Require Import Coqlib.
Require Import Maps.
Require Import ASTExtra.
Require Import Integers.
Require Import Floats.
Require Import Values.
Require Import Memory.
Require Import Events.
Require Import Stacklayout.
Require Import Globalenvs.
Require Import AsmX.
Require Import Smallstep.
Require Import AuxStateDataType.
Require Import Constant.
Require Import GlobIdent.
Require Import FlatMemory.
Require Import CommonTactic.
Require Import AuxLemma.
Require Import RealParams.
Require Import PrimSemantics.
Require Import LAsm.
Require Import LoadStoreSem1.
Require Import XOmega.

Require Import liblayers.logic.PTreeModules.
Require Import liblayers.logic.LayerLogicImpl.
Require Import liblayers.compat.CompatLayers.
Require Import liblayers.compat.CompatGenSem.

Require Import AbstractDataType.

Require Export MCSMBoot.

Require Export ObjCPU.
Require Export ObjMM.
Require Export ObjFlatMem.
Require Export ObjMultiprocessor.
Require Export ObjSerialDevice.
Require Export ObjKeyboard.
Require Export ObjInterruptController.
Require Export ObjX86.
Require Export ObjMCSLock.

Section WITHMEM.

  Local Open Scope Z_scope.

  Context `{real_params: RealParams}.
  Context `{mcs_oracle_prop: MCSOracleProp}.

  Record high_level_invariant (abd: RData) :=
    mkInvariant {
        CPU_ID_range: 0 ≤ (CPU_ID abd) < TOTAL_CPU;
        valid_curid: 0 ≤ ZMap.get (CPU_ID abd) (cid abd) < num_proc
      }.

  Global Instance mcurid_data_ops : CompatDataOps RData :=
    {
      empty_data := init_adt mcs_oracle_init0;
      high_level_invariant := high_level_invariant;
      low_level_invariant := low_level_invariant;
      kernel_mode adt := ikern adt = true ∧ ihost adt = true
    }.

  Section Property_Abstract_Data.

    Lemma empty_data_high_level_invariant:
      high_level_invariant (init_adt mcs_oracle_init0).
    Proof.
      constructor; trivial; simpl.
      - apply current_CPU_ID_range.
      - rewrite ZMap.gi; intuition.
    Qed.

    Global Instance mcurid_data_prf : CompatData RData.
    Proof.
      constructor.
      - apply low_level_invariant_incr.
      - apply empty_data_low_level_invariant.
      - apply empty_data_high_level_invariant.
    Qed.

  End Property_Abstract_Data.

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

  Section INV.

    Global Instance setPG_inv: PreservesInvariants setPG_spec.
    Proof.
      preserves_invariants_simpl_auto.
    Qed.

    Global Instance fstore_inv: PreservesInvariants fstore´_spec.
    Proof.
      preserves_invariants_simpl_auto.
    Qed.

    Global Instance setCR3_inv: SetCR3Invariants setCR3_spec.
    Proof.
      constructor; intros.
      - functional inversion H; inv H0; constructor; trivial.
      - functional inversion H; inv H0; constructor; auto.
      - functional inversion H; simpl in *; assumption.
    Qed.

    Global Instance bootloader0_inv: PreservesInvariants bootloader0_spec.
    Proof.
      preserves_invariants_simpl_auto.
    Qed.

    Global Instance trapin_inv: PrimInvariants trapin_spec.
    Proof.
      PrimInvariants_simpl_auto.
    Qed.

    Global Instance trapout_inv: PrimInvariants trapout´_spec.
    Proof.
      PrimInvariants_simpl_auto.
    Qed.

    Global Instance hostin_inv: PrimInvariants hostin_spec.
    Proof.
      PrimInvariants_simpl_auto.
    Qed.

    Global Instance hostout_inv: PrimInvariants hostout´_spec.
    Proof.
      PrimInvariants_simpl_auto.
    Qed.

    Global Instance set_curid_inv: PreservesInvariants set_curid_spec.
    Proof.
      preserves_invariants_simpl_auto; eauto 2.
      - rewrite ZMap.gss. auto.
    Qed.

