diff --git a/core/includes/theme.inc b/core/includes/theme.inc
index f98df80..63515ed 100644
--- a/core/includes/theme.inc
+++ b/core/includes/theme.inc
@@ -615,6 +615,9 @@ function _theme($hook, $variables = array()) {
     if (isset($info['path'])) {
       $template_file = $info['path'] . '/' . $template_file;
     }
+    if (!file_exists($template_file)) {
+      return;
+    }
     // Add the theme suggestions to the variables array just before rendering
     // the template for backwards compatibility with template engines.
     $variables['theme_hook_suggestions'] = $suggestions;
@@ -2746,31 +2749,24 @@ function drupal_common_theme() {
     // From theme.inc.
     'html' => array(
       'variables' => array('page_object' => NULL),
-      'template' => 'html',
     ),
     'page' => array(
       'render element' => 'page',
-      'template' => 'page',
     ),
     'region' => array(
       'render element' => 'elements',
-      'template' => 'region',
     ),
     'datetime' => array(
       'variables' => array('timestamp' => NULL, 'text' => NULL, 'attributes' => array(), 'html' => FALSE),
-      'template' => 'datetime',
     ),
     'status_messages' => array(
       'variables' => array('display' => NULL),
-      'template' => 'status-messages',
     ),
     'links' => array(
       'variables' => array('links' => array(), 'attributes' => array('class' => array('links')), 'heading' => array(), 'set_active_class' => FALSE),
-      'template' => 'links',
     ),
     'dropbutton_wrapper' => array(
       'variables' => array('children' => NULL),
-      'template' => 'dropbutton-wrapper',
     ),
     'image' => array(
       // HTML 4 and XHTML 1.0 always require an alt attribute. The HTML 5 draft
@@ -2786,51 +2782,47 @@ function drupal_common_theme() {
       // The title attribute is optional in all cases, so it is omitted by
       // default.
       'variables' => array('uri' => NULL, 'width' => NULL, 'height' => NULL, 'alt' => '', 'title' => NULL, 'attributes' => array()),
-      'template' => 'image',
     ),
     'breadcrumb' => array(
       'variables' => array('breadcrumb' => NULL),
-      'template' => 'breadcrumb',
     ),
     'table' => array(
       'variables' => array('header' => NULL, 'rows' => NULL, 'attributes' => array(), 'caption' => NULL, 'colgroups' => array(), 'sticky' => FALSE, 'responsive' => TRUE, 'empty' => ''),
     ),
     'tablesort_indicator' => array(
       'variables' => array('style' => NULL),
-      'template' => 'tablesort-indicator',
     ),
     'mark' => array(
       'variables' => array('status' => MARK_NEW),
+      'function' => 'theme_mark',
     ),
     'item_list' => array(
       'variables' => array('items' => array(), 'title' => '', 'list_type' => 'ul', 'attributes' => array(), 'empty' => NULL),
-      'template' => 'item-list',
     ),
     'feed_icon' => array(
       'variables' => array('url' => NULL, 'title' => NULL),
-      'template' => 'feed-icon',
     ),
     'more_link' => array(
-      'variables' => array('url' => NULL, 'title' => NULL)
+      'variables' => array('url' => NULL, 'title' => NULL),
+      'function' => 'theme_more_link',
     ),
     'progress_bar' => array(
       'variables' => array('label' => NULL, 'percent' => NULL, 'message' => NULL),
-      'template' => 'progress-bar',
     ),
     'indentation' => array(
       'variables' => array('size' => 1),
+      'function' => 'theme_indentation',
     ),
     // From theme.maintenance.inc.
     'maintenance_page' => array(
       'variables' => array('content' => NULL, 'show_messages' => TRUE, 'page' => array()),
-      'template' => 'maintenance-page',
     ),
     'install_page' => array(
       'variables' => array('content' => NULL, 'show_messages' => TRUE, 'page' => array()),
-      'template' => 'install-page',
     ),
     'task_list' => array(
       'variables' => array('items' => NULL, 'active' => NULL,  'variant' => NULL),
+      'function' => 'theme_task_list',
     ),
     'authorize_message' => array(
       'variables' => array('message' => NULL, 'success' => TRUE),
@@ -2841,87 +2833,86 @@ function drupal_common_theme() {
     // From pager.inc.
