@@ -633,10 +633,10 @@ class Analyzer(
633633   *    it into the plan tree. 
634634   */  
635635  object  ExtractWindowExpressions  extends  Rule [LogicalPlan ] {
636-     def  hasWindowFunction (projectList : Seq [NamedExpression ]):  Boolean  = 
636+     private   def  hasWindowFunction (projectList : Seq [NamedExpression ]):  Boolean  = 
637637      projectList.exists(hasWindowFunction)
638638
639-     def  hasWindowFunction (expr : NamedExpression ):  Boolean  =  {
639+     private   def  hasWindowFunction (expr : NamedExpression ):  Boolean  =  {
640640      expr.find {
641641        case  window : WindowExpression  =>  true 
642642        case  _ =>  false 
@@ -647,7 +647,7 @@ class Analyzer(
647647     * From a Seq of [[NamedExpression ]]s, extract expressions containing window expressions and 
648648     * other regular expressions that do not contain any window expression. 
649649     */  
650-     def  extractRegularExpressions (
650+     private   def  extractRegularExpressions (
651651        expressions : Seq [NamedExpression ]):  (Seq [NamedExpression ], Seq [NamedExpression ]) =  {
652652      //  First, we partition the input expressions to two part. For the first part,
653653      //  every expression in it contain at least one WindowExpression.
@@ -709,12 +709,12 @@ class Analyzer(
709709      }
710710
711711      (newExpressionsWithWindowFunctions, regularExpressions ++  extractedExprBuffer)
712-     }
712+     }  //  end of extractRegularExpressions 
713713
714714    /**  
715715     * Adds operators for Window Expressions. Every Window operator handles a single Window Spec. 
716716     */  
717-     def  addWindow (
717+     private   def  addWindow (
718718        expressionsWithWindowFunctions : Seq [NamedExpression ],
719719        child : LogicalPlan ):  LogicalPlan  =  {
720720      //  First, we need to extract all WindowExpressions from expressionsWithWindowFunctions
@@ -779,7 +779,7 @@ class Analyzer(
779779      //  Finally, we create a Project to output currentChild's output
780780      //  newExpressionsWithWindowFunctions.
781781      Project (currentChild.output ++  newExpressionsWithWindowFunctions, currentChild)
782-     }
782+     }  //  end of addWindow 
783783
784784    //  We have to use transformDown at here to make sure the rule of
785785    //  "Aggregate with Having clause" will be triggered.
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