example of custom Walker for nav

walker-nav-example.php

// Menu output mods
class description_walker extends Walker_Nav_Menu
{
      function start_el(&$output, $item, $depth, $args)
      {
			global $wp_query;
			$indent = ( $depth ) ? str_repeat( "\t", $depth ) : '';
			
			$class_names = $value = '';
			
			// If the item has children, add the dropdown class for bootstrap
			if ( $args->has_children ) {
				$class_names = "dropdown ";
			}
			
			$classes = empty( $item->classes ) ? array() : (array) $item->classes;
			
			$class_names .= join( ' ', apply_filters( 'nav_menu_css_class', array_filter( $classes ), $item ) );
			$class_names = ' class="'. esc_attr( $class_names ) . '"';
           
           	$output .= $indent . '<li id="menu-item-'. $item->ID . '"' . $value . $class_names .'>';

           	$attributes  = ! empty( $item->attr_title ) ? ' title="'  . esc_attr( $item->attr_title ) .'"' : '';
           	$attributes .= ! empty( $item->target )     ? ' target="' . esc_attr( $item->target     ) .'"' : '';
           	$attributes .= ! empty( $item->xfn )        ? ' rel="'    . esc_attr( $item->xfn        ) .'"' : '';
           	$attributes .= ! empty( $item->url )        ? ' href="'   . esc_attr( $item->url        ) .'"' : '';
           	// if the item has children add these two attributes to the anchor tag
           	if ( $args->has_children ) {
				$attributes .= ' class="dropdown-toggle" data-toggle="dropdown"';
			}

            $item_output = $args->before;
            $item_output .= '<a'. $attributes .'>';
            $item_output .= $args->link_before .apply_filters( 'the_title', $item->title, $item->ID );
            $item_output .= $args->link_after;
            // if the item has children add the caret just before closing the anchor tag
            if ( $args->has_children ) {
            	$item_output .= '<b class="caret"></b></a>';
            }
            else{
            	$item_output .= '</a>';
            }
            $item_output .= $args->after;

            $output .= apply_filters( 'walker_nav_menu_start_el', $item_output, $item, $depth, $args );
            }
            
        function start_lvl(&$output, $depth) {
            $indent = str_repeat("\t", $depth);
            $output .= "\n$indent<ul class=\"dropdown-menu\">\n";
        }
            
      	function display_element( $element, &$children_elements, $max_depth, $depth=0, $args, &$output )
      	    {
      	        $id_field = $this->db_fields['id'];
      	        if ( is_object( $args[0] ) ) {
      	            $args[0]->has_children = ! empty( $children_elements[$element->$id_field] );
      	        }
      	        return parent::display_element( $element, $children_elements, $max_depth, $depth, $args, $output );
      	    }
      	
            
}