the halting problem is only true for _arbitrary_ programs
but there are always sets of programs for which it is clearly possible to guarantee their termination
e.g. the program `return 1+1;` is guaranteed to halt
e.g. given program like `while condition(&mut state) { ... }` with where `condition()` is guaranteed to halt but otherwise unknown is not guaranteed to halt, but if you turn it into `for _ in 0..1000 { if !condition(&mut state) { break; } ... }` then it is guaranteed to halt after at most 1000 iterations
or in other words eBPF only accepts programs which it can proof will halt in at most maxins "instruction" (through it's more strict then my example, i.e. you would need to unroll the for-loop to make it pass validation)
the thing with programs which are provable halting is that they tend to also not be very convenient to write and/or quite limited in what you can do with them, i.e. they are not suitable as general purpose programming languages at all
but there are always sets of programs for which it is clearly possible to guarantee their termination
e.g. the program `return 1+1;` is guaranteed to halt
e.g. given program like `while condition(&mut state) { ... }` with where `condition()` is guaranteed to halt but otherwise unknown is not guaranteed to halt, but if you turn it into `for _ in 0..1000 { if !condition(&mut state) { break; } ... }` then it is guaranteed to halt after at most 1000 iterations
or in other words eBPF only accepts programs which it can proof will halt in at most maxins "instruction" (through it's more strict then my example, i.e. you would need to unroll the for-loop to make it pass validation)
the thing with programs which are provable halting is that they tend to also not be very convenient to write and/or quite limited in what you can do with them, i.e. they are not suitable as general purpose programming languages at all