The CCR framework unifies refinement and separation logic to provide ownership-based modular reasoning and transitive incremental reasoning in open settings that involve unverified code. However, when reasoning about function invocations, the reasoning principles available to clients remain confined to pre- and postconditions, which struggle to capture effectful behaviors such as I/O actions or interactions with arbitrary unverified code. This limitation becomes particularly acute in hybrid verification , where a mixture of different verification techniques is applied and some code is never formally verified but instead tested or model-checked. To overcome this limitation, we introduce imaginary specifications —a novel notion that freely mixes executable code with ownership assertions—and reasoning principles for their use. Through key technical developments, we present CRIS (Contextual Refinement with Imaginary Specifications), a framework that generalizes CCR with support for imaginary specifications. We demonstrate CRIS’s expressiveness and reasoning power through examples involving hybrid verification with unverified code exhibiting arbitrary side effects such as I/O or divergence, with complete mechanization in Rocq.

@article{paperbot3724,
  title = {CRIS: The Power of Imagination in Hybrid Verification},
  author = {Yonghee Kim and Taeyoung Yoon and Sanghyun Yi and Jaehyung Lee and Soonwon Moon and Yeji Han and Seonho Lee and Taeyoung Rhee and Yujin Im and Donghyun Nam and Jieung Kim and Chung-Kil Hur},
  journal = {Proceedings of the ACM on Programming Languages},
  volume = {10},
  number = {PLDI},
  year = {2026},
  doi = {10.1145/3808317}
}