Gemara

Mishnah - R. Meir: Even though R. Gamliel says that we do not interrupt a series of fasts if a fast falls on Rosh Chodesh, Chanukah or Purim, he agrees that we do not complete the fast (until night).

The same applies when Tish'ah b'Av is on Erev Shabbos.

Eruvin 40b - Question (Rabah and other Talmidim of Rav Huna): If a Talmid fasts on Erev Shabbos, should he complete the fast?

Rav Huna and Rav Yehudah could not answer.

Answer (Rava - Beraisa): When Tishah b'Av falls on Erev Shabbos, he may eat k'Beitzah (of food before Shabbos), in order that he not enter Shabbos amidst affliction;

(Beraisa - R. Yehudah): Once, Tishah b'Av fell on Erev Shabbos. They brought a roasted egg for R. Akiva; he ate it without salt. He was not hungry, he just wanted to show the Halachah to Talmidim.

R. Yosi says, he must complete the fast.

R. Yosi: You agree that when Tishah b'Av falls on Motza'ei Shabbos, one must stop eating (on Shabbos) while it is still day. Just like one may end Shabbos amidst (the beginning of) a fast, one may enter Shabbos amidst affliction!

Chachamim: One may end Shabbos amidst a fast, for he ate and drank the entire day (he is satiated). One may not enter amidst affliction of having fasted the entire day!

(Ula): The Halachah follows R. Yosi.

Question: The Halachah does not follow R. Yosi!

(Mishnah - R. Meir: Even though R. Gamliel says that if we started fasting and a fast fell on Rosh Chodesh, Chanukah or Purim we do not interrupt, he agrees that we do not complete the fast;

The same applies when Tishah b'Av falls on Erev Shabbos.

(Beraisa): After R. Gamliel died, R. Yehoshua came to overturn his words (and say that we complete the fast).

R. Yochanan ben Nuri: The body must follow the head. As long as R. Gamliel (or Nasi) was alive, the Halachah followed him. Will we now annul his words?! No! The Halachah was fixed like him!

No one argued with R. Yochanan ben Nuri.

Answer: R. Gamliel's generation followed him, but R. Yosi's generation follows R. Yosi!

Question: R. Gamliel's generation did not follow him!

(Beraisa - R. Eliezer b'Ribi Tzadok): Once, Tishah b'Av fell on Shabbos; the fast was postponed to the 10th. My family did not complete the fast, for it is our Yom Tov (my family used to bring wood for the Mizbe'ach on this day).

Inference: If the fast was not on their Yom Tov, rather, on the day before their Yom Tov, they would complete the fast!

Answer (Ravina): A Yom Tov mid'Rabanan is different. Since one may fast part of the day (e.g. when Tishah b'Av is postponed to the 10th), we finish a fast before it. One may not fast on Shabbos at all, so we do not finish a fast before it.

(Mishnah): We not decree fasts... (starting) on Rosh Chodesh... (R. Meir says, R. Gamliel agrees that we do not complete a fast that falls on one of these days).

(Rav Yehudah): This is R. Gamliel's opinion according to R. Meir, but Chachamim say that one fasts and completes the fast.

Suggestion: He refers to all of the days R. Meir discusses (including Erev Shabbos, and he says that Chachamim say that we complete the fast)!

Rejection: No, he refers only to (Rosh Chodesh,) Chanukah and Purim (which R. Gamliel himself discussed).

Support: He cannot refer to all of them, for Rav Yehudah was unable to answer Rabah's question (about Erev Shabbos, at the beginning of our Sugya)!

Rejection: Mar Zutra said that Rav Huna that the Halachah is that one completes the fast, even though Rav Huna did not answer Rabah's question!

We must say that Rav Huna did not know at first, and later he heard the Halachah. We can say similarly about Rav Yehudah!

(Mar Zutra citing Rav Huna): The Halachah is, one completes the fast.

Rishonim

R. Chananel (Eruvin 41a): We have a tradition that doctors told R. Akiva to eat an egg because he was dangerously sick; R. Yehudah was unaware of this.

