I'm Mister Satori

ITT: Give me a program, and I'll tell you if it terminates.

Suppose you had a function, foo, which takes in as it's input a function, and returns 1 or 0, depending on whether that function terminates or not (1 if it does, else 0)

Consider the following program:


int main()
{
    int x = foo(main);
    return 0;
}

Since main terminates, x is assigned 1
Now consider


int main()
{
    int x = foo(main);
    while (x) {}
    return 0;
}

If foo returned 1, implying main terminates, we would enter this infinite loop, hence main doesn't terminate.
If main is self-terminating, then it isn't self-terminating

Suppose then, foo returned 0, implying main wasn't self-terminating, we would skip pass the infinite loop, and hence main would become self-terminating.
If main isn't self-terminating, it terminates

The conclusion is that the problem of determinating whether a proposed function (which may be extended to a program) terminates or not is beyond the power of current computational models, and hence this thread is a complete sham.