God did, after all, provide more information on that in Exodus 20.
3. Destroy - Both persons and goods, kill all that live, and consume all things without life, for I will have no name nor remnant of that people left, whom long since I have devoted to utter destruction. Spare not - Shew no compassion or favour to any of them. The same thing repeated to prevent mistake, and oblige Saul to the exact performance hereof. Slay, &c. - Which was not unjust, because God is the supreme Lord of life, and can require his own when he pleaseth; infants likewise are born in sin, and therefore liable to God's wrath. Their death also was rather a mercy than a curse, as being the occasion of preventing their sin and punishment.