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 LAsmModuleSemAux.
Require Import LayerCalculusLemma.
Require Import AbstractDataType.

Require Import PUCtxtIntro.
Require Import PProc.

Require Import GlobalOracleProp.

Require Import ProcGenSpec.

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 := pproc_data_ops) HDATA).
  Notation LDATAOps := (cdata (cdata_ops := pqthread_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;

          kctxt_re: kctxt_inj f num_proc (kctxt hadt) (kctxt ladt);
          uctxt_re: uctxt_inj f (uctxt hadt) (uctxt ladt);
          
          syncchpool_re: syncchpool hadt = syncchpool 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.
        - eapply uctxt_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.

      Section FRESH_PRIM.

        Lemma proc_start_user_spec_ref:
          compatsim (crel HDATA LDATA)
                    (primcall_start_user_compatsem proc_start_user_spec)
                    proc_start_user_spec_low.
        Proof.
          compatsim_simpl (@match_AbData).
          intros.
          inv match_extcall_states.
          exploit proc_start_user_exist; eauto 1.
          eapply valid_curid; eauto.
          intros (d2´ & rs2´ & HM & HR & HReg & He & Hrange´).
          subst.
          refine_split´.
          - econstructor.
            + eauto.
            + eapply reg_symbol_inject; eassumption.
            + eauto.
            + reflexivity.
            + eauto.
            + eauto.
            + eauto.
          - econstructor; eauto.
            constructor; try eassumption.
            econstructor.
            val_inject_simpl; try (eapply HReg; omega).
        Qed.

        Lemma proc_exit_user_spec_ref:
          compatsim (crel HDATA LDATA)
                    (primcall_exit_user_compatsem proc_exit_user_spec)
                    proc_exit_user_spec_low.
        Proof.
          compatsim_simpl (@match_AbData).
          intros.
          inv H4. inv match_extcall_states.
          exploit proc_exit_user_exist; eauto 1.
          - subst uctx4 uctx3 uctx2 uctx1.
            intros. inv_proc. rewrite ZMap.gi. constructor.
          - intros [d2´[HM HR]].
            refine_split; try econstructor; eauto.
            eapply reg_symbol_inject; eassumption.
            + exploit (extcall_args_inject (D1:= HDATAOps) (D2:= LDATAOps)); eauto.
              instantiate (3:= d1´).
              apply extcall_args_with_data; eauto.
              instantiate (1:= d2).
              intros [?[? Hinv]]. inv_val_inject.
              apply extcall_args_without_data in H; eauto.
            + specialize (match_reg ESP); unfold Pregmap.get in match_reg.
              inv match_reg; congruence.
            + intros.
              specialize (match_reg ESP); unfold Pregmap.get in match_reg.
              inv match_reg; try congruence.
              specialize (HESP_STACK _ _ (eq_sym H1)).
              replace b1 with b2 by congruence.
              split.
              × apply Ple_trans with b0;
                [ apply HESP_STACK | apply (match_inject_forward _ _ _ H3) ].
              × apply (Mem.valid_block_inject_2 _ _ _ _ _ _ H3 match_inject).
            + econstructor; eauto. constructor.
            + val_inject_simpl.
        Qed.

        Lemma proc_start_user_spec_ref2:
          compatsim (crel HDATA LDATA)
                    (primcall_start_user_compatsem2 proc_start_user_spec)
                    proc_start_user_spec_low2.
        Proof.
          compatsim_simpl (@match_AbData).
          intros.
          inv match_extcall_states.
          exploit proc_start_user_exist; eauto 1.
          eapply valid_curid; eauto.
          intros (d2´ & rs2´ & HM & HR & HReg & He & Hrange´).
          subst.
          refine_split´.
          - econstructor.
            + eauto.
            + eapply reg_symbol_inject; eassumption.
            + eauto.
            + reflexivity.
            + eauto.
            + eauto.
            + eauto.
          - econstructor; eauto.
            constructor; try eassumption.
            econstructor.
            val_inject_simpl; try (eapply HReg; omega).
        Qed.