     'pager' => array(
       'variables' => array('tags' => array(), 'element' => 0, 'parameters' => array(), 'quantity' => 9),
-      'template' => 'pager',
     ),
     // From menu.inc.
     'menu_link' => array(
       'render element' => 'element',
+      'function' => 'theme_menu_link',
     ),
     'menu_tree' => array(
       'render element' => 'tree',
+      'function' => 'theme_menu_tree',
     ),
     'menu_local_task' => array(
       'render element' => 'element',
+      'function' => 'theme_menu_local_task',
     ),
     'menu_local_action' => array(
       'render element' => 'element',
+      'function' => 'theme_menu_local_action',
     ),
     'menu_local_tasks' => array(
       'variables' => array('primary' => array(), 'secondary' => array()),
+      'function' => 'theme_menu_local_tasks',
     ),
     // From form.inc.
     'input' => array(
       'render element' => 'element',
+      'function' => 'theme_input',
     ),
     'select' => array(
       'render element' => 'element',
-      'template' => 'select',
     ),
     'fieldset' => array(
       'render element' => 'element',
-      'template' => 'fieldset',
     ),
     'details' => array(
       'render element' => 'element',
-      'template' => 'details',
     ),
     'radios' => array(
       'render element' => 'element',
-      'template' => 'radios',
     ),
     'date' => array(
       'render element' => 'element',
+      'function' => 'theme_date',
     ),
     'checkboxes' => array(
       'render element' => 'element',
+      'function' => 'theme_checkboxes',
     ),
     'form' => array(
       'render element' => 'element',
-      'template' => 'form',
     ),
     'textarea' => array(
       'render element' => 'element',
-      'template' => 'textarea',
     ),
     'tableselect' => array(
       'render element' => 'element',
+      'function' => 'theme_tableselect',
     ),
     'form_element' => array(
       'render element' => 'element',
-      'template' => 'form-element',
     ),
     'form_required_marker' => array(
       'render element' => 'element',
+      'function' => 'theme_form_required_marker',
     ),
     'form_element_label' => array(
       'render element' => 'element',
+      'function' => 'theme_form_element_label',
     ),
     'vertical_tabs' => array(
       'render element' => 'element',
-      'template' => 'vertical-tabs',
     ),
     'container' => array(
       'render element' => 'element',
-      'template' => 'container',
     ),
     // From field system.
     'field' => array(
       'render element' => 'element',
-      'template' => 'field',
     ),
     'field_multiple_value_form' => array(
       'render element' => 'element',
-      'template' => 'field-multiple-value-form',
     ),
   );
 }
diff --git a/core/lib/Drupal/Core/Theme/Registry.php b/core/lib/Drupal/Core/Theme/Registry.php
index e84b33b..ee5f8ec 100644
--- a/core/lib/Drupal/Core/Theme/Registry.php
+++ b/core/lib/Drupal/Core/Theme/Registry.php
@@ -426,7 +426,8 @@ protected function processExtension(&$cache, $name, $type, $theme, $path) {
         // If function and file are omitted, default to standard naming
         // conventions.
         if (!isset($info['template']) && !isset($info['function'])) {
-          $result[$hook]['function'] = ($type == 'module' ? 'theme_' : $name . '_') . $hook;
+          $info['template'] = strtr($hook, '_', '-');
+          $result[$hook]['template'] = strtr($hook, '_', '-');
         }
 
         if (isset($cache[$hook]['includes'])) {
diff --git a/core/modules/toolbar/toolbar.module b/core/modules/toolbar/toolbar.module
index 29773f1..767bf56 100644
--- a/core/modules/toolbar/toolbar.module
+++ b/core/modules/toolbar/toolbar.module
@@ -52,6 +52,7 @@ function toolbar_theme($existing, $type, $theme, $path) {
   );
   $items['toolbar_item'] = array(
     'render element' => 'element',
+    'function' => 'theme_toolbar_item',
   );
 
   return $items;