You may have the action value that you'd like, as the following HTML indicates:
The way your form is currently set up, by default, it results in a GET request. However, your PHP tests for a form submitted as a POST request! If you really intend to submit the form as a POST request then you must specify that in the action attribute as action="POST". Then, change your test of the submitted form to check whether the POST has a value or not, as follows:
Note: when the method is POST, the portion ?query=string does not reflect a GET variable but rather a QUERY_STRING. When this form is submitted it redirects to testform.php?query=string.
Incidentally, a handy function for parsing the resulting query string is parse_str and you can use it to create a variable or an associative array that contains the "string" value, as follows:
See http://3v4l.org/DC27Y