        Lemma proc_exit_user_spec_ref2:
          compatsim (crel HDATA LDATA)
                    (primcall_exit_user_compatsem2 proc_exit_user_spec)
                    proc_exit_user_spec_low2.
        Proof.
          compatsim_simpl (@match_AbData).
          intros.
          inv H4. inv match_extcall_states.
          exploit proc_exit_user_exist; eauto 1.
          - subst uctx4 uctx3 uctx2 uctx1.
            intros. inv_proc. rewrite ZMap.gi. constructor.
          - intros [d2´[HM HR]].
            refine_split; try econstructor; eauto.
            eapply reg_symbol_inject; eassumption.
            + exploit (extcall_args_inject (D1:= HDATAOps) (D2:= LDATAOps)); eauto.
              instantiate (3:= d1´).
              apply extcall_args_with_data; eauto.
              instantiate (1:= d2).
              intros [?[? Hinv]]. inv_val_inject.
              apply extcall_args_without_data in H; eauto.
            + specialize (match_reg ESP); unfold Pregmap.get in match_reg.
              inv match_reg; congruence.
            + intros.
              specialize (match_reg ESP); unfold Pregmap.get in match_reg.
              inv match_reg; try congruence.
              specialize (HESP_STACK _ _ (eq_sym H1)).
              replace b1 with b2 by congruence.
              split.
              × apply Ple_trans with b0;
                [ apply HESP_STACK | apply (match_inject_forward _ _ _ H3) ].
              × apply (Mem.valid_block_inject_2 _ _ _ _ _ _ H3 match_inject).
            + econstructor; eauto. constructor.
            + val_inject_simpl.
        Qed.

        Lemma biglow_proc_create_kernel_mode:
          ∀ d2 d2´ b b´ b2 ofs_uc q,
            biglow_proc_create_spec d2 b b´ b2 ofs_uc q = Some d2´
            → kernel_mode d2.
        Proof.
          unfold biglow_proc_create_spec; intros.
          simpl; subdestruct. auto.
        Qed.

        Lemma biglow_proc_create_spec_ref:
          compatsim (crel HDATA LDATA) (proc_create_compatsem biglow_proc_create_spec) proc_create_spec_low.
        Proof.
          compatsim_simpl (@match_AbData).
          generalize biglow_proc_create_exist.

          exploit biglow_proc_create_exist; eauto 1.
          intros (labd´ & HP & HM).
          destruct H9 as [fun_id Hsymbol].
          exploit (stencil_find_symbol_inject´ s ι fun_id buc); eauto.
          intros HFB.
          refine_split; try econstructor; eauto.
          - eapply biglow_proc_create_kernel_mode; 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) pproc_passthrough puctxtintro.
        Proof.
          sim_oplus.
          - apply fload_sim.
          - apply fstore_sim.
          - apply vmxinfo_get_sim.
          - apply palloc_sim.
          - apply setPT_sim.
          - apply ptRead_sim.
          - apply ptResv_sim.
          - apply shared_mem_status_sim.
          - apply offer_shared_mem_sim.

          - apply biglow_thread_wakeup_sim.
          - apply biglow_thread_yield_sim.
          - apply biglow_thread_sleep_sim.
          - apply biglow_sched_init_sim.

          - apply uctx_get_sim.
          - apply uctx_set_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 acquire_lock_SC_sim.
          - apply release_lock_SC_sim.
          - apply get_sync_chan_busy_sim.
          - apply set_sync_chan_busy_sim.
          - apply ipc_send_body_sim.
          - apply ipc_receive_body_sim.

          - 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 hostin_sim.
          - apply hostout_sim.
          - apply proc_create_postinit_sim.
          - apply trap_info_get_sim.
          - apply trap_info_ret_sim.
          - layer_sim_simpl.
            + eapply load_correct2.
            + eapply store_correct2.
        Qed.

      End PASSTHROUGH_PRIM.

    End OneStep_Forward_Relation.

  End WITHMEM.

End Refinement.