Estrutura Sintática I Aulas 1,2 e 3

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Estrutura Sintática I
Ao final desta aula, você será capaz de:
Study the word classes (parts of speech): nouns, adjectives, articles, numerals, pronouns, verbs, adverbs, prepositions and conjunctions and analyze their relation with clause elements in the discourse.
Introdução
Hello everybody! Welcome to our first class of syntactic structure. Syntax is a word which comes from the Greek. It means, in that language, the joining of several things together; and, as used by grammarians, it means those principles and rules which teach us how to put words together so as to form sentences. It means, in short, sentence-making. Having been taught by the rules of Etymology what are the relationships of words, how words grow out of each other, how they are varied in their letters in order to correspond with the variation in the circumstances to which they apply, Syntax will teach you how to give all your words their proper situations or places, when you come to put them together into sentences.
Syntactic Structure I
Word Class (Parts of Speech) - A word class may be defined as a set of words that display the same formal properties, especially their inflections and distribution.
What is a word?
A word is the smallest free form found in a language. A free form is an element that can occur in isolation. It does not have an entirely fixed position.
e.g.
the birds left
birds avoid cats
cats chase birds
Words can be put together to build larger elements of language, such as phrases (a red rock), clauses (I threw a rock), and sentences (He threw a rock too but he missed).
The Term Word
The term word may refer to a spoken word or to a written word, or sometimes to the abstract concept behind either. Spoken words are made up of units of sound called phonemes, and written words of symbols called graphemes, such as the letters of the English alphabet.
Following Sentence
Words are fundamental units in every sentence, so we will begin by looking at these. Consider the words in the following sentence:     
My brother drives a big car  
We can tell almost instinctively that brother and car are the same type of word, and also that brother and drives are different types of words. By this we mean that brother and car belong to the same word class. Similarly, when we recognize that brother and drives are different types, we mean that they belong to different word classes.
Word Classes
If you noticed, indefinite and demonstrative pronouns are placed as pronouns or determiners. What’s the difference? Let’s analyze some examples:
“Both of the students came - In this case, both is a determiner, as it which co-occurs with a noun (students). 
Both came.. - In this case, both is a pronoun, as it is replacing a noun (students).”
“Try to ignore the few who sneer.
Try to ignore the few people who sneer.”
“This is a fast moving train.
This train is moving fast.”
1 - Almost all English words belong to one or another of the eight word classes. A word is placed in a particular class according to how it is used in building phrases: nouns are used in noun phrases, verbs in verb phrases, adjectives in adjective phrases, adverbs in adverb phrases and prepositions in prepositional phrases.
2 - Determiners (including the articles “a” and “the”) are used in connection with nouns. Pronouns are used to replace either single nouns or whole noun phrases. Conjunctions are used to connect the clauses that make up compound and complex sentences.
3 - Some words, such as NUMBERS, do not fit in any of the word classes given above. They can behave as adjectives (one loaf or two?) or pronouns (I want one now!).
NOTE: There are some authors that will divide them:
a) Nouns, verbs, adjectives, adverbs, pronouns, prepositions, conjunctions and interjections.
b) Lexical verbs, nouns, adjectives, adverbs, auxiliary verbs, numerals, determiners, pronouns, prepositions, conjunctions.
Functional Classification
Some word classes are OPEN (OR FORM CLASSES), that is, new words can be added to the class as the need arises. The class of nouns, for instance, is potentially infinite, since it is continually being expanded as new scientific discoveries are made, new products are developed, and new ideas are explored. They are:
Nouns
Lexical Verbs (or Full Verbs)
Adjectives
Adverbs
Interjections
The words in open classes are called CONTENT (OR LEXICAL) WORDS. They are words which have meaning in themselves.
On the other hand, we never invent new prepositions, determiners, or conjunctions. They are called CLOSED (OR STRUCTURE CLASSES) WORD CLASSES because they are made up of finite sets of words which are never expanded (though their members may change their spelling, for example, over long periods of time). They are:
Auxiliary Verbs (primary and modal verbs)
Determiners
Pronouns
Prepositions
Conjunctions
The words in open classes are called FUNCTION WORDS. They are words which have little or no meaning other than the grammatical idea they express. There are only about 300 in English.
