Expressiveness + Automation + Soundness: Towards Combining SMT Solvers and Interactive Proof Assistants

Pascal Fontaine 1 Jean-Yves Marion 2 Stephan Merz 1 Leonor Prensa Nieto 1 Alwen Tiu 2
1 MOSEL - Proof-oriented development of computer-based systems
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
2 CALLIGRAMME - Linear logic, proof networks and categorial grammars
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : Formal system development needs expressive specification languages, but also calls for highly automated tools. These two goals are not easy to reconcile, especially if one also aims at high assurances for correctness. In this paper, we describe a combination of Isabelle/HOL with a proof-producing SMT (Satisfiability Modulo Theories) solver that contains a SAT engine and a decision procedure for quantifier-free first-order logic with equality. As a result, a user benefits from the expressiveness of Isabelle/HOL when modeling a system, but obtains much better automation for those fragments of the proofs that fall within the scope of the (automatic) SMT solver. Soundness is not compromised because all proofs are submitted to the trusted kernel of Isabelle for certification. This architecture is straightforward to extend for other interactive proof assistants and proof-producing reasoners.
Keywords : theorem proving decision procedures tool integration proof certification SMT solver
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Conference papers
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https://hal.inria.fr/inria-00001088
Contributor : Stephan Merz <>
Submitted on : Thursday, February 2, 2006 - 5:06:57 PM
Last modification on : Thursday, January 11, 2018 - 6:19:52 AM

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Pascal Fontaine, Jean-Yves Marion, Stephan Merz, Leonor Prensa Nieto, Alwen Tiu. Expressiveness + Automation + Soundness: Towards Combining SMT Solvers and Interactive Proof Assistants. 12th International Conference on Tools and Algorithms for the Construction and Analysis of Systems - TACAS'06, Mar 2006, Vienna/Austria, pp.167-181, ⟨10.1007/11691372_11⟩. ⟨inria-00001088⟩

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