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The Tur (O.C. 487) observes the custom observed in some communities to recite the full hallel, with the introductory and concluding berakhot, in the synagogue on the first night of Pesach (and, in the Diaspora, on the second night), after arvit. The source of this practice, as cited by the Tur, is Masekhet Sofrim (20:9), which lists the first night of Pesach among the occasions when the full hallel is recited. The reason for this custom, the Tur explains, is that we will not have to recite a berakha over the hallel recitation at the seder that night. It seems that in principle, the hallel recitation at the seder requires a berakha, but in practice, a berakha is not recited, and so the custom evolved to recite hallel in the synagogue with a berakha to satisfy the requirement to recite a berakha. The likely explanation is that at the seder we divide the hallel into two sections – reciting the beginning of the hallel text at the end of maggid, before the meal, and reciting the rest of hallel after the meal. The meal would constitute an interruption in between the introductory berakha and the rest of hallel, and so we cannot recite the introductory berakha at the seder. According to the Tur, this is the reason why it became customary to recite hallel in the synagogue.
Others, however, explain this practice differently. The Tosefta (Pesachim 10:8), cited by Tosafot (Berakhot 14a), indicates that it became customary in some places to recite hallel in the synagogue for the benefit of those who were unable to recite it themselves. In communities where there were people who did not know the hallel text by heart and did not have access to printed texts, hallel was read for them in the synagogue, so they could fulfill their requirement by listening to its recitation. Conceivably, this is the origin of the practice observed in some communities to recite hallel in the synagogue on the night of the seder.
Yet another view is cited by the Ran (Pesachim 26b in the Rif) in the name of the Rashba, who maintained that “ikar takanat keri’ato be-veit ha-kenesset haya, ve-lo ba-bayit” – the primary hallel obligation on this night is to recite hallel after arvit in the synagogue. According to the Rashba, the synagogue recitation fulfills the formal hallel obligation of this night, which is why a berakha is recited over this recitation. This is in contradistinction to the conventional understanding – and the Tur’s explanation – that the primary obligation is to recite hallel at the seder, and the recitation in the synagogue is merely a custom that developed later.
The Shulchan Arukh (487:4) records this custom, whereas the Rama observed that Ashkenazic communities in his time did not recite hallel in the synagogue on the night of the seder. The Vilna Gaon (Bi’ur Ha-Gra) suggests that these two views reflect the different opinions as to the origin of this practice. The Rama perhaps maintained that this custom developed for the sake of those who were unable to recite it themselves, and so nowadays, when people can recite it themselves, there is no need to recite hallel in the synagogue. The Shulchan Aruch, by contrast, followed the position that Chazal established a formal requirement to recite hallel in the synagogue on this night, and so this practice must be observed even in our times.
Interestingly, the Vilna Gaon in a separate context seems to point to a different perspective on the halllel recitation in the synagogue on the first night of Pesach. Commenting on the practice to light Chanukah candles in the synagogue each night (Bi’ur Ha-Gra to O.C. 671:7), the Vilna Gaon writes that this custom resembles the custom to recite hallel in the synagogue on the night of the seder. In both instances, the Gaon explains, the custom developed to perform publicly, in the synagogue, a mitzva which is performed in one’s home, for the purpose of pirsumei nisa – to make a public celebration of the miracle. According to the Vilna Gaon, then, the custom to recite hallel in the synagogue on the first night of Pesach serves to publicize the miracle of the Exodus. (See Minchat Asher – Moadim, vol. 3, chapter 7.)
Conceivably, these different approaches would affect the question of whether one who, for whatever reason, cannot attend the synagogue on this night nevertheless recites hallel after arvit, if this is his normal custom when praying in the synagogue. If this hallel recitation continues the ancient practice of reciting hallel in the synagogue for the benefit of those who could not recite it on their own, then it would seem that this custom requires reciting hallel only in the synagogue. And, certainly, according to the Vilna Gaon, who understood that the purpose of this custom is to make a public celebration, it applies only when praying publicly. According to the Tur, however, hallel is recited after arvit to avoid having to recite the berakha over hallel at the seder, and this is relevant even if one prays privately.
Regardless, Rav Asher Weiss (Minchat Asher – Corona, pp. 262-265) ruled that in those communities which follow the practice of reciting hallel in the synagogue on the first night of Pesach, even one who prays privately recites hallel after arvit. Although this halakha should depend on the reason for the synagogue halllel recitation, as discussed, Rav Weiss explains that since this practice is based on Sephardic custom, its parameters are determined based on that original custom. And a number of Sephardic poskim, including the Chida (Birkei Yosef, 487:8; Sheyarei Berakha, 487:3; Moreh Be-etzba, 207) and the Kaf Ha-chayim (487:39-42), mention that even those who pray privately recite hallel after arvit. Therefore, this is the policy that should be followed by those who normally recite hallel in the synagogue on the first night of Pesach but now find themselves praying privately.