I think you are muddling the concepts of infinity, as in the digits of pi; and undecidability

Perhaps, but in practice, aren't there cases where the difference doesn't actually matter? If we don't know whether a lazy function will halt for all possible inputs, wouldn't we just give it the input we've got and let it run until either it does halt or the user takes some action to cause us to stop it (either by way of the program's own interface or an OS process management facility)?

Don't get me wrong -- I think lazy evaluation is a great idea. But it's not going to solve any unsolveable problems, just golf down some of the solveable ones.

Right, I agree with that entirely. This is what I meant when I said that lazy eval doesn't create GLooP (a theoretical more-than-Turing language), but nonetheless can be terribly convenient.

(Hmmm... OTOH, if we wanted to let something run in the background, we'd probably use fork rather than lazy. Still, I think lazy will be useful.)