We propose a method for mechanically translating iterative dataflow analysis (IDA) algorithms to algebraic program analysis (APA) algorithms capable of computing exactly the same set of dataflow facts. The method is useful because while most of the dataflow analysis algorithms used in practice are expressed as iterative procedures, APA provides an alternative and inherently-compositional approach to solving dataflow problems, thus making it well suited for certain applications (e.g., incremental analysis of a program that goes through frequent code changes, or amortizing the cost of answering a large number of dataflow queries for the same program). However, manually crafting an APA algorithm not only is labor intensive and error prone but also can lead to suboptimal performance. Our method overcomes the limitation by providing a mechanical translation that guarantees to be correct by construction. Our method handles a broad class of dataflow analysis problems — the only requirements are that (1) the set of dataflow facts is finite and (2) the dataflow functions distribute over the confluence operation (e.g., set union). They include classical dataflow problems whose IDA algorithms can be expressed using Gen/Kill sets, such as reaching definitions, live variables, and available expressions. They also include non Gen/Kill problems such as copy constant propagation, truly-live variables, and possibly-initialized variables. Our experimental evaluation shows that the translated APA algorithms are not only simpler and easier to understand, but also significantly faster than manually-designed APA algorithms, especially for incremental program analysis.

@article{paperbot3851,
  title = {Mechanically Translating Iterative Dataflow Analysis to Algebraic Program Analysis},
  author = {Chenyu Zhou and Jingbo Wang and Chao Wang},
  journal = {Proceedings of the ACM on Programming Languages},
  volume = {10},
  number = {OOPSLA1},
  year = {2026},
  doi = {10.1145/3798216}
}