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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 ${\mathcal {L}}$ 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]

Examples

Some examples of formal languages include:

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
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:

Strings produced by some formal grammar (see Chomsky hierarchy)
Strings described or matched by a regular expression
Strings accepted by some automaton, such as a Turing machine or finite state automaton
Strings indicated by a decision procedure (a set of related yes/no questions) where the answer is 'yes'

Related pages

Language for languages in general
Syntax for the form of a language in general
Semantics for the meanings in a language
Natural language for languages that are not formal
Computer language for application of formal languages in computing
Programming language for the application of formal languages to program computers

References

↑ "Comprehensive List of Logic Symbols". Math Vault. 2020-04-06. Retrieved 2020-10-09.
↑ "Definition of formal language | Dictionary.com". www.dictionary.com. Retrieved 2020-10-09.
↑ "1.11. Formal and Natural Languages — How to Think like a Computer Scientist: Interactive Edition". runestone.academy. Retrieved 2020-10-09.

Other websites

http://icalp06.dsi.unive.it/ ICALP 2006 33rd International Colloquium on Automata, Languages and Programming.
http://www.cs.auckland.ac.nz/CDMTCS/conferences/dlt/DLTConfSeries.html International Conferences on Developments in Language Theory

[1] "Comprehensive List of Logic Symbols". Math Vault. 2020-04-06. Retrieved 2020-10-09.

[2] "Definition of formal language | Dictionary.com". www.dictionary.com. Retrieved 2020-10-09.

[3] "1.11. Formal and Natural Languages — How to Think like a Computer Scientist: Interactive Edition". runestone.academy. Retrieved 2020-10-09.

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-In mathematics, a '''formal language''' is one that has a particular set of symbols that are made according to a particular kind of rule.
+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 <math>\mathcal{L}</math> is often used as a [[variable]] for formal languages in [[logic]].<ref>{{Cite web|date=2020-04-06|title=Comprehensive List of Logic Symbols|url=https://mathvault.ca/hub/higher-math/math-symbols/logic-symbols/|access-date=2020-10-09|website=Math Vault|language=en-US}}</ref>
+Unlike [[Natural language|natural languages]], the symbols and formulas in formal languages are syntactically and semantically related to one another in a precise way.<ref>{{Cite web|title=Definition of formal language {{!}} Dictionary.com|url=https://www.dictionary.com/browse/formal-language|access-date=2020-10-09|website=www.dictionary.com|language=en}}</ref> As a result, formal languages are completely (or almost completely) void of [[ambiguity]].<ref>{{Cite web|title=1.11. Formal and Natural Languages — How to Think like a Computer Scientist: Interactive Edition|url=https://runestone.academy/runestone/books/published/thinkcspy/GeneralIntro/FormalandNaturalLanguages.html|access-date=2020-10-09|website=runestone.academy}}</ref>
 == Examples ==
-Some examples of formal languages:
+Some examples of formal languages include:
-* the set of all words over <math>{a, b}\,</math>
+* The set of all words over <math>{a, b}\,</math>
-* the set <math>\left \{ a^{n}\right\}</math>, where <math>n\,</math> is a [[natural number]] and <math>a^n\,</math> means <math>a\,</math> repeated <math>n\,</math> times
+* The set <math>\left \{ a^{n}\right\}</math>, where <math>n\,</math> is a [[natural number]] and <math>a^n\,</math> means <math>a\,</math> repeated <math>n</math> times
-* finite languages, such as <math>\{\{a,b\},\{a, aa, bba\}\}\,</math>
+* Finite languages, such as <math>\{\{a,b\},\{a, aa, bba\}\}\,</math>
-* the set of syntactically correct programs in a given programming language; or
+* The set of syntactically correct programs in a given programming language
-* the set of inputs upon which a certain [[Turing machine]] halts.
+* 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:
-* Strings produced by some [[formal grammar]] (see [[Chomsky hierarchy]]);
+* Strings produced by some [[formal grammar]] (see [[Chomsky hierarchy]])
-* Strings described or matched by a [[regular expression]];
+* Strings described or matched by a [[regular expression]]
-* Strings accepted by some [[automaton]], such as a [[Turing machine]] or [[Finite state machine|finite state automaton]];
+* Strings accepted by some [[automaton]], such as a [[Turing machine]] or [[Finite state machine|finite state automaton]]
-* Strings indicated by a [[decision problem|decision procedure]] (a set of related YES/NO questions) where the answer is YES.
+* Strings indicated by a [[decision problem|decision procedure]] (a set of related yes/no questions) where the answer is 'yes'
 ==Related pages==
@@ Line 25: / Line 27: @@
 * [[Computer language]] for application of formal languages in computing
 * [[Programming language]] for the application of formal languages to program computers
+== References ==
+<references />
 == Further reading ==