Adam Clarke on John 8:56

Abraham rejoiced to see my day - Or, he earnestly desired to see my day; ηγαλλιασατο, from αγαν, very much, and ἁλλομαι, I leap - his soul leaped forward in earnest hope and strong expectation that he might see the incarnation of Jesus Christ. The metaphor appears to be taken from a person who, desiring to see a long-expected friend who is coming, runs forward, now and then jumping up to see if he can discover him. There is a saying very like this in Sohar Numer fol. 61: "Abraham rejoiced because he could know, and perceive, and cleave to the Divine Name." The Divine name is יהוה Yehovah; and by this they simply mean God himself.

And he saw it - Not only in the first promise, Gen 3:15, for the other patriarchs saw this as well as he; and not only in that promise which was made particularly to himself, Gen 12:7; Gen 22:18, (compared with Gal 3:16), that the Messiah should spring from his family; but he saw this day especially when Jehovah appeared to him in a human form, Gen 18:2, Gen 18:17, which many suppose to have been a manifestation of the Lord Jesus.