Helper file to reason through http://www.lel.ed.ac.uk/~gpullum/loopsnoop.html
See the video linked from http://cs.indstate.edu/info/coding-demos.html for a walk-through

Suppose program P solves the halting problem.  So,
	P(prog, input) = 'Bad' if prog never halts
	P(prog, input) = 'Good' if prog halts

Okay, create a program Q that uses P as follows,
      Q(A)
	result = P(A, A)
        if result = 'Bad' then stop
       	if result = 'Good' then do not halt

Now, what will the output of Q(Q) be?  Let's see.
     result = P(Q, Q)
     // if result = 'Bad', P's definition says Q(Q) does not halt
       // Q's definition says that Q(Q) does not halt when P(Q, Q)='Good'
         // this would mean that result is 'Good'
	   // So if result is 'Bad', it must be that result is 'Good'

     // what if result = 'Good'.  trace through the same steps, and you
     // will find that it must be that result is 'Bad'
If result is 'Bad', result must be 'Good'.  If result is 'Good', result must be 'Bad'.
That doesn't make sense, so it must be that P cannot exist.