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System description: Leo — A higher-order theorem prover [chapter]

Christoph Benzmüller, Michael Kohlhase
1998 Lecture Notes in Computer Science  
, there are proof problems which lie beyond the capabilities of first-order theorem provers, but instead can be solved easily by an higher-order theorem prover (HOATP) like Leo.  ...  Leo uses a higher-order Logic based upon Church's simply typed λ-calculus, so that the comprehension axioms are implicitly handled by αβη-equality.  ...  Experiments Leo is able to solve a variety of simple higher-order theorems such as Cantor's theorem and it is specialized in solving theorems with embedded propositions.  ... 
doi:10.1007/bfb0054256 fatcat:acvfqu3bijervbmasdm4fmh5si

Can a Higher-Order and a First-Order Theorem Prover Cooperate? [chapter]

Christoph Benzmüller, Volker Sorge, Mateja Jamnik, Manfred Kerber
2005 Lecture Notes in Computer Science  
We present a solution to this challenge by combining a higher-order and a first-order automated theorem prover, both based on the resolution principle, in a flexible and distributed environment.  ...  We demonstrate the effectiveness of our approach on a set of problems still considered non-trivial for many first-order theorem provers.  ...  theorem provers could also be evaluated against higher-order systems (and vice versa).  ... 
doi:10.1007/978-3-540-32275-7_27 fatcat:vllvzeicvbdixmzafcjhtee7ca

LEO-II - A Cooperative Automatic Theorem Prover for Classical Higher-Order Logic (System Description) [chapter]

Christoph Benzmüller, Lawrence C. Paulson, Frank Theiss, Arnaud Fietzke
Lecture Notes in Computer Science  
LEO-II is a standalone, resolution-based higher-order theorem prover designed for effective cooperation with specialist provers for natural fragments of higher-order logic.  ...  At present LEO-II can cooperate with the first-order automated theorem provers E, SPASS, and Vampire.  ...  Overview of LEO-II The one year project "LEO-II: An Effective Higher-Order Theorem Prover" was funded by EPSRC at Cambridge University, UK under grant EP/D070511/1.  ... 
doi:10.1007/978-3-540-71070-7_14 fatcat:i6575xhhubg6bf5xvrwb2w634e

Update report: LEO-II version 1.5 [article]

Christoph Benzmüller, Nik Sultana
2013 arXiv   pre-print
Recent improvements of the LEO-II theorem prover are presented.  ...  These improvements include a revised ATP interface, new translations into first-order logic, rule support for the axiom of choice, detection of defined equality, and more flexible strategy scheduling.  ...  The second author was supported by a grant from the German Academic Exchange Service (DAAD) during a visit to Freie Universität Berlin, during which the work described in this paper was carried out.  ... 
arXiv:1303.3761v2 fatcat:7hjtn4fgkjeapmt4yxstiedmlu

Extensional Higher-Order Paramodulation in Leo-III [article]

Alexander Steen, Christoph Benzmüller
2021 arXiv   pre-print
Leo-III is an automated theorem prover for extensional type theory with Henkin semantics and choice.  ...  The prover may cooperate with multiple external specialist reasoning systems such as first-order provers and SMT solvers.  ...  Introduction Leo-III is an automated theorem prover (ATP) for classical higher-order logic (HOL) with Henkin semantics and choice.  ... 
arXiv:1907.11501v2 fatcat:hv3uysew6fdrtixvtv5d7ydgb4

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

Alexander Steen
2019 Künstliche Intelligenz  
In the practically motivated main part of this thesis, the design and architecture of the new higher-order theorem prover Leo-III is presented.  ...  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  ...  This list is by no means exhaustive; a more extensive description of higher-order reasoning systems is presented by Benzmüller and Miller [BM14] . Figure 2: The logo of the Leo-III theorem prover.  ... 
doi:10.1007/s13218-019-00628-8 fatcat:b6yfenxgxndb3myskqushsm6uy

Leo-III Version 1.1 (System description)

Christoph Benzmüller, Alexander Steen, Max Wisniewski
unpublished
Leo-III is an automated theorem prover for (polymorphic) higher-order logic which supports all common TPTP dialects, including THF, TFF and FOF as well as their rank-1 polymorphic derivatives.  ...  It is based on a paramodulation calculus with ordering constraints and, in tradition of its predecessor LEO-II, heavily relies on cooperation with external first-order theorem provers.Unlike LEO-II, asynchronous  ...  Example Summary and Further Work Leo-III is a cooperative higher-order theorem prover, which extends and further improves on the ideas underlying its predecessor system LEO-II.  ... 
doi:10.29007/grmx fatcat:yhliautngvb47gt2tpgqkqzwaa

Experiments with an Agent-Oriented Reasoning System [chapter]

Christoph Benzmüller, Manfred Kerber, Mateja Jamnik, Volker Sorge
2001 Lecture Notes in Computer Science  
It particularly supports cooperative proofs between reasoning systems which are strong in different application areas, e.g., higher-order and first-order theorem provers and computer algebra systems.  ...  The approach combines ideas from two subfields of AI (theorem proving/proof planning and multi-agent systems) and makes use of state of the art distribution techniques to decentralise and spread its reasoning  ...  Currently our system links up with the computer algebra systems Maple and Gap running in Saarbrücken, and locally with the higher-order theorem provers Leo and Tps, the first-order theorem prover Otter  ... 
doi:10.1007/3-540-45422-5_29 fatcat:6twdpntxvbexxl5g7l5uc7tqru