Important: One used as a noun-substitute (as in the red dress and the blue one). The verbs be, have, do, will, would, shall, should, can, could, may, might, must (auxiliaries).  These verbs are stressed when they come at the end of the sentence and when they are used in tag questions.
Note: The same lexical word can function as either content or function word depending on it's function in an utterance.
“I have come to see you", "have" is a function word (auxiliary verb)
"I have three apples", "have" is a content word (full verb)
"One has one's principles", "one" is a function word (pronoun)  
"I have one apple", "one" is a content word (numeral)
"I have no more money", "no" is a function word (a negative particle)
"No. I am not coming", "no" is a content word (Yes/No answer)
One Word, Multiple Classes
The word class of a word is  a permanent characteristic of a word and part of its definition, but many words can belong to more than one word class. It depends on:
The meaning of the word (less important). 
The grammatical characteristics of the word (more important).
Neither written nor spoken English generally marks words as belonging to one part of speech or another, as they tend to be understood in the context of the sentence. Words like neigh, break, outlaw, laser, microwave, and telephone might all be either VERB FORMS OR NOUNS. 
Although -ly is a frequent adverb marker, not all adverbs end in -ly (-wise is another common adverb marker) and not all words ending in -ly are adverbs. 
For instance, tomorrow, fast, very can all be adverbs, while early, friendly, ugly are all adjectives (though early can also function as an adverb).
Verbs can also be used as adjectives: 
The unfolding spectacle astonished the child (verb)
The astonished child watched the spectacle unfold (adjective)
In certain circumstances, even words with primarily grammatical functions can be used as verbs or nouns, as in "We must look to the how's and not just the why's" or "Miranda was to-ing and fro-ing and not paying attention".
Items may belong to more than one class. In most instances, we can only assign a word to a word class when we encounter it in context.
 Looks is a verb in 'It looks good, but a noun in 'She has good looks'; 
 That is a conjunction in 'I know that they are abroad, but a pronoun in 'I know that' and a determiner in 'I know that man'; 
 One is a generic pronoun in 'One must be careful not to offend them, but a numeral in 'Give me one good reason.
Note: A dictionary does not (or should not) prescribe, but indicates the word class or part of speech where a word is usually placed. But in a given sentence, if the speaker or writer has used it as if it were in a different class, then this is where it should be placed. 
For example, toilet is usually classified as a noun. But UK primary school teachers often speak of toileting children (I had to toilet John twice today). In describing such a sentence, you should be guided by theinternal grammar of the sentence (syntax) rather than the dictionary. Here toilet is a transitive verb. If this usage becomes standard, lexicographers will record it. This kind of word formation is called conversion, a self-explanatory name.
The Word Classes and the Clause Elements
There is a close connection between the eight word classes and the seven clause elements—subjects, verbs (verb elements), objects, predicatives, complements, adnominal functors and adverbials. The various types of phrase function as one or another of the clause elements; they are the “constituents” of the clause elements in other words.
Noun 
In English, a noun (from the Latin "nomen") is a word used to name a person, animal, place, thing, and abstract idea. Nouns are usually the first words which small children learn. The highlighted words in the following sentences are all nouns:
Late last year our neighbors bought a goat. 
Portia White was an opera singer. 
The bus inspector looked at all the passengers' passes. 
According to Plutarch, the library at Alexandria was destroyed in 48 B.C.
Substantive
The word "substantive" comes from the Latin words sub + sto (stans, stantis...), and literally means "standing in place of."  A substantive is a term covering all words that can function like a noun. In general, they are the HEAD of a phrase (sintagma). Substantives include nouns, gerunds, adjectival nouns and pronouns.
The studio is large.
Studying is good for you.
The rich are here.
This is a good book.
Let’s see: 
1. big bananas (‘big’ is an adnominal functor) 
2. a big banana (‘a’ and ‘big’ are adnominal functors) 
3. this big banana (‘this’ and ‘big’ are adnominal functors) 
4. a very big banana (‘a’, ‘very’ ‘big’ are adnominal functors) 
More sentences analysis:
Estrutura Sintática I
1. Analyze the types of prepositions and their use;
2. study the semantic meaning of the prepositions.
Introdução
Hello everybody! Anybody who has tried to learn another language knows the importance of prepositions, and how frustrating they can be to properly use. Prepositions are often very small words – like in, of, as, by, for, or to. But a preposition can be the most important word for understanding some sentences.
