Program synthesis and library learning generate useful operations, but the resulting artifacts are often treated merely as derivations or search traces rather than reusable operational objects. This paper introduces FormCraft, a framework that represents both primitive and composed operations as first-class capabilities in a uniform well-formed space $\mathfrak{F}$, separating instance-independent formation and public callability from optional persistence through a verification gate. By retaining formation provenance while exposing composites through the same public interface as primitives, the framework aims to make persistent library growth possible and to eliminate the need to reconstruct historical derivation chains at reuse time, a claim backed by a paired experiment showing orders-of-magnitude reductions in search work.

Symbolic regression search spaces suffer from structural redundancy: expression DAGs with $k$ internal nodes admit $\Theta(k!)$ distinct node-numberings that encode the same mathematical expression. This paper proposes IsalSR, a representation framework that computes a pruned canonical string—a complete labeled-DAG isomorphism invariant—to collapse all equivalent forms into a single canonical representation. The approach promises to reduce effective search space size by $O(k!)$ and can be integrated into any existing SR algorithm as a preprocessing step.