Does "החג" include שמיני עצרת?
I commonly see "החג" (or "חג"), literally "the holiday", explained as referring to the holiday of Sukos. I wonder whether it's correct or whether, as I suspect, it refers to the combined celebrations of Sukos and Sh'mini Atzeres. The reasons for that my suspicion are:
- that the prayer for rain is said on Sh'mini Atzeres, and the mishna in Rosh Hashana says that God passes judgement about rain on "החג";
- that Shulchan Aruch, OC 644:1, says that we say halel on "all the eight days of החג"; and
- that the combination has no other name that I know of, so it makes sense to give it this name, whereas Sukos has another name, so doesn't need a new one.
Do any sources explicitly address the possibility the "החג" refers to the entire period? Do they accept or reject it and why?