7.Convert the following BNF to EBNF + | | → ** | → () | id
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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![### Converting BNF to EBNF
**Exercise:**
Convert the following BNF (Backus-Naur Form) to EBNF (Extended Backus-Naur Form).
**BNF Grammar:**
```
<expr> ::= <expr> + <term>
| <expr> - <term>
| <term>
<term> ::= <term> * <factor>
| <term> / <factor>
| <factor>
<factor> ::= <exp> ** <factor>
| <exp>
<exp> ::= (<expr>)
| id
```
**Explanation:**
This BNF grammar consists of four non-terminal symbols `expr`, `term`, `factor`, and `exp`. Each of these non-terminals can be expanded to represent other non-terminals or terminals. The goal is to convert this representation from BNF to EBNF, which provides syntactic sugar to make the notation more concise.
**Conversion:**
Let's simplify the above rules using EBNF notation.
1. **Expression (`<expr>`)**
In BNF:
```
<expr> ::= <expr> + <term>
| <expr> - <term>
| <term>
```
In EBNF, we can use `{}` to denote repetition (zero or more times) and `[]` for optional elements:
```
<expr> ::= <term> { ("+" | "-") <term> }
```
2. **Term (`<term>`)**
In BNF:
```
<term> ::= <term> * <factor>
| <term> / <factor>
| <factor>
```
In EBNF:
```
<term> ::= <factor> { ("*" | "/") <factor> }
```
3. **Factor (`<factor>`)**
In BNF:
```
<factor> ::= <exp> ** <factor>
| <exp>
```
In EBNF:
```
<factor> ::= <exp> [ "**" <factor> ]
```
4. **Expression Operand (`<exp>`)**
In BNF:
```
<exp> ::= (<expr>)
| id
```
In EBNF:
```
<exp>](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad1b3f56-a3c9-4d59-9a30-165fb680e6c9%2Fd268a29a-ecef-4009-acfb-08a4d79915aa%2Fj6iexcc_processed.png&w=3840&q=75)
Transcribed Image Text:### Converting BNF to EBNF
**Exercise:**
Convert the following BNF (Backus-Naur Form) to EBNF (Extended Backus-Naur Form).
**BNF Grammar:**
```
<expr> ::= <expr> + <term>
| <expr> - <term>
| <term>
<term> ::= <term> * <factor>
| <term> / <factor>
| <factor>
<factor> ::= <exp> ** <factor>
| <exp>
<exp> ::= (<expr>)
| id
```
**Explanation:**
This BNF grammar consists of four non-terminal symbols `expr`, `term`, `factor`, and `exp`. Each of these non-terminals can be expanded to represent other non-terminals or terminals. The goal is to convert this representation from BNF to EBNF, which provides syntactic sugar to make the notation more concise.
**Conversion:**
Let's simplify the above rules using EBNF notation.
1. **Expression (`<expr>`)**
In BNF:
```
<expr> ::= <expr> + <term>
| <expr> - <term>
| <term>
```
In EBNF, we can use `{}` to denote repetition (zero or more times) and `[]` for optional elements:
```
<expr> ::= <term> { ("+" | "-") <term> }
```
2. **Term (`<term>`)**
In BNF:
```
<term> ::= <term> * <factor>
| <term> / <factor>
| <factor>
```
In EBNF:
```
<term> ::= <factor> { ("*" | "/") <factor> }
```
3. **Factor (`<factor>`)**
In BNF:
```
<factor> ::= <exp> ** <factor>
| <exp>
```
In EBNF:
```
<factor> ::= <exp> [ "**" <factor> ]
```
4. **Expression Operand (`<exp>`)**
In BNF:
```
<exp> ::= (<expr>)
| id
```
In EBNF:
```
<exp>
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