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# Formal language

In mathematics, a formal language is one that has a particular set of symbols that are made according to a particular kind of rule.

## Examples

Some examples of formal languages:

• the set of all words over ${a, b}\,$
• the set $\left \{ a^{n}\right\}$, where $n\,$ is a natural number and $a^n\,$ means $a\,$ repeated $n\,$ times
• finite languages, such as $\{\{a,b\},\{a, aa, bba\}\}\,$
• the set of syntactically correct programs in a given programming language; or
• the set of inputs upon which a certain Turing machine halts.

## Specification

A formal language can be specified in a great variety of ways, such as:

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