Library mcertikos.mm.MContainer

***********************************************************************
*                                                                     *
*            The CertiKOS Certified Kit Operating System              *
*                                                                     *
*                   The FLINT Group, Yale University                  *
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*  Copyright The FLINT Group, Yale University.  All rights reserved.  *
*  This file is distributed under the terms of the Yale University    *
*  Non-Commercial License Agreement.                                  *
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This file defines the raw abstract data and the primitives for the MBoot layer, which is also the bottom layer of memory management

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 DeviceStateDataType.
Require Import Constant.
Require Import GlobIdent.
Require Import FlatMemory.
Require Import CommonTactic.
Require Import FutureTactic.
Require Import AuxLemma.
Require Import RealParams.
Require Import PrimSemantics.
Require Import LAsm.
Require Import LoadStoreSem1.

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

Require Import INVLemmaContainer.
Require Import INVLemmaDevice.

Require Import AbstractDataType.
Require Import DeviceStateDataType.

Require Export ObjCPU.
Require Export ObjMM.
Require Export ObjFlatMem.
Require Export ObjContainer.
Require Export ObjSerialDevice.
Require Export ObjConsole.
Require Export ObjSerialDriver.
Require Export ObjInterruptController.
Require Export ObjInterruptManagement.

Section WITHMEM.

Local Open Scope Z_scope.

Context `{real_params: RealParams}.

Invariants at this layer

  Record high_level_invariant (abd: RData) :=
    mkInvariant {
      valid_container: Container_valid (AC abd);
      valid_preinit_container: init abd = false →
        ∀ x, 0 ≤ x < num_id → cused (ZMap.get x (AC abd)) ≠ true;
      valid_cons_buf_rpos: 0 ≤ rpos (console abd) < CONSOLE_BUFFER_SIZE;
      valid_cons_buf_length: 0 ≤ Zlength (cons_buf (console abd)) < CONSOLE_BUFFER_SIZE
    }.

Definition of the abstract state ops

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

Proofs that the initial abstract_data should satisfy the invariants

  Section Property_Abstract_Data.

    Lemma empty_data_high_level_invariant:
      high_level_invariant init_adt.
    Proof.
      constructor.
      - apply empty_container_valid.
      - intros; simpl; rewrite ZMap.gi; discriminate.
      - simpl; omega.
      - simpl; solve_list; omega.
    Qed.

Definition of the abstract state

    Global Instance mcontainer_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.MemoryModel}.
  Context `{Hmwd: UseMemWithData mem}.

Proofs that the primitives satisfies the invariants at this layer

Section INV.

MContainer primitives

    Global Instance container_init_inv: PreservesInvariants container_init_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant.
      apply AC_init_container_valid.
    Qed.

    Global Instance container_split_inv: PreservesInvariants container_split_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant.
      rewrite <- H0 in H2.
      exploit split_container_valid; eauto.
      subst c; contradiction (valid_preinit_container0 H (Int.unsigned i)).
      inv valid_container0; auto.
    Qed.

    Fact remove_in {A} : ∀ (l : list A) eq a1 a2, a1 ≠ a2 → In a2 l → In a2 (remove eq a1 l).
    Proof.
      induction l; simpl; intros; auto.
      destruct H0; subst.
      destruct (eq a1 a2); simpl; auto; contradiction.
      destruct (eq a1 a); simpl; auto.
    Qed.

    Fact remove_in_rev {A} : ∀ (l : list A) eq a1 a2, In a2 (remove eq a1 l) → a1 ≠ a2 ∧ In a2 l.
    Proof.
      induction l; simpl; intros; auto.
      destruct (eq a1 a); subst.
      apply IHl in H; destruct H; auto.
      simpl in H; destruct H; subst; auto.
      apply IHl in H; destruct H; auto.
    Qed.

