In various places the Torah refers to מַלְאַךְ ה׳; e.g., twice in Bereishis 22. Mechon Mamre’s JPS translation renders this as “the angel of the LORD”, but is the definite article implicit in this form of the word מלאך, or should it be translated as “an angel of the LORD”?
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… which is not the way I think of it, and I'm not sure it's a good way of thinking of it, but maybe. Anyway, let me explain:
A noun phrase in Hebrew sometimes consists of a construct noun and another noun following. The construct noun is something like "מַלְאַךְ" and the noun following it can be "ה׳". In that case, the first, construct noun is definite, i.e. it means "the [something] of", here "the messenger of" or "the angel of". (There are exceptions.)
Note, though, that the definiteness can mean various things. In particular, it need not mean that the messenger/angel under consideration is God's only messenger/angel. (This is like in English, where we say "give him the green folder": there's certainly more than one green folder, but only one under consideration at the moment.) In Genesis 22, the first "מַלְאַךְ ה׳" can't easily be read as referring to a specific messenger/angel mentioned earlier in the text, so the definiteness must be weaker, perhaps something like "the specific messenger/angel that God sent this time". Perhaps some of the commentators there discuss this, but that wasn't your question.
I don't have a definitive source, but the following is according to how I learned it (in a biblical Hebrew grammar class at Hebrew U).
The definite/indefinite quality of the construct state depends entirely on the following word (the one in absolute state). For example:
סוּס הַמֶּלֶךְ - the horse of the king
סוּס מֶלֶךְ - a horse of a king -- a king's horse (where no particular horse is intended)
For example, Isaiah 34:8 has "שְׁנַת שָׁלוֹם", where JPS translates "a year of recompense".
In particular, since ה׳ is definite, מַלְאַךְ ה׳ would be "the angel of Hashem".
I can't account for Wikipedia's account of the construct being always semantically definite, but for Gesenius, as quoted in the previous answer, I think many of the examples where I would say indefinite and Gesenius writes "the" are more a function of how we write things in English. For example, he writes "the terror of a king", where I would understand that as meaning "any terror of a king", hence indefinite.
See also his point 2(e), where he writes כּסִיל אָדָם (a fool of a man), or in 2(a) (the second one -- on the page marking on the left, it's right before page 418), where we have אִישׁ דְּבָרִים (a man of words) and אִישׁ לָשׁוֹן (a slanderer). There's also the very common example of תַּלְמִיד חָכָם (lit. a student of a wise man).
Sorry I can't post link to Wikipedia and Gesenius (links that are in msh210's answer), and also that I'm not attaching this as a comment to the previous answer, as my reputation currently doesn't allow it.