WordPress/wp-includes/widgets/class-wp-widget-search.php

<?php
/**
 * Widget API: WP_Widget_Search class
 *
 * @package WordPress
 * @subpackage Widgets
 * @since 4.4.0
 */

/**
 * Core class used to implement a Search widget.
 *
 * @since 2.8.0
 *
 * @see WP_Widget
 */
class WP_Widget_Search extends WP_Widget {

	public function __construct() {
		$widget_ops = array('classname' => 'widget_search', 'description' => __( "A search form for your site.") );
		parent::__construct( 'search', _x( 'Search', 'Search widget' ), $widget_ops );
	}

	/**
	 * @param array $args
	 * @param array $instance
	 */
	public function widget( $args, $instance ) {
		/** This filter is documented in wp-includes/widgets/class-wp-widget-pages.php */
		$title = apply_filters( 'widget_title', empty( $instance['title'] ) ? '' : $instance['title'], $instance, $this->id_base );

		echo $args['before_widget'];
		if ( $title ) {
			echo $args['before_title'] . $title . $args['after_title'];
		}

		// Use current theme search form if it exists
		get_search_form();

		echo $args['after_widget'];
	}

	/**
	 * @param array $instance
	 */
	public function form( $instance ) {
		$instance = wp_parse_args( (array) $instance, array( 'title' => '') );
		$title = $instance['title'];
?>
		<p><label for="<?php echo $this->get_field_id('title'); ?>"><?php _e('Title:'); ?> <input class="widefat" id="<?php echo $this->get_field_id('title'); ?>" name="<?php echo $this->get_field_name('title'); ?>" type="text" value="<?php echo esc_attr($title); ?>" /></label></p>
<?php
	}

	/**
	 * @param array $new_instance
	 * @param array $old_instance
	 * @return array
	 */
	public function update( $new_instance, $old_instance ) {
		$instance = $old_instance;
		$new_instance = wp_parse_args((array) $new_instance, array( 'title' => ''));
		$instance['title'] = sanitize_text_field( $new_instance['title'] );
		return $instance;
	}

}