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 ?