AGENTIC-SYSTEMSApril 30, 20261 min read6 views

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

DreamProver is an agentic framework that leverages a 'wake-sleep' paradigm to discover and evolve reusable lemma libraries, significantly improving the success rate and efficiency of formal theorem proving.

Computer Science > Artificial Intelligence

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

View PDF HTML (experimental)Abstract:We introduce DreamProver, an agentic framework that leverages a "wake-sleep" program induction paradigm to discover reusable lemmas for formal theorem proving. Existing approaches either rely on fixed lemma libraries, which limit adaptability, or synthesize highly specific intermediate lemmas tailored to individual theorems, thereby lacking generality. DreamProver addresses this gap through an iterative two-stage process. In the wake stage, DreamProver attempts to prove theorems from a training set using the current lemma library while proposing new candidate lemmas. In the "sleep" stage, it abstracts, refines, and consolidates these candidates to compress and optimize the library. Through this alternating cycle, DreamProver progressively evolves a compact set of high-level, transferable lemmas that can be effectively used to prove unseen theorems in related domains. Experimental results demonstrate that DreamProver substantially improves proof success rates across a diverse set of mathematical benchmarks, while also producing more concise proofs and reducing computational cost.

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Source: arXiv cs.AI Recent

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