CAPRI is presented, a contract-aware repair workflow in which Isabelle checks the proof and an independent checker enforces a machine-readable edit contract, in which Isabelle checks the proof and an independent checker enforces a machine-readable edit contract.
Abstract
We address the use of large language models (LLMs) to help discover Isabelle proofs. An Isabelle build establishes that the submitted theory is accepted, but not that an LLM changed only what the developer authorised. We present CAPRI, a contract-aware repair workflow in which Isabelle checks the proof and an independent checker enforces a machine-readable edit contract. Prompts, proposals, candidate repositories, diagnostics, verdicts, and hashes are retained for audit. We evaluate five workflows on twelve failed proofs from four developments, with three replicates per task and condition, giving 180 runs and 138 valid repairs. Of 144 terminal candidates accepted by Isabelle, six had modified protected text; all arose in iterative workflows that could edit a complete theory. A proof-body-only interface produced 29/36 valid repairs and no contract violations, compared with 31/36 for the corresponding full-theory workflow. One-shot repair produced 22/36, while a later prospectively frozen iterative workflow produced 32/36; these figures compare complete workflows rather than individual mechanisms. A separate post hoc OpenRouter campaign found no improvement in the designated Luna comparisons. A Sol configuration with matched demonstrations produced 33/36 repairs, compared with 29/36 in the frozen OpenAI Responses condition, but the difference was not statistically significant in a one-sided exact McNemar test ($p=0.0625$).
Large language models can propose proofs for interactive theorem provers, but a successful build does not show the surrounding verification task was preserved. We study this problem in an Isabelle development of a sampled-data double-tank controller. The work began with nine theories and ten unfinished obligations, grew to a 16-theory build without sorry, oops, added axiomatisation, or oracle use, and accumulated 23 stable and 36 broken proof states. A retrospective audit found material changes in 16 of the 100 original declarations, including a weakened end-to-end assurance theorem that assumed three of the four requirements in its conclusion. We used CAPRI, a contract-aware proof-repair tool, to govern a reconstruction by combining Isabelle acceptance with an independent check of repository changes against machine-readable edit contracts. The reconstruction discharged all ten scoped obligations within the original nine-theory structure. A secondary replay by a co-author reproduced the R10 build, contract checks, control tests, and principal audit findings; independent replication remains future work. Operational end-to-end verification remains incomplete: we still need to connect operational executions to the reconstructed quantitative trace contract, a task requiring an extended contract.
Jim Woodcock, Gabriel Leite, Augusto Sampaio et al.· 0 citations
LLM-based Lean proving systems increasingly organize a proof as a blueprint: a dependency graph of formal statements. We introduce BlueprintRepair, a repair interface that lets a model change this graph through ten schema-checked local operations. An operation names the node it edits, so the target theorem cannot be changed. Lean checks every applied change, and an accepted repair must declare every blueprint lemma its proof uses. We also construct BlueprintTrace, a benchmark of 142 controlled failures with complete accepted and rejected repair trajectories. We compare typed edits, exact source patches, and complete module rewrites under matched source, feedback, model, and budget, one episode per state and interface. With DeepSeek-V4-Flash, the three interfaces solve almost the same number of the benchmark's localized failures. Typed repair is the cheapest per solved state (patching is 1.30x as expensive, rewriting 2.06x), and within 10,000 completion tokens per task it reaches almost all of its final coverage, while both free-form interfaces are well behind. A second model, Qwen3.6-Flash, solves fewer states but keeps typed repair cheapest, puts it ahead on the proof-authoring states, and repeats the localized pattern.
This work presents StructureClaw, an artifact-centered workbench in which LLM agents operate through governed engineering skills, typed tools, shared artifact state, and local analysis backends, together with StructureClaw-Bench, an executable benchmark of 150 controlled scenarios spanning standard workflows, interactive robustness, and multimodal structural-model reconstruction.
Sizhong Qin, Yi Gu, Yao Jiang et al.· arXiv.org· 0 citations
The case suggests that explicit failure records, fixtures, port-owned proofs, and validating imports can make agent-assisted systems more auditable and controlled ablations and external replications are needed to test whether such infrastructure causally improves development outcomes.
FLEX is presented, a foundational Constrained Horn Clause (CHC) solver implemented in LEAN, that reduces the trusted base to the kernel alone, and allows using LEAN's entire proof ecosystem to verify low-level systems code, via three contributions.
J. Khan, Petros Markopoulos, Nicolás Lehmann et al.· arXiv.org· 0 citations
SymCert is presented, a framework implemented in Lean for building verified SMT-based analyses of Cedar policies that provide a verified symbolic compiler and authorizer for reducing policies to SMT formulas, a hierarchy enforcer for ensuring well-formedness of counterexamples, and a counterex-ample extractor for proving analysis completeness.
Emina Torlak· 0 citations
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