1. Grammars

2. Grammars A formal definition of the syntactic structure of a language
Set of rules that tell you whether a sentence is correctly structured
a sentence is a well-formed string in the language
rules specify the order of components and their sub-components in a sentence

3. Languages Natural language language spoken or written by humans
English, French, Italian, Spanish, …
English and other natural languages clearly have structure
subjects, nouns, verbs, …
In contrast we have programming languages
languages used to communicate with computers
Java, C, C++, …
programming languages also have structure
expressions, statements, methods, …

4. English grammar
A set of rules for combining words into well-formed phrases and clauses

5. Clauses
A clause is a group of related words containing a subject and a verb
building blocks of sentences
Independent clause
can stand alone as complete sentence
Tammy is great!
Dependent clause
unable to stand alone as complete sentence
Although Tammy is great
“Although” is a dependent word: allows clause to be embedded in another sentence
Although Tammy is great, this class is still boring.

6. Phrases
A phrase is a group of related words that does not contain a subject-verb relationship
can consist of a single word or a group of words
noun-phrases and verb-phrases
Dogs bite.
Some dogs bite.
The mean dog in the park bites.
Some dogs bite people.
a noun-phrase can be contained in a verb-phrase
bite people
the noun people is the object of the verb bite

7. An English grammar
<SENTENCE> => <NOUN-PHRASE> <VERB-PHRASE>
<NOUN-PHRASE> => <NOUN> | <ARTICLE> <NOUN> |
<ARTICLE> <ADJECTIVE> <NOUN>
<VERB-PHRASE> => <VERB> | <VERB> <NOUN-PHRASE>
The above grammar specifies the rules for generating a syntactically correct English sentence
This means …
given lists of nouns, articles, adjectives, and verbs, we can generate any number of syntactically correct English sentences

8. Example
<NOUN> => DOG | CAT | WATER
<VERB> => BIT | SNIFFED | DRANK | SCRATCHED
<ARTICLE> => THE | A
<ADJECTIVE> => STINKY | HAPPY | MEAN
According to our grammar, the following sentences are syntactically correct:
THE HAPPY DOG SNIFFED THE STINKY CAT
A MEAN CAT SCRATCHED THE DOG
THE CAT BIT THE DOG
A STINKY DOG DRANK THE WATER
THE HAPPY WATER DRANK THE STINKY DOG
THE MEAN WATER SCRATCHED THE HAPPY CAT

9. THE HAPPY DOG SNIFFED THE STINKY CAT
Recognition
Grammars can also be used to recognize syntactically correct sentences. For example, the sentence
THE HAPPY DOG SNIFFED THE STINKY CAT
can be fit to the grammar in the following way
<SENTENCE>
<NOUN-PHRASE>
<VERB-PHRASE>
<ARTICLE> <ADJECTIVE> <NOUN>
<VERB>
THE HAPPY DOG SNIFFED THE STINKY CAT

10. Optional parts of speech
Our grammar provided us with options for the phrases, we can also fit the sentence
THE DOG SNIFFED THE CAT
to the grammar
<ARTICLE> <NOUN>
<ARTICLE> <NOUN>
<SENTENCE>
<NOUN-PHRASE>
<VERB-PHRASE>
<VERB>
THE DOG SNIFFED THE CAT

11. Syntax and semantics
Syntax only tells you if the sentence is constructed correctly
Semantics tells you whether a correctly structured sentence makes any sense
The sentences
THE HAPPY WATER DRANK THE STINKY DOG
THE MEAN WATER SCRATCHED THE HAPPY CAT
are correct syntactically speaking but something appears wrong …
water usually isn’t happy or mean and usually doesn’t drink or scratch either

12. Parsing
Process of taking sentence and fitting it to grammar is called parsing
DOG BIT CAT
<NOUN> <VERB> <NOUN>
<NOUN-PHRASE> <VERB-PHRASE>
<SENTENCE>
Parsing English is complex because of context dependence
Natural language understanding is one of the hardest problems of artificial intelligence
human language is complex, irregular and diverse
philosophical problems of meaning

13. Formal specifications
Need a precise notation of syntax of a language
grammars can be used for generation and recognition
Context-free grammars
<name> => sequence of letters and/or
digits that begins with a letter
<name> => gikB
<name> => msg42
Substitute as many times as necessary. All legal statements can be generated this way 

14. Context-free grammar person = firstname + " " + lastname;
How do we get this from our grammar?
Unlike natural languages like English, all the legal strings in a programming language can be specified using a context-free grammar

15. Recursive Sentence Generator
Constructs sentences, paragraphs, and even papers that fit a prescribed format.
The format is specified by a set of rules called a grammar
A grammar consists of a set of definitions
Each definition is a set of productions
Examples of grammars (Lab 7)
Extension request
College rejection letter
Poem

16. Poem Grammar All grammars begin with start rule{
<start>
The <object> <verb> tonight. ; }
Nonterminals are indicated by angle brackets
<object>
waves ;
big yellow flowers ;
slugs ;

17. More on the poem grammar
Nonterminals can refer to other nonterminals {
<verb>
sigh <adverb> ;
portend like <object> ; }
<adverb>
warily ;
grumpily and <adverb> ;

18. Generating a poem <start> All sentences start with <start>
Only one production in the definition of <start>
The <object> <verb> tonight.
Expand each grammar element from left to right
The is a terminal, so it is simply printed
<object> is a non-terminal, so it must be expanded
Choose one:
waves
big yellow flowers
slugs
Suppose that slugs is chosen

19. Generating a poem The slugs <verb> tonight.
<verb> is a non-terminal, so it must be expanded
Choose one:
sigh <adverb>
portend like <object>
The slugs sigh <adverb> tonight.
<adverb> is a non-terminal, so it must be expanded
warily
grumpily
Suppose that grumpily is chosen

20. A complete poem The slugs sigh grumpily tonight.
tonight. is a terminal so it is simply printed
There are no more non-terminals to expand!
The grammar has generated a complete poem
Question:
Why is this called a recursive sentence generator?