I read 2 Samuel 1 this morning, (from the REB) leaving out the gory bits (about the death of the Amalekite messenger). Why do translations write about the book of Jashar (REB and loads of others)? The construct (עַל־סֵפֶר הַיָּשָֽׁר) implies that Jashar is not a proper name.
Note Lambdin - a proper name does not take the definite article, and a proper name does not require a definite article to make the phrase include 'the' in English. So this is not 'the book of Jasher' but the book of the upright.
Upright gives more poignancy to the lament of David that follows. Jonathan and Saul - in spite of all the difficulty are still written in the Book of the Just. (Good news).
and he said to teach the children of Judah --- behold, it is written in the book of the upright...
וַיֹּאמֶר לְלַמֵּד בְּנֵֽי־יְהוּדָה קָשֶׁת הִנֵּה כְתוּבָה עַל־סֵפֶר הַיָּשָֽׁר׃
Now - what's קָשֶׁת (bow) doing in that sentence?