_wp_ajax_menu_quick_search

function _wp_ajax_menu_quick_search( $request = array() ) {
	$args            = array();
	$type            = isset( $request['type'] ) ? $request['type'] : '';
	$object_type     = isset( $request['object_type'] ) ? $request['object_type'] : '';
	$query           = isset( $request['q'] ) ? $request['q'] : '';
	$response_format = isset( $request['response-format'] ) ? $request['response-format'] : '';

	if ( ! $response_format || ! in_array( $response_format, array( 'json', 'markup' ), true ) ) {
		$response_format = 'json';
	}

	if ( 'markup' === $response_format ) {
		$args['walker'] = new Walker_Nav_Menu_Checklist;
	}

	if ( 'get-post-item' === $type ) {
		if ( post_type_exists( $object_type ) ) {
			if ( isset( $request['ID'] ) ) {
				$object_id = (int) $request['ID'];
				if ( 'markup' === $response_format ) {
					echo walk_nav_menu_tree( array_map( 'wp_setup_nav_menu_item', array( get_post( $object_id ) ) ), 0, (object) $args );
				} elseif ( 'json' === $response_format ) {
					echo wp_json_encode(
						array(
							'ID'         => $object_id,
							'post_title' => get_the_title( $object_id ),
							'post_type'  => get_post_type( $object_id ),
						)
					);
					echo "\n";
				}
			}
		} elseif ( taxonomy_exists( $object_type ) ) {
			if ( isset( $request['ID'] ) ) {
				$object_id = (int) $request['ID'];
				if ( 'markup' === $response_format ) {
					echo walk_nav_menu_tree( array_map( 'wp_setup_nav_menu_item', array( get_term( $object_id, $object_type ) ) ), 0, (object) $args );
				} elseif ( 'json' === $response_format ) {
					$post_obj = get_term( $object_id, $object_type );
					echo wp_json_encode(
						array(
							'ID'         => $object_id,
							'post_title' => $post_obj->name,
							'post_type'  => $object_type,
						)
					);
					echo "\n";
				}
			}
		}
	} elseif ( preg_match( '/quick-search-(posttype|taxonomy)-([a-zA-Z_-]*\b)/', $type, $matches ) ) {
		if ( 'posttype' === $matches[1] && get_post_type_object( $matches[2] ) ) {
			$post_type_obj = _wp_nav_menu_meta_box_object( get_post_type_object( $matches[2] ) );
			$args          = array_merge(
				$args,
				array(
					'no_found_rows'          => true,
					'update_post_meta_cache' => false,
					'update_post_term_cache' => false,
					'posts_per_page'         => 10,
					'post_type'              => $matches[2],
					's'                      => $query,
				)
			);
			if ( isset( $post_type_obj->_default_query ) ) {
				$args = array_merge( $args, (array) $post_type_obj->_default_query );
			}
			$search_results_query = new WP_Query( $args );
			if ( ! $search_results_query->have_posts() ) {
				return;
			}
			while ( $search_results_query->have_posts() ) {
				$post = $search_results_query->next_post();
				if ( 'markup' === $response_format ) {
					$var_by_ref = $post->ID;
					echo walk_nav_menu_tree( array_map( 'wp_setup_nav_menu_item', array( get_post( $var_by_ref ) ) ), 0, (object) $args );
				} elseif ( 'json' === $response_format ) {
					echo wp_json_encode(
						array(
							'ID'         => $post->ID,
							'post_title' => get_the_title( $post->ID ),
							'post_type'  => $matches[2],
						)
					);
					echo "\n";
				}
			}
		} elseif ( 'taxonomy' === $matches[1] ) {
			$terms = get_terms(
				array(
					'taxonomy'   => $matches[2],
					'name__like' => $query,
					'number'     => 10,
					'hide_empty' => false,
				)
			);
			if ( empty( $terms ) || is_wp_error( $terms ) ) {
				return;
			}
			foreach ( (array) $terms as $term ) {
				if ( 'markup' === $response_format ) {
					echo walk_nav_menu_tree( array_map( 'wp_setup_nav_menu_item', array( $term ) ), 0, (object) $args );
				} elseif ( 'json' === $response_format ) {
					echo wp_json_encode(
						array(
							'ID'         => $term->term_id,
							'post_title' => $term->name,
							'post_type'  => $matches[2],
						)
					);
					echo "\n";
				}
			}
		}
	}
}