Rif and Rosh (2:25): The Halachah is, one completes a fast on Erev Shabbos.

Rosh (ibid.): This applies even to an individual's fast. The Yerushalmi says that if he did not stipulate that he fasts only until the Tzibur prays (Ma'ariv), he may fast until Tzeis ha'Kochavim. This is not considered fasting on Shabbos, because a fast that does not last until Shki'ah is not a fast.

Korban Nesan'el (60): It is optional to complete an individual fast until Tzeis ha'Kochavim. This is obligatory for a Ta'anis Tzibur, for one cannot stipulate about it.

Rambam (Hilchos Ta'anis 5:5): If one of the four fasts fell on Erev Shabbos we fast on that day.

Magid Mishnah: The Ra'avad says that 'completing the fast' means fasting until Shki'ah. At Shki'ah one may not fast, due to the Kedushah of Tosefes Shabbos.

Hagahos Maimoniyos (1:3): The Halachah is, we complete the fast. Tosfos (Eruvin 41b DH v'Hilchesa) explains that one may complete it. Avi ha'Ezri and the Roke'ach say that one must complete it. Completing the fast means fasting until after Ma'ariv, even if it is before Shki'ah. However, one completes a Ta'anis Chalom until Tzeis ha'Kochavim, for it is due to danger, to annul a bad dream. Perhaps he will not annul it unless he fasts until Tzeis. Also, one may fast Ta'anis Chalom on Shabbos itself. Regarding any other fast, one who wants to complete it may eat immediately after Ma'ariv. Some do not want to complete it, so they eat after the time of Minchah.

Rosh (Rosh Hashanah 4:14): Rav Hai Gaon says that many generations were unsure whether or not one who fasts on Erev Shabbos completes the fast, until it was decided that he does.

Poskim

Shulchan Aruch (249:4): If one accepted to fast on Erev Shabbos he must fast until Tzeis ha'Kochavim, unless he stipulated to fast only until the Tzibur finishes Ma'ariv.

Taz (2): L'Chatchilah one should stipulate so he will not need to fast on part of Shabbos.

Kaf ha'Chayim (24): It suffices if he intended in his heart.

Taz (3): Our custom is to complete a Ta'anis Chalom.

Rema: Some say that he should not finish; he should eat immediately after leaving the Beis ha'Keneses. Therefore, one should not complete an individual fast. It is good to stipulate when accepting it. One should complete a Ta'anis Tzibur; this is the custom.

Mishnah Berurah (22): A fast for a Yartzite or Erev Rosh Chodesh is considered an individual fast. Some say that if the first time he fasted until Tzeis ha'Kochavim he must always do so, for presumably he intended for this (unless he specified otherwise). Some say that this is even if the first time was not Erev Shabbos. Some are lenient even if the first time was Erev Shabbos. One may rely on them if he is in pain.

Shulchan Aruch: One must fast until Tzeis ha'Kochavim for a Ta'anis Chalom (even on Erev Shabbos).

Beis Yosef (249 DH u'Mah she'Chosav Rabeinu b'Shem): The Mordechai says that once Asarah b'Teves fell on Erev Shabbos and the Ri tasted food before Ma'ariv, to avoid entering Shabbos amidst Inuy. He holds that the question was whether or not it is permitted to complete the fast, but it is better not to. Hagahos Maimoniyos says that one must complete a Ta'anis Chalom; the Or Zaru'a permits eating after Ma'ariv.

Darchei Moshe: Hagahos Ashri (1:12) permits eating after Ma'ariv even on a weekday.

Rema (YD 402:12): It is a Mitzvah to fast on the day one's parent died... if it falls on Erev Shabbos, it is like other Ta'aneisim.

Taz (OC 249:3): The Maharshal says that one completes a Ta'anis Yartzite on Erev Shabbos, except for the first year. It is like a Neder. Since it takes effect on Chol (Erev Shabbos), it takes effect even on Shabbos. This is not clear. One is exempt when the Yartzite falls on Shabbos, even if he previously fasted when it was on Chol. Also, why is it different than a regular fast that an individual accepted? One need not be stringent about this, especially if he is in pain.