Compositional Loop Invariant Inference for Multiphase Programs via Structured Neurosymbolic Reasoning

Mingxiu Wang, Jiawei Wang, Shuangxiang Kan, Angela Huo, Yuekang Li +2

Loop invariants are essential for deductive program verification, yet automatically inferring them for {multiphase programs}, whose loops contain conditional branches that induce multiple execution phases with distinct behaviors, remains an open problem. Existing LLM-based methods either reason about loops as a whole or use explicit branch information to generate atomic assertions jointly across branches, without maintaining complete candidate sub-invariants for independent generation and targeted repair. We present CLOVER, a structured neurosymbolic reasoning framework for multiphase invariant inference built on two interlinked mechanisms. First, compositional inference: CLOVER statically decomposes a loop into symbolic {loop branch sequences}, conjunctions of the loop guard and branch conditions that characterize distinct execution scenarios, and guides the LLM to generate candidate sub-invariants for each one independently, so that each LLM query focuses on a single execution scenario rather than the entire loop. Second, counterexample-guided localized refinement: when SMT verification rejects a composed disjunctive invariant, CLOVER traces the counterexample back through the…