Drive extension functions from ExtensionFunction::Run. The

extensions/browser/api/async_api_function.h

Index: extensions/browser/api/async_api_function.h
diff --git a/extensions/browser/api/async_api_function.h b/extensions/browser/api/async_api_function.h
index b18ec4da4e711bd1f9dc5dcf3813d2c517e567cb..dd586f185933470db65fbba2d9ab90d89fcd8475 100644
--- a/extensions/browser/api/async_api_function.h
+++ b/extensions/browser/api/async_api_function.h
@@ -12,7 +12,7 @@ namespace extensions {
 
 // AsyncApiFunction provides convenient thread management for APIs that need to
 // do essentially all their work on a thread other than the UI thread.
-class AsyncApiFunction : public UIThreadExtensionFunction {
+class AsyncApiFunction : public AsyncExtensionFunction {
  protected:
   AsyncApiFunction();
   virtual ~AsyncApiFunction();
@@ -38,8 +38,8 @@ class AsyncApiFunction : public UIThreadExtensionFunction {
   // Respond. Guaranteed to happen on UI thread.
   virtual bool Respond() = 0;
 
-  // ExtensionFunction::RunImpl()
-  virtual bool RunImpl() OVERRIDE;
+  // ExtensionFunction::RunAsync()
+  virtual bool RunAsync() OVERRIDE;
 
  protected:
   content::BrowserThread::ID work_thread_id() const { return work_thread_id_; }