diff -u b/core/includes/theme.inc b/core/includes/theme.inc
--- b/core/includes/theme.inc
+++ b/core/includes/theme.inc
@@ -2551,7 +2551,6 @@
     'mark' => array(
       'variables' => array('status' => MARK_NEW),
       'template' => 'mark',
-      'function' => 'theme_mark',
     ),
     'item_list' => array(
       'variables' => array('items' => array(), 'title' => '', 'list_type' => 'ul', 'attributes' => array(), 'empty' => NULL),
@@ -2628,7 +2627,6 @@
     'input' => array(
       'render element' => 'element',
       'template' => 'input',
-      'function' => 'theme_input',
     ),
     'select' => array(
       'render element' => 'element',
@@ -2669,7 +2667,6 @@
     'form_element_label' => array(
       'render element' => 'element',
       'template' => 'form-element-label',
-      'function' => 'theme_form_element_label',
     ),
     'vertical_tabs' => array(
       'render element' => 'element',
reverted:
--- b/core/modules/file/file.module
+++ a/core/modules/file/file.module
@@ -587,12 +587,10 @@
     'file_link' => array(
       'variables' => array('file' => NULL, 'icon_directory' => NULL, 'description' => NULL, 'attributes' => array()),
       'template' => 'file-link',
-      'function' => 'theme_file_link',
     ),
     'file_managed_file' => array(
       'render element' => 'element',
       'template' => 'file-managed-file',
-      'function' => 'theme_file_managed_file',
     ),
 
     // From file.field.inc.
@@ -600,19 +598,16 @@
       'render element' => 'element',
       'template' => 'file-widget',
       'file' => 'file.field.inc',
-      'function' => 'theme_file_widget',
     ),
     'file_widget_multiple' => array(
       'render element' => 'element',
       'template' => 'file-widget-multiple',
       'file' => 'file.field.inc',
-      'function' => 'theme_file_widget_multiple',
     ),
     'file_upload_help' => array(
       'variables' => array('description' => NULL, 'upload_validators' => NULL, 'cardinality' => NULL),
       'template' => 'file-upload-help',
       'file' => 'file.field.inc',
-      'function' => 'theme_file_upload_help',
     ),
   );
 }
diff -u b/core/modules/image/image.module b/core/modules/image/image.module
--- b/core/modules/image/image.module
+++ b/core/modules/image/image.module
@@ -121,33 +121,27 @@
       'variables' => array('style' => NULL),
       'file' => 'image.admin.inc',
       'template' => 'image-style-preview',
-      'function' => 'theme_image_style_preview',
     ),
     'image_anchor' => array(
       'render element' => 'element',
       'file' => 'image.admin.inc',
       'template' => 'image-anchor',
-      'function' => 'theme_image_anchor',
     ),
     'image_resize_summary' => array(
       'variables' => array('data' => NULL, 'effect' => array()),
       'template' => 'image-resize-summary',
-      'function' => 'theme_image_resize_summary',
     ),
     'image_scale_summary' => array(
       'variables' => array('data' => NULL, 'effect' => array()),
       'template' => 'image-scale-summary',
-      'function' => 'theme_image_scale_summary',
     ),
     'image_crop_summary' => array(
       'variables' => array('data' => NULL, 'effect' => array()),
       'template' => 'image-crop-summary',
-      'function' => 'theme_image_crop_summary',
     ),
     'image_rotate_summary' => array(
       'variables' => array('data' => NULL, 'effect' => array()),
       'template' => 'image-rotate-summary',
-      'function' => 'theme_image_rotate_summary',
     ),
 
     // Theme functions in image.field.inc.
@@ -155,13 +149,11 @@
       'render element' => 'element',
       'file' => 'image.field.inc',
       'template' => 'image-widget',
-      'function' => 'theme_image_widget',
     ),
     'image_formatter' => array(
       'variables' => array('item' => NULL, 'item_attributes' => NULL, 'path' => NULL, 'image_style' => NULL),
       'file' => 'image.field.inc',
       'template' => 'image-formatter',
-      'function' => 'theme_image_formatter',
     ),
   );
 }
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
@@ -119,7 +119,6 @@
       'render element' => 'form',
       'file' => 'language.admin.inc',
       'template' => 'language-negotiation-configure-form',
-      'function' => 'theme_language_negotiation_configure_form',
     ),
     'language_negotiation_configure_browser_form_table' => array(
       'render element' => 'form',
diff -u b/core/modules/system/system.module b/core/modules/system/system.module
--- b/core/modules/system/system.module
+++ b/core/modules/system/system.module
@@ -180,7 +180,6 @@
     'system_config_form' => array(
       'render element' => 'form',
       'template' => 'system-config-form',
-      'function' => 'theme_system_config_form',
     ),
     'confirm_form' => array(
       'render element' => 'form',
diff -u b/core/modules/update/update.module b/core/modules/update/update.module
--- b/core/modules/update/update.module
+++ b/core/modules/update/update.module
@@ -180,7 +180,6 @@
     'update_last_check' => array(
       'variables' => array('last' => 0),
       'template' => 'update-last-check',
-      'function' => 'theme_update_last_check',
     ),
     'update_report' => array(
       'variables' => array('data' => NULL),