The halting problem’s undecidability prevents you from writing a program that is guaranteed to prove whether other arbitrary programs halt or not. You can’t write a halting-checker program and then feed it the source code to your AGI and have it say “this halts” or “this doesn’t halt”.
You can prove that some specific programs halt. If you’re trying to prove it about a program that you are writing at the time, it can even be easy. I have written many programs that halt on all input sequences, and then proved this fact about them.
Here’s a super-easy example: print “hello world” provably always halts.
The halting problem’s undecidability prevents you from writing a program that is guaranteed to prove whether other arbitrary programs halt or not. You can’t write a halting-checker program and then feed it the source code to your AGI and have it say “this halts” or “this doesn’t halt”.
You can prove that some specific programs halt. If you’re trying to prove it about a program that you are writing at the time, it can even be easy. I have written many programs that halt on all input sequences, and then proved this fact about them.
Here’s a super-easy example: print “hello world” provably always halts.