This document discusses Backus-Naur Form (BNF), which is a notation technique used to describe the syntax of computer languages. BNF uses terminal and non-terminal symbols with production rules of the form left-hand side ::= right-hand side to formally define a language's grammar. John Backus first proposed BNF to describe the syntax of ALGOL 58. Examples are given to write BNF grammars for University of Lucknow course codes and palindromes. The document also discusses ambiguity in grammars, where a grammar has more than one parse tree for a string.

1. Compiler Design
BNF
Ambiquity

2. BNF-Backus Naur Form
• Backus normal form (BNF) is a notation technique for context-free
grammars.
• It is often used to describe the syntax of languages used in
computing.
• Such as computer programming languages, document formats,
instruction sets and communication protocols.
• They are applied wherever exact descriptions of languages are
needed.
• John Backus, a programming language designer at IBM, proposed
a metalanguage of "metalinguistic formulas" to describe the
syntax of the new programming language IAL, known today
as ALGOL 58 (1959). His notation was first used in the ALGOL 60
report.
• It is used to formally define the grammar of a language.
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3. Contd…..
• It is a formal mathematical way to describe a language.
• It is used to describe the syntax of the programming languages.
• It is a way of defining syntax.
• It consists of…..
 a set of terminal symbols
 a set of non-terminal symbols
 a set of production rules of the form
 Left - Hand- Side ::= Right- Hand- Side
 where the LHS is a non-terminal symbol & the RHS is a sequence
of symbols (terminals or non-terminals).
 The meaning of the production rule is that the non-terminal on
the LHS may be replaced by the expression on the RHS.
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4. Example:-Write a BNF grammar for the language of
University of Lucknow course codes.
• Example sentences:
• CSI3125
• MAT2743
• PHY1200
• CHE6581
• CSI9999
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5. Solution:
• <coursecode> ::= <acadunit> <coursenumber>
• <acadunit> ::= <letter> <letter> <letter>
• <coursenumber> ::= <year> <semesters> <digit> <digit>
• <year> ::= <ugrad> | <grad>
• <ugrad> ::= 0 | 1 | 2 | 3 | 4
• <grad> ::= 5 | 6 | 7 | 9
• <semesters> ::= <onesemester> | <twosemesters>
• <onesemester> ::= <frenchone> | <englishone> | <bilingual>
• <frenchone> ::= 5 | 7
• <englishone> ::= 1 | 3
• <bilingual> ::= 9
• <twosemesters> ::= <frenchtwo> | <englishtwo>
• <frenchtwo> ::= 6 | 8
• <englishtwo> ::= 2 | 4
• <digit> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
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6. Write a BNF grammar for the language of palindromes
• Examples (spaces don't count!):
• aba
• pop
• pop a pop
• elu par cette crapule
• a man a plan a canal panama
• Solution:
 <palindrome> ::= a <palindrome> a | b <palindrome> b |
c <palindrome> c | d <palindrome> d |
e <palindrome> e | ...
|z <palindrome> z
<palindrome> ::= <letter>
<letter> ::= a | b | c | ... | y | z
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7. Ambiguity or Ambiguous
Grammar
• A grammar G is said to be ambiguous if it has more
than one parse tree (left or right derivation) for at
least one string.
• C, C++, and Java have a large number of –
operators and – precedence levels.
• Instead of using a large grammar, we can: –
Write a smaller ambiguous grammar, and –
Give separate precedence and associativity.
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8. Contd……
• An Ambiguous Expression Grammar G1
Expr → Expr Op Expr | ( Expr ) | Integer
Op → + | - | * | / | % | **
Ambiguous Parse of 5-4+3
Using Grammar G1
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Exp
3+
ExpOpExp
ExpOpExp
-
45

9. Contd……
• E → E + E
• E → E – E
• E → id
For the string id + id – id, the above grammar
generates two parse trees:
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10. THANKS