Program termination is a classic non-safety property whose falsification cannot in general be witnessed by a finite trace. This makes testing for non-termination challenging, and also a natural target for symbolic proof. Several works in the literature apply non-termination proving to small, self-contained benchmarks, but it has not been developed for large, real-world projects; as such, despite its allure, non-termination proving has had limited practical impact. We develop a compositional theory for non-termination proving, paving the way for its scalable application to large codebases. Discovering non-termination is an under-approximate problem, and we present UNT er , a sound and complete under-approximate logic for proving non-termination. We then extend UNT er with separation logic and develop UNTer SL for heap-manipulating programs, yielding a compositional proof method amenable to automation via under-approximation and bi-abduction. We extend the Pulse analyser from Meta and develop Pulse ∞ , an automated, compositional prover for non-termination based onx UNTer SL . We have run Pulse ∞ on large codebases and libraries, each comprising hundreds of thousands of lines of code, including OpenSSL, libxml2, libxpm and CryptoPP; we discovered several previously-unknown non-termination bugs and have reported them to developers of these libraries.

@article{RaadVO24,
  title = {Non-termination Proving at Scale},
  author = {Azalea Raad and Julien Vanegue and Peter O’Hearn},
  journal = {Proceedings of the ACM on Programming Languages},
  volume = {8},
  number = {OOPSLA2},
  year = {2024},
  doi = {10.1145/3689720}
}