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I am learning about context free grammars and have been through few texts in a undetailed manner on these topic . I think I should know the exact , rigorous ,technical definition of what exactly a "grammar" means .

I could see that ,in all of these lessons, a sequence of equations as follow :

 a = bc
 b = ed
 c = gh

I was tempted to conclude that "a grammar is a collection of symbols which are related by a set of equations which dictate rules for substitution of a symbol by a series of symbols "

Then I got to know that , not in all series of equations can we substitute one symbol by a series of another symbol .We can do it only in case of "context-free grammars " . Then I went through one of the stackexchange post and through a brilliant answer got to know what context free exactly means .

So , I thought before I proceed ahead I better seek for the exact rigorous definition of a grammar . What exactly is the mathematical/technical definition of a grammar ?

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    $\begingroup$ Any textbook covering formal languages provides a formal definition of a grammar, i.e., regular, context-free, context sensitive, etc. What is unclear with these definitions? Why do you think they are not "mathematical/technical "? $\endgroup$ – fade2black Nov 1 '17 at 20:35
  • $\begingroup$ @fade2black : Need to check my book again . Actually it's not a book on theory of formal languages but is basically headed towards compiler design . $\endgroup$ – Eddie Dorphy Nov 15 '17 at 19:27
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A grammar is a set of production rules for symbol sequences.

But you knew that already. If you edit the question to make it more specific, we can offer more specific answers.

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  • $\begingroup$ J.H : For the time being , that's it about grammar . Just wanted to be sure what I am concluding is correct . $\endgroup$ – Eddie Dorphy Nov 15 '17 at 19:25
  • $\begingroup$ I like this kind of answer; it is concise and clear. $\endgroup$ – David A. Gray Dec 2 '17 at 6:56

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