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The field of formal language theory studies primarily the purely syntactic aspects of such languages—that is, their internal structural patterns. Formal language theory sprang out of linguistics, as a way of understanding the syntactic regularities of natural languages .
The Chomsky hierarchy in the fields of formal language theory, computer science, and linguistics, is a containment hierarchy of classes of formal grammars. A formal grammar describes how to form strings from a language's vocabulary (or alphabet) that are valid according to the language's syntax.
Methods of formal linguistics were introduced by semioticians such as Charles Sanders Peirce and Louis Hjelmslev.Building on the work of David Hilbert and Rudolf Carnap, Hjelmslev proposed the use of formal grammars to analyse, generate and explain language in his 1943 book Prolegomena to a Theory of Language.
Rudolph Carnap defined the meaning of the adjective formal in 1934 as follows: "A theory, a rule, a definition, or the like is to be called formal when no reference is made in it either to the meaning of the symbols (for example, the words) or to the sense of the expressions (e.g. the sentences), but simply and solely to the kinds and order of the symbols from which the expressions are ...
Formal language theory, the discipline that studies formal grammars and languages, is a branch of applied mathematics. Its applications are found in theoretical computer science , theoretical linguistics , formal semantics , mathematical logic , and other areas.
This has led to a nomenclature where the term regular expression has different meanings in formal language theory and pattern matching. For this reason, some people have taken to using the term regex, regexp, or simply pattern to describe the latter. Larry Wall, author of the Perl programming language, writes in an essay about the design of Raku:
In formal language theory, a context-free grammar, G, is said to be in Chomsky normal form (first described by Noam Chomsky) [1] if all of its production rules are of the form: [2] [3] A → BC, or A → a, or S → ε,
Conjunctive grammars are a class of formal grammars studied in formal language theory. They extend the basic type of grammars, the context-free grammars , with a conjunction operation. Besides explicit conjunction, conjunctive grammars allow implicit disjunction represented by multiple rules for a single nonterminal symbol, which is the only ...
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