A formal language L over an alphabet Σ is a subset of Σ*, that is, a set of words over that alphabet.
In computer science and mathematics, which do not usually deal with natural languages, the adjective "formal" is often omitted as redundant.
While formal language theory usually concerns itself with formal languages that are described by some syntactical rules, the actual definition of the concept "formal language" is only as above: a (possibly infinite) set of finite-length strings, no more nor less. In practice, there are many languages that can be described by rules, such as regular languages or context-free languages. The notion of a formal grammar may be closer to the intuitive concept of a "language," one described by syntactic rules. By an abuse of the definition, a particular formal language is often thought of as being equipped with a formal grammar that describes it.
Read more about Formal Language: Examples, Language-specification Formalisms, Operations On Languages
Famous quotes containing the words formal and/or language:
“True variety is in that plenitude of real and unexpected elements, in the branch charged with blue flowers thrusting itself, against all expectations, from the springtime hedge which seems already too full, while the purely formal imitation of variety ... is but void and uniformity, that is, that which is most opposed to variety....”
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—Mark Twain [Samuel Langhorne Clemens] (1835–1910)