What grammatical roles do infinitives and participles assume when used predicatively?

Question

A non-academic grammar site I was reading says:

A linking verb will always be completed by an adjective (a predicate adjective) or a noun (a predicate nominative).

...

A linking verb can only be completed by a predicate adjective or a predicate nominative (i.e., a noun or a pronoun). (source)

This, of course, is incorrect. I am thinking participles, infinitives, and predicative clauses which I am not sure fall under either one. But it occurred to me that I don't know what the former two are called grammatically. I know in a sentence predicate a clause would be a predicative clause, a gerund a predicate nominative. And those mentioned are probably all predicative expressions.

She is running. (present participle)

She is stunned. (past participle)

The only thing she can do right now is wait. (infinitive)

So do these have specific names in grammar?

Answer 1

The question wouldn't arise if there weren't a false dichotomy between some uses of auxiliary verbs and others. Be is not a "linking verb". That's a term for grade school students. Be is an auxiliary verb. It is required whenever the main predicate is not a tensed verb:

• This gentleman is the one who phoned you. (predicate NP)
• That gentleman is rather ill. (predicate AdjP)
• The other gentleman is on the sofa. (predicate PP)

Of course, be is not the only auxiliary verb in English, but it is the most prominent one, and it's always an auxiliary verb. That is, it has no meaning; it's strictly part of the grammatical machinery, like the do in Do you like cilantro?.

Other uses of auxiliary be occur with various verb forms, participial and infinitive, in what are called Constructions in syntax. These are often called "tenses" or "voices" by grammar-school texts, but English only has two inflectional tenses (present and past), and no inflectional cases, moods, voices, or aspects at all, unlike other European languages. English does everything with constructions.

There is the Progressive (or Continuous) construction, which uses auxiliary be (in present or past tense), followed immediately by the present participle (the -ing form) of the next verb (which could be the main verb):

• He was looking at his phone.
• It's raining.
• I'm thinking about it.

Then there's the Passive construction, which uses be, also available in present or past, followed by the past participle (the -en/ed form, like taken or written, and often the same form as the past tense) of the next verb:

• His phone was stolen yesterday.
• This book was written by my friend.
• The children are fed by the nanny.

But those are in the verb chain and can be used together, along with modals and the Perfect construction, e.g,

• She will have been being photographed for 6 hours by then.

Auxiliary be doesn't occur with an infinitive in the verb chain; but it does occur in a specialized future construction for scheduled events:

• Frank is to leave tomorrow.

There's no special name for this construction, afaik; it's one of several ways of indicating the future in English.

Answer 2

English grammars traditionally consider to be + -ing forms a verbal phrase expressing a tense into itself (present continuous). So we can put She is running aside, because there is nothing after "is running".

Other than that, within "grammar", it is convenient to differentiate between the syntactic function of a word (what work it does in the sentence), and the semantic function of a word (what type of word it is, i.e. noun, adjective, adverb, etc.).

Another thing to remember is that participles such as "stunned" and infinitives such as "wait" are both "verbals". Verbals are words derived from vebs, but which can be semantically equivalent to adjectives and nouns respectively.

That said: whatever comes after a linking (copulative) verb is, by definition, a predicative construction (syntactically). That predicative construction can be formed by a noun, by an adjective, or even by an adverb. (Or by multi-word construnctions having those types of words as a nucleus).

She is pretty => adjective

She is very pretty => adjectival construction

She is gold => substantive

She is a true angel => substantive construction

She is well => adverb

She is very well => adverbial construction

She is stunned => participle (working as an adjective)

She is very stunned by the crash => participial (hence adjectival) construction

All she does is wait => infinitive (working as a noun)

All she does is always wait in line for bread => infinitive (hence nominal) consruction

And every single example after "is", in all the examples, is a "predicative construction".