Inputs to Program to Illustrate Halting Problem

Question

Is this illustration of the haling problem correct?

function halts(func) {
  // Insert code here that returns "true" if "func" halts and "false" otherwise.
}

function deceiver() {
  if(halts(deceiver))
    while(true) { }
}

If so, why do so many descriptions involve a function which takes two arguments, where one is the program and the other is the same program as program input?

E.g.:

Assume we have a function Halts(P, W) that halts if program P halts on input W. Then we write this perfectly-valid Python function:

    def K(P):
        if (Halts(P, P)):
            while True: pass # run forever
        else:
            return 42 # halt!

Now, what happens when we call K(K)? If Halts(K,K) is True, then K(K) hangs (runs forever) If Halts(K,K) is False, then K(K) halts So either way, Halts(K,K) is wrong. Thus, the Halts function cannot exist!

Answer 1

The two input parameters are just a trick for the construction of the proof by contradiction, showing the non-existence of an algorithm for the halting problem.

There are a lot of sketches for the proof online, e.g. https://www.youtube.com/watch?v=macM_MtS_w4