Formal language

In mathematics, computer science, and linguistics, a formal language is a set of strings of symbols that may be constrained by rules that are specific to it.

Set of symbols

The alphabet of a formal language is the set of symbols, letters, or tokens from which the strings of the language may be formed; frequently it is required to be finite.

Words

The strings formed from this alphabet are called words, and the words that belong to a particular formal language are sometimes called well-formed words or well-formed formulas.

Formal grammar

A formal language is often defined by means of a formal grammar such as a regular grammar or context-free grammar, also called its formation rule.

Syntax

The field of formal language theory studies primarily the purely syntactical aspects of such languages -- that is, their internal structural patterns.

Natural language

Formal language theory sprang out of linguistics, as a way of understanding the syntactic regularities of natural languages.

Computer science

In computer science, formal languages are used among others as the basis for defining the grammar of programming languages and formalized versions of subsets of natural languages in which the words of the language represent concepts that are associated with particular meanings or semantics.

Computational complexity theory

In computational complexity theory, decision problems are typically defined as formal languages, and complexity classes are defined as the sets of the formal languages that can be parsed by machines with limited computational power.

Logic and mathematics

In logic and the foundations of mathematics, formal languages are used to represent the syntax of axiomatic systems, and mathematical formalism is the philosophy that all of mathematics can be reduced to the syntactic manipulation of formal languages in this way.

Database schema

A database schema is a formal language which describes the structure of a database.

See also

• Alphabet (formal language)
• Associative array
• Combinatorics on words
• Computer science
• Constructed language
• Database schema
• Formal grammar
• Formal language theory
• Formal method
• Formal system
• Free variables and bound variables
• Grammar framework
• Mathematical logic
• Mathematical notation
• Mathematics
• String (computer science)

External links

• Formal language @ Wikipedia