See accompanying blog post, http://simonpadbury.github.io/2016/03/09/bootstrap-4-navbar-with-dropdowns-for-wordwress.html

bootstrap-4-nav-walker.php

<?php

/*
Bootstrap 4.0.0-alpha2 nav walker extension class
=================================================
Add this to your `functions.php`
*/

class bootstrap_4_walker_nav_menu extends Walker_Nav_menu {
    
    function start_lvl( &$output, $depth ){ // ul
        $indent = str_repeat("\t",$depth); // indents the outputted HTML
        $submenu = ($depth > 0) ? ' sub-menu' : '';
        $output .= "\n$indent<ul class=\"dropdown-menu$submenu depth_$depth\">\n";
    }
  
  function start_el( &$output, $item, $depth = 0, $args = array(), $id = 0 ){ // li a span
        
    $indent = ( $depth ) ? str_repeat("\t",$depth) : '';
    
    $li_attributes = '';
        $class_names = $value = '';
    
        $classes = empty( $item->classes ) ? array() : (array) $item->classes;
        
        $classes[] = ($args->walker->has_children) ? 'dropdown' : '';
        $classes[] = ($item->current || $item->current_item_anchestor) ? 'active' : '';
        $classes[] = 'nav-item';
        $classes[] = 'nav-item-' . $item->ID;
        if( $depth && $args->walker->has_children ){
            $classes[] = 'dropdown-menu';
        }
        
        $class_names =  join(' ', apply_filters('nav_menu_css_class', array_filter( $classes ), $item, $args ) );
        $class_names = ' class="' . esc_attr($class_names) . '"';
        
        $id = apply_filters('nav_menu_item_id', 'menu-item-'.$item->ID, $item, $args);
        $id = strlen( $id ) ? ' id="' . esc_attr( $id ) . '"' : '';
        
        $output .= $indent . '<li ' . $id . $value . $class_names . $li_attributes . '>';
        
        $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) . '"' : '';
        
        $attributes .= ( $args->walker->has_children ) ? ' class="nav-link dropdown-toggle" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false"' : ' class="nav-link"';
        
        $item_output = $args->before;
        $item_output .= ( $depth > 0 ) ? '<a class="dropdown-item"' . $attributes . '>' : '<a' . $attributes . '>';
        $item_output .= $args->link_before . apply_filters( 'the_title', $item->title, $item->ID ) . $args->link_after;
        $item_output .= '</a>';
        $item_output .= $args->after;
        
        $output .= apply_filters ( 'walker_nav_menu_start_el', $item_output, $item, $depth, $args );
    
    }
    
}

/*
Register Navbar
*/

register_nav_menu('navbar', __('Navbar', 'your-theme'));

bootstrap-4-navbar.css

/*
Bootstrap 4.0.0-alpha2 navbar with dropdown menus
=================================================
A small CSS modification is required. Add this to your theme CSS.
*/

.navbar .dropdown-menu li {
  width: 100%;
  margin-left: 0 !important;
}

bootstrap-4-navbar.html

<!--
Bootstrap 4.0.0-alpha2 navbar with dropdown menus
=================================================
Add this to your `header.php`
-->

<nav class="navbar navbar-topbar navbar-dark bg-primary">
  <button class="navbar-toggler hidden-sm-up" type="button" data-toggle="collapse" data-target="#collapsingNavbar">
    &#9776;
  </button>
  <div class="collapse navbar-toggleable-xs" id="collapsingNavbar">
    <a class="navbar-brand" href="<?php echo home_url('/'); ?>"><?php bloginfo('name'); ?></a>
    <?php
        wp_nav_menu( array(
          'theme_location' => 'navbar',
          'container'      => false,
          'menu_class'     => 'nav navbar-nav',
          'fallback_cb'    => '__return_false',
          'items_wrap'     => '<ul id="%1$s" class="%2$s">%3$s</ul>',
          'depth'          => 2,
          'walker'         => new bootstrap_4_walker_nav_menu()
       ) );
    ?>
    <?php get_template_part('navbar-search'); ?>
  </div>
</nav>