    Fact remove_nodup {A} : ∀ (l : list A) eq a, NoDup l → NoDup (remove eq a l).
    Proof.
      induction l; simpl; intros.
      constructor.
      inv H; destruct (eq a0 a); subst; auto.
      constructor; auto.
      intro H´; contradiction H2.
      apply remove_in_rev in H´; destruct H´; auto.
    Qed.

    Global Instance container_alloc_inv: PreservesInvariants container_alloc_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant.
      exploit alloc_container_valid; eauto.
    Qed.

passthrough primitives

    Global Instance setPG_inv: PreservesInvariants setPG_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant; 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 trapin_inv: PrimInvariants trapin_spec.
    Proof.
      PrimInvariants_simpl H H0.
    Qed.

    Global Instance trapout_inv: PrimInvariants trapout´_spec.
    Proof.
      PrimInvariants_simpl H H0.
    Qed.

    Global Instance hostin_inv: PrimInvariants hostin_spec.
    Proof.
      PrimInvariants_simpl H H0.
    Qed.

    Global Instance hostout_inv: PrimInvariants hostout´_spec.
    Proof.
      PrimInvariants_simpl H H0.
    Qed.

    Global Instance fstore_inv: PreservesInvariants fstore´_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant; auto.
    Qed.

    Global Instance bootloader_inv: PreservesInvariants bootloader_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant; eauto.
    Qed.

    Global Instance flatmem_copy_inv: PreservesInvariants flatmem_copy´_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant; eauto.
    Qed.

    Require Export ObjInterruptController.
    Global Instance cli_inv: PreservesInvariants cli_spec.
    Proof.
      preserves_invariants_direct low_level_invariant high_level_invariant; eauto 2.
    Qed.

    Global Instance sti_inv: PreservesInvariants sti_spec.
    Proof.
      preserves_invariants_direct low_level_invariant high_level_invariant; eauto 2.
    Qed.

    Require Export ObjConsole.
    Require Import INVLemmaDriver.
    Global Instance cons_buf_read_inv:
      PreservesInvariants cons_buf_read_spec.
    Proof.
      preserves_invariants_nested low_level_invariant high_level_invariant; eauto 2.
    Qed.

    Require Export ObjSerialDriver.
    Global Instance serial_putc_inv:
      PreservesInvariants serial_putc_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant; eauto 2.
    Qed.

    Require Export ObjInterruptManagement.
    Require Import INVLemmaInterrupt.
    Global Instance serial_intr_disable_inv: PreservesInvariants serial_intr_disable_spec.
    Proof.
      constructor; simpl; intros; inv_generic_sem H.
      - inversion H0; econstructor; eauto 2 with serial_intr_disable_invariantdb.
        generalize (serial_intr_disable_preserves_tf _ _ H2); intro tmprw; rewrite <- tmprw; assumption.
      - inversion H0; econstructor; eauto 2 with serial_intr_disable_invariantdb.
      - eauto 2 with serial_intr_disable_invariantdb.
    Qed.

    Global Instance serial_intr_enable_inv: PreservesInvariants serial_intr_enable_spec.
    Proof.
      constructor; simpl; intros; inv_generic_sem H.
      - inversion H0; econstructor; eauto 2 with serial_intr_enable_invariantdb.
        generalize (serial_intr_enable_preserves_tf _ _ H2); intro tmprw; rewrite <- tmprw; assumption.
      - inversion H0; econstructor; eauto 2 with serial_intr_enable_invariantdb.
      - eauto 2 with serial_intr_enable_invariantdb.
    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.

Layer Definition

  Definition mcontainer_fresh : compatlayer (cdata RData) :=
    container_init ↦ gensem container_init_spec
           ⊕ container_get_parent ↦ gensem container_get_parent_spec
           ⊕ container_get_quota ↦ gensem container_get_quota_spec
           ⊕ container_get_usage ↦ gensem container_get_usage_spec
           ⊕ container_can_consume ↦ gensem container_can_consume_spec
           ⊕ container_split ↦ gensem container_split_spec
           ⊕ container_alloc ↦ gensem container_alloc_spec.

Layer Definition passthrough