Principle of Definition by Structural Induction

Theorem
Let $\mathcal L$ be a formal language.

Let the formal grammar of $\mathcal L$ be a bottom-up grammar.

A definition (in the metalanguage of $\mathcal L$) for all well-formed formulas of $\mathcal L$ is uniquely specified by:


 * A definition for the letters of $\mathcal L$
 * For each rule of formation for $\mathcal L$, a definition of the resultant WFF in terms of the constituent WFFs' definitions.