wp_list_categories( array|string $args = '' )

function wp_list_categories( $args = '' ) {
	$defaults = array(
		'child_of'            => 0,
		'current_category'    => 0,
		'depth'               => 0,
		'echo'                => 1,
		'exclude'             => '',
		'exclude_tree'        => '',
		'feed'                => '',
		'feed_image'          => '',
		'feed_type'           => '',
		'hide_empty'          => 1,
		'hide_title_if_empty' => false,
		'hierarchical'        => true,
		'order'               => 'ASC',
		'orderby'             => 'name',
		'separator'           => '<br />',
		'show_count'          => 0,
		'show_option_all'     => '',
		'show_option_none'    => __( 'No categories' ),
		'style'               => 'list',
		'taxonomy'            => 'category',
		'title_li'            => __( 'Categories' ),
		'use_desc_for_title'  => 1,
	);

	$r = wp_parse_args( $args, $defaults );

	if ( !isset( $r['pad_counts'] ) && $r['show_count'] && $r['hierarchical'] )
		$r['pad_counts'] = true;

	// Descendants of exclusions should be excluded too.
	if ( true == $r['hierarchical'] ) {
		$exclude_tree = array();

		if ( $r['exclude_tree'] ) {
			$exclude_tree = array_merge( $exclude_tree, wp_parse_id_list( $r['exclude_tree'] ) );
		}

		if ( $r['exclude'] ) {
			$exclude_tree = array_merge( $exclude_tree, wp_parse_id_list( $r['exclude'] ) );
		}

		$r['exclude_tree'] = $exclude_tree;
		$r['exclude'] = '';
	}

	if ( ! isset( $r['class'] ) )
		$r['class'] = ( 'category' == $r['taxonomy'] ) ? 'categories' : $r['taxonomy'];

	if ( ! taxonomy_exists( $r['taxonomy'] ) ) {
		return false;
	}

	$show_option_all = $r['show_option_all'];
	$show_option_none = $r['show_option_none'];

	$categories = get_categories( $r );

	$output = '';
	if ( $r['title_li'] && 'list' == $r['style'] && ( ! empty( $categories ) || ! $r['hide_title_if_empty'] ) ) {
		$output = '<li class="' . esc_attr( $r['class'] ) . '">' . $r['title_li'] . '<ul>';
	}
	if ( empty( $categories ) ) {
		if ( ! empty( $show_option_none ) ) {
			if ( 'list' == $r['style'] ) {
				$output .= '<li class="cat-item-none">' . $show_option_none . '</li>';
			} else {
				$output .= $show_option_none;
			}
		}
	} else {
		if ( ! empty( $show_option_all ) ) {

			$posts_page = '';

			// For taxonomies that belong only to custom post types, point to a valid archive.
			$taxonomy_object = get_taxonomy( $r['taxonomy'] );
			if ( ! in_array( 'post', $taxonomy_object->object_type ) && ! in_array( 'page', $taxonomy_object->object_type ) ) {
				foreach ( $taxonomy_object->object_type as $object_type ) {
					$_object_type = get_post_type_object( $object_type );

					// Grab the first one.
					if ( ! empty( $_object_type->has_archive ) ) {
						$posts_page = get_post_type_archive_link( $object_type );
						break;
					}
				}
			}

			// Fallback for the 'All' link is the posts page.
			if ( ! $posts_page ) {
				if ( 'page' == get_option( 'show_on_front' ) && get_option( 'page_for_posts' ) ) {
					$posts_page = get_permalink( get_option( 'page_for_posts' ) );
				} else {
					$posts_page = home_url( '/' );
				}
			}

			$posts_page = esc_url( $posts_page );
			if ( 'list' == $r['style'] ) {
				$output .= "<li class='cat-item-all'><a href='$posts_page'>$show_option_all</a></li>";
			} else {
				$output .= "<a href='$posts_page'>$show_option_all</a>";
			}
		}

		if ( empty( $r['current_category'] ) && ( is_category() || is_tax() || is_tag() ) ) {
			$current_term_object = get_queried_object();
			if ( $current_term_object && $r['taxonomy'] === $current_term_object->taxonomy ) {
				$r['current_category'] = get_queried_object_id();
			}
		}

		if ( $r['hierarchical'] ) {
			$depth = $r['depth'];
		} else {
			$depth = -1; // Flat.
		}
		$output .= walk_category_tree( $categories, $depth, $r );
	}

	if ( $r['title_li'] && 'list' == $r['style'] && ( ! empty( $categories ) || ! $r['hide_title_if_empty'] ) ) {
		$output .= '</ul></li>';
	}

	/**
	 * Filters the HTML output of a taxonomy list.
	 *
	 * @since WP-2.1.0
	 *
	 * @param string $output HTML output.
	 * @param array  $args   An array of taxonomy-listing arguments.
	 */
	$html = apply_filters( 'wp_list_categories', $output, $args );

	if ( $r['echo'] ) {
		echo $html;
	} else {
		return $html;
	}
}