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Towards Selfverification of HOL Light
 In International Joint Conference on Automated Reasoning
, 2006
"... Abstract. The HOL Light prover is based on a logical kernel consisting of about 400 lines of mostly functional OCaml, whose complete formal verification seems to be quite feasible. We would like to formally verify (i) that the abstract HOL logic is indeed correct, and (ii) that the OCaml code does c ..."
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Abstract. The HOL Light prover is based on a logical kernel consisting of about 400 lines of mostly functional OCaml, whose complete formal verification seems to be quite feasible. We would like to formally verify (i) that the abstract HOL logic is indeed correct, and (ii) that the OCaml code does correctly implement this logic. We have performed a full verification of an imperfect but quite detailed model of the basic HOL Light core, without definitional mechanisms, and this verification is entirely conducted with respect to a settheoretic semantics within HOL Light itself. We will duly explain why the obvious logical and pragmatic difficulties do not vitiate this approach, even though it looks impossible or useless at first sight. Extension to include definitional mechanisms seems straightforward enough, and the results so far allay most of our practical worries. 1 Introduction: quis custodiet ipsos custodes? Mathematical proofs are subjected to peer review before publication, but there
Formalized proof, computation, and the construction problem in algebraic geometry
, 2004
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Theoretical Computer Science Group
"... Hiermit versichere ich, die vorliegende Diplomarbeit ohne Hilfe Dritter und nur mit den angegebenen Quellen und Hilfsmitteln angefertigt zu haben. Alle Stellen, die aus den Quellen entnommen wurden, sind als solche kenntlich gemacht worden. Diese Arbeit hat in gleicher oder ähnlicher Form noch keine ..."
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Hiermit versichere ich, die vorliegende Diplomarbeit ohne Hilfe Dritter und nur mit den angegebenen Quellen und Hilfsmitteln angefertigt zu haben. Alle Stellen, die aus den Quellen entnommen wurden, sind als solche kenntlich gemacht worden. Diese Arbeit hat in gleicher oder ähnlicher Form noch keiner Prüfungsbehörde vorgelegen.
4 FORMALIZED PROOF, COMPUTATION, AND THE CONSTRUCTION PROBLEM IN ALGEBRAIC GEOMETRY
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Formal Correctness Proof for DPLL Procedure ∗
, 2008
"... Abstract. The DPLL procedure for the SAT problem is one of the fundamental algorithms in computer science, with many applications in a range of domains, including software and hardware verification. Most of the modern SAT solvers are based on this procedure, extending it with different heuristics. I ..."
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Abstract. The DPLL procedure for the SAT problem is one of the fundamental algorithms in computer science, with many applications in a range of domains, including software and hardware verification. Most of the modern SAT solvers are based on this procedure, extending it with different heuristics. In this paper we present a formal proof that the DPLL procedure is correct. As far as we know, this is the first such proof. The proof was formalized within the Isabelle/Isar proof assistant system. This proof adds to the growing body of formalized mathematical knowledge and it also provides a number of lemmas relevant for proving correctness of modern SAT and SMT solvers.