alt Hacker NewsAn infinite loop doesn’t mean that you can’t prove whatever property you want to prove about your program, if you’ve designed it for that. The limitations coming from undecidability don’t really affect our everyday applications. Unless your application is exactly to determine whether another arbitrary program will halt, that is. But that’s not what the vast majority of software whose bugs we might be concerned about is about.
“We can’t write bug-free software due to the halting problem anyway” is an incorrect argument.
You can't prove a program completed successfully if you can't prove a program even completes at all.
I don't know what properties you think people are trying to pragmatically prove about arbitrary programs but "did the program complete successfully" will always be an important, pragmatic property in software development. Especially in the pragmatic world where so much of our software is chaining smaller programs together to solve a task.
I'm saying we can't write perfectly bug-free software because of the Halting Problem and the inability to prove any given loop will not be infinite until running that loop. Perfect remains the enemy of the good and we certainly write a lot of "bug-free-enough" software without worrying about the Halting Problem day-to-day. But if you are saying the world needs to write perfectly bug free code starting tomorrow because LLMs will find all the vulnerabilities and sandbox escapes the Halting Problem is absolutely one of the reasons we can't ever provably hit that "perfect" target. We still need to find "good enough" or we give up on software development altogether and that's not what I'm advocating. Perfect is the enemy of the good. Mathematically perfect provably does not exist. Software will always have bugs, especially in the world with a threat model of active brute force machines.