1. 4장 보조자료

2. BNF BNF uses following notations: (i) Non-terminals : < >
(ii) Rules X ::= Y
(1) X : Nonterminal.
(2) Y : a terminal, nonterminal, or concatenation of terminal
and nonterminals
(3) metasymbol : ::=, |
Example: <S>::= a < S > |a
Notation ε : Used to represent an empty string

3. EBNF(Extended BNF) Additional Metasymbols [ ] for optional structures
{ } for repetitive structures
( ) for grouping

4. Conversion from EBNF to BNF and Vice Versa
BNF to EBNF:
(i) Look for recursion in grammar:
A::= aA | a
A::= a{a}
(ii) Look for common string that can be factored out with grouping and options.
A ::=aB |a
A := a [B]

5. EBNF to BNF: (i) Option: [] (ii) Repetition: {} A::= a[B]C
A’::=aNC N::=B| ε
(ii) Repetition: {}
A ::=a{ B1B2... Bn}C
A’::=aNC N::=B1B2...BnN| ε

6. <expr> ::= <digits> <digits> ::= <digit> | <digit><digits>

7. <expr> ::= <digit>{<digit>}

8. <expr> ::= <digits>
<digits> ::= empty
| <digit><digits>

9. <expr> ::= {<digit>}

10. <id> ::= <letter> | <id><letter> | <id><digit>

11. <id> ::= <letter> {<letter> | <digit>}

12. Notes on use of EBNF
Use {…} only for left recursive rules with associativity: BNF : expr → expr + term | term
EBNF : expr → term {+ term }
For right recursive rules use [ ... ] instead: BNF : expr => term + expr | term
EBNF : expr => term [ + expr ]
=> left associativity

13. expr => { - } term … Do not start a rule with {…}: write
expr → term {+ term }, not expr → {term +} term
exception: left { x } is OK for simple token
expr => { - } term …
Square brackets can be used anywhere, however: expr → expr + term | term | - term
should be written as expr → [-] term {+ term }

14. EBNF Examples Repetition Optional BNF: expr → expr + term | term
EBNF: expr → term { + term }
Optional
BNF: if-stmt → if ( expr ) stmt | if ( expr ) stmt else stmt
EBNF: if-stmt → if ( expr ) stmt [ else stmt ]

15. expr => expr + term
=> expr + term + term
=> expr + term + term + term
=> term term + term

16. BNF: EBNF: <expr> -> <expr> + <term>
<term> -> <term> * <factor>
| <term> / <factor>
| <factor>
EBNF:
<expr> -> <term> {(+ | -) <term>}
<term> -> <factor> {(* | /) <factor>}

17. Syntax Diagram Examples
Repetition
EBNF: expr → term { + term }
Optional
EBNF: if-stmt → if ( expr ) stmt [ else stmt ]
expr
term +
if-stmt if (
expr )
stmt
else
stmt

18. 모호성 제거 방법 해법1: 우선순위(precedence) 부여 해법2: 결합순서(associativity) 부여
+보다 *가 우선적으로 결합되도록
E ::= E + E | E -E | T (G2)
T ::= T * T | ( E ) | N
문법(G2)는 * 5에 대해서 모호성 해결
해법2: 결합순서(associativity) 부여
E ::= E + T | E -T | T (G3)
T ::= T * F | F
F ::= ( E ) | N

19. <expr> -> <expr> <op> <expr> | const