal _ a).
            destruct HTDQ as [head0[tail0[HTDQ[Head HTail]]]].
            inv HTDQ. rewrite H0 in Hdestruct4. inv Hdestruct4.
            rewrite zle_lt_true; [|omega].
            refine_split´; eauto.
            econstructor; eauto.
        Qed.

      End Exists.

      Section FRESH_PRIM.

        Lemma queue_rmv_spec_ref:
          compatsim (crel HDATA LDATA) (gensem queue_rmv_spec)
                    queue_rmv_spec_low.
        Proof.
          compatsim_simpl (@match_AbData).
          exploit queue_rmv_exist; eauto 1.
          intros [labd´ [HP [HM Hkern]]].
          refine_split; try econstructor; eauto. constructor.
        Qed.

        Lemma tdqueue_init_spec_ref:
          compatsim (crel HDATA LDATA) (gensem tdqueue_init_spec)
                    tdqueue_init_spec_low.
        Proof.
          compatsim_simpl (@match_AbData).
          exploit tdqueue_init_exist; eauto 1.
          intros [labd´ [HP [HM Hkern]]].
          refine_split; try econstructor; eauto. constructor.
        Qed.

        Lemma enqueue_spec_ref:
          compatsim (crel HDATA LDATA) (gensem enqueue_spec)
                    enqueue_spec_low.
        Proof.
          compatsim_simpl (@match_AbData).
          exploit enqueue_exist; eauto 1.
          intros [labd´ [HP [HM Hkern]]].
          refine_split; try econstructor; eauto. constructor.
        Qed.

        Lemma dequeue_spec_ref:
          compatsim (crel HDATA LDATA) (gensem dequeue_spec)
                    dequeue_spec_low.
        Proof.
          compatsim_simpl (@match_AbData).
          exploit dequeue_exist; eauto 1.
          intros [labd´ [HP [HM Hkern]]].
          refine_split; try econstructor; 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) pqueueinit_passthrough pqueueintro.
        Proof.
          sim_oplus.
          - apply fload_sim.
          - apply fstore_sim.
          - apply flatmem_copy_sim.
          - apply vmxinfo_get_sim.
          - apply palloc_sim.
          - apply pfree_sim.
          - apply setPT_sim.
          - apply ptRead_sim.
          - apply ptResv_sim.
          - apply kctxt_new_sim.
          - apply shared_mem_status_sim.
          - apply offer_shared_mem_sim.
          - apply get_state_sim.
          - apply set_state_sim.
          - apply ptin_sim.
          - apply ptout_sim.
          - apply container_get_quota_sim.
          - apply container_get_usage_sim.
          - apply container_can_consume_sim.
          - apply trapin_sim.
          - apply trapout_sim.
          - apply hostin_sim.
          - apply hostout_sim.
          - apply trap_info_get_sim.
          - apply trap_info_ret_sim.
          - apply kctxt_switch_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.
          - layer_sim_simpl.
            + eapply load_correct2.
            + eapply store_correct2.
        Qed.

      End PASSTHROUGH_RPIM.

    End OneStep_Forward_Relation.

  End WITHMEM.

End Refinement.