A Structure-preserving Clause Form Translation
Journal of Symbolic Computation
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
A machine program for theorem-proving
Communications of the ACM
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Automated Proof Construction in Type Theory Using Resolution
Journal of Automated Reasoning
Using Reflection to Build Efficient and Certified Decision Procedures
TACS '97 Proceedings of the Third International Symposium on Theoretical Aspects of Computer Software
Minimizing the Number of Clauses by Renaming
Proceedings of the 10th International Conference on Automated Deduction
On Generating Small Clause Normal Forms
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
Simplify: a theorem prover for program checking
Journal of the ACM (JACM)
Type-safe modular hash-consing
Proceedings of the 2006 workshop on ML
Automation for interactive proof: first prototype
Information and Computation - Special issue: Combining logical systems
Zenon: an extensible automated theorem prover producing checkable proofs
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
Deciding equality in the constructor theory
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
Proving equalities in a commutative ring done right in coq
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
Reflecting proofs in first-order logic with equality
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
A modular integration of SAT/SMT solvers to coq through proof witnesses
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
SAT Solving for Termination Proofs with Recursive Path Orders and Dependency Pairs
Journal of Automated Reasoning
A bisimulation between DPLL(T) and a proof-search strategy for the focused sequent calculus
Proceedings of the Eighth ACM SIGPLAN international workshop on Logical frameworks & meta-languages: theory & practice
Square root and division elimination in PVS
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
| Hi-index | 0.00 |
In an attempt to improve automation capabilities in the Coq proof assistant, we develop a tactic for the propositional fragment based on the DPLL procedure. Although formulas naturally arising in interactive proofs do not require a state-of-the-art SAT solver, the conversion to clausal form required by DPLL strongly damages the performance of the procedure. In this paper, we present a reflexive DPLL algorithm formalized in Coq which outperforms the existing tactics. It is tightly coupled with a lazy CNF conversion scheme which, unlike Tseitin-style approaches, does not disrupt the procedure. This conversion relies on a lazy mechanism which requires slight adaptations of the original DPLL. As far as we know, this is the first formal proof of this mechanism and its Coq implementation raises interesting challenges.