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Let $\LL$ be a formal language whose alphabet is $\AA$.
A bottom-up grammar for $\LL$ is a formal grammar whose rules of formation allow the user to build well-formed formulas from primitive symbols, in the following way:
- Letters are well-formed formulas.
- A collection of specified collations of well-formed formulas, possibly labeled with additional signs, are also well-formed formulas.
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
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.