claimcheck: Measuring and Improving Specification Faithfulness

Formal verification proves that a program satisfies its specification, but says nothing about whether the specification captures what the author meant. As LLMs increasingly write both code and specifications, a gap between the author's natural-language requirement and the specification becomes a live risk. A machine-checked proof of a property narrower than the one requested is worthless but passes every check. Closing this gap is solving the spec formalization problem: given a natural-language requirement, produce a formal artifact whose meaning matches it. To measure the gap, we curate an end-to-end benchmark for spec formalization spanning four formal languages: Dafny contracts and Lean 4, Isabelle and Rocq theorem statements. Each of its 3,234 rows pairs a natural-language requirement with a formal artifact and a label established by execution, by proof, or by the benchmark it is drawn from. A third of the rows are meaning-preserving rewrites of the artifact that keep the faithful label, so a judge cannot score by detecting that a row was edited. We introduce claimcheck, a tool that detects incorrect formalizations: the formal artifact is translated back into plain English by a model that never sees the requirement, and a separate model, the judge, decides whether the informalization and the requirement express the same guarantee. On all four languages it gains 8.2 to 9.8 points of macro recall over a single call shown the requirement and the artifact, and 4.2 to 6.0 over that call handed the same list of meaning-preserving rewrites. Showing the judge the artifact as well costs 1.4 to 4.5 points. Across four judges that also see the artifact, the gain shrinks as the judge gets stronger, to within a point of the informed single call for the strongest.