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 Calculus, an example of a top-down grammar