Question

Give production rules in Backus–Naur form that generate all identifiers in the C programming language. In ‘C’ an identifier starts with a letter or an underscore (_) that is followed by one or more lowercase letters, uppercase letters, underscores, and digits.

Several extensions to Backus–Naur form are commonly used to define phrase-structure grammars. In one such extension, a question mark (?) indicates that the symbol, or group of symbols inside parentheses, to its left can appear zero or once (that is, it is optional), an asterisk (*) indicates that the symbol to its left can appear zero or more times, and a plus (+) indicates that the symbol to its left can appear one or more times. These extensions are part of extended Backus–Naur form (EBNF), and the symbols?, *, and + are called metacharacters. In EBNF the brackets used to denote nonterminal are usually not shown.

Short answer

Backus-Naur form

<Identifier> ::==<letterorus><string>

<letterorus> ::==<lcletter>|<ucletter>|_

<String> ::==<symbol>|<symbole><string>

<Symbol> ::==<lcletter>|<ucletter>|_|<diigits>

<Digits>: ==0|1|23|4|5|6|7|8|9

<Lcletter> ::==a | b | c | d | e | f | g | h | i | j | k | l | m | n | o | p | q | r | s | t | u | v| w |x | y| z

<Ucletter>::==A | B | C | D | E | F | G | H | I | J | K| L | M| N| O |P | Q |R | S |T | U | V | W |X | Y | Z

Step-by-step solution

About Backus-Nour form

The Backus-Naur form could be a notation for specifying a kind 2 grammar.

Productions during a type 2 grammar have one non-terminal symbol on the left.

Rather of listing all the productions separately, we will merge all those with the identical non terminal symbol on the left-hand side into one statement rather than using the symbolàin a very production,

we use the symbol:: =

We enclose all non-terminal symbols in brackets <>, and that we list all right-hand sides of productions within the same statement, separating them by bars.

Find the result

Backus-Naur form

<Identifier> ::==<letterorus><string>

<letterorus> ::==<lcletter>|<ucletter>|_

<String> ::==<symbol>|<symbole><string>

<Symbol> ::==<lcletter>|<ucletter>|_|<diigits>

<Digits>: ==0 |1 | 2| 3 | 4| 5 | 6 | 7 | 8 |9

<Lcletter> ::==a | b | c | d | e | f | g | h | i | j | k | l | m | n | o | p | q | r | s | t | u | v| w |x | y| z

<Ucletter>::==A | B | C | D | E | F | G | H | I | J | K| L | M| N| O |P | Q |R | S |T | U | V | W |X | Y | Z

Therefore, this can be the require Back-Naur form.