The present Mekhilta cannot, however, be the one composed by Ishmael, as is proved by the references in it to Ishmael's pupils and to other later "tannaim". Both Maimonides and the author of the "Halakhot Gedolot," moreover, refer, evidently on the basis of a tradition, to a much larger Mekhilta extending from Exodus 1 to the end of the Torah, while the midrash here considered discusses only certain passages of Exodus. It must be assumed, therefore, that Ishmael composed an explanatory midrash to the last four books of the Torah, and that his pupils amplified it.