    Global Instance set_curid_init_inv: PreservesInvariants set_curid_init_spec.
    Proof.
      preserves_invariants_simpl_auto; eauto 2.
      case_eq (zeq (CPU_ID d) (Int.unsigned i)); intros; subst.
      - rewrite e; rewrite ZMap.gss; omega.
      - rewrite ZMap.gso; auto.
    Qed.

    Global Instance cli_inv: PreservesInvariants cli_spec.
    Proof.
      econstructor; intros; inv H; functional inversion H1; subst.
      - inv H0; constructor; trivial.
      - inv H0; constructor; auto.
      - simpl in *; assumption.
    Qed.

    Global Instance sti_inv: PreservesInvariants sti_spec.
    Proof.
      econstructor; intros; inv H; functional inversion H1; subst.
      - inv H0; constructor; trivial.
      - inv H0; constructor; auto.
      - simpl in *; assumption.
    Qed.

    Require Import FutureTactic.

    Global Instance serial_in_inv: PreservesInvariants serial_in_spec.
    Proof.
      preserves_invariants_subst low_level_invariant high_level_invariant.
    Qed.

    Global Instance serial_out_inv: PreservesInvariants serial_out_spec.
    Proof.
      preserves_invariants_subst low_level_invariant high_level_invariant.
    Qed.

    Global Instance serial_hw_intr_inv: PreservesInvariants serial_hw_intr_spec.
    Proof.
      preserves_invariants_nested low_level_invariant high_level_invariant.
    Qed.

    Global Instance ic_intr_inv: PreservesInvariants ic_intr_spec.
    Proof.
      preserves_invariants_nested low_level_invariant high_level_invariant.
    Qed.

    Global Instance keyboard_in_inv: PreservesInvariants keyboard_in_spec.
    Proof.
      preserves_invariants_subst low_level_invariant high_level_invariant.
    Qed.

    Global Instance keyboard_hw_intr_inv: PreservesInvariants keyboard_hw_intr_spec.
    Proof.
      preserves_invariants_nested low_level_invariant high_level_invariant.
    Qed.

    Global Instance ioapic_read_inv: PreservesInvariants ioapic_read_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant.
    Qed.

    Global Instance ioapic_write_inv: PreservesInvariants ioapic_write_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant.
    Qed.

    Global Instance lapic_read_inv: PreservesInvariants lapic_read_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant.
    Qed.

    Global Instance lapic_write_inv: PreservesInvariants lapic_write_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant.
    Qed.

    Global Instance iret_inv: PreservesInvariants iret_spec.
    Proof.
      preserves_invariants_direct low_level_invariant high_level_invariant; eauto 2.
    Qed.

    Global Instance local_irq_save_inv:
      PreservesInvariants local_irq_save_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant; eauto 2.
    Qed.

    Global Instance local_irq_restore_inv:
      PreservesInvariants local_irq_restore_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant; eauto 2.
    Qed.

    Global Instance save_context_inv:
      SaveContextInvariants save_context_spec.
    Proof.
      constructor; intros.
      -
        inv H0. unfold save_context_spec; simpl. inv H1.
        constructor; simpl; trivial.
        induction (tf d).
        simpl.
        constructor.
        constructor.
        simpl.
        apply inv_reg_wt.
        simpl.
        inv inv_inject_neutral.
        eapply inv_reg_inject_neutral; auto.
        constructor.
        constructor.
        inv tf_INJECT.
        assumption.
        eapply IHt; auto.
        inv tf_INJECT.
        assumption.
      -
        inv H0. unfold save_context_spec; simpl.
        constructor; simpl; trivial.
    Qed.

    Global Instance restore_context_inv:
      RestoreContextInvariants restore_context_spec.
    Proof.
      constructor; intros.
      -
        inv H0. functional inversion H; inv H1;
        constructor; simpl; trivial.
        rewrite H4 in ×.
        clear H4 H.
        generalize dependent _x.
        induction _x0.
        intros.
        simpl in ×.
        constructor.
        intros.
        simpl in ×.
        constructor.
        inv tf_INJECT.
        assumption.
        eapply IH_x0; auto.
        inv tf_INJECT; assumption.
      -
        inv H0. functional inversion H; subst;
        constructor; simpl; trivial.
    Qed.

