JavaScript はページを更新せずに PHP 関数を呼び出すにはどうすればよいでしょうか?

$.ajax({
    type: "POST",
    url: 'your_functions_address.php',
    dataType: 'json',
    data: {functionname: 'add', arguments: [1, 2]},

    success: function (obj, textstatus) {
                  if( !('error' in obj) ) {
                      yourVariable = obj.result;
                  }
                  else {
                      console.log(obj.error);
                  }
            }
});

header('Content-Type: application/json');

$aResult = array();

if( !isset($_POST['functionname']) ) { $aResult['error'] = 'No function name!'; }

if( !isset($_POST['arguments']) ) { $aResult['error'] = 'No function arguments!'; }

if( !isset($aResult['error']) ) {

    switch($_POST['functionname']) {
        case 'add':
               if( !is_array($_POST['arguments']) || (count($_POST['arguments']) < 2) ) {
                   $aResult['error'] = 'Error in arguments!';
               }
               else {
                   $aResult['result'] = add(floatval($_POST['arguments'][0]), floatval($_POST['arguments'][1]));
               }
               break;

        default:
               $aResult['error'] = 'Not found function '.$_POST['functionname'].'!';
               break;
    }

}

echo json_encode($aResult);