Help wanted with shortcode to display categories / posts

Hi,

When I add this code to a template file it will display a nice list of my Categories and Posts:

<?php  $cats = get_categories('hide_empty=0&orderby=name&order=asc');

foreach ($cats as $cat) :

	echo '<ul class="list"><li class="name-cat"><a href="' . get_category_link( $cat->term_id ) . '" title="' . $cat->name . '" >' . $cat->name . '</a></li>';

$args = array(
	'posts_per_page' => -1, // max number of post per category
	'cat' => $cat->term_id
);

query_posts($args); 

if (have_posts()) :

	while (have_posts()) : the_post(); ?>
		<li class="name-post">
		<a href="<?php the_permalink() ?>" rel="bookmark" title="<?php printf(__('Permalink to %s', 'translation'), the_title_attribute('echo=0')); ?>"> <?php the_title(); ?></a>
		</li>
	<?php endwhile;
endif;

wp_reset_query(); ?>

<?php echo '</ul>'; ?>

<?php endforeach; ?>

Code above works 100%. But I want to turn this into a shortcode, so I can add this shortcode while creating a post/page.

But, simply adding this before and after this code results in an error:

function display_posts_function() {
My code above
}

Btw, of course I have added this too, otherwise nothing happens:

function register_shortcodes(){
   add_shortcode('myshortcode', 'display_posts_function');
}
add_action( 'init', 'register_shortcodes');

So, who can help me?

Guido