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Metalanguages have their own metasyntax each composed of terminal symbols, nonterminal symbols, and metasymbols. 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 ...
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 ...
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
This production rule defines the nonterminal digit which is on the left side of the assignment. The vertical bar represents an alternative and the terminal symbols are enclosed with quotation marks followed by a semicolon as terminating character. Hence a digit is a 0 or a digit excluding zero that can be 1 or 2 or 3 and so forth until 9.
Nonterminal symbols are blue and terminal symbols are red. In formal language theory, a context-free grammar (CFG) is a formal grammar whose production rules can be applied to a nonterminal symbol regardless of its context. In particular, in a context-free grammar, each production rule is of the form
The right side may be the empty string, or a single terminal symbol, or a single terminal symbol followed by a nonterminal symbol, but nothing else. (Sometimes a broader definition is used: one can allow longer strings of terminals or single nonterminals without anything else, making languages easier to denote while still defining the same ...
Each semantic function deals with attributes of symbols occurring only in one production rule: both semantic function parameters and its result are attributes of symbols from one particular rule. When a semantic function defines the value of an attribute of the symbol on the left hand side of the rule, the attribute is called synthesized ...
Similar to a CFG, a probabilistic context-free grammar G can be defined by a quintuple: = (,,,,) where M is the set of non-terminal symbols; T is the set of terminal symbols; R is the set of production rules; S is the start symbol; P is the set of probabilities on production rules