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HFEPX · Eval paper review

ImProver: Agent-Based Automated Proof Optimization

Riyaz Ahuja, Jeremy Avigad, Prasad Tetali, Sean Welleck

Published

Oct 7, 2024

Citations

0

Trust level

Low

Usefulness score

0/100 (Low)

Extraction confidence

15% (Low)

Derived from extracted protocol signals and abstract evidence.

Rater population

Not reported

Signals refreshed

May 21, 2026

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Should you rely on this paper?

This paper is adjacent to HFEPX scope and is best used for background context, not as a primary protocol reference.

Use this as background context only. Do not make protocol decisions from this page alone.

Best use

Background context only

Use if you need

Background context only.

What to verify

Read the full paper before copying any benchmark, metric, or protocol choices.

Main weakness

This paper looks adjacent to evaluation work, but not like a strong protocol reference.

Human feedback signal
Not explicit
Not explicit in abstract metadata
Evaluation signal
Weak or implicit
Validate from full paper
Usefulness for eval research
0/100
Adjacent candidate

Treat as adjacent context, not a core eval-method reference.

If you are doing eval pipeline work, start here

Human Eval Papers LLM-as-Judge Papers Pairwise Preference Papers Tool-Use Evaluation Search

Abstract

Large language models (LLMs) have been used to generate formal proofs of mathematical theorems in proofs assistants such as Lean. However, we often want to optimize a formal proof with respect to various criteria, depending on its downstream use. For example, we may want a proof to adhere to a certain style, or to be readable, concise, or modularly structured. Having suitably optimized proofs is also important for learning tasks, especially since human-written proofs may not optimal for that purpose. To this end, we study a new problem of automated proof optimization: rewriting a proof so that it is correct and optimizes for an arbitrary criterion, such as length or readability. As a first method for automated proof optimization, we present ImProver, a large-language-model agent that rewrites proofs to optimize arbitrary user-defined metrics in Lean. We find that naively applying LLMs to proof optimization falls short, and we incorporate various improvements into ImProver, such as the use of symbolic Lean context in a novel Chain-of-States technique, as well as error-correction and retrieval. We test ImProver on rewriting real-world undergraduate, competition, and research-level mathematics theorems, finding that ImProver is capable of rewriting proofs so that they are substantially shorter, more modular, and more readable.

What we could verify

These are the protocol signals we could actually recover from the available paper metadata. Use them to decide whether this paper is worth deeper reading.

Human Feedback Types

missing

None explicit

No explicit feedback protocol extracted.

"Large language models (LLMs) have been used to generate formal proofs of mathematical theorems in proofs assistants such as Lean."

Evaluation Modes

missing

None explicit

Validate eval design from full paper text.

"Large language models (LLMs) have been used to generate formal proofs of mathematical theorems in proofs assistants such as Lean."

Quality Controls

missing

Not reported

No explicit QC controls found.

"Large language models (LLMs) have been used to generate formal proofs of mathematical theorems in proofs assistants such as Lean."

Benchmarks / Datasets

missing

Not extracted

No benchmark anchors detected.

"Large language models (LLMs) have been used to generate formal proofs of mathematical theorems in proofs assistants such as Lean."

Reported Metrics

missing

Not extracted

No metric anchors detected.

"Large language models (LLMs) have been used to generate formal proofs of mathematical theorems in proofs assistants such as Lean."

Benchmarks and datasets

No benchmark or dataset names were extracted from the available abstract.

Reported metrics

No metric terms were extracted from the available abstract.

Human feedback details
Uses human feedback
No
Feedback types
None
Rater population
Not reported
Expertise required
Math
Evaluation details
Evaluation modes
None
Agentic eval
None
Quality controls
Not reported
Evidence quality
Low
Use this page as
Background context only

Research brief

Metadata summary

Large language models (LLMs) have been used to generate formal proofs of mathematical theorems in proofs assistants such as Lean.

Based on abstract + metadata only. Check the source paper before making high-confidence protocol decisions.

Key takeaways

  • Large language models (LLMs) have been used to generate formal proofs of mathematical theorems in proofs assistants such as Lean.
  • However, we often want to optimize a formal proof with respect to various criteria, depending on its downstream use.
  • For example, we may want a proof to adhere to a certain style, or to be readable, concise, or modularly structured.

Researcher actions

  • Compare this paper against nearby papers in the same arXiv category before using it for protocol decisions.
  • Check the full text for explicit evaluation design choices (raters, protocol, and metrics).
  • Use related-paper links to find stronger protocol-specific references.

Caveats

  • Generated from abstract + metadata only; no PDF parsing.
  • Signals below are heuristic and may miss details reported outside the abstract.

Recommended queries

Contribution summary

  • Having suitably optimized proofs is also important for learning tasks, especially since human-written proofs may not optimal for that purpose.
  • As a first method for automated proof optimization, we present ImProver, a large-language-model agent that rewrites proofs to optimize arbitrary user-defined metrics in Lean.

Why it matters for eval

  • Having suitably optimized proofs is also important for learning tasks, especially since human-written proofs may not optimal for that purpose.
  • As a first method for automated proof optimization, we present ImProver, a large-language-model agent that rewrites proofs to optimize arbitrary user-defined metrics in Lean.

Researcher checklist

  • Human feedback protocol is explicit

    No explicit human feedback protocol detected.

  • Evaluation mode is explicit

    No clear evaluation mode extracted.

  • Quality control reporting appears

    No calibration/adjudication/IAA control explicitly detected.

  • Benchmark or dataset anchors are present

    No benchmark/dataset anchor extracted from abstract.

  • Metric reporting is present

    No metric terms extracted.