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 FutureTactic.

Require Import AbstractDataType.
Require Import LayerCalculusLemma.

Require Import PAbQueueAtomic.
Require Import AbQueueAtomicGenSpec.

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 (cdata_ops := pabqueue_data_ops) HDATA).
  Notation LDATAOps := (cdata (cdata_ops := pabqueue_data_ops) 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;

          abq_re: abq ladt = abq hadt;
          syncchpool_re: syncchpool ladt = syncchpool hadt;
          
          abtcb_re: abtcb ladt = abtcb hadt;
          sleeper_re: sleeper ladt = sleeper hadt;

          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
      }.

    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.

    End Rel_Property.


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

    Section OneStep_Forward_Relation.

      Ltac pattern2_refinement_simpl:=
        pattern2_refinement_simpl´ (@relate_AbData).

      Section FRESH_PRIM.
        Lemma enqueue_atomic_spec_ref:
          compatsim (crel HDATA LDATA) (gensem enqueue_atomic_spec)
                    enqueue_atomic_spec_low.
        Proof.
          compatsim_simpl (@match_AbData).
          exploit enqueue_atomic_exist; eauto 1.
          intros [labd´ [HP HM]].
          refine_split; try econstructor; eauto.
          - econstructor; functional inversion HP;
            unfold acquire_lock_ABTCB_spec in H0;
            subdestruct; reflexivity.
          - functional inversion H1. inv match_related. econstructor; eauto.
        Qed.

        Lemma dequeue_atomic_spec_ref:
          compatsim (crel HDATA LDATA) (gensem dequeue_atomic_spec)
                    dequeue_atomic_spec_low.
        Proof.
          compatsim_simpl (@match_AbData).
          exploit dequeue_atomic_exist; eauto 1.
          intros [labd´ [HP HM]].
          refine_split; try econstructor; eauto.
          - econstructor; functional inversion HP;
              unfold acquire_lock_ABTCB_spec in H2;
              subdestruct; reflexivity.
          - functional inversion H1. inv match_related. econstructor; eauto.
        Qed.

      End FRESH_PRIM.

      Lemma release_lock_exist:
        ∀ i ofs e habd habd´ labd f,
          release_lock_spec2 i ofs e habd = Some habd´
          → relate_RData f habd labd
          → ∃ labd´, release_lock_spec2 i ofs e labd = Some labd´ ∧
                     relate_RData f habd´ labd´.
      Proof.
        unfold release_lock_spec; intros.
        pose proof H0 as HR. inv H0.
        revert H.
        subrewrite.
        subdestruct. inv HQ.
        inv multi_log_re0.
        subrewrite´.
        refine_split´; trivial.
        constructor; eauto; simpl.
      Qed.

      Require Import LAsmModuleSemAux.

      Lemma release_lock_sim2 :
        ∀ id,
          sim (crel RData RData) (id ↦ primcall_release_lock_compatsem id release_lock_spec2)
              (id ↦ primcall_release_lock_compatsem id release_lock_spec2).
      Proof.
        intros. layer_sim_simpl. compatsim_simpl (@match_AbData).
        inv match_extcall_states.
        exploit release_lock_exist; eauto 1; intros (labd´ & HP & HM).
        eapply (extcall_args_with_data (D:= HDATAOps) d1) in H11.
        exploit (extcall_args_inject (D1:= HDATAOps) (D2:= HDATAOps) d1 d2); eauto.
        intros (varg´ & Hargs & Hlist).
        eapply extcall_args_without_data in Hargs.
        refine_split.
        - econstructor; try eapply H7; eauto; try (eapply reg_symbol_inject; eassumption).
          exploit Mem.loadbytes_inject; eauto.
          { eapply stencil_find_symbol_inject´; eauto. }
          intros (bytes2 & HLD & Hlist).
          eapply list_forall2_bytelist_inject_eq in Hlist. subst.
          change (0 + 0) with 0 in HLD. trivial.
        - repeat (econstructor; eauto).
          subst rs´. val_inject_simpl.
      Qed.

      Lemma acquire_lock_exist:
        ∀ bound i ofs habd habd´ labd f p l,
          acquire_lock_spec2 bound i ofs habd = Some (habd´, p, l)
          → relate_RData f habd labd
          → (∃ labd´, acquire_lock_spec2 bound i ofs labd = Some (labd´, p, l) ∧
                      relate_RData f habd´ labd´)
            ∧ Shared2ID2 i = Some p.
      Proof.
        unfold acquire_lock_spec; intros.
        pose proof H0 as HR. inv H0.
        revert H.
        subrewrite.
        subdestruct. inv HQ.
        inv multi_log_re0.
        subrewrite´.
        refine_split´; trivial.
        constructor; eauto; simpl.
      Qed.

      Lemma acquire_lock_sim2:
        ∀ id,
          sim (crel RData RData)
              (id ↦ primcall_acquire_lock_compatsem acquire_lock_spec2)
              (id ↦ primcall_acquire_lock_compatsem acquire_lock_spec2).
      Proof.
        intros. layer_sim_simpl. compatsim_simpl (@match_AbData).
        inv match_extcall_states.
        exploit acquire_lock_exist; eauto 1; intros ((labd´ & HP & HM) & HS).
        eapply (extcall_args_with_data (D:= HDATAOps) d1) in H10.
        destruct l; subst.
        {
          exploit Mem.storebytes_mapped_inject; eauto.
          { eapply stencil_find_symbol_inject´; eauto. }
          { eapply list_forall2_bytelist_inject; eauto. }
          intros (m2´ & Hst & Hinj).
          exploit (extcall_args_inject (D1:= HDATAOps) (D2:= HDATAOps) d1 d2); eauto.
          intros (varg´ & Hargs & Hlist).
          eapply extcall_args_without_data in Hargs.
          match_external_states_simpl.
          - simpl; trivial.
          -
            erewrite Mem.nextblock_storebytes; eauto.
            eapply Mem.nextblock_storebytes in Hst; eauto.
            rewrite Hst. assumption.
          -
            intros. inv H.
          -
            subst rs´.
            val_inject_simpl.
        }
        {
          exploit (extcall_args_inject (D1:= HDATAOps) (D2:= HDATAOps) d1 d2); eauto.
          intros (varg´ & Hargs & Hlist).
          eapply extcall_args_without_data in Hargs.
          match_external_states_simpl.
          subst rs´. val_inject_simpl.
        }
      Qed.

      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) pabqueue_atomic_passthrough pabqueue.
        Proof.
          unfold_layers. sim_oplus_split_straight.
          - 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 kctxt_new_sim.
          - apply shared_mem_status_sim.
          - apply offer_shared_mem_sim.
          - apply get_state0_sim.
          - apply set_state0_sim.
          - intros. layer_sim_simpl. compatsim_simpl (@match_AbData).
            match_external_states_simpl.
            erewrite get_abtcb_CPU_ID_exist; eauto. reflexivity.           - eapply set_abtcb_CPU_ID_sim.
          - eapply acquire_lock_ABTCB_sim.
          - eapply release_lock_ABTCB_sim.
          - eapply tdqueue_init0_sim.
          - eapply enqueue0_sim.
          - eapply dequeue0_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 sleeper_inc_sim.
          - apply sleeper_dec_sim.
          - apply sleeper_zzz_sim.

          - eapply release_lock_sim2.
          - eapply acquire_lock_sim2; eauto.
          - 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.