Researchers unlock hidden math power in AI proof systems
A team has fixed a long-standing gap in automated theorem proving by enabling specialized math solvers to handle floating-point arithmetic—the backbone of scientific computing. The upgrade significantly boosts success rates in formal verification, a critical tool for ensuring software reliability in safety-critical applications like aviation and autonomous systems.
Originaltitel: Hammering Floating-Point Arithmetic
<p>Sledgehammer, a component of the interactive proof assistant Isabelle/HOL, 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 Sledgehammer's 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/HOL. 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-point arithmetic.</p>