HOL2P - A System of Classical Higher Order Logic with Second Order Polymorphism

Völker, Norbert

doi:10.1007/978-3-540-74591-4_25

Cited by 9 publications

(7 citation statements)

References 16 publications

(18 reference statements)

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“…Furthermore, Andrews' system Q [And65] and Melham's so-called "Extended HOL" [Mel93] permit quantification over types, and even more general systems account for type abstraction as e.g. the one underlying HOL2P [Völ07].…”

Section: Related Systemsmentioning

confidence: 99%

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

Steen

2019

Künstl Intell

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In this thesis the theoretical foundations and the practical components for implementing an effective automated theorem proving system for higher-order logic are presented. A primary focus of this thesis is the provision of evidence that a paramodulation-based proof calculus can effectively be employed for performant equational reasoning in Extensional Type Theory (higher-order logic). To that end, a sound and complete paramodulation calculus for extensional higherorder logic with Henkin semantics is presented. The completeness proof hereby unifies and simplifies existing abstract consistency techniques for a formulation of higher-order logic that is based on primitive equality as sole logical connective. In the practically motivated main part of this thesis, the design and architecture of the new higher-order theorem prover Leo-III is presented. Leo-III is based on the above paramodulation calculus and implements additional practically motivated inference rules including equational simplification routines such as heuristic rewriting and support for reasoning with choice. The system encompasses a flexible mechanism for asynchronous cooperation with first-order reasoning systems, a powerful proof search procedure and a sophisticated and efficient set of underlying data structures. Pragmatic and practically significant features of Leo-III are discussed, including its native support for polymorphic higher-order logic and reasoning in higher-order quantified modal logics. An evaluation on a heterogeneous set of benchmark problems confirms that Leo-III is one of the most effective and versatile higher-order automated reasoning systems to date. vii The dissertation project was conducted within the "Leo-III" project funded by the German Research Foundation (DFG) under grant BE 2501/11-1, and the project "Consistent Rational Argumentation in Politics" funded by the Volkswagenstiftung. All source code related to work presented in this thesis is publicly available (under BSD-3 license) at https://github.com/leoprover/Leo-III.

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Section: Related Systemsmentioning

confidence: 99%

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

Steen

2019

Künstl Intell

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“…Another approach to higher order logic theory operations is to extend the logic so that theories can be directly represented with theorems [33,17]. The goal of the present work is to implement a theory infrastructure on top of the existing logic, but extending the logic has the significant advantage of supporting theory operations without replaying proofs.…”

Section: Related Workmentioning

confidence: 99%

The OpenTheory Standard Theory Library

Hurd

2011

Lecture Notes in Computer Science

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Abstract. Interactive theorem proving is tackling ever larger formalization and verification projects, and there is a critical need for theory engineering techniques to support these efforts. One such technique is cross-prover package management, which has the potential to simplify the development of logical theories and effectively share theories between different theorem prover implementations. The OpenTheory project has developed standards for packaging theories of the higher order logic implemented by the HOL family of theorem provers. What is currently missing is a standard theory library that can serve as a published contract of interoperability and contain proofs of basic properties that would otherwise appear in many theory packages. The core contribution of this paper is the presentation of a standard theory library for higher order logic represented as an OpenTheory package. We identify the core theory set of the HOL family of theorem provers, and describe the process of instrumenting the HOL Light theorem prover to extract a standardized version of its core theory development. We profile the axioms and theorems of our standard theory library and investigate the performance cost of separating the standard theory library into coherent hierarchical theory packages.

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“…Here we present its design, implementation, and the challenges encountered. (HOL2P [54] is another example of a logical system built by modifying HOL Light. )…”

Section: Introductionmentioning

confidence: 99%

HOL Light QE

Carette

Farmer

Laskowski

2018

Interactive Theorem Proving

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We are interested in algorithms that manipulate mathematical expressions in mathematically meaningful ways. Expressions are syntactic, but most logics do not allow one to discuss syntax. cttqe is a version of Church's type theory that includes quotation and evaluation operators, akin to quote and eval in the Lisp programming language. Since the HOL logic is also a version of Church's type theory, we decided to add quotation and evaluation to HOL Light to demonstrate the implementability of cttqe and the benefits of having quotation and evaluation in a proof assistant. The resulting system is called HOL Light QE. Here we document the design of HOL Light QE and the challenges that needed to be overcome. The resulting implementation is freely available.

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HOL2P - A System of Classical Higher Order Logic with Second Order Polymorphism

Cited by 9 publications

References 16 publications

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

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

The OpenTheory Standard Theory Library

HOL Light QE

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