the program isn't the proof. you have to prove that the program always gives the correct answer, and works inside some time bound. what if, say, it generates th

the program isn't the proof. you have to prove that the program always gives the correct answer, and works inside some time bound. what if, say, it generates the Collatz sequence as a subroutine? good luck proving that the program is polynomial when we can't even prove that sequence always converges.