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

@article{Vukmirovic2019ExtendingAB, title={Extending a brainiac prover to lambda-free higher-order logic}, author={Petar Vukmirovic and Jasmin Christian Blanchette and Simon Cruanes and Stephan Schulz}, journal={International Journal on Software Tools for Technology Transfer}, year={2019}, volume={24}, pages={67-87} }

Decades of work have gone into developing efficient proof calculi, data structures, algorithms, and heuristics for first-order automatic theorem proving. Higher-order provers lag behind in terms of efficiency. Instead of developing a new higher-order prover from the ground up, we propose to start with the state-of-the-art superposition prover E and gradually enrich it with higher-order features. We explain how to extend the prover’s data structures, algorithms, and heuristics to $$\lambda…

## 23 Citations

Superposition for Lambda-Free Higher-Order Logic

- Computer ScienceIJCAR
- 2018

Refutationally complete superposition calculi for intentional and extensional \(\lambda \)-free higher-order logic, two formalisms that allow partial application and applied variables, appear promising as a stepping stone towards complete, efficient automatic theorem provers for full higher- order logic.

Extending a High-Performance Prover to Higher-Order Logic

- Computer Science
- 2022

This work extends E to full higher-order logic, and finds the resulting prover is the strongest one on benchmarks coming from a proof assistant, and the second strongest on TPTP benchmarks.

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.

Restricted Combinatory Unification

- Computer ScienceCADE
- 2019

A restricted version of Dougherty's algorithm that is incomplete, terminating and does not require polymorphism is presented, including a novel use of a substitution tree as a filtering index for higher-order unification.

Formalizing the metatheory of logical calculi and automatic provers in Isabelle/HOL (invited talk)

- Computer ScienceCPP
- 2019

This paper describes and reflects on three verification subprojects to which I contributed: a first-order resolution prover, an imperative SAT solver, and generalized term orders for λ-free higher-order logic.

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.

New Techniques for Higher-Order Superposition

- Computer Science
- 2020

Techniques that address the need for new heuristics to curb the explosion of specific higher-order rules in the Zipperposition theorem prover are described.

Superposition with First-class Booleans and Inprocessing Clausification

- Computer ScienceCADE
- 2021

A complete superposition calculus for first-order logic with an interpreted Boolean type to lay the foundation for refutationally complete calculi in more expressive logics with Booleans, and to make superposition work efficiently on problems that would be obfuscated when using clausification as preprocessing.

Extending SMT solvers to Higher-Order Logic ( Technical Report )

- Computer Science
- 2019

This work proposes a pragmatic extension of SMT solvers to natively support higher-order reasoning without compromising their performance on FOL problems, thus leveraging the extensive research and implementation efforts dedicated to efficient FOL solving.

Extending SMT Solvers to Higher-Order Logic

- Computer ScienceCADE
- 2019

This work proposes 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.

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