The result is even stronger: we can prove that it will sometimes not terminate!
Still that's not too bad, since type checking is always conservative: if a program passes, we know it's correct(ly typed). If it doesn't pass, we don't gain any knowledge: it may be incorrect, or it may be correct in a way which the type checker's limited algorithm cannot determine (ie. a Goedel sentence).
I'm very concerned whether my programs terminate/coterminate, since having to kill them part-way-through could cause corruption and other nastiness. Whether the type-checker terminates or not I don't really care about; I can just kill it after a certain timeout and keep fiddling with my code until it passes, just like any other type error.
Of course, a timeout removes Turing-completeness, but that timeout is under my control at the commandline, rather than being an inherent property of the algorithm.
Still that's not too bad, since type checking is always conservative: if a program passes, we know it's correct(ly typed). If it doesn't pass, we don't gain any knowledge: it may be incorrect, or it may be correct in a way which the type checker's limited algorithm cannot determine (ie. a Goedel sentence).
I'm very concerned whether my programs terminate/coterminate, since having to kill them part-way-through could cause corruption and other nastiness. Whether the type-checker terminates or not I don't really care about; I can just kill it after a certain timeout and keep fiddling with my code until it passes, just like any other type error.
Of course, a timeout removes Turing-completeness, but that timeout is under my control at the commandline, rather than being an inherent property of the algorithm.