The verb you're looking for is "perform". Perform a function, but fulfil a requirement. (Yes, you also need a/the before function: "...the verb performs the function of a predicate") For your example sentence, I'm not sure what you mean by "serve". Do you mean "provide", or "serve as"? I've also looked at your previous question about precedent and I really can't imagine a proper way to express it. Unfortunately, I've found Russian linguistic theory doesn't make much sense when applied to English... I mean, no native English speaker would try to explain it in such a way, so the texts I've read by Russian speakers explaining English really look like nonsense. Perhaps if you gave an example of "precedent names" in this context, then I might be able to to find an analogy.

I am not sure what you mean. Here are some synonyms for fulfill: http://www.collinsdictionary.com/dictionary/english-thesaurus/fulfill