theme_links() override has no effect So I want menus to output in a custom way. I would not output the following HTML.

&lt;ul attributes&gt;
    &lt;li attributes&gt;
       &lt;a href="foo"&gt;foo&lt;/a&gt;
    &lt;/li&gt;
    &lt;li attributes&gt;
       &lt;a href="bar"&gt;bar&lt;/a&gt;
    &lt;/li&gt;
 &lt;/ul&gt;


I would replace it with the following one.

&lt;nav attributes&gt;
   &lt;a attributes href="foo"&gt;foo&lt;/a&gt;
   &lt;a attributes href="bar"&gt;bar&lt;/a&gt;
&lt;/nav&gt;


So I put in the template.php file the following function (my theme is called mFAC).

function mFAC_links($variables) {
    // custom stuff
}


I am starting with a light alteration, but nothing seems to have any effect. I cleared the cache.

Is there anything I am missing?
You can override the menu wrapper in this manner:

function YOURTHEME_menu_tree__MENU_NAME($variables) {
  return '&lt;nav class="menu'.$variables['delta'].'"&gt;' . $variables['tree'] . '&lt;/nav&gt;';
}