Many natural program correctness properties can be stated in terms of symmetries, but existing formal methods have little support for reasoning about such properties. We consider how to formally verify a broad class of symmetry properties expressed in terms of group actions. To specify these properties, we design a syntax for group actions, supporting standard constructions and a natural notion of entailment. Then, we develop a Hoare-style logic for verifying symmetry properties of imperative programs, where group actions take the place of the typical pre- and post-condition assertions. Finally, we develop a prototype tool SymVerif, and use it to verify symmetry properties on a series of handcrafted benchmarks. Our tool uncovered an error in a model of a dynamical system described by McLachlan and Quispel [Acta Numerica 2002].

@article{paperbot2962,
  title = {A Hoare Logic for Symmetry Properties},
  author = {Vaibhav Mehta and Justin Hsu},
  journal = {Proceedings of the ACM on Programming Languages},
  volume = {9},
  number = {OOPSLA2},
  year = {2025},
  doi = {10.1145/3763080}
}