A presentation, in english, about the importance of grammars and syntax in the definition of a language. I used it to present a "class sample" for a job as teacher for K12 teachers (normal superior).

2. A grammar is a formula
to build phrases
in a given language

3. The nature of the
language is
not important

4. Languages
Programming
Languages
UML
Mind Maps
Graphical
Languages
Symbolic
Languages
Boolean
Logic
Python
Natural
LanguagesEnglish
Conceptual Maps
Java
Spanish
Math

5. There are two basic forms
to describe (document)
a grammar

6. Graphically → Syntax Diagrams

8. bubbles
describes
lexems

9. bubbles
describes
lexems
boxes
describes
syntagms

10. bubbles
describes
lexems
boxes
describes
syntagms
arrows
describes
correct paths

11. a Compulsory (1 time)

12. a
a
Compulsory (1 time)
Optional (0 or 1 times)

13. a
b
a
a
Compulsory (1 time)
Optional (0 or 1 times)
Selection (“a” or “b”)

14. a
b
a
a
a
Compulsory (1 time)
Optional (0 or 1 times)
Selection (“a” or “b”)
Repetition (1 or more times)

15. 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)

16. Textually → EBNF Notation

18. syntagm

19. syntagm lexem

20. syntagm lexem
is defined as

21. 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 }*

22. 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> )

23. ~ A ^ B v A ^ ~ B

24. ~ A ^ B v A ^ ~ B
we run the
expression from
left to right

25. ~ A ^ B v A ^ ~ B
negation
first

26. ~
~ A ^ B v A ^ ~ B

27. ~
A ^ B v A ^ ~ B

28. ~
A ^ B v A ^ ~ B
then
the other
negation

29. ~
A ^ B v A ^ ~ B
~

30. ~
A ^ B v A ^ B
~

31. ~
A ^ B v A ^ B
~
then
the AND
conjuntion

32. ~
^
A ^ B v A ^ B
~

33. ~
^
A B v A ^ B
~

34. ~
^
A B v A ^ B
~
and the other
AND
conjunción

35. ~
^
A B v A ^ B
~
^

36. ~
^
A B v A B
~
^

37. ~
^
A B v A B
~
^
The OR
disyuntion
at the last

38. ~
^
A B v A B
~
^
v

39. ~
^
A B A B
~
^
v

40. ~
^
A B A B
~
^
v finished
tree!

41. ~
^
A B A B
~
^
v

42. 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.