The Gemara in Taanis [12b] derives that it is forbidden to do melacha on a fast - by day only.
Rav Chisda said that Rav Yirmeya bar Abba said as that the verse states: “Sanctify a fast, call a solemn assembly, gather the elders” (Joel 1:14), this indicates that a fast day is like a day of assembly. Just as on a day of assembly, i.e., a Festival, it is prohibited to engage in working, so too,on a fast it is prohibited to engage in working.
אי מה עצרת מאורתא אף תענית נמי מאורתא אמר רבי זירא לדידי מיפרשא לי מיניה דר' ירמיה בר אבא אמר קרא אספו זקנים דומיא דאסיפת זקנים מה אסיפת זקנים ביום אף צום נמי ביום ואימא מטיהרא אמר רב שישא בריה דרב אידי מסייע ליה לרב הונא דאמר מצפרא כינופיא
The Gemara asks: If so, one could say: Just as on a day of assembly it is prohibited to work from the previous evening, so too, on a fast it should be prohibited to work from the evening. Rabbi Zeira said: This was explained to me by Rabbi Yirmeya bar Abba himself: The verse states: “Sanctify a fast, call a solemn assembly, gather the elders,” indicating that a fast is similar to a gathering of elders: Just as the gathering of elders is performed by day, so too, the time for a fast is also by day.
Question: If the source of the limmud is עצרת [i.e. Yom Tov] then just as on Yom Tov one may not perform melacha at night - so too on the fast. How does the Gemara employ a היקש למחצה - half equation??
והדברים פלואים!!!
This question is THANKFULLY discussed in this shiur, that also presents HUUUUGE yesodos in the Avoda of Yom Tov!!