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Concept
Terminal and nonterminal symbols
Summary
In formal languages, terminal and nonterminal symbols are the lexical elements used in specifying the production rules constituting a formal grammar. Terminal symbols are the elementary symbols of the language defined as part of a formal grammar. Nonterminal symbols (or syntactic variables) are replaced by groups of terminal symbols according to the production rules.
The terminals and nonterminals of a particular grammar are in two completely separate sets.
Terminal symbols are symbols that may appear in the outputs of the production rules of a formal grammar and which cannot be changed using the rules of the grammar. Applying the rules recursively to a source string of symbols will usually terminate in a final output string consisting only of terminal symbols.
Consider a grammar defined by two rules. In this grammar, the symbol Б is a terminal symbol and Ψ is both a non-terminal symbol and the start symbol. The production rules for creating strings are as follows:
The symbol Ψ can become БΨ
The symbol Ψ can become Б
Here Б is a terminal symbol because no rule exists which would change it into something else. On the other hand, Ψ has two rules that can change it, thus it is nonterminal. A formal language defined or generated by a particular grammar is the set of strings that can be produced by the grammar and that consist only of terminal symbols. Diagram 1 illustrates a string that can be produced with this grammar.
Nonterminal symbols are those symbols that can be replaced. They may also be called simply syntactic variables. A formal grammar includes a start symbol, a designated member of the set of nonterminals from which all the strings in the language may be derived by successive applications of the production rules. In fact, the language defined by a grammar is precisely the set of terminal strings that can be so derived.
Context-free grammars are those grammars in which the left-hand side of each production rule consists of only a single nonterminal symbol. This restriction is non-trivial; not all languages can be generated by context-free grammars.
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