How to quit a Windows GUI program gracefully with Python under Cygwin?

[KB]

Hi,

I want to write a Python script that controls and automates a Windows
GUI computation program.

My problem is that I do not know how to quit the Windows GUI program
gracefully with a command (program's or Python) in Cygwin.  'kill' or
CTRL-C command in Cygwin does not finish it gracefully, meaning that
some outputs do not come out normally.  The only thing I know is to
click 'File-Exit' menu, but
this requires a manual intervention that prevents scripting.

Is there a way to quit a Windows GUI program gracefully with Python
under Cygwin, of course, after the program finishes
normal execution?

Thanks,

KB