grammars and syntax

A grammar is a formulato build phrases

in a given language

The nature of the

language is

not important

Languages

ProgrammingLanguages

UML

Mind Maps

GraphicalLanguages

SymbolicLanguages

BooleanLogic

Python

NaturalLanguagesEnglish

Conceptual Maps

Java

Spanish

Math

There are two basic forms

to describe (document)

a grammar

Graphically → Syntax Diagrams

bubblesdescribes

lexems

bubblesdescribes

lexems

boxesdescribessyntagms

bubblesdescribes

lexems

boxesdescribessyntagms

arrowsdescribes

correct paths

a Compulsory (1 time)

a

a

Compulsory (1 time)

Optional (0 or 1 times)

a

b

a

a

Compulsory (1 time)

Optional (0 or 1 times)

Selection (“a” or “b”)

a

b

a

a

a

Compulsory (1 time)

Optional (0 or 1 times)

Selection (“a” or “b”)

Repetition (1 or more times)

a

b

a

a

a

a

Compulsory (1 time)

Optional (0 or 1 times)

Selection (“a” or “b”)

Repetition (1 or more times)

Repetition (0 or more times)

Textually → EBNF Notation

syntagm

syntagm lexem

syntagm lexem

is defined as

a

b

a

a

a

a

Compulsory (1 time)

Optional (0 or 1 times)

Selection (“a” or “b”)

Repetition (1 or more times)

Repetition (0 or more times)

[ a ]

a

[ a | b ]

{ a }+

{ a }*

for example...

<boolean_expr> ::= <boolean_term> | <boolean_expr> v <boolean_term>

<boolean_term> ::= <boolean_element> | <boolean_element> ^ <boolean_element>

<boolean_element> ::= true | false | variable |~ ( <boolean_expr> ) | ( <boolean_expr> )

~ A ^ B v A ^ ~ B

~ A ^ B v A ^ ~ B

we run theexpression from

left to right

~ A ^ B v A ^ ~ B

negationfirst

~

~ A ^ B v A ^ ~ B

~

A ^ B v A ^ ~ B

~

A ^ B v A ^ ~ B

then the othernegation

~

A ^ B v A ^ ~ B

~

~

A ^ B v A ^ B

~

~

A ^ B v A ^ B

~

thenthe ANDconjuntion

~

^

A ^ B v A ^ B

~

~

^

A B v A ^ B

~

~

^

A B v A ^ B

~

and the otherAND

conjunción

~

^

A B v A ^ B

~

^

~

^

A B v A B

~

^

~

^

A B v A B

~

^The OR

disyuntionat the last

~

^

A B v A B

~

^

v

~

^

A B A B

~

^

v

~

^

A B A B

~

^

v finishedtree!

~

^

A B A B

~

^

v

Homework

Define a simple grammar for the sentences in English. Then test it with this phrases:

My friend runs slowly.The cat ate a mouse.