I’ve always thought of the 的 after 有 as making 有的 noun-like, as in: - Some have understood it, some haven’t. The 有的 acts as ‘some’ and is noun-like not verb-like in the construction. This would be ungrammatical: - 有看懂了，有没看懂 But I’m not a Chinese teacher, so I can’t get much more technical than that, sorry. Hope that helps.

After chatting about this with someone a bit more knowledgeable, I should note that context, as ever, is important. Compare these two: - 有些学生发现这本书太难了。 有的看懂了，有的没看懂。 - 我读过这本书，但很难。 有的看懂了，有的没看懂。 Mmm...

有的 is a word. It means "some".

的 means the thing that you understand. 有 followed by 的 which makes 有的 become a noun.

有的 看懂了， 有的 没 看懂 = Some (things, words, ideas) (I, they, anyone) understood, some -- didn't understand.