Definition:Formal Grammar

Definition
Let $\LL$ be a formal language whose alphabet is $\AA$.

The formal grammar of $\LL$ comprises of rules of formation, which determine whether collations in $\AA$ belong to $\LL$ or not.

Roughly speaking, there are two types of formal grammar: top-down grammar and bottom-up grammar.

Also known as
The formal grammar may also be called syntax; however, a convenient viewpoint is to think of the formal grammar as explicating the syntax for the associated formal language.

Thus the formal grammar is a means to obtain a syntax for $\LL$, and multiple formal grammars may yield the same syntax.

Some sources call this merely a grammar, the term formal being taken for granted by the fact that a formal language is under discussion.