nonterminal

A nonterminal is a fundamental concept in the field of formal languages and automata theory, particularly in the context of context-free grammars and parsing. It refers to a symbol in a grammar that can be expanded into a sequence of terminals and/or nonterminals. Nonterminals are used to represent syntactic categories or constructs in a language, such as expressions, statements, or declarations.

In a context-free grammar, a nonterminal is defined by a set of production rules, which specify how the nonterminal can be rewritten. Each production rule consists of a nonterminal on the left-hand side and a sequence of terminals and/or nonterminals on the right-hand side. The process of applying production rules to a nonterminal is known as derivation or expansion.

Nonterminals play a crucial role in parsing, the process of analyzing a string of terminals to determine its syntactic structure according to a given grammar. Parsers use nonterminals to build a parse tree or syntax tree, which represents the hierarchical structure of the input string.

In summary, a nonterminal is a symbol in a grammar that can be expanded into a sequence of terminals and/or nonterminals, representing syntactic categories or constructs in a language. Nonterminals are defined by production rules and are essential for parsing and understanding the syntactic structure of a language.