Data processing frameworks like Apache Spark and Flink provide built-in support for user-defined aggregation functions (UDAFs), enabling the integration of domain-specific logic. However, for these frameworks to support efficient UDAF execution, the function needs to satisfy a homomorphism property, which ensures that partial results from independent computations can be merged correctly Motivated by this problem, this paper introduces a novel homomorphism calculus that can both verify and refute whether a UDAF is a dataframe homomorphism. If so, our calculus also enables the construction of a corresponding merge operator which can be used for incremental computation and parallel execution. We have implemented an algorithm based on our proposed calculus and evaluate it on real-world UDAFs, demonstrating that our approach significantly outperforms two leading synthesizers.

@article{paperbot2935,
  title = {Homomorphism Calculus for User-Defined Aggregations},
  author = {Ziteng Wang and Ruijie Fang and Linus Zheng and Dixin Tang and Işıl Dillig},
  journal = {Proceedings of the ACM on Programming Languages},
  volume = {9},
  number = {OOPSLA2},
  year = {2025},
  doi = {10.1145/3763072}
}