shortcode.php

<?php

function display_posts_function() {

	$return = "";

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

	foreach ($cats as $cat) :

		$return .= '<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
		);

		$posts = get_posts($args); 

		if ( count($posts) > 0 ) :

		foreach( $posts AS $single_post ) :
	
			$return .=  '<li class="name-post">';
			$return .=  '<a href="'.get_permalink( $single_post->ID ).'" rel="bookmark">'.get_the_title( $single_post->ID ).'</a>';
			$return .=  '</li>';
		
		endforeach;
		
		endif;
	
	$return .=  '</ul>';
		
	endforeach;
	
	return $return;
}


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

add_action( 'init', 'register_shortcodes');

// [myshortcode]