Lean Copilot

In-editor Lean 4 neural theorem-proving framework combining LLM tactic generation, premise selection, and a best-first proof search tactic that uses the model confidence as score.

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The loop

  1. Proposes

    Native CTranslate2 models running inside Lean 4 propose tactics and retrieve premises for the active proof goal.

  2. Judged by

    The Lean 4 kernel checks each tactic application and returns updated subgoal states.

  3. Steers

    A best-first search tactic (`search_proof`) with the model confidence as score explores the proof tree until all goals close.

Headline result

Automates proof goals directly inside Lean 4 workflows with 3.8x faster tactic inference than Python RPC bridges.

What this does not prove

Designed for interactive lemma and subgoal automation rather than multi-hour distributed search.

How it generalizes the harness

A native Lean 4 best-first search engine invokes the neural tactic generator and verifies every node in the Lean kernel.

Classification

Classification of Lean Copilot
What it proposesProof tactic
Generative modelReProver / ByT5 tactic and premise models
Algorithmic authorityLean 4 kernel and best-first proof search
FeedbackProof state
What gets updatedSearch tree
When it runsAt inference time
ValidityFormal (machine-checked)
EvidenceCode released
LineageDerivative