  In resolving instances of a computational problem, if multiple instances of
interest share a feature in common, it may be fruitful to compile this feature
into a format that allows for more efficient resolution, even if the
compilation is relatively expensive. In this article, we introduce a formal
framework for classifying problems according to their compilability. The basic
object in our framework is that of a parameterized problem, which here is a
language along with a parameterization---a map which provides, for each
instance, a so-called parameter on which compilation may be performed. Our
framework is positioned within the paradigm of parameterized complexity, and
our notions are relatable to established concepts in the theory of
parameterized complexity. Indeed, we view our framework as playing a unifying
role, integrating together parameterized complexity and compilability theory.
