Commenting on Rav Yehudah Amar Shmuel, the Maharsha explains that had the Torah not explicitly inserted the Shirah that Moshe and Yisrael sang, we would have assumed that they said Hallel. But now that the Torah does specify the Shirah that was sung, it is clear that it was not they who composed Halel, but rather the Nevi'im of Yisrael.

The Maharsha adds that this is the opinion of Rebbi Elazar b'Rebbi Yossi, quoted in the Beraisa. Rebbi Meir however, maintains that Moshe and Yisrael must have sung Hallel (over and above the Shirah), even though it is not recorded in the Torah.

be'Virchas Kol Tuv

Eliezer Chrysler