Formal Grammars
A formal grammar of this type consists of:
- a finite set of production rules (left-hand side right-hand side) where each side consists of a sequence of these symbols
- a finite set of nonterminal symbols (indicating that some production rule can yet be applied)
- a finite set of terminal symbols (indicating that no production rule can be applied)
- a start symbol (a distinguished nonterminal symbol)
A formal grammar defines (or generates) a formal language, which is a (usually infinite) set of finite-length sequences of symbols (i.e. strings) that may be constructed by applying production rules to another sequence of symbols which initially contains just the start symbol. A rule may be applied to a sequence of symbols by replacing an occurrence of the symbols on the left-hand side of the rule with those that appear on the right-hand side. A sequence of rule applications is called a derivation. Such a grammar defines the formal language: all words consisting solely of terminal symbols which can be reached by a derivation from the start symbol.
Nonterminals are usually represented by uppercase letters, terminals by lowercase letters, and the start symbol by . For example, the grammar with terminals, nonterminals, production rules
- ε (where ε is the empty string)
and start symbol, defines the language of all words of the form (i.e. copies of followed by copies of ). The following is a simpler grammar that defines the same language: Terminals, Nonterminals, Start symbol, Production rules
- ε
Read more about this topic: Chomsky Hierarchy
Famous quotes containing the words formal and/or grammars:
“The spiritual kinship between Lincoln and Whitman was founded upon their Americanism, their essential Westernism. Whitman had grown up without much formal education; Lincoln had scarcely any education. One had become the notable poet of the day; one the orator of the Gettsyburg Address. It was inevitable that Whitman as a poet should turn with a feeling of kinship to Lincoln, and even without any association or contact feel that Lincoln was his.”
—Edgar Lee Masters (1869–1950)
“The violent illiteracies of the graffiti, the clenched silence of the adolescent, the nonsense cries from the stage-happening, are resolutely strategic. The insurgent and the freak-out have broken off discourse with a cultural system which they despise as a cruel, antiquated fraud. They will not bandy words with it. Accept, even momentarily, the conventions of literate linguistic exchange, and you are caught in the net of the old values, of the grammars that can condescend or enslave.”
—George Steiner (b. 1929)