Midrash su Salmi 72:20

(Fol. 117) R. Juda, in the name of Samuel, said: "The Bible song (Ex. 15) was uttered by Moses and Israel when they ascended from the Red Sea. But who recited the Hallel? The prophets among them ordained that Israel shall say it on every momentous occasion; and whenever trouble overtakes them and they are delivered [by God] from it, they should say it [as praise] for their deliverance." We are taught that R. Meier has said: "All the songs and praises which are uttered in the Book of Psalms were uttered by David, as it is said (Ps. 72, 20) Here are ended the prayers of David, the son of Jesse. Do not read Kalu (here ended) but read it Kal elu (all these are). And who said Hallel? R. Jose says: "My son, Elazar, holds that Moses and Israel uttered them when they were ascending the Red Sea. But his associates differ from him and say that David uttered them. And to me it seems that my son's opinion is more correct than that of his associates; for how is it possible that Israel could slay the Passover offering and take the palm branches (on Succoth) and utter no praise to God?"