Form Validation - Error Message for Anonoymous Function

You need to wrap it in another array and specify a message string name as the first parameter.

PHP Code:

$this->form_validation->set_rules(
        'referral-code', 'Referral Code',
        array(
                'required',
                'regex_match[/^[a-zA-Z0-9]+$/]',
                array(
                        'referral-code_callable',
                        function($str)
                        {
                                // Check validity of $str and return TRUE or FALSE
                        }
                )
        ),
        array(
                'required'               =>'Please enter a valid referral code',
                'regex_match'            =>'Invalid referral code',
                'referral-code_callable' => 'The code did not pass the test'
        )
);