This presentation includes all the details regarding the Backus Naur Form and the Extended Backus Naur Form.For more information visit : https://www.youtube.com/watch?v=hl2NLbIaU7U&t=255s

1. BNF EBNF

2. • What is BNF?
• Why need BNF?
• What does BNF look like?
• Examples of BNF
• Parse trees
• Examples of parse trees
• Origin of EBNF
• Examples

3. What is BNF?
• BNF = Backus-Naur Form
• It is a formal, mathematical way to specify context-free grammars
• BNF is Meta language (Meta language - a language that describes a
language, which can describe a programming language).
• It is precise and unambiguous

4. Why need BNF?
• Before BNF, people specified programming languages ambiguously,
i.e., with English
“He fed her cat food.”
Can have different meanings,
• He fed a woman’s cat some food.
• He fed a woman some food that was intended for cats.
• He somehow encouraged some cat food to eat something.

5. Peter NaurJohn Backus

6. What does BNF look like?
BNF grammar consists of 4 parts,
• The set of tokens
• The set of non terminal symbols
• The start symbol
• The set of productions
LHS = RHS
Non-terminals = Terminals/non-terminals

7. “or”
“is defined as”
Assign -> id := expr
id -> A|B|C
expr -> id+ expr | id * expr |(expr)|id
Terminal
Nonterminal
What does BNF look like?

8. Example 1
A := B*(A+C)
Solution -->
Assign -> id := expr
A := expr
A := id*expr
A := B*(expr)
A := B*(id + expr)
A := B*(A + expr)
A := B*(A + id)
A := B*(A + C)

9. Example 2
A := (B * A) + C
Solution -->
Assign -> id := expr
A := (expr)
A := (id*expr)
A := (B*expr)
A := (B*(expr))
This cannot be derived.

10. Example 3
A:=A+B*C
Solution -->
Assign -> id := expr
A:=id+expr
A:=A+expr
A:=A+id*expr
A:=A+B*expr
A:=A+B*id
A:=A+B*C

11. Parse Trees
• A Parse tree is a hierarchical representation of a derivation.

12. • A grammar is ambiguous if it generates a sentential form that has two
or more distinct parse trees.

13. Example 1
A := B*(A+C)
<assign>
id := <expr>
A id * <expr>
B ( expr )
id + expr
A id
C

14. Example 3
A:=A+B*C
<assign>
Id := <expr>
A id + <expr>
A id * <expr>
B id
C

15. <assign>
Id := <expr>
A <expr> + <expr>
id <expr> * <expr>
A id id
B C

16. Origin of EBNF
• Stands for “Extended Backus-Naur Form”.
• Increase readability and write ability.

17. • Optional [ ]
<if_cond> if <logic> then <stmt>
• Repetition { }
<stmts> <stmt> { ; <stmt> } * 0 or more
+ 1 or more
eg:- digit { digit } digit can be 1 or more
• Group ( )
value + integer | - integer
value ( + | - )integer
+

18. Syntax Graphs
• <stmt> <var> = <expr>
var = expr
• <var> A | B | C
A
B
C
<var>
<stmt>

19. <stmt> <stmt> | ; <stmt>
<var> a | ab
<stmt>
;
a
b

20. Example 1
<expr> <term> + <term> | <term> - <term>
Example 2
<program> begin <stmt_list> end
<term> <term>
-
+
<expr>
begin end<stmt_list>

21. Example 3
<stmt> <var> = <expression>
<var> = <expression>
<stmt>