A Reflexive Formalization of a SAT Solver in Coq

We present a Coq formalization of an algorithm deciding the satisfiability of propositional formulas (SAT). This SAT solver is described as a set of inference rules in a manner that is independent of the actual representation of propositional variables and formulas. We prove soundness and completeness for this system, and instantiate our solver directly on the propositional fragment of Coq’s logic in order to obtain a fully reflexive tactic. Such a tactic represents a first and important step towards our ultimate goal of embedding an automated theorem prover inside the Coq system. We also extract a certified Ocaml implementation of the algorithm.

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