Concept of Backus Normal Form

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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PROFESSOR JIT
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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