diff -u b/core/includes/theme.inc b/core/includes/theme.inc
--- b/core/includes/theme.inc
+++ b/core/includes/theme.inc
@@ -2299,6 +2299,7 @@
     ),
     'indentation' => array(
       'variables' => array('size' => 1),
+      'function' => 'theme_indentation',
     ),
     // From theme.maintenance.inc.
     'maintenance_page' => array(
@@ -2315,9 +2316,11 @@
     ),
     'authorize_message' => array(
       'variables' => array('message' => NULL, 'success' => TRUE),
+      'function' => 'theme_authorize_message',
     ),
     'authorize_report' => array(
       'variables' => array('messages' => array()),
+      'function' => 'theme_authorize_report',
     ),
     // From pager.inc.
     'pager' => array(
@@ -2327,6 +2330,9 @@
     // From menu.inc.
     'menu_link' => array(
       'render element' => 'element',
+      'function' => 'theme_menu_link',
+      'path' => 'core/includes',
+      'file' => 'menu.inc',
     ),
     'menu_tree' => array(
       'render element' => 'tree',
@@ -2342,7 +2348,6 @@
     ),
     'indentation' => array(
       'variables' => array('size' => 1),
-      'function' => 'theme_indentation',
     ),
     // From theme.maintenance.inc.
     'maintenance_page' => array(
@@ -2359,11 +2364,9 @@
     ),
     'authorize_message' => array(
       'variables' => array('message' => NULL, 'success' => TRUE),
-      'function' => 'theme_authorize_message',
     ),
     'authorize_report' => array(
       'variables' => array('messages' => array()),
-      'function' => 'theme_authorize_report',
     ),
     // From pager.inc.
     'pager' => array(
@@ -2373,9 +2376,6 @@
     // From menu.inc.
     'menu_link' => array(
       'render element' => 'element',
-      'function' => 'theme_menu_link',
-      'path' => 'core/includes',
-      'file' => 'menu.inc',
     ),
     'menu_tree' => array(
       'render element' => 'tree',
diff -u b/core/modules/field_ui/field_ui.module b/core/modules/field_ui/field_ui.module
--- b/core/modules/field_ui/field_ui.module
+++ b/core/modules/field_ui/field_ui.module
@@ -66,6 +66,7 @@
   return array(
     'field_ui_table' => array(
       'render element' => 'elements',
+      'function' => 'theme_field_ui_table',
     ),
   );
 }
@@ -96,7 +97,6 @@
   return array(
     'field_ui_table' => array(
       'render element' => 'elements',
-      'function' => 'theme_field_ui_table',
     ),
   );
 }
diff -u b/core/modules/language/language.module b/core/modules/language/language.module
--- b/core/modules/language/language.module
+++ b/core/modules/language/language.module
@@ -100,10 +100,12 @@
     'language_negotiation_configure_browser_form_table' => array(
       'render element' => 'form',
       'file' => 'language.admin.inc',
+      'function' => 'theme_language_negotiation_configure_browser_form_table',
     ),
     'language_content_settings_table' => array(
       'render element' => 'element',
       'file' => 'language.admin.inc',
+      'function' => 'theme_language_content_settings_table',
     ),
   );
 }
@@ -111,12 +113,10 @@
     'language_negotiation_configure_browser_form_table' => array(
       'render element' => 'form',
       'file' => 'language.admin.inc',
-      'function' => 'theme_language_negotiation_configure_browser_form_table',
     ),
     'language_content_settings_table' => array(
       'render element' => 'element',
       'file' => 'language.admin.inc',
-      'function' => 'theme_language_content_settings_table',
     ),
   );
 }
diff -u b/core/modules/locale/locale.module b/core/modules/locale/locale.module
--- b/core/modules/locale/locale.module
+++ b/core/modules/locale/locale.module
@@ -181,6 +181,7 @@
     'locale_translate_edit_form_strings' => array(
       'render element' => 'form',
       'file' => 'locale.pages.inc',
+      'function' => 'theme_locale_translate_edit_form_strings',
     ),
     'locale_translation_last_check' => array(
       'variables' => array('last' => NULL),
@@ -193,7 +194,6 @@
     'locale_translate_edit_form_strings' => array(
       'render element' => 'form',
       'file' => 'locale.pages.inc',
-      'function' => 'theme_locale_translate_edit_form_strings',
     ),
     'locale_translation_last_check' => array(
