Formal language

set of strings of symbols that may be constrained by rules that are specific to it; words whose letters are taken from an alphabet and are well-formed according to a specific set of rules

In mathematics, computer science and linguistics, a formal language is one that has a particular set of symbols, and whose expressions are made according to a particular set of rules. The symbol is often used as a variable for formal languages in logic.[1]

Unlike natural languages, the symbols and formulas in formal languages are syntactically and semantically related to one another in a precise way.[2] As a result, formal languages are completely (or almost completely) void of ambiguity.[3]



Some examples of formal languages include:

  • The set of all words over  
  • The set  , where   is a natural number and   means   repeated   times
  • Finite languages, such as  
  • The set of syntactically correct programs in a given programming language
  • The set of inputs upon which a certain Turing machine halts



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



  1. "Comprehensive List of Logic Symbols". Math Vault. 2020-04-06. Retrieved 2020-10-09.
  2. "Definition of formal language |". Retrieved 2020-10-09.
  3. "1.11. Formal and Natural Languages — How to Think like a Computer Scientist: Interactive Edition". Retrieved 2020-10-09.

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