Change WokerThread to use a blink::WebThread.

Source/core/inspector/WorkerDebuggerAgent.cpp

 /*
  * Copyright (C) 2011 Google Inc. All rights reserved.
  *
  * Redistribution and use in source and binary forms, with or without
  * modification, are permitted provided that the following conditions are
  * met:
  *
  *     * Redistributions of source code must retain the above copyright
  * notice, this list of conditions and the following disclaimer.
  *     * Redistributions in binary form must reproduce the above
@@ skipping 46 matching lines @@
 
 class RunInspectorCommandsTask FINAL : public ScriptDebugServer::Task {
 public:
     explicit RunInspectorCommandsTask(WorkerThread* thread)
         : m_thread(thread) { }
     virtual ~RunInspectorCommandsTask() { }
     virtual void run() OVERRIDE
     {
         // Process all queued debugger commands. WorkerThread is certainly
         // alive if this task is being executed.
-        while (MessageQueueMessageReceived == m_thread->runDebuggerTask(WorkerRunLoop::DontWaitForMessage)) { }
+        m_thread->willEnterNestedLoop();
+        while (MessageQueueMessageReceived == m_thread->runDebuggerTask(WorkerThread::DontWaitForMessage)) { }
+        m_thread->didLeaveNestedLoop();
     }
 
 private:
     WorkerThread* m_thread;
 };
 
 } // namespace
 
 PassOwnPtr<WorkerDebuggerAgent> WorkerDebuggerAgent::create(WorkerScriptDebugServer* scriptDebugServer, WorkerGlobalScope* inspectedWorkerGlobalScope, InjectedScriptManager* injectedScriptManager)
 {
@@ skipping 52 matching lines @@
 {
     // We don't need to mute console for workers.
 }
 
 void WorkerDebuggerAgent::unmuteConsole()
 {
     // We don't need to mute console for workers.
 }
 
 } // namespace blink