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
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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>
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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