Download PDFOpen PDF in browserOracle Integration of Floating-Point Solvers with IsabelleEasyChair Preprint 864018 pages•Date: August 11, 2022AbstractSledgehammer, a component of the interactive proof assistant Isabelle, aims to increase proof automation by automatically discharging proof goals with the help of external provers. Among these provers are a group of satisfiability modulo theories (SMT) solvers with support for the SMT-LIB input language. Despite existing formalizations of IEEE floating-point arithmetic in both Isabelle/HOL and SMT-LIB, Sledgehammer employs an abstract translation of floating-point types and constants, depriving the SMT solvers of the opportunity to make use of their dedicated decision procedures for floating-point arithmetic. We show that, by extending the translation from the language of Isabelle/HOL into SMT-LIB with an interpretation of floating-point types and constants, floating-point reasoning in SMT solvers can be made available to Isabelle. Our main contribution is a description and implementation of such an extension. An evaluation of the extended translation shows a significant increase of Sledgehammer's success rate on proof goals involving floating-points. In particular, this enhancement enables Sledgehammer to prove more non-trivial goals -- thereby increasing proof automation for floating-point arithmetic in Isabelle. Keyphrases: SMT solvers, Sledgehammer, floating-points
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