System description: Leo — A higher-order theorem prover

1998 ◽  
pp. 139-143 ◽  
Author(s):  
Christoph Benzmüller ◽  
Michael Kohlhase
Keyword(s):  
Higher Order ◽  
Theorem Prover ◽  
System Description

scholarly journals Leo-III Version 1.1 (System description)

10.29007/grmx ◽  
2018 ◽  
Author(s):  
Christoph Benzmüller ◽  
Alexander Steen ◽  
Max Wisniewski
Keyword(s):  
Higher Order ◽  
Order Logic ◽  
Theorem Prover ◽  
Higher Order Logic ◽  
System Description ◽  
Agent Based ◽  
First Order ◽  
Theorem Provers ◽  
Automated Theorem Prover ◽  
Ordering Constraints

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 cooperation with typed first-order provers and an agent-based internal cooperation scheme is supported. In this paper, we sketch Leo-III's underlying calculus, survey implementation details and give examples of use.

scholarly journals Invariants and Robustness of BIP Models

10.29007/prxp ◽  
2018 ◽  
Author(s):  
Jan Olaf Blech ◽  
Thanh-Hung Nguyen ◽  
Michael Perin
Keyword(s):  
Embedded Systems ◽  
Higher Order ◽  
Theorem Prover ◽  
Important Goal ◽  
Invariant Generation ◽  
Execution Traces ◽  
Verification Tool ◽  
Verification Tools ◽  
Generation Mechanisms ◽  
Natural Way

In this paper we present on-going work addressing the problem of automatically generating realistic and guaranteed correct invariants. Since invariant generation mechanisms are error-prone, after the computation of invariants by a verification tool, we formally prove that the generated invariants are indeed invariants of the considered systems using a higher-order theorem prover and automated techniques. We regard invariants for BIP models. BIP (behavior, interaction, priority) is a language for specifying asynchronous component based systems. Proving that an invariant holds often requires an induction on possible system execution traces. For this reason, apart from generating invariants that precisely capture a system’s behavior, inductiveness of invariants is an important goal. We establish a notion of robust BIP models. These can be automatically constructed from our original non-robust BIP models and over-approximate their behavior. We motivate that invariants of robust BIP models capture the behavior of systems in a more natural way than invariants of corresponding non-robust BIP models. Robust BIP models take imprecision due to values delivered by sensors into account. Invariants of robust BIP models tend to be inductive and are also invariants of the original non-robust BIP model. Therefore they may be used by our verification tools and it is easy to show their correctness in a higher-order theorem prover. The presented work is developed to verify the results of a deadlock-checking tool for embedded systems after their computations. Therewith, we gain confidence in the provided analysis results.

scholarly journals The Lean Theorem Prover (System Description)

2015 ◽  
pp. 378-388 ◽  
Author(s):  
Leonardo de Moura ◽  
Soonho Kong ◽  
Jeremy Avigad ◽  
Floris van Doorn ◽  
Jakob von Raumer
Keyword(s):  
Theorem Prover ◽  
System Description

scholarly journals Higher-order theorem proving and its applications

2019 ◽  
Vol 61 (4) ◽  
pp. 187-191
Author(s):  
Alexander Steen
Keyword(s):  
Theorem Proving ◽  
Formal Analysis ◽  
Logical Consequence ◽  
Effective Means ◽  
Industrial Applications ◽  
Higher Order ◽  
Hardware Verification ◽  
Theorem Prover ◽  
Computer Assisted ◽  
Higher Order Logic

Abstract Automated theorem proving systems validate or refute whether a conjecture is a logical consequence of a given set of assumptions. Higher-order provers have been successfully applied in academic and industrial applications, such as planning, software and hardware verification, or knowledge-based systems. Recent studies moreover suggest that automation of higher-order logic, in particular, yields effective means for reasoning within expressive non-classical logics, enabling a whole new range of applications, including computer-assisted formal analysis of arguments in metaphysics. My work focuses on the theoretical foundations, effective implementation and practical application of higher-order theorem proving systems. This article briefly introduces higher-order reasoning in general and presents an overview of the design and implementation of the higher-order theorem prover Leo-III. In the second part, some example applications of Leo-III are discussed.

A prototype theorem-prover for a higher-order functional language

1985 ◽  
Vol 10 (4) ◽  
pp. 72-74
Author(s):  
Bob Boyer ◽  
Matt Kaufmann
Keyword(s):  
Higher Order ◽  
Theorem Prover ◽  
Functional Language

scholarly journals Understanding LEO-II’s proofs

10.29007/x9c9 ◽  
2018 ◽  
Author(s):  
Nik Sultana ◽  
Christoph Benzmüller
Keyword(s):  
Theorem Proving ◽  
Automated Theorem Proving ◽  
Higher Order ◽  
Target Audience ◽  
Theorem Prover ◽  
First Order

The LEO and LEO-II provers have pioneered the integration of higher-order and first-order automated theorem proving. To date, the LEO-II system is, to our knowledge, the only automated higher-order theorem prover which is capable of generating joint higher-order–first-order proof objects in TPTP format. This paper discusses LEO-II’s proof objects. The target audience are practitioners with an interest in using LEO-II proofs within other systems.

scholarly journals Making Higher-Order Superposition Work

2021 ◽  
pp. 415-432
Author(s):  
Petar Vukmirović ◽  
Alexander Bentkamp ◽  
Jasmin Blanchette ◽  
Simon Cruanes ◽  
Visa Nummelin ◽  
...  
Keyword(s):  
Higher Order ◽  
Order Logic ◽  
Theorem Prover ◽  
First Order Logic ◽  
Inference Rules ◽  
Higher Order Logic ◽  
First Order ◽  
New Challenges

AbstractSuperposition is among the most successful calculi for first-order logic. Its extension to higher-order logic introduces new challenges 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. We describe techniques that address these issues and extensively evaluate their implementation in the Zipperposition theorem prover. Largely thanks to their use, Zipperposition won the higher-order division of the CASC-J10 competition.

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