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Chapter 13: Problem 33

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

Short Answer

Expert verified
::= | ::= ['a'-'z' | 'A'-'Z' | '_'] ::= | | ::= '0'-'9' ::= '_'

Step by step solution

01

Define the Identifier

Identify the components that make up a valid identifier in C. An identifier starts with a letter (uppercase or lowercase) or an underscore (_), followed by a sequence of letters, underscores, or digits.
02

Create Non-terminal Symbols

Set up non-terminal symbols that will represent the different parts of the identifier.
03

Define Terminal Symbols

Create terminal symbols that cover the acceptable characters: letters (both uppercase and lowercase), digits, and the underscore.
04

Formulate the Production Rules

Write the production rules in Backus-Naur form. Use the non-terminal symbols defined earlier to show how an identifier is constructed.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Production Rules
Production rules in Backus-Naur Form (BNF) lay the groundwork for defining the syntax of programming languages. They demonstrate how complex structures can be built from simpler ones. In the context of C programming identifiers, these rules dictate the formation of valid variable names.
For C identifiers, production rules outline that an identifier begins with a letter or an underscore, followed by letters, underscores, or digits. This ensures all identifiers conform to the defined syntax.
C Programming Identifiers
In C programming, identifiers are names used to identify a variable, function, or any other user-defined item. These identifiers must follow specific rules:
  • They can only start with a letter (a-z, A-Z) or an underscore (_).
  • The subsequent characters can be letters, digits (0-9), or underscores.
  • Identifiers are case-sensitive which means 'Variable' and 'variable' would be considered different.
  • They cannot use reserved keywords like int, float, return, etc.
Understanding these rules is crucial for writing error-free code in C.
BNF Syntax
Backus-Naur Form (BNF) is a notation technique for context-free grammars. It is widely used to describe the syntax of computer languages. Each rule in BNF consists of a non-terminal symbol, the '::=', and an expression that describes a sequence of terminals and non-terminals.
For example, to define a C identifier in BNF syntax, we might write:

identifier ::= letter (letter | digit | _)*
letter ::= a | b | c | ... | z | A | B | ... | Z
digit ::= 0 | 1 | 2 | ... | 9

Here, 'identifier' is expanded into 'letter' followed by any combination of 'letter', 'digit', or '_'. This clearly lays out how identifiers should be structured.
Non-terminal Symbols
Non-terminal symbols are the building blocks of BNF production rules. They represent sets of strings in the language. Unlike terminal symbols, which correspond to actual symbols in the language, non-terminal symbols are abstract and are used to define the structure of the language.
In the case of defining C identifiers, non-terminal symbols might include:
  • 'identifier': Represents the entire valid identifier.
  • 'letter': Represents any alphabetical character.
  • 'digit': Represents any numerical digit.
These non-terminal symbols create a road map for constructing valid identifiers in the language.

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Most popular questions from this chapter

Let \(M=\left(S, I, f, s_{0}, F\right)\) be a deterministic finite-state automaton. Show that the language recognized by \(M, L(M),\) is infinite if and only if there is a word \(x\) recognized by \(M\) with \(l(x) \geq|S|\) .

Construct a Turing machine with tape symbols 0, 1, and B that, when given a bit string as input, replaces the first 0 with a 1 and does not change any of the other symbols on the tape.

Construct a finite-state machine for entering a security code into an automatic teller machine (ATM) that implements these rules: A user enters a string of four digits, one digit at a time. If the user enters the correct four digits of the password, the ATM displays a welcome screen. When the user enters an incorrect string of four digits, the ATM displays a screen that informs the user that an incorrect password was entered. If a user enters the incorrect password three times, the account is locked.

a) Construct a phrase-structure grammar that generates all signed decimal numbers, consisting of a sign, either \(+\) or \(-;\) a nonnegative integer; and a decimal fraction that is either the empty string or a decimal point followed by a positive integer, where initial zeros in an integer are allowed. b) Give the Backus-Naur form of this grammar. c) Construct a derivation tree for \(-31.4\) in this grammar.

Find a deterministic finite-state automaton that recognizes each of these sets. $$\begin{array}{ll}{\text { a) }\\{0\\}} & {\text { b) }\\{1,00\\}} \\ {\text { c) }\left\\{1^{n} | n=2,3,4, \ldots\right\\}}\end{array}$$
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