# Extending SMT Solvers to Higher-Order Logic

@inproceedings{Barbosa2019ExtendingSS, title={Extending SMT Solvers to Higher-Order Logic}, author={Haniel Barbosa and Andrew Reynolds and Daniel El Ouraoui and Cesare Tinelli and Clark W. Barrett}, booktitle={CADE}, year={2019} }

SMT solvers have throughout the years been able to cope with increasingly expressive formulas, from ground logics to full first-order logic (FOL). In contrast, the extension of SMT solvers to higher-order logic (HOL) is mostly unexplored. We propose a pragmatic extension for SMT solvers to support HOL reasoning natively without compromising performance on FOL reasoning, thus leveraging the extensive research and implementation efforts dedicated to efficient SMT solving. We show how to…

## 22 Citations

Extensional Higher-Order Paramodulation in Leo-III

- Computer ScienceJ. Autom. Reason.
- 2021

Leo-III is an automated theorem prover for extensional type theory with Henkin semantics and choice that supports reasoning in polymorphic first-order and higher-order logic, in all normal quantified modal logics, as well as in different deontic logics.

How to Safely Use Extensionality in Liquid Haskell

- Computer Science
- 2021

A new approach to equality in Liquid Haskell is developed: a propositional equality in a library the authors call PEq, which avoids the unsoundness while still proving useful equalities at higher types; its use in several case studies is demonstrated.

Functional Extensionality for Refinement Types

- Computer ScienceArXiv
- 2021

A new approach to equality in Liquid Haskell is developed: a propositional equality in a library the authors call PEq, which avoids the unsoundness while still proving useful equalities at higher types; its use in several case studies is demonstrated.

HoCHC: A Refutationally Complete and Semantically Invariant System of Higher-order Logic Modulo Theories

- Mathematics2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
- 2019

This work presents a simple resolution proof system for higher-order constrained Horn clauses (HoCHC) and proves its soundness and refutational completeness w.r.t. both standard and Henkin semantics.

Extending a brainiac prover to lambda-free higher-order logic

- Computer ScienceTACAS
- 2019

This work proposes to start with the state-of-the-art superposition prover E and gradually enrich it with higher-order features, explaining how to extend the prover’s data structures, algorithms, and heuristics to higher- order logic, a formalism that supports partial application and applied variables.

Making Higher-Order Superposition Work

- Computer ScienceCADE
- 2021

Techniques that address issues such as infinitely branching inference rules, new possibilities such as reasoning about formulas, and the need to curb the explosion of specific higher-order rules are described and extensively evaluated in the Zipperposition theorem prover.

Boolean Reasoning in a Higher-Order Superposition Prover

- Computer SciencePAAR+SC²@IJCAI
- 2020

We present a pragmatic approach to extending a Boolean-free higher-order superposition calculus to support Boolean reasoning. Our approach extends inference rules that have been used only in a…

Proceedings of the Second International Workshop on Automated Reasoning: Challenges, Applications, Directions, Exemplary Achievements

- Computer ScienceElectronic Proceedings in Theoretical Computer Science
- 2019

The contributions to automated reasoning made in the context of the project Matryoshka, funded for five years by the European Research Council, are presented, whose general aim is to bridge the gap between ATP and ITP by strengthening higher-order proof automation.

Superposition with Lambdas

- Computer ScienceCADE
- 2019

A superposition calculus for a clausal fragment of extensional polymorphic higher-order logic that includes anonymous functions but excludes Booleans is designed and implemented in the Zipperposition prover and evaluated on TPTP and Isabelle benchmarks.

Summing Up Smart Transitions

- Computer ScienceCAV
- 2021

A generalization of first-order logic which can express the unbounded sum of balances is presented and the decidablity of one of the extensions and the undecidability of a slightly richer one are proved.

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