# Definition:Formal Grammar/Bottom-Up

## Definition

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

A bottom-up grammar for $\mathcal L$ is a formal grammar whose rules of formation allow the user to build well-formed formulas from primitive symbols, in the following way:

In certain use cases, the first clause is adjusted to allow for more complex situations, for example in the bottom-up specification of predicate logic

### Extremal Clause

The extremal clause of a bottom-up grammar is the final rule which excludes all collations other than those specified in the formation rules from being well-formed formulas.