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| A '''two-level grammar''' is a [[formal grammar]] that is used to generate another formal grammar [http://web.cs.wpi.edu/~jshutt/adapt/2level.html], such as one with an infinite rule set [http://www.metanotion.net/misc/thesis.pdf#search=%22van%20Wijngaarden%20grammar%20Algol68%20ACM%20Portal%22]. This is how a [[Van Wijngaarden grammar]] was used to specify Algol68 [http://burks.bton.ac.uk/burks/language/other/a68rr/rrtoc.htm]. A [[context free grammar]] that defines the rules for a second grammar can yield an effectively infinite set of rules for the derived grammar. This makes such two-level grammars more powerful than a single layer of context free grammar, because generative two-level grammars have actually been shown to be [[Turing complete]].<ref>Sintzoff, M. "Existence of van Wijngaarden syntax for every recursively enumerable set", Annales de la Société Scientifique de Bruxelles 2 (1967), 115-118.</ref>
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| ''Two-level grammar'' can also refer to a formal grammar for a two-level [[formal language]], which is a formal language specified at two levels, for example, the levels of words and sentences.{{Citation needed|date=February 2007}}
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| ==Example==
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| A well-known non-context-free language is
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| :<math>\{a^n b^n a^n | n \ge 1\}.</math>
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| A two-level grammar for this language is the metagrammar
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| :N ::= 1 | N1
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| :X ::= a | b
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| together with grammar schema
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| :Start ::= <math> \langle a^N \rangle\langle b^N \rangle\langle a^N \rangle </math>
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| :<math> \langle X^{N1} \rangle</math> ::= <math>\langle X^N \rangle X </math>
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| :<math> \langle X^1 \rangle</math> ::= X
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| ==See also==
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| *[[Affix grammar]]
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| *[[Attribute grammar]]
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| *[[Van Wijngaarden grammar]]
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| ==References==
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| <references/>
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| ==External links==
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| * Petersson, Kent (1990), "Syntax and Semantics of Programming Languages", Draft Lecture Notes, [http://www.cs.chalmers.se/~kentp/proglang.pdf PDF text].
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| {{DEFAULTSORT:Two-Level Grammar}}
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| [[Category:Formal languages]]
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| {{compu-lang-stub}}
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Also visit my webpage ... clash of Clans hack without survey