How do we differentiate whether 'up' is an adverb or an adjective in these two sentences?:

1) Your time is up.

2) The sun is up.
1. This is an idiomatic use of "up" - time's up or your time is up means that you are out of time, or the time allocated to the task has expired. You shouldn't think think of up in the normal sense, so it is neither an adjective nor an adverb.

2. I'm tempted to say this is idiomatic too. You say "What time does the sun come up tomorrow" or "We'll leave at sun-up" which just means sunrise - and "the sun is up" just means the sun has risen. But it's literal too - as you watch the sun rise (something I prefer not to be up to do!), it does come UP over the horizon. Now here is where I fail you - I cannot remember what this construction is called - the sun has risen. CJ or a few others will be along shortly to remind me.
I don't think there are any sentences in English with the pattern

noun is adverb

I've heard of a predicate noun and of a predicate adjective, but never of a predicate adverb.

Therefore up is an adjective in both cases, equivalent to the adjectives expired and risen, respectively.

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I've always had the impression that 'up' is an adjective until I checked the dictionaries which have me quite confused.

The sentences were taken from Merriam Webster online, which actually defines 'up' in the first as an adverb and in the second as an adjective. Oxford Advanced Learners' defines it similarly.

Does the pattern noun is adverb also include a sentence such as: "He is here."? Here, it seems like 'here' is an adverb since it describes where the person is.

In my thesaurus, up in "the sun is up" is also an adj.

And here in "he's here" is an adj, too.
I've noticed that Oxford Advanced Learner's Dictionary doesn't list out here as an adjective. I'm wondering why it does not. It's rather odd.



And this famous dictionary takes up in the following examples as adverb:

Time is up.

What's up?

be up to sb.


I'm totally bewildered.
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My American Heritage Dictionary of the English Language lists up as both adverb and adjective. Under adjective one of the definitions is

finished; over. His time was up.

here is listed only as an adverb, however, so the question of how to analyze It is here is indeed somewhat bewildering!

The fact that such questions arise at all illustrates the limitations of the traditional parts-of-speech analysis of grammatical structures. Shall we grant that here can be an adjective and preserve the idea that noun is adverb is really non-existent in English? Or shall we keep here as an adverb - never an adjective, and expand the possible structures in English to include what we will call a "predicate adverb", thus allowing noun is adverb as a possibility? Or shall we just accept that the traditional analytical machinery is insufficient to address every possibility we might encounter in the structure of English -- and move on?

What about "He is on the way up."?

What's the part of speech of "up"? And, what does it modify?
I'd say it's an adverb. It says in which direction he is making his way.
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