# Effective Normalization Techniques for HOL

@inproceedings{Wisniewski2016EffectiveNT, title={Effective Normalization Techniques for HOL}, author={Max Wisniewski and Alexander Steen and Kim Kern and Christoph Benzm{\"u}ller}, booktitle={IJCAR}, year={2016} }

Normalization procedures are an important component of most automated theorem provers. In this work we present an adaption of advanced first-order normalization techniques for higher-order theorem proving which have been bundled in a stand-alone tool. It can be used in conjunction with any higher-order theorem prover, even though the implemented techniques are primarily targeted on resolution-based provers. We evaluated the normalization procedure on selected problems of the TPTP using multiple…

## 10 Citations

A Clausal Normal Form Translation for FOOL

- Computer ScienceGCAI
- 2016

A new CNF translation algorithm for FOOL that is friendly and efficient for superposition-based first-order provers, implemented in the Vampire theorem prover and evaluated on a large number of problems coming from formalisation of mathematics and program analysis.

Extensional Paramodulation for Higher-Order Logic and Its Effective Implementation Leo-III

- Computer ScienceKI - Künstliche Intelligenz
- 2019

In this dissertation, both the theoretical and the practical challenges of designing an effective higher-order reasoning system are studied and the resulting system, the automated theorem prover Leo-III, is one of the most effective and versatile systems, in terms of supported logical formalisms, to date.

Automated Theorem Proving with Extensions of First-Order Logic

- Computer Science
- 2018

This thesis develops an extension of first-order logic named FOOL, which contains syntactical features of programming languages and more expressive logics, is friendly for translation of problems from various domains, and can be efficiently supported by existing theorem provers.

Towards Strong Higher-Order Automation for Fast Interactive Verification

- Computer ScienceARCADE@CADE
- 2017

The Matryoshka project aims to enrich superposition and SMT with higher-order reasoning in a careful manner, to preserve their good properties and bring a new level of automation to the users of proof assistants.

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…

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.

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.

A Transfinite Knuth-Bendix Order for Lambda-Free Higher-Order Terms

- MathematicsCADE
- 2017

The Knuth–Bendix order is generalized to higher-order terms without \(\lambda \)-abstraction and appears promising as the basis of a higher- order superposition calculus.

Agent-Based HOL Reasoning

- Computer ScienceICMS
- 2016

Key goals of the system’s development involve parallelism on various levels of the proof search, adaptability for different external specialists, and native support for reasoning in expressive non-classical logics.

The 8th IJCAR automated theorem proving system competition - CASC-J8

- Computer ScienceAI Commun.
- 2016

## References

SHOWING 1-10 OF 20 REFERENCES

A Generic Tableau Prover and its Integration with Isabelle

- Computer ScienceJ. Univers. Comput. Sci.
- 1999

A generic tableau prover that has been implemented and integrated with Isabelle (Paulson, 1994), which has numerous extensions that allow it to reason with any supplied set of tableau rules.

Automated Reasoning in Higher-Order Logic using the TPTP THF Infrastructure

- Computer ScienceJ. Formaliz. Reason.
- 2010

Key developments have been the specification of the THF language, the addition of higher-order problems to theTPTP, the development of the TPTP THF infrastructure, several ATP systems for higher- order logic, and the use of higher -order ATP in a range of domains.

Isabelle/HOL: A Proof Assistant for Higher-Order Logic

- Computer Science
- 2002

This presentation discusses Functional Programming in HOL, which aims to provide students with an understanding of the programming language through the lens of Haskell.

The TPTP Problem Library and Associated Infrastructure

- Computer ScienceJournal of Automated Reasoning
- 2009

This paper describes the First-Order Form (FOF) and Clause Normal Form (CNF) parts of the TPTP problem library, and the associated infrastructure. TPTP v3.5.0 was the last release containing only FOF…

Satallax: An Automatic Higher-Order Prover

- BusinessIJCAR
- 2012

Satallax is an automatic higher-order theorem prover that generates propositional clauses encoding (ground) tableau rules and uses MiniSat to test for unsatisfiability. We describe the…

SPASS & FLOTTER Version 0.42

- Computer ScienceCADE
- 1996

The algorithm implemented by FLOTTER includes an improved form of the renaming technique developed by Thierry Boy de la Tour], the optimized Skolemization technique by Ohlbach and Weidenbach 7] and some improvements leading to smallerSkolem function.

The Leo-III Project

- Mathematics
- 2014

LEO-II, a resolution based theorem prover for classical higher-order logic, is currently being developed in a one year research project at the University of Cambridge, UK, with support from Saarland…

Cut-Simulation and Impredicativity

- PhilosophyLog. Methods Comput. Sci.
- 2009

It is illustrated that adding simple axioms such as Leibniz equations to a calculus for an impredicative logic is like adding cut, and calls for the development of calculi where these principles are built-in instead of being treated axiomatically.

Cvc4

- Computer ScienceCAV
- 2011

The system architecture, subsystems of note, and discuss some applications and continuing work of CVC4 are described, which is a lighter-weight and higher-performing tool than CVC3.

Neighbourhood Structures: Bisimilarity and Basic Model Theory

- MathematicsLog. Methods Comput. Sci.
- 2009

An analogue of Van Benthem's characterisation theorem and a model-theoretic proof of Craig interpolation for classical modal logic are proved and a notion of modal saturation for neighbourhood models is introduced, and its relationship with denability and image-niteness is investigated.