Prepositions - Initial Considerations
A preposition is a connector that introduces a prepositional phrase. It usually connects a noun or noun phrase to the part of the sentence modified by the whole prepositional phrase, and it shows the relation between the two.
Consider a professor's desk and all the prepositions we can use while talking about it.
You can sit before the desk (or in front of the desk). The professor can sit on the desk (when he's being informal) or behind the desk, and then his feet are under the desk or beneath the desk. He can stand beside the desk (meaning next to the desk), before the desk, between the desk and you, or even on the desk (if he's really strange). If he's clumsy, he can bump into the desk or try to walk through the desk (and stuff would fall off the desk).
Passing his hands over the desk or resting his elbows upon the desk, he often looks across the desk and speaks of the desk or concerning the desk as if there were nothing else like the desk. Because he thinks of nothing except the desk, sometimes you wonder about the desk, what's in the desk, what he paid for the desk, and if he could live without the desk. You can walk toward the desk, to the desk, around the desk, by the desk, and even past the desk while he sits at the desk or leans against the desk.
All of this happens, of course, in time: during the class, before the class, until the class, throughout the class, after the class, etc. And the professor can sit there in a bad mood.
Those words in bold are all prepositions.
Some prepositions do other things besides locate in space or time, for example:
My brother is like my father."
"Everyone in the class except me got the answer."
But nearly all of them modify in one way or another. Is it any wonder that prepositions create such troubles for students for whom English is a second language? We say we are at the hospital to visit a friend who is in the hospital. We lie in bed but on the couch. We watch a film at the theater but on television.
The choice of preposition in a sentence is often idiomatic, and may depend either on the verb preceding it or on the noun which it governs: it is often not clear from the sense which preposition is appropriate. Different languages and regional dialects often have different conventions. Learning the conventionally preferred word is a matter of exposure to examples.
For example, most dialects of American English have "to wait in line", but some have "to wait on line". Because of this, prepositions are often cited as one of the most difficult aspects of a language to learn, for both non-native speakers and native speakers.
Where a preposition is required in one language, it may not be in another. In translations, prepositions must be dealt with on a case-by-case basis, and one may be either supplied or omitted.
Classification
Simple prepositions consist of a single word, while complex prepositions consist of a group of words that act as one unit. Some examples of complex prepositions in English are: in spite of, with respect to, except for, by dint of, next to.
What are the 49 prepositions in order?
Aboard, about, above, across, after, against, along, among, around, at, before, behind, below, beneath, beside, between, beyond, but, by, down, during, except, for, from, in, inside, into, like, near, of, off, on, out, outside, over, past, since through, throughout, to, toward, under, underneath, until, up, upon, with, within, without.
"To & for" comparados a "para"
Preposições são palavras de significado pouco claro e muito variável. São mais partículas funcionais do que palavras de conteúdo semântico definido. A maioria das ocorrências de preposições, não segue um padrão lógico ou regular. Além disso, entre o português e o inglês, as preposições não apresentam uma correlação muito estreita. Cobrem normalmente diferentes áreas de significado, sendo umas de uso mais amplo que outras.
É particularmente notória a dificuldade para nós, brasileiros, quando temos que decidir qual preposição usar em inglês, to ou for, quando em português a ideia seria expressa através da preposição para. Em geral, pode-se dizer que to está ligado à ideia de direção, movimento, correspondendo muitas vezes também à preposição a do português; enquanto que for está relacionado com a ideia de benefício, substituição, intenção ou destinação, correspondendo, às vezes, ao português por. Esta diferença de significado, entretanto, não é sempre clara. Mesmo assim, for e to raramente podem ser usados como sinônimos.
Frequentemente to e for introduzem o objeto indireto e é neste caso que as duas preposições normalmente correspondem ao português para. Objeto indireto em inglês é sempre um nome ou pronome que precede ou sucede o objeto direto nos verbos bitransitivos. Quando posicionado antes do objeto direto, não vem acompanhado de preposição. Quando posicionado após o objeto direto, virá invariavelmente acompanhado da preposição to ou for. Neste caso, a preposição certa dependerá do verbo, não havendo regra para isso. Observe os seguintes exemplos:
To verbs
I gave a present to him.	 > I gave him a present.
I'll show the figures to you. > 	I'll show you the figures.
He sold a car to me. > He sold me a car.
He sent a letter to Mary. > He sent Mary a letter.
