Formal language

Formal language is a set of strings of symbols that may be constrained by rules that are specific to it. These strings can be defined by a formal system such as a computational model. Formal languages are used in mathematics, computer science, and linguistics.

Definition

A formal language is a set of words, i.e. finite strings of letters, symbols, or tokens. The set of words is often defined by a set of rules – these rules can be specific to the language, or can be general rules of syntax and grammar from a higher-level language. The letters and symbols of a formal language are formed from a finite alphabet.

Usage

Formal languages are used in many areas of computer science and mathematics. They are used in the definition of programming languages, where they describe the syntax of the language. They are also used in automata theory and formal grammars, where they describe the behavior of automata and the structure of languages.

Formal systems

A formal system is a system used to derive one string from another, according to a set of rules. These rules can be used to manipulate strings in a formal language. Examples of formal systems include logic systems, proof systems, and computation models.

Formal grammar

A formal grammar is a set of production rules for strings in a formal language. The rules describe how to form strings from the language's alphabet that are valid according to the language's syntax. Formal grammars are used in computer science to parse and generate languages, and in linguistics to model natural languages.

See also

• Automata theory
• Formal system
• Formal grammar
• Programming language
• Computational model