       'variables' => array('last' => NULL),
diff -u b/core/modules/menu_ui/menu_ui.module b/core/modules/menu_ui/menu_ui.module
--- b/core/modules/menu_ui/menu_ui.module
+++ b/core/modules/menu_ui/menu_ui.module
@@ -78,6 +78,7 @@
     'menu_overview_form' => array(
       'file' => 'menu_ui.admin.inc',
       'render element' => 'form',
+      'function' => 'theme_menu_overview_form',
     ),
   );
 }
@@ -89,7 +90,6 @@
     'menu_overview_form' => array(
       'file' => 'menu_ui.admin.inc',
       'render element' => 'form',
-      'function' => 'theme_menu_overview_form',
     ),
   );
 }
diff -u b/core/modules/node/node.module b/core/modules/node/node.module
--- b/core/modules/node/node.module
+++ b/core/modules/node/node.module
@@ -140,6 +140,7 @@
     ),
     'node_search_admin' => array(
       'render element' => 'form',
+      'function' => 'theme_node_search_admin',
     ),
     'node_add_list' => array(
       'variables' => array('content' => NULL),
@@ -163,7 +164,6 @@
     ),
     'node_search_admin' => array(
       'render element' => 'form',
-      'function' => 'theme_node_search_admin',
     ),
     'node_add_list' => array(
       'variables' => array('content' => NULL),
diff -u b/core/modules/toolbar/toolbar.module b/core/modules/toolbar/toolbar.module
--- b/core/modules/toolbar/toolbar.module
+++ b/core/modules/toolbar/toolbar.module
@@ -41,9 +41,6 @@
     'render element' => 'element',
     'template' => 'toolbar',
   );
-  $items['toolbar_item'] = array(
-    'render element' => 'element',
-  );
 
   return $items;
 }
@@ -52,6 +49,9 @@
     'render element' => 'element',
     'template' => 'toolbar',
   );
+  $items['toolbar_item'] = array(
+    'render element' => 'element',
+  );
 
   return $items;
 }
@@ -82,7 +82,6 @@
   // property contains a renderable array.
   $elements['toolbar_item'] = array(
     '#pre_render' => array('toolbar_pre_render_item'),
-    '#theme' => 'toolbar_item',
     'tab' => array(
       '#type' => 'link',
       '#title' => NULL,
@@ -93,6 +92,7 @@
   // property contains a renderable array.
   $elements['toolbar_item'] = array(
     '#pre_render' => array('toolbar_pre_render_item'),
+    '#theme' => 'toolbar_item',
     'tab' => array(
       '#type' => 'link',
       '#title' => NULL,
only in patch2:
unchanged:
--- a/core/modules/system/system.api.php
+++ b/core/modules/system/system.api.php
@@ -1098,16 +1098,16 @@ function hook_help($route_name, \Drupal\Core\Routing\RouteMatchInterface $route_
  *     path, include it here. This path should be relative to the Drupal root
  *     directory.
  *   - template: If specified, this theme implementation is a template, and
- *     this is the template file without an extension. Do not put .html.twig on
- *     this file; that extension will be added automatically by the default
- *     rendering engine (which is Twig). If 'path' above is specified, the
- *     template should also be in this path.
+ *     this is the template file without an extension. If neither 'template'
+ *     nor 'function' is specified, a default template name will be assumed.
+ *     For example, if a module registers the 'node' theme hook, 'node'
+ *     will be assigned to its template. Do not put .html.twig on this file;
+ *     that extension will be added automatically by the default rendering
+ *     engine (which is Twig). If 'path' above is specified, the template should
+ *     also be in this path.
  *   - function: If specified, this will be the function name to invoke for
- *     this implementation. If neither 'template' nor 'function' is specified,
- *     a default function name will be assumed. For example, if a module
- *     registers the 'node' theme hook, 'theme_node' will be assigned to its
- *     function. If the chameleon theme registers the node hook, it will be
- *     assigned 'chameleon_node' as its function.
+ *     this implementation. If the chameleon theme registers the node hook,
+ *     it will be assigned 'chameleon_node' as its function.
  *   - base hook: Used for _theme() suggestions only: the base theme hook name.
  *     Instead of this suggestion's implementation being used directly, the base
  *     hook will be invoked with this implementation as its first suggestion.