Can you lend this book to me? > Can you lend me this book?
For verbs
Let me buy a present for you. >	Let me buy you a present.
I got some food for you. >	I got you some food.
She made a sandwich for me.	> She made me a sandwich.
Did she cook dinner for you?	> Did she cook you dinner?
Existem também verbos que só aceitam o objeto indireto quando acompanhado de preposição. Exemplos:
Toverbs
The teacher said "Good morning" to the students.
He's going to introduce Mary to his family.
I already explained the project to the staff.
Mr. Cole described the new house to his wife.
I sometimes speak English to (with) my wife.
To verbs
Can you carry the suitcases for me?
Could you open the door for me?
He asked the bank teller to cash a check for him.
Doctors like to prescribe medicine for the patients.
She is going to prepare the meal for the guests.
Na verdade, quase qualquer verbo aceita o adjunto preposicional for. São portanto ilimitadas as possibilidades de FOR VERBS neste segundo grupo. Observe-se que mesmo os TO VERBS, além de aceitarem o objeto indireto precedido pela preposição to, também aceitam o adjunto preposicional for, porém com outro sentido. Ex:
I sent a letter to Mary.
I sent a letter for Mary.
No primeiro exemplo, Mary mora noutro lugar e eu lhe escrevi mandando notícias. No segundo exemplo, Mary escreveu uma carta para alguém, estava talvez muito ocupada para ir ao correio, e eu fui em lugar dela.
http://www.sk.com.br/sk-perg8.html#249
Prepositions of Place
Prepositions “in, on or at” are usually used for different places.
“In” is usually used for place which have some boundary (boundary may physical or virtual).
“On” is  used for surface. 
“At” is used for specific place. 
Preposition of Agent (By)
Preposition for agent is used for a thing which is cause of another thing in the sentence. Such prepositions are by, with etc. Following examples will help in better understanding. Examples:
This book is written by Shakespeare.
The work was completed by him.
The room was decorated by her.
The tub is filled with water.
Preposition of Device, Instrument or Machine
Different preposition are used by different devices, instruments or machines. e.g. by, with, on etc. Following examples will help in better understanding. Examples:
She comes by bus daily.
He opened the lock with key.
Prepositions of Direction (and Place)
VER ANEXO “PREPOSITIONS OF DIRECTION (AND PLACE)” – IMPORTANTE
British X American
All and all of - Before a noun with a determiner (e.g. the, this, my), all and all of are both possible in British English. American English usually has all of.
She has eaten all (of) the cake. (GB) 
She has eaten all of the cake. (US)
All (of) my friends like riding. (GB) 
All of my friends like riding. (US)
United States
Different from/than 
Check something (out) 
Do something over/again 
Live on X street 
On a team 
Monday through/to Friday
Great Britain
Different from/to 
Check something
Do something again 
Live in X street 
In a team 
Monday to Friday
Informal use of like - In an informal style, like is often used instead of as if/though, especially in American English. This is not considered correct in a formal style.
It seems like it is going to rain.
He sat there smiling like it was his birthday.
On - In American English, it is common to leave out on before the days of the week.
I am seeing her Sunday morning. (US) 
British people say at the weekend; Americans say on the weekend.
What did you do at the weekend? (GB) 
What did you do on the weekend? (US)
In and for - In American English, in can be used, like for, to talk about periods up to the present. (British English only for).
I haven’t seen her in years. (US)
Unnecessary Prepositions
In everyday speech, we fall into some bad habits, using prepositions where they are not necessary. It would be a good idea to eliminate these words altogether, but we must be especially careful not to use them in formal, academic prose.
She met up with the new coach in the hallway.
The book fell off of the desk.
He threw the book out of the window.
She wouldn't let the cat inside of the house. [or use "in"]
Where did they go to?
Put the lamp in back of the couch. [use "behind" instead]
Where is your college at?
Prepositions in Parallel Form
When two words or phrases are used in parallel and require the same preposition to be idiomatically correct, the preposition does not have to be used twice.
You can wear that outfit in summer and in winter.
The female was both attracted by and distracted by the male's dance.
 
However, when the idiomatic use of phrases calls for different prepositions, we must be careful not to omit one of them.
The children were interested in and disgusted by the movie.
It was clear that this player could both contribute to and learn from every game he played.
