LeanSAT is a collection of utilities for SAT work. This includes:

  • Encoding utilities
  • Solver APIs
  • Printers and parsers for common file formats

This repository is an active research code base using the Research Codebase Manifesto, and the core library (in LeanSAT/) is not very stable yet.

We would love to hear from any projects using LeanSAT! Contact @JamesGallicchio by email or mastodon.

Getting it

Add the following to your project's lakefile:

require «lean-sat» from git
  "https://github.com/JamesGallicchio/LeanSAT" @ "main"

The main branch is currently on Lean v4.7.0, and Lean still has breaking changes every minor revision, so expect it to not compile on any other version of Lean.

As this project relies on mathlib, we recommend running lake exe cache get after modifying your lakefile. This downloads a precompiled version of mathlib.


In your files, import LeanSAT will import everything in the library.

Everything in the library is under the LeanSAT namespace, so we generally assume you also have open LeanSAT at the top of your files.

Important types:

  • PropFun: The mathematical model of a propositional formula. Two PropFuns are equal iff they have the same interpretation under all assignments.
  • EncCNF: The encoding monad. This monad allows you to build up a CNF via do-notation. See Examples/Encoding for example usage.
  • VEncCNF: Verified encoding. Similar to EncCNF, constrained to provably encode some predicate over assignments. This connects EncCNF to the PropFun math model.
  • Solver, Solver.ModelCount, Solver.ModelSample: Solver interfaces. These are each typeclasses. The idea is that you should have an instance of the Solver typeclass in scope when you go to solve a CNF formula. See Examples/Cadical.lean for how to declare a solver instance.


TODO(JG): describe available notation for PropFun, PropForm

Planned scope

  • Support (verified?) encoding to non-CNF formulas (KNF, d-DNNF, XOR-CNF, ...)
  • Add verified checkers for sat certificates
  • Add verified model counting
  • Add verified pre-processing


This project is licensed under the Apache 2.0 license (see LICENSE). If you want to use the library but need it to be released under different terms, please contact us or open an issue.


PRs are welcome and appreciated. That said, because the repository is quite unstable, please open an issue or comment on an existing one to let us know what you are working on!


@vtec234 @ccodel @JamesGallicchio