Drupal 7: Change structure of all menus from pattern [ ul > li > a ] to a valid html5 pattern [ nav > a ]

d7_html5_menus.php

<?php
  /*
  * Replace all menu tree <ul> elements with <nav>.
  */
  function foo_menu_tree(&$variables) {
    return '<nav>' . $variables['tree'] . '</nav>';
  }
  /*
  * Removes <li> from all menu links, leaving only <a>s.
  */
  function foo_menu_link(&$variables) {
    $element = $variables['element'];
    $sub_menu = '';
    if ($element['#below']) {
      $sub_menu = drupal_render($element['#below']);
    }
    $output = l($element['#title'], $element['#href'], $element['#localized_options']);
    return $output . $sub_menu;
  }
?>