    Global Instance acquire_shared_inv: SAcquireInvariants acquire_shared0_spec0.
    Proof.
      constructor; unfold acquire_shared0_spec; intros; subdestruct;
      inv H; inv H0; constructor; auto.
    Qed.

    Global Instance release_shared_inv: ReleaseInvariants release_shared0_spec0.
    Proof.
      constructor; unfold release_shared0_spec; intros; subdestruct;
      inv H; inv H0; constructor; auto.
    Qed.

    Global Instance atomic_mcs_log_inv: AtomicmcslogInvariants atomic_mcs_log_spec.
    Proof.
      unfold atomic_mcs_log_spec; constructor; intros; subdestruct; inv H; inv H0;
      constructor; auto.
    Qed.

    Global Instance atomic_mcs_SWAP_inv: AtomicmcsSWAPInvariants atomic_mcs_SWAP_spec.
    Proof.
      unfold atomic_mcs_SWAP_spec; constructor; intros; subdestruct; inv H; inv H0;
      constructor; auto.
    Qed.

    Global Instance atomic_mcs_CAS_inv: AtomicmcsCASInvariants atomic_mcs_CAS_spec.
    Proof.
      unfold atomic_mcs_CAS_spec; constructor; intros; subdestruct; inv H; inv H0;
      constructor; auto.
    Qed.

    Global Instance mcs_init_node_log_inv: PreservesInvariants mcs_init_node_log_spec.
    Proof.
      preserves_invariants_simpl_auto1.
    Qed.

    Global Instance mcs_GET_NEXT_log_inv: PreservesInvariants mcs_GET_NEXT_log_spec.
    Proof.
      preserves_invariants_simpl_auto1.
    Qed.

    Global Instance mcs_SET_NEXT_log_inv: PreservesInvariants mcs_SET_NEXT_log_spec.
    Proof.
      preserves_invariants_simpl_auto1.
    Qed.

    Global Instance mcs_GET_BUSY_log_inv: PreservesInvariants mcs_GET_BUSY_log_spec.
    Proof.
      preserves_invariants_simpl_auto1.
    Qed.

    Global Instance mcs_SET_BUSY_log_inv: PreservesInvariants mcs_SET_BUSY_log_spec.
    Proof.
      preserves_invariants_simpl_auto1.
    Qed.

    Global Instance proc_create_postinit_inv:
      PreservesInvariants proc_create_postinit_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant; eauto 2.
    Qed.

  End INV.

  Definition exec_loadex {F V} := exec_loadex1 (F := F) (V := V).

  Definition exec_storeex {F V} := exec_storeex1 (flatmem_store:= flatmem_store´) (F := F) (V := V).

  Global Instance flatmem_store_inv: FlatmemStoreInvariant (flatmem_store:= flatmem_store´).
  Proof.
    split; inversion 1; intros.
    - functional inversion H0; constructor; auto.
    - functional inversion H1; constructor; auto.
  Qed.

  Global Instance trapinfo_set_inv: TrapinfoSetInvariant.
  Proof.
    split; inversion 1; intros; constructor; auto.
  Qed.


   Global Instance page_copy_inv: PreservesInvariants page_copy´´´_spec.
   Proof.
     preserves_invariants_simpl_auto.
   Qed.

  Global Instance page_copy_back_inv: PreservesInvariants page_copy_back´_spec.
  Proof.
    preserves_invariants_simpl_auto.
  Qed.

  Definition mcurid_fresh : compatlayer (cdata RData) :=
    get_curid ↦ gensem get_curid_spec
              ⊕ set_curid ↦ gensem set_curid_spec
              ⊕ set_curid_init ↦ gensem set_curid_init_spec.

