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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.
A nonterminal symbol is called productive, or generating, if there is a derivation for some string of terminal symbols. X {\displaystyle X} is called reachable if there is a derivation S ⇒ ∗ α X β {\displaystyle S{\stackrel {*}{\Rightarrow }}\alpha X\beta } for some strings α , β {\displaystyle \alpha ,\beta } of nonterminal and ...
A context-sensitive grammar is a noncontracting grammar in which all rules are of the form αAβ → αγβ, where A is a nonterminal, and γ is a nonempty string of nonterminal and/or terminal symbols. However, some authors use the term context-sensitive grammar to refer to noncontracting grammars in general. [1]
where A, B, and C are nonterminal symbols, the letter a is a terminal symbol (a symbol that represents a constant value), S is the start symbol, and ε denotes the empty string. Also, neither B nor C may be the start symbol, and the third production rule can only appear if ε is in L(G), the language produced by the context-free grammar G.
A terminal symbol, such as a word or a token, is a stand-alone structure in a language being defined. A nonterminal symbol represents a syntactic category, which defines one or more valid phrasal or sentence structure consisted of an n-element subset. Metasymbols provide syntactic information for denotational purposes in a given metasyntax.
An unrestricted grammar is a formal grammar = (,,,), where . is a finite set of nonterminal symbols,; is a finite set of terminal symbols with and disjoint, [note 1]; is a finite set of production rules of the form , where and are strings of symbols in and is not the empty string, and
is the set of terminal symbols; is the set of productions; is the distinguished, or start, symbol; Then, given a string of nonterminal symbols and an attribute name , . is a synthesized attribute if all three of these conditions are met:
Given a natural number , a context-free grammar = (,,,) is an LL(k) grammar if . for each terminal symbol string of length up to symbols,; for each nonterminal symbol , and; for each terminal symbol string ,