Ours Is to Reason Why [chapter]

Cliff B. Jones, Leo Freitas, Andrius Velykis
2013 Lecture Notes in Computer Science  
Modern theorem proving tools greatly simplify the discharge of such proof obligations.  ...  In many formal approaches, a "posit and prove" approach allows a designer to record an engineering design decision from which a collection of "proof obligations" are generated; their discharge justifies  ...  The first author is grateful to Aaron Sloman for a useful discussion at the Birmingham BCTCS meeting.  ... 
doi:10.1007/978-3-642-39698-4_14 fatcat:nvcnfk3lbzdoni6zqbrn4ajc6q

An Axiomatic Value Model for Isabelle/UTP [chapter]

Frank Zeyda, Simon Foster, Leo Freitas
2017 Lecture Notes in Computer Science  
Several mechanisations of the UTP in HOL theorem provers have been developed. All of them, however, succumb to a trade off in how they encode the value model of UTP theories.  ...  We carefully craft a definitional mechanism in the Isabelle/HOL prover that guarantees soundness.  ...  Isabelle/HOL Isabelle/HOL [13] is a popular theorem prover for Higher-Order Logic (HOL).  ... 
doi:10.1007/978-3-319-52228-9_8 fatcat:attpodbcbjfg7cxrsghgif5tny

A Model for Capturing and Replaying Proof Strategies [chapter]

Leo Freitas, Cliff B. Jones, Andrius Velykis, Iain Whiteside
2014 Lecture Notes in Computer Science  
Modern theorem provers can discharge a significant proportion of Proof Obligations (POs) that arise in the use of Formal Methods (FMs).  ...  This paper outlines a system that will identify and characterise ways of discharging POs of a family by tracking an interactive proof of one member of the family.  ...  This abstract description of the AI 4 FM system can be implemented in different ways.  ... 
doi:10.1007/978-3-319-12154-3_12 fatcat:nxedgu6v2vfnjahd4aebddfali

Mechanising Mondex with Z/Eves

Leo Freitas, Jim Woodcock
2007 Formal Aspects of Computing  
We describe our experiences in mechanising the specification, refinement, and proof of the Mondex Electronic Purse using the Z/Eves theorem prover.  ...  We took a conservative approach and mechanised the original L A T E X sources without changing their technical content, except to correct errors.  ...  It is useful to understand how the theorem prover works, in order to explain how to handle a specification as big and complex as Mondex.  ... 
doi:10.1007/s00165-007-0059-y fatcat:rlikrbxz7bgjrlpoqo3kmdhy5q

POSIX file store in Z/Eves: an experiment in the verified software repository

Leo Freitas, Zheng Fu, Jim Woodcock
2007 12th IEEE International Conference on Engineering Complex Computer Systems (ICECCS 2007)  
We present results from the second pilot project in the international Verification Grand Challenge: a formally verified specification of a POSIX-compliant file store using the Z/Eves theorem prover.  ...  Our specification of the file store is based on Morgan & Sufrin's specification of the UNIX filing system; the proof and its mechanisation in Z/Eves are novel.  ...  Yet another indirect use could be to validate some JML properties in a theorem prover from the lifted JML description of HashMaps. And this idea has also been already done for Java sets [10] .  ... 
doi:10.1109/iceccs.2007.36 dblp:conf/iceccs/FreitasFW07 fatcat:tavqvnoqz5a4hajbrjylyvqcle

Mechanising a formal model of flash memory

Andrew Butterfield, Leo Freitas, Jim Woodcock
2009 Science of Computer Programming  
The model is intended as a key part of a pilot project to develop a verified file store system based on flash memory.  ...  The project was proposed by Joshi and Holzmann as a contribution to the Grand Challenge in Verified Software, and involves constructing a highly assured flash file store for use in spaceflight missions  ...  Acknowledgements We are grateful to Rajeev Joshi and Gerard Holzmann from NASA/JPL who originally suggested the flash file store as a grand challenge pilot project.  ... 
doi:10.1016/j.scico.2008.09.014 fatcat:xwgyuos3onei5hpa2vm6r3ovm4

The Space of Mathematical Software Systems – A Survey of Paradigmatic Systems [article]

Katja Bercic, Jacques Carette, William M. Farmer, Michael Kohlhase, Dennis Müller, Florian Rabe, Yasmine Sharoda
2020 arXiv   pre-print
Mathematical software systems are becoming more and more important in pure and applied mathematics in order to deal with the complexity and scalability issues inherent in mathematics.  ...  In this survey, we focus on the commonalities and differences of these systems from the perspective of a future multi-aspect system.  ...  Automated provers for higher-order logics are much harder to develop but are gaining strength. Example systems are Leo [Ben+08] and Satallax [Bro12] .  ... 
arXiv:2002.04955v1 fatcat:th2h5qrd4rcazhw2eqbqmy2zmq
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