He was fascinated by and enamored of this beguiling woman.
Semantic Classification
Prepositions  can be used to express a wide range of semantic relations between their complement and the rest of the context. The following list is not an exhaustive classification:
Estrutura Sintática I
1. Learn the definition of Prepositional Phrases;
2. analyze the meaning of some prepositional phrases;
3. analyze the particularities of some prepositional phrases.
Introdução
The woman in the blue coat is looking for her dog. The above sentence contains two prepositional phrases: "in the blue coat" and "for her dog."
Prepositional Phrases
Prepositions are words which begin prepositional phrases. A prepositional phrase is a group of words containing a preposition, a noun or pronoun object of the preposition, and any modifiers of the object. A preposition sits in front of (is “pre-positioned” before) its object. The bolded phrases are examples of prepositional phrases in English:
She is on the computer. 
He could hear her across the room. 
Sarah walked down the ramp. 
They walked to their school. 
Garrett ate in the kitchen.
The prepositional phrase in this sentence is composed of two parts: a preposition and a noun phrase. 
The preposition is in the head position, and the noun phrase is in the complement position.
After several minutes, we located the key for the door.
after several minutes = prepositional phrase
after = preposition
several minutes = object of preposition
The flock of tiny swallows flew over the trees near the lake
a) of tiny swallows = prepositional phrase
of = preposition
tiny swallows = object of preposition
b) over the trees = prepositional phrase
over = preposition
the trees = object of preposition
c) near the lake = prepositional phrase
near = preposition
the lake = object of preposition
Do not confound object of preposition and direct object:
Compare:
We drove to the store
To the store is a prepositional phrase.
Store is the object of the preposition to, not the direct object of the verb drove.
We drove our car to the grocery store.
Car is the direct object of the verb drove.
To the grocery store is a prepositional phrase. 
Important:
Some verbs need a preposition before an object or another verb. The preposition is only grammatical, it doesn't change the meaning of the verb.
Particle
A prepositional phrase should not be confused with the sequence formed by the particle and the direct object of a phrasal verb, as in turn on the light. This sequence is structurally distinct from a prepositional phrase. In this case, "on" and "the light" do not form a unit; they combine independently with the verb "turn". A word that looks like a preposition but is actually part of a verb is called a Particle.
Four armed men held up the bank. (Held up is a verb meaning “to rob.”)
Therefore, up is not a preposition, and bank is not the object of a preposition.
Instead, bank is the direct object of the verb held up.
In order to avoid confusing prepositions with particles, test by moving the word (up) and words following it to the front of the sentence: Up the bank four armed men held.
If the resulting sentence does not make sense, then the word belongs with the verb and is a particle, not a preposition.
Note the difference:
We ran up the hill.
Test: Up the hill we ran.
The resulting sentence makes sense. Therefore, up is a preposition.
We ran up the bill. (to run up = toaccumulate indebtedness)
Test: Up the bill we ran.
The resulting sentence does not make sense. Therefore, up is a particle in this sentence. 
Other examples:
1. He came by the office in a hurry (by = preposition)
He came by his fortune honestly (by = particle)
 
2. She turned up that street (up = preposition)
She turned up her nose (up = particle)
 
3. Tom lived down the street (down = preposition)
We finally lived down that accident (down = particle)
Prepositions and Their Respective Nouns, Adjectives and Verbs (VER PDF PREPOSITIONS AND THEIR RESPECTIVE NOUNS, ADJECTIVES AND VERBS.)
Made of / Made from
"Paper is made from trees."
"Wine is made from grapes." 
"This cake is made from all natural ingredients."
You can notice that there's a common theme - a common pattern. The cotton in the shirt is still cotton – it hasn't changed its form and become something else. In the same way, the bricks in the walls of the house – they're still bricks. They didn't stop being bricks when the house was made. And the plastic in my computer keyboard is still plastic.
On the other hand, the trees in the example where we say:
"The paper is made from trees." - These trees are not trees anymore – they stopped being trees when they became paper. 
"Wine is made from grapes." - The grapes are no longer grapes – they've been changed into a different type of stuff – a different type of substance - in this case, wine.
"This cake is made from all natural ingredients." - And the flour and the eggs and the sugar in the example about the cake; these have all changed their forms as well when they became cake.
So this is the rule:
If something keeps its form, we use 'made of'.
