LeanAide translation: Natural language to Lean 4

Stream: lean4

[Siddhartha Gadgil]

We have been working on a tool for AI based translation from natural language to Lean 4 with a convenient interface.

• A quick demo of this in action: leanaide-translation.gif
  
• A brief video: https://youtu.be/_NMquXd0Qos
  

The code is at https://github.com/siddhartha-gadgil/LeanAide. The Lean code was written by @Anand Rao and myself, and is part of a collaboration with @Ayush Agrawal @Ashvni Narayanan and Navin Goyal.

Quickstart

Our translation is based on Codex, to use which you need an OpenAI key. We also use a server for sentence similarity. To get started please configure environment variables using the following bash commands or equivalent in your shell:

export LEANAIDE_IP="34.100.184.111:5000"
export OPENAI_API_KEY=<your-open-ai-key>

Build this repository with the following commands

lake build mathlib
lake build

After this open the folder in VS code (or equivalent) with Lean 4 and go to the file LeanCodePrompts/TranslateExample.lean. Place the cursor anywhere on one of the comments below and invoke the code action to translate by clicking on the lightbulbor using ctrl-.

You can add your own comments and try to translate using the same method. In general, you can import LeanCodePrompts.CodeActions in a lean file and use the code-action to translate. You should usually also include import Mathbin.All to include the (partly broken) binary port of mathlib.

In case translation fails please look at the troubleshooting section in the README or ping us here.

How this works

The translation is based on Codex with input-dependent prompting and post-processing. Our steps are:

• given a natural language statement to be translated we find similar doc-strings in mathlib and build a prompt roughly with these and the corresponding code, with the natural language statement to be translated appended in the guise of a doc-string.
• the prompt is sent to the Codex server, which returns a bunch of completions (we specify := as the termination token).
• these are then post-processed: we (attempt to) translate identifiers from Lean 3 to Lean 4, do some auto-correction, and filter out those that fail to elaborate.

More details are in a note at the 2nd Math AI workshop and in more detail (along with related work) in a preprint.

Limitations and road-map

We have a reasonable success rate with typical doc-strings with translations that are valid for the present state of the binary port of mathlib. We plan to work on many improvements, including

• translating to definitions as well as theorems,
• handling more complex mathematical idioms,
• more generally improving our success rate,
• using the info-panel to offer many choices to the user,
• using the translation of identifiers from mathlib3port and Lean's fuzzy finder in place of (or in addition to) our (hacky) translation and auto-correction.

We further plan to migrate to mathlib4 as the target once its coverage is adequate. So suggestions, feature requests, contributions are most welcome over the next few months as we hope this tool moves to practical usability.

Thanks

This work was only possible because of a lot of help we got here from the Lean community. We also got help from a few collaborators at Microsoft Research and Microsoft. Support to host the sentence similarity server comes from Google cloud research credits.