CLEVER: A Curated Benchmark for Formally Verified Code Generation

TL;DR

CLEVER is a curated benchmark of 161 verified code generation problems in Lean, designed to evaluate the ability of language models to produce correct, verifiable code without relying on test cases or leaked specifications.

Contribution

It introduces a high-quality, curated benchmark for verified code generation that avoids common pitfalls and provides post-hoc verification, setting a new standard for evaluating formal code synthesis.

Findings

State-of-the-art models struggle to fully verify generated code.

Benchmark reveals the difficulty of achieving complete formal verification.

Provides a challenging testbed for future research in verified program synthesis.

Abstract

We introduce ${\rm C{\small LEVER}}$, a high-quality, curated benchmark of 161 problems for end-to-end verified code generation in Lean. Each problem consists of (1) the task of generating a specification that matches a held-out ground-truth specification, and (2) the task of generating a Lean implementation that provably satisfies this specification. Unlike prior benchmarks, ${\rm C{\small LEVER}}$ avoids test-case supervision, LLM-generated annotations, and specifications that leak implementation logic or allow vacuous solutions. All outputs are verified post-hoc using Lean's type checker to ensure machine-checkable correctness. We use ${\rm C{\small LEVER}}$ to evaluate several few-shot and agentic approaches based on state-of-the-art language models. These methods all struggle to achieve full verification, establishing it as a challenging frontier benchmark for program synthesis and formal reasoning. Our benchmark can be found on GitHub(https://github.com/trishullab/clever) as well as HuggingFace(https://huggingface.co/datasets/amitayusht/clever). All our evaluation code is also available online(https://github.com/trishullab/clever-prover).