But if the form is changed during the process of making, then we use 'made from'. 
If there is a list of ingredients, we use ‘made with’.
The table is made of wood. (It is still recognizably wood).
Wine is made from grapes. (We cannot see the grapes in the wine).
The cake was made with flour, butter, eggs, sugar and fruit. (a number of different ingredients).
Home At Home
Compare these sentences:
A: Is Mr. Jones in (the house)?
B: No, I am afraid he is out.
A: Is Mr. Jones at home?
B: No, I am afraid he is not at home.
 
At is the only preposition used with home. No preposition is used with verbs of movement,
A: What time did he arrive home? (What time did he arrive at his house?).
B: He got home at ten o’clock (He got to his house at ten o’clock).
Position of a Preposition
Misconception: A sentence must not end in a preposition. Mignon Fogarty ("Grammar Girl") says, "nearly all grammarians agree that it's fine to end sentences with prepositions, at least in some cases." Fowler's Modern English Usage says that "One of the most persistent myths about prepositions in English is that they properly belong before the word or words they govern and should not be placed at the end of a clause or sentence. Preposition stranding was in use long before any English speakers considered it to be incorrect. This idea probably began in the 17th century, owing to an essay by the poet John Dryden, and it is still taught in schools today.
But, "every major grammarian for more than a century has tried to debunk" this idea; "it's perfectly natural to put a preposition at the end of a sentence, and it has been since Anglo-Saxon times." "Great literature from Chaucer to Milton, to Shakespeare, to the King James version of the Bible was full of so called terminal prepositions." Winston Churchill is said to have written, "This is the sort of nonsense up with which I will not put, illustrating the awkwardness that could result from a rule prohibiting sentence-ending prepositions.
When Can a Sentence End with a Preposition?
English has a type of verb called a phrasal verb. These are verbs made up of multiple words, and one is always a preposition. “Cheer up,” “run over,” “log on,” and “leave off” are all examples of phrasal verbs, and often sentences that use phrasal verbs end with a preposition:
I wish he would cheer up.
You should leave it off.
It’s also OK to end a sentence with a preposition sometimes even when you aren’t using a phrasal verb. For example, although you could rewrite the following sentences to avoid ending them with a preposition, you don’t need to.
She displayed the good humor she’s known for. (Could be rewritten as “She displayed the good humor for which she’s known.”)
I want to know where he came from. (Could be rewritten as “I want to know from where he came.”)
What's this about? (Could be rewritten as “About what is this?”)
Which book are you referring to? (Could be rewritten as “To which book are you referring?”)
What did you step on? (Could be rewritten as “On what did you step?”)
When Can't You End a Sentence with a Preposition?  
But, you can't always end sentences with prepositions. When you could leave off the preposition and it wouldn't change the meaning, you should leave it off. Here is a cell phone commercial: 
Where are you at?
The problem is that “Where are you at?” doesn't need the preposition at the end. If you say “Where are you?” it means the same thing. So the "at" is unnecessary. You should leave it off. 
Other positions:
1. Some prepositions can appear on either side of their complement; these can be called ambipositions:
He slept {through the whole night}/{the whole night through}.
2.  Another preposition surrounds its complement, called a circumposition. A circumposition has two parts, which surround the complement to form a circumpositional phrase. 
English: from now on
3. Interposition is used for prepositions in the structures such as the following:
word for word, page upon page.
Classification by Complement
Prepositional phrases generally act as complements and adjuncts of noun phrases (adjectives) and verb phrases (indirect object, prepositional object or adverbs). For example: 
The man from China was enjoying his noodles. (Adjunct of a noun phrase - adjective).
She ran under him. (Adjunct of a verb phrase - adverb).
A student of physics. (Complement of a noun phrase - adjective).
She argued with him. (Complement of a verb phrase – prepositional object).
She handed the money to me. (Complement of a verb phrase – indirect object).
Give this man your name. (Complement of a verb phrase – indirect object with preposition understood).
Let’s analyze:  The boy from the shop is waiting at the corner.
at the corner: The head of this prepositional phrase is the preposition at. The function of the phrase is adverbial - it does the work of an adverb by modifying the verb waiting. It answers the question: where is he waiting?
at the corner: The head of this prepositional phrase is the preposition at. The function of the phrase is adverbial - it does the work of an adverb by modifying the verb waiting. It answers the question: where is he waiting?