Definition:Formal Grammar/Top-Down
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Definition
Let $\LL$ be a formal language whose alphabet is $\AA$.
A top-down grammar for $\LL$ 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 $\AA$.
- A metasymbol may be replaced by certain collations labeled with metasymbols and signs of $\AA$.
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