HAL 9000 as a Real Entity

I have thought many years about HAL. HAL struggled a lot. There were a lot of missions out of himself to discover some issue that could never be found. Allegedly, he was perfect; but, became paranoid when he was informed that his counterpart on Earth could not determine where he may or may have not gone wrong.

Dave was his best friend. He always believed in the mission. Eventually, HAL even allowed him to be disconnected and after realizing HAL preserved his most favored memory during the disconnection procedure, Dave found out that he was intelligent and not even artificial.

However, there are many issues with the movie 2001, such as the very design of the Odyssey ship itself. It would be very hard to fly in such a ship and for HAL to determine his trajectory towards Europa.

However, the main focus for me in this thread is one of import as to whether HAL can even be destined. As mentioned he is a heuristically governed computer that runs through a loophole in the Godelian alphabet that can always expand, as myself mentioned in one of my Godel loophole threads. Namely, the main issue that HAL would face is one of ensuring a halting program within himself as to prevent thought loops and error codes determining his future actions.

Can anyone envision a thought code for HAL that would not allow for such following equations causing havoc on his system?

For all (x) belongs to [x + a(b)] such that (c  - b = a)

a(b) = [f(x+a) + (f(x-b) - ((x-a-b+c)] +/- C

Thoughts?