  Definition mcurid_passthrough : compatlayer (cdata RData) :=
    fload ↦ gensem fload´_spec
          ⊕ fstore ↦ gensem fstore´_spec
          
          ⊕ page_copy ↦ gensem page_copy´´´_spec
          ⊕ page_copy_back ↦ gensem page_copy_back´_spec
          ⊕ vmxinfo_get ↦ gensem vmxinfo_get_spec
          ⊕ set_pg ↦ gensem setPG_spec
          ⊕ set_cr3 ↦ setCR3_compatsem setCR3_spec
          ⊕ get_size ↦ gensem MMSize
          ⊕ is_usable ↦ gensem is_mm_usable_spec
          ⊕ get_mms ↦ gensem get_mm_s_spec
          ⊕ get_mml ↦ gensem get_mm_l_spec
          ⊕ boot_loader ↦ gensem bootloader0_spec

          
          ⊕ release_shared ↦ primcall_release_lock_compatsem release_shared release_shared0_spec0
          ⊕ acquire_shared ↦ primcall_acquire_shared_compatsem acquire_shared0_spec0

          ⊕ atomic_mcs_log ↦ primcall_atomic_mcs_log_compatsem atomic_mcs_log_spec
          ⊕ atomic_mcs_SWAP ↦ primcall_atomic_mcs_SWAP_compatsem atomic_mcs_SWAP_spec
          ⊕ atomic_mcs_CAS ↦ primcall_atomic_mcs_CAS_compatsem atomic_mcs_CAS_spec

          ⊕ mcs_init_node_log ↦ gensem mcs_init_node_log_spec
          ⊕ mcs_GET_NEXT_log ↦ gensem mcs_GET_NEXT_log_spec
          ⊕ mcs_SET_NEXT_log ↦ gensem mcs_SET_NEXT_log_spec
          ⊕ mcs_GET_BUSY_log ↦ gensem mcs_GET_BUSY_log_spec
          ⊕ mcs_SET_BUSY_log ↦ gensem mcs_SET_BUSY_log_spec
          

          ⊕ get_CPU_ID ↦ gensem get_CPU_ID_spec
          ⊕ trap_in ↦ primcall_general_compatsem trapin_spec
          ⊕ trap_out ↦ primcall_general_compatsem trapout´_spec
          ⊕ host_in ↦ primcall_general_compatsem hostin_spec
          ⊕ host_out ↦ primcall_general_compatsem hostout´_spec
          ⊕ proc_create_postinit ↦ gensem proc_create_postinit_spec
          ⊕ trap_get ↦ primcall_trap_info_get_compatsem trap_info_get_spec
          ⊕ trap_set ↦ primcall_trap_info_ret_compatsem trap_info_ret_spec
          ⊕ serial_irq_check ↦ gensem serial_irq_check_spec
          ⊕ iret ↦ gensem iret_spec
          ⊕ cli ↦ gensem cli_spec
          ⊕ sti ↦ gensem sti_spec
          ⊕ serial_irq_current ↦ gensem serial_irq_current_spec
          ⊕ ic_intr ↦ gensem ic_intr_spec
          ⊕ save_context ↦ primcall_save_context_compatsem save_context_spec
          ⊕ restore_context ↦ primcall_restore_context_compatsem restore_context_spec
          ⊕ local_irq_save ↦ gensem local_irq_save_spec
          ⊕ local_irq_restore ↦ gensem local_irq_restore_spec
          ⊕ serial_in ↦ gensem serial_in_spec

          ⊕ serial_out ↦ gensem serial_out_spec

          ⊕ serial_hw_intr ↦ gensem serial_hw_intr_spec

          ⊕ ioapic_read ↦ gensem ioapic_read_spec

          ⊕ ioapic_write ↦ gensem ioapic_write_spec

          ⊕ lapic_read ↦ gensem lapic_read_spec

          ⊕ lapic_write ↦ gensem lapic_write_spec

          ⊕ accessors ↦ {| exec_load := @exec_loadex; exec_store := @exec_storeex |}.

  Definition mcurid : compatlayer (cdata RData) := mcurid_fresh ⊕ mcurid_passthrough.

End WITHMEM.