A Turing machine is a theoretical construct that needs an infintely long tape, so any implementation has to be a subset, without invoking religion (-: and then you first have to prove that the g.d you use really exists :-).

So isn't it a bit non-gracious to complain about an infinite list?

I mean, it wouldn't be impossible to use a tied array. (The semantics for how a list is created makes that impossible, I think?)