Library mcertikos.proc.PUCtxtIntro

***********************************************************************
*                                                                     *
*            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 abstract data and the primitives for the UCtxtIntro layer, which will introduce the primtives of thread

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 LoadStoreSem2.
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 CalRealPTPool.
Require Import CalRealPT.
Require Import CalRealIDPDE.
Require Import CalRealInitPTE.
Require Import CalRealPTB.
Require Import CalRealSMSPool.
Require Import CalRealProcModule.

Require Import INVLemmaMemory.
Require Import INVLemmaThread.
Require Import INVLemmaProc.

Require Import AbstractDataType.
Require Export PIPC.
Require Export PUCtxtIntroDef.

Abstract Data and Primitives at this layer

Section WITHMEM.

Local Open Scope Z_scope.

Context `{real_params: RealParams}.

**Definition of the raw data at MPTBit layer

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

Proofs that the primitives satisfies the invariants at this layer

  Section INV.

    Global Instance uctx_set_inv: PreservesInvariants uctx_set_spec.
    Proof.
      preserves_invariants_simpl low_level_invariant high_level_invariant; eauto 2.
      eapply uctxt_inject_neutral_gss; eauto.
      eapply uctxt_inject_neutral0_gss; eauto.
      eapply uctxt_inject_neutral0_Vint.
    Qed.

    Global Instance uctx_set_eip_inv: UCTXSetEIPInvariants uctx_set_eip_spec.
    Proof.
      constructor; intros.
      -
        inv H1. functional inversion H; inv H.
        constructor; trivial.
        eapply uctxt_inject_neutral_gss; eauto.
        eapply uctxt_inject_neutral0_gss; eauto.
        eapply uctxt_inject_neutral0_Vptr_flat; eauto.
      -
        inv H0. functional inversion H; inv H.
        constructor; trivial.
      -
        functional inversion H; inv H.
        constructor; trivial.
    Qed.

    Global Instance save_uctx_inv: SaveUCtxInvariants save_uctx_spec.
    Proof.
      constructor; intros.
      -
        inv H0. functional inversion H; inv H.
        constructor; trivial.
        eapply uctxt_inject_neutral_gss; eauto.
        repeat eapply uctxt_inject_neutral0_gss;
          try eapply uctxt_inject_neutral0_Vint.
        apply uctxt_inject_neutral0_init; eauto.
      -
        inv H0. functional inversion H; inv H.
        constructor; trivial.
      -
        functional inversion H; inv H.
        constructor; trivial.
    Qed.

    Global Instance restore_uctx_inv: RestoreUCtxInvariants restore_uctx_spec.
    Proof.
      constructor; intros.
      -
        inv H0. functional inversion H; inv H.
        constructor; trivial.
      -
        inv H0. functional inversion H; inv H.
        subst. constructor; auto; simpl in *; intros; try congruence.
    Qed.

  End INV.

Layer Definition