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Does an official set of production rules (formal grammar) for English exist? Something along the lines of:

Sentence -> Clause EndPunctuation
Clause -> Subject Predicate
Subject -> NounPhrase
NounPhrase -> Determiner Noun
            | Adjective Noun
EndPunctuation -> EndPunctuation EndPunctuation
                | .
                | !
                | ?

If so, where can it be found?

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No. (I don't know what "official" would mean, here.) The closest thing I know to that is the book GPSG (see Generalized Phrase Structure Grammar), which however does not claim to give a comprehensive account of English, and would not give a practical parser. It would have to be supplemented with a lexicon. It is a context free phrase structure grammar for a part of English, though.

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