General Grammars:

. General Grammars:
A grammar is a set of rules which are used to construct a language (combine words to generate sentences).
Definition: A grammar is a quadruple (?, V, S, P), where:
1. ? is a finite nonempty set called the terminal alphabet. The elements of ? are called the terminals.
2. V is a finite nonempty set disjoint from ?. The elements of V are called the nonterminals or variables.
3. S ? V is a distinguished nonterminal called the start symbol.
4. P is a finite set of productions (or rules) of the form
???
where ? ? (?UV )*V (?UV )* and ? ? (?UV )*, i.e. ? is a string of terminals and nonterminals containing at least one nonterminal and ? is a string of terminals and nonterminals.

Derivation:
A derivation is a sequence of rewriting operations that starts with the string ? = S and then repeats the following until ? contains only terminals.
A left-most derivation(?(??lm )) is one in which the left-most non-terminal is always chosen as the next non-terminal to expand(Always replace the left-most variable by one of its rule-bodies).
A right-most derivation(?(??rm )) is one in which the right-most non-terminal is always chosen as the next non-terminal to expand(Always replace the rightmost variable by one of its rule-bodies).