Berger, Ulrich and Lawrence, Andrew and Forsberg, Fredrik Nordvall and Seisenberger, Monika - Extracting verified decision procedures: DPLL and Resolution

lmcs:766 - Logical Methods in Computer Science, March 10, 2015, Volume 11, Issue 1
Extracting verified decision procedures: DPLL and Resolution

Authors: Berger, Ulrich and Lawrence, Andrew and Forsberg, Fredrik Nordvall and Seisenberger, Monika

This article is concerned with the application of the program extraction technique to a new class of problems: the synthesis of decision procedures for the classical satisfiability problem that are correct by construction. To this end, we formalize a completeness proof for the DPLL proof system and extract a SAT solver from it. When applied to a propositional formula in conjunctive normal form the program produces either a satisfying assignment or a DPLL derivation showing its unsatisfiability. We use non-computational quantifiers to remove redundant computational content from the extracted program and translate it into Haskell to improve performance. We also prove the equivalence between the resolution proof system and the DPLL proof system with a bound on the size of the resulting resolution proof. This demonstrates that it is possible to capture quantitative information about the extracted program on the proof level. The formalization is carried out in the interactive proof assistant Minlog.


Source : oai:arXiv.org:1502.02131
DOI : 10.2168/LMCS-11(1:6)2015
Volume: Volume 11, Issue 1
Published on: March 10, 2015
Submitted on: November 11, 2013
Keywords: Computer Science - Logic in Computer Science


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