LLMLean

LLMlean integrates LLMs and Lean for tactic suggestions, proof completion, and more.

Here's an example of using LLMLean on problems from Mathematics in Lean:

llmlean_example.mp4

You can use an LLM running on your laptop, or an LLM from the Open AI API or Together.ai API:

LLM in the cloud (default):

1. Get an OpenAI API key.

2. Modify ~/.config/llmlean/config.toml (or C:\Users\<Username>\AppData\Roaming\llmlean\config.toml on Windows), and enter the following:

api = "openai"
model = "gpt-4o"
apiKey = "<your-openai-api-key>"

(Alternatively, you may set the API key using the environment variable LLMLEAN_API_KEY or using set_option llmlean.apiKey "<your-api-key>".) Similarly, to set up an Anthropic LLM, use

api = "anthropic"
model = "claude-3-7-sonnet-20250219"
apiKey = "<your-anthropic-api-key>"

1. Add llmlean to lakefile:

require llmlean from git
  "https://github.com/cmu-l3/llmlean.git"

1. Import:

import LLMlean

Now use a tactic described below.

Option 2: LLM on your laptop:

1. Install ollama.

2. Pull a language model:

ollama pull wellecks/ntpctx-llama3-8b

3. Set 2 configuration variables in ~/.config/llmlean/config.toml:

api = "ollama"
model = "wellecks/ntpctx-llama3-8b" # model name from above

Then do steps (3) and (4) above. Now use a tactic described below.

Option 3: LLM in the cloud (together.ai):

1. Get a together.ai API key.

2. Set 2 configuration variables in ~/.config/llmlean/config.toml:

api = "together"
apiKey = "<your-together-api-key>"

Then do steps (3) and (4) above. Now use a tactic described below.

Tactics

llmstep tactic

Next-tactic suggestions via llmstep "{prefix}". Examples:

• llmstep ""

  

• llmstep "apply "

  

The suggestions are checked in Lean.

llmqed tactic

Complete the current proof via llmqed. Examples:

• 

The suggestions are checked in Lean.

For the best performance, especially for the llmqed tactic, we recommend using the Open AI API.

Demo in PFR

Here is an example of proving a lemma with llmqed (OpenAI GPT-4o):

And using llmqed to make part of an existing proof simpler:

Customization

Please see the following:

• Customization

Testing

Rebuild LLMLean with the config test=on:

lake -R -Ktest=on update
lake build

Then manually check llmlean on the files under LLMleanTest.