Final answer:
In compiler design, the lexeme of a variable name is obtained from a context-free grammar rule that defines an identifier, often with a production rule like 'identifier → letter (letter | digit)*', which is used by the lexical analyzer to recognize variable names.
Step-by-step explanation:
In the context of compiler design, a context-free grammar (CFG) rule that yields the lexeme of a variable name typically involves a production rule that defines an identifier. Identifiers in programming languages are names given to various programming entities such as variables, functions, and types. The production rule for an identifier in a CFG might look like:
identifier → letter (letter | digit)*
Here, the rule states that an identifier starts with a letter, followed by zero or more occurrences of either letters or digits. This CFG rule is used by the lexical analyzer component of a compiler to recognize and create tokens corresponding to variable names in the source code.