Higher-Order SMT Solving (Work in Progress)

Haniel Barbosa (1) , Andrew Reynolds (1) , Pascal Fontaine (2, 3) , Daniel El Ouraoui (3) , Cesare Tinelli (1)

1 University of Iowa [Iowa City]
2 MOSEL - Proof-oriented development of computer-based systems
3 VERIDIS - Modeling and Verification of Distributed Algorithms and Systems

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 (HOSMT) is still little explored. In this preliminary report we discuss how to extend SMT solvers to natively support higherorder reasoning without compromising their performances on FO problems. We present a pragmatic extension of the cvc4 solver in which we generalize existing data structures and algorithms to HOSMT, thus leveraging the extensive research and implementation efforts dedicated to efficient FO solving. Our evaluation shows that the initial implementation does not add significant overhead to FO problems and its performance is on par with the encoding-based approach for HOSMT. We also discuss an alternative extension being implemented in veriT, in which new data structures and algorithms are being developed from scratch to best support HOSMT, thus avoiding the inherent difficulties of generalizing in a graceful way existing infrastructure not indented to higher-order reasoning.

Domaines: Logique en informatique [cs.LO]

Haniel Barbosa, Andrew Reynolds, Pascal Fontaine, Daniel El Ouraoui, Cesare Tinelli. Higher-Order SMT Solving (Work in Progress). SMT 2018 - 16th International Workshop on Satisfiability Modulo Theories, Jul 2018, Oxford, United Kingdom. ⟨hal-03049044⟩