# Definition:Formal Grammar/Top-Down

## Definition

Let $\mathcal L$ be a formal language whose alphabet is $\mathcal A$.

A **top-down grammar** for $\mathcal L$ is a formal grammar which allows well-formed formulas to be built from a single metasymbol.

Such a grammar can be made explicit by declaring that:

- A metasymbol may be replaced by a letter of $\mathcal A$.

- A metasymbol may be replaced by certain collations labeled with metasymbols and signs of $\mathcal A$.

From the words thus generated, those not containing any metasymbols are the well-formed formulas.

## Also see

- BNF Specification of Propositional Logic, an example of a
**top-down grammar**