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SATurne

A purely functional verified SAT solver which produces proofs

SATurne is a simple purely functional SAT solver written and verified in Coq. It's a tiny solver absolutely not designed for performances nor scalability. It is, however, intended to be well-documented, easy to understand and extremely trustworthy.

SATurne is progressively integrated as the SAT solver behind the Modulus SMT solver.

Few words on SATurn design

At it's core, SATurne is a ridiculously simple solver very similar to the one described in this article.

Features

SATurne is not only a solver. It is also a collection of Coq theories formalizing the boolean logic and the associated proof systems (e.g. the resolution system).

SATurne is shipped with a proof checker to check proofs of unsatisfiability based on the resolution system. This checker is proven to be correct and can be extracted to a self contained OCaml module.

Since SATurne solve only formulas in clausal form, it also features a verified CNF converter.

Coq Sources

The sources are located in the src folder. A _CoqProject and a makefile are provided. Simply type make at the project root SATurne is ready to be loaded in your favorite Coq editor.

Structure/TODOs

src/
  Clauses.v     -> Theories of literals, clauses and set of clauses
  Cnf.v         -> conversion into cnf
  Proof.v       -> proof checker
  Evaluation.v  -> (old) models in boolean logic
  Sat.v         -> (old) facts about satisfiability
  Solver_aux.v  -> (old) useful facts used to prove the solver
  Solver.v      -> (old) verified solver