SOFTWARE & SYSTEMS

Lean 4 formal theorem proving

Lean 4 formal theorem proving is an OpenEnv-compatible reinforcement learning environment in our Software & Systems catalog. An agent acts through the tools below, and a deterministic verifier scores every episode, so the reward can be used for GRPO or other RLVR post-training.

Task and verification

Prove held-out mathlib theorems in their original module context. The target declaration is withheld; Lean elaboration, forbidden-token checks, and kernel axiom auditing determine correctness.

Tools and runtime

Lean 4 + mathlib v4.33.1 + C++ kernel axiom audit

OPENENV / LEAN

Related Software & Systems gyms

• Kernel / Triton GPU optimization
• SQL transformation & query optimization
• Database query plan performance tuning
• Compiler optimization pass verification
• Concurrency race & deadlock repair
• Production incident reproduction & RCA
• Mutation testing & test suite hardening
• Automated software migrations & refactoring
• Enterprise network verification (Batfish)
• Protocols & distributed safety (TLA+)
• Quantum-circuit compilation & routing
• Research mathematics & symbolic conjectures
• Desktop OS agentic computer use (QEMU)
• Cloud cost optimization under strict SLOs

See how these environments are run privately on the custom RL environments page, and how their rewards are made hard to game in our verifier design guide.

Plan a training run

Check the environment’s availability, compatible models and compute in Studio. A catalog entry does not guarantee that hosted training is enabled for your workspace.