My daughter asked me what would happen if someone started the day not fasting -- intentionally! He wakes and says "this is dumb so I'm having breakfast." Then, due to some intervening act or realization, he became a bal tshuva during the morning. Would this person then start fasting in order to fast for the rest of the day or is the opportunity to fast gone once one intentionally does not fast?
Though I know that there are rules for someone who has accidentally eaten, I wonder how those rules apply when someone intentionally ate. Is the obligation still incumbent upon him once it has been intentionally violated (the way I assume Shabbos is -- if someone broke shabbos, he is still bound to observe it 5 minutes later) or is a fast something that requires the intent to observe it for the entire time and someone can't invoke an obligation and be yotzei that requirement later in the process? Is one getting credit for not eating, or simply discharging an obligation by not eating? Is every moment of not eating a positive point, or do the moments have no value if they are not part of the complete fulfillment of a "fast day"?
Does this hinge on whether the fast is a halachically ordained one (so the obligation exists for the entire time) or a personally accepted one which he then gives up on, and then desires to return to?