Sorry to say, this example has nothing to do with the halting problem. Rather, I would say, it's a reformulation of a(n unsolved) mathematical problem to the qu

Sorry to say, this example has nothing to do with the halting problem. Rather, I would say, it's a reformulation of a(n unsolved) mathematical problem to the question whether a certain function halts on a certain input (being "no input", as the function is nullary). Or, if you insist, we can regard it as a trivial instance of the halting problem. An instance of the halting problem asks, given (a partial recursive) function F, whether there is an decision algorithm A (aka. Boolean valued algorithm) on the universe of inputs U of F that calculates the domain of F (those inputs where F takes a value, ie. halts; ie, A(x) <=> F halts on x, where x in U). For any finite subset S = {s_1, ..., s_n} of U, there is a trivial decision algorithm on U that calculates S: def A_S(x): for s in (s_1, ..., s_n): if x == s: return True return False Therefore if the domain D of F is finite, the answer to the halting problem of F is trivially yes: A_D is a decision algorithm for F. (This has noting to do with the question whether we know D or not!) If U is finite, then D is finite, so the answer to the halting problem of F is trivially yes. If F is a thunk (nullary function), then U is finite, ie. the singleton set of "no input", so the answer to the halting problem of F is trivially yes. odd_perfect_number is a thunk.