\begin{definition}[Definition:Bottom-Up Form of Top-Down Grammar]
Let $\LL$ be a formal language.
Let $\LL$ be given by a top-down formal grammar $\TT$.
The '''bottom-up form of $\TT$''' is the formal grammar $\BB$ defined by declaring that:
:Each letter of $\LL$ is a $\BB$-WFF
and, for each rule of formation $\mathbf R$ of $\TT$ of the form:
:A metasymbol may be replaced by the collation $\phi$ with metasymbols $\phi_1, \ldots, \phi_n$
declaring that $\BB$ has the rule of formation $\mathbf R_\BB$:
:If $\phi_1, \ldots, \phi_n$ are $\BB$-WFFs, so is $\phi$.
\end{definition}