diff --git a/Arrangement_on_surface_2/include/CGAL/Arrangement_2/Arrangement_on_surface_2_impl.h b/Arrangement_on_surface_2/include/CGAL/Arrangement_2/Arrangement_on_surface_2_impl.h
index 599e7e7e1a8..dbc0f2c4a07 100644
--- a/Arrangement_on_surface_2/include/CGAL/Arrangement_2/Arrangement_on_surface_2_impl.h
+++ b/Arrangement_on_surface_2/include/CGAL/Arrangement_2/Arrangement_on_surface_2_impl.h
@@ -54,31 +54,31 @@ Arrangement_on_surface_2<GeomTraits, TopTraits>::Arrangement_on_surface_2 () :
 {
   
   typedef has_Left_side_category<GeomTraits> Cond_left;
-  typedef internal::Validate_left_side_tag< GeomTraits, Cond_left::value > 
-    Validate_left_side_tag;
-  void (Validate_left_side_tag::*pleft)(void) =
-    &Validate_left_side_tag::missing__Left_side_category;
+  typedef internal::Validate_left_side_category< GeomTraits, Cond_left::value > 
+    Validate_left_side_category;
+  void (Validate_left_side_category::*pleft)(void) =
+    &Validate_left_side_category::missing__Left_side_category;
   (void)pleft;
   
  typedef has_Bottom_side_category<GeomTraits> Cond_bottom;
-  typedef internal::Validate_bottom_side_tag< GeomTraits, Cond_bottom::value > 
-    Validate_bottom_side_tag;
-  void (Validate_bottom_side_tag::*pbottom)(void) =
-    &Validate_bottom_side_tag::missing__Bottom_side_category;
+  typedef internal::Validate_bottom_side_category< GeomTraits, Cond_bottom::value > 
+    Validate_bottom_side_category;
+  void (Validate_bottom_side_category::*pbottom)(void) =
+    &Validate_bottom_side_category::missing__Bottom_side_category;
   (void)pbottom;
 
  typedef has_Top_side_category<GeomTraits> Cond_top;
-  typedef internal::Validate_top_side_tag< GeomTraits, Cond_top::value > 
-    Validate_top_side_tag;
-  void (Validate_top_side_tag::*ptop)(void) =
-    &Validate_top_side_tag::missing__Top_side_category;
+  typedef internal::Validate_top_side_category< GeomTraits, Cond_top::value > 
+    Validate_top_side_category;
+  void (Validate_top_side_category::*ptop)(void) =
+    &Validate_top_side_category::missing__Top_side_category;
   (void)ptop;
 
  typedef has_Right_side_category<GeomTraits> Cond_right;
-  typedef internal::Validate_right_side_tag< GeomTraits, Cond_right::value > 
-    Validate_right_side_tag;
-  void (Validate_right_side_tag::*pright)(void) =
-    &Validate_right_side_tag::missing__Right_side_category;
+  typedef internal::Validate_right_side_category< GeomTraits, Cond_right::value > 
+    Validate_right_side_category;
+  void (Validate_right_side_category::*pright)(void) =
+    &Validate_right_side_category::missing__Right_side_category;
   (void)pright;
 
   // Initialize the DCEL structure to represent an empty arrangement.
@@ -111,31 +111,31 @@ Arrangement_on_surface_2(const Geometry_traits_2 * geom_traits) :
 {
   
  typedef has_Left_side_category<GeomTraits> Cond_left;
-  typedef internal::Validate_left_side_tag< GeomTraits, Cond_left::value > 
-    Validate_left_side_tag;
-  void (Validate_left_side_tag::*pleft)(void) =
-    &Validate_left_side_tag::missing__Left_side_category;
+  typedef internal::Validate_left_side_category< GeomTraits, Cond_left::value > 
+    Validate_left_side_category;
+  void (Validate_left_side_category::*pleft)(void) =
+    &Validate_left_side_category::missing__Left_side_category;
   (void)pleft;
   
  typedef has_Bottom_side_category<GeomTraits> Cond_bottom;
-  typedef internal::Validate_bottom_side_tag< GeomTraits, Cond_bottom::value > 
-    Validate_bottom_side_tag;
-  void (Validate_bottom_side_tag::*pbottom)(void) =
-    &Validate_bottom_side_tag::missing__Bottom_side_category;
+  typedef internal::Validate_bottom_side_category< GeomTraits, Cond_bottom::value > 
+    Validate_bottom_side_category;
+  void (Validate_bottom_side_category::*pbottom)(void) =
+    &Validate_bottom_side_category::missing__Bottom_side_category;
   (void)pbottom;
 
  typedef has_Top_side_category<GeomTraits> Cond_top;
-  typedef internal::Validate_top_side_tag< GeomTraits, Cond_top::value > 
-    Validate_top_side_tag;
-  void (Validate_top_side_tag::*ptop)(void) =
-    &Validate_top_side_tag::missing__Top_side_category;
+  typedef internal::Validate_top_side_category< GeomTraits, Cond_top::value > 
+    Validate_top_side_category;
+  void (Validate_top_side_category::*ptop)(void) =
+    &Validate_top_side_category::missing__Top_side_category;
   (void)ptop;
 
  typedef has_Right_side_category<GeomTraits> Cond_right;
-  typedef internal::Validate_right_side_tag< GeomTraits, Cond_right::value > 
-    Validate_right_side_tag;
-  void (Validate_right_side_tag::*pright)(void) =
-    &Validate_right_side_tag::missing__Right_side_category;
+  typedef internal::Validate_right_side_category< GeomTraits, Cond_right::value > 
+    Validate_right_side_category;
+  void (Validate_right_side_category::*pright)(void) =
+    &Validate_right_side_category::missing__Right_side_category;
   (void)pright;
 
   // Initialize the DCEL structure to represent an empty arrangement.