DreamProver: Evolving Transferable Lemma Libraries via a Wake-Sleep Theorem-Proving Agent

2026-04-29 · Source: Artificial Intelligence · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, quick

Summary

DreamProver is an agentic framework designed to discover and evolve reusable lemmas for formal theorem proving, addressing limitations of existing methods that use fixed or overly specific lemma libraries. It operates through an iterative "wake-sleep" program induction paradigm. In the "wake" stage, DreamProver attempts to prove theorems from a training set using its current lemma library and proposes new candidate lemmas. The subsequent "sleep" stage involves abstracting, refining, and consolidating these candidates to optimize and compress the library. This alternating cycle enables DreamProver to progressively develop a compact set of high-level, transferable lemmas. Experimental results indicate that DreamProver significantly improves proof success rates across various mathematical benchmarks, while also generating more concise proofs and lowering computational costs.

Key takeaway

For AI Scientists developing automated theorem provers, DreamProver's "wake-sleep" approach offers a robust method for generating more generalizable and efficient lemma libraries. You should consider integrating iterative lemma evolution into your proof systems to enhance adaptability and reduce computational overhead, moving beyond static or highly specialized lemma sets.

Key insights

DreamProver uses a wake-sleep paradigm to evolve transferable lemma libraries for formal theorem proving.

Principles

• Iterative refinement improves lemma generality
• Abstracting candidates optimizes lemma libraries

Method

DreamProver employs a two-stage "wake-sleep" cycle: proving theorems and proposing lemmas in the wake stage, then abstracting and consolidating candidates in the sleep stage to evolve a compact lemma library.

In practice

• Apply wake-sleep for program induction
• Consolidate intermediate steps for generality

Topics

• DreamProver
• Formal Theorem Proving
• Lemma Libraries
• Wake-Sleep Paradigm
• Program Induction

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Artificial Intelligence.