Partially-static data structures are a well-known technique for improving binding times.
However, they are often defined in an ad-hoc manner, without a unifying framework to ensure full use of the equations associated with each operation.
We present a foundational view of partially-static data structures as free extensions of algebras for suitable equational theories, i.e. the coproduct of an algebra and a free algebra in the category of algebras and their homomorphisms.
By precalculating these free extensions, we construct a high-level library of partially static data representations for common algebraic structures.
We demonstrate our library with common use-cases from the literature: string and list manipulation, linear algebra, and numerical simplification.