A Theory of Arrays (ToA) Union Find

This article discusses enhancements to union find data structures, focusing on edge annotations that support destructive store/substitution. It reviews previous work on annotating roots with semilattices and edges with groups, then presents a non-group annotation approach using offset union finds. The author provides code examples in Python for an offset union find implementation and hints at interactions between edge and root annotations for program analyses. The content is technical and relevant to data structures, algorithms, and software engineering.