Language and Proofs for Higher-Order SMT (Work in Progress)

TL;DR

This paper introduces an extension to the SMT-LIB language and proof format to support higher-order logic, aiming to enhance the reasoning capabilities of SMT solvers beyond first-order logic.

Contribution

It presents a novel extension of SMT-LIB and proof formats to incorporate higher-order constructs, advancing SMT solver expressiveness.

Findings

Extended SMT-LIB language with higher-order features

Augmented veriT proof format for higher-order reasoning

Preliminary framework for higher-order SMT solving

Abstract

Satisfiability modulo theories (SMT) solvers have throughout the years been able to cope with increasingly expressive formulas, from ground logics to full first-order logic modulo theories. Nevertheless, higher-order logic within SMT is still little explored. One main goal of the Matryoshka project, which started in March 2017, is to extend the reasoning capabilities of SMT solvers and other automatic provers beyond first-order logic. In this preliminary report, we report on an extension of the SMT-LIB language, the standard input format of SMT solvers, to handle higher-order constructs. We also discuss how to augment the proof format of the SMT solver veriT to accommodate these new constructs and the solving techniques they require.