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Grammar
Formally, a grammar is an ordered fourtuple G = (T,N,S,P), where
N and T are finite alphabets, S is a distinguished symbol
of N, and P is a finite non-empty set pairs (L,R)
such that L and R are in (N U T)* and G
is called a Context Free Grammar (CFG) if L is in N.
The symbols of N are called nonterminal symbols.
The symbols of T are called
terminal symbols. According to above definition
of a grammar G, the sets N and T are disjoint in every grammar. The
nonterminal symbol S is called the initial symbol, axiom or
root, and is used to start the derivations of the sentences of the language.
The ordered pairs in P are called rewriting rules or productions
and will be written in the form L ---> R where the symbol ---> (derives)
is, of course,
not in N U T. Productions are used to derive new sentences
from given ones by replacing a part equal to the
left-hand side of a rule by the right-hand side of the same rule.
In such a way, taking always S as the starting symbol, it is possible to derive
from S and just applying productions in P, a set (possibly infinite) of sentences
that is called the language generated by G, L(G).
See following grammar example: nLPD grammar