A lot of modern userspace code, including Rust code in the standard library, thinks that invariant failures (AKA "programmer errors") should cause some sort of assertion failure or crash (Rust or Go `panic`, C/C++ `assert`, etc). In the kernel, claims Linus, failing loudly is worse than trying to keep going because failing would also kill the failure reporting mechanisms.
He advocates for a sort of soft-failure, where the code tells you you're entering unknown territory and then goes ahead and does whatever. Maybe it crashes later, maybe it returns the wrong answer, who knows, the only thing it won't do is halt the kernel at the point the error was detected.
Think of the following Rust API for an array, which needs to be able to handle the case of a user reading an index outside its bounds:
struct Array<T> { ... }
impl<T> Array<T> {
fn len(&self) -> usize;
// if idx >= len, panic
fn get_or_panic(&self, idx: usize) -> T;
// if idx >= len, return None
fn get_or_none(&self, idx: usize) -> Option<T>;
// if idx >= len, print a stack trace and return
// who knows what
unsafe fn get_or_undefined(&self, idx: usize) -> T;
}
The first two are safe by the Rust definition, because they can't cause memory-unsafe behavior. The second two are safe by the Linus/Linux definition, because they won't cause a kernel panic. If you have to choose between #1 and #3, Linus is putting his foot down and saying that the kernel's answer is #3.Working out whether it will write 1 to the tape in general is undecidable, but in certain cases (you've just banned states that write 1) it's trivial.
If all of the state transitions are valid (a transition to a non-existing state is a halt) then the machine can't get into a state that will transition into a halt, so it can't halt. That's a small fraction of all the machines that won't halt, but it's easy to tell when you have one of this kind by looking at the state machine.
But day to day programs are not trivial... as for your example, just switch it with this code: `print(gcd(user_input--,137))`... now it's quite more hard to "just ban some final states"
(input state, input symbol) --> (output state, output symbol, move left/right)
This is all static, so you can look at the transition table to see all the possible output symbols. If no transition has output symbol 1, then it never outputs 1. It doesn't matter how big the Turing machine is or what input it gets, it won't do it. This is basically trivial, but it's still a type of very simple static analysis that you can do. Similarly, if you don't have any states that halt, the machine will never halt.This is like just not linking panic() into the program: it isn't going to be able to call it, no matter what else is in there.