Making Higher-Order Superposition Work

Vukmirović, Petar; Bentkamp, Alexander; Blanchette, Jasmin Christian; Cruanes, Simon; Nummelin, Visa; Tourret, Sophie

doi:10.1007/978-3-030-79876-5_24

Cited by 16 publications

(7 citation statements)

References 52 publications

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“…Preprocessing. Our experience with Zipperposition showed the importance of flexibility in preprocessing the higher-order problems [40]. Therefore, we implemented a flexible preprocessing module in λE.…”

Section: Preprocessing Calculus and Extensionsmentioning

confidence: 99%

“…For Zipperposition, Vukmirović et al developed a variant of the saturation procedure that interleaves computing unifiers and scheduling inferences to be performed [40]. Since completeness was not a design goal for λE, we did not implement this version of the saturation procedure.…”

Section: Preprocessing Calculus and Extensionsmentioning

confidence: 99%

“…Finally, λE treats induction axioms specially. Like Zipperposition [40,Sect. 4], it abstracts literals from the goal clauses and instantiates induction axioms with these abstractions.…”

Section: Preprocessing Calculus and Extensionsmentioning

confidence: 99%

See 2 more Smart Citations

Extending a High-Performance Prover to Higher-Order Logic

Vukmirović

Blanchette

Schulz

2023

Lecture Notes in Computer Science

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Most users of proof assistants want more proof automation. Some proof assistants discharge goals by translating them to first-order logic and invoking an efficient prover on them, but much is lost in translation. Instead, we propose to extend first-order provers with native support for higher-order features. Building on our extension of E to $$\lambda $$ λ -free higher-order logic, we extend E to full higher-order logic. The result is the strongest prover on benchmarks exported from a proof assistant.

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Section: Preprocessing Calculus and Extensionsmentioning

confidence: 99%

Section: Preprocessing Calculus and Extensionsmentioning

confidence: 99%

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Extending a High-Performance Prover to Higher-Order Logic

Vukmirović

Blanchette

Schulz

2023

Lecture Notes in Computer Science

Self Cite

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“…The basic calculus of Satallax is a complete ground tableau calculus [2,5,6]. In recent years the top systems of the THF division of CASC are primarily based on resolution and superposition [3,8,11]. At the moment it is an open question whether there is a research and development path via which a tableau based prover could again become competitive.…”

Section: Introductionmentioning

confidence: 99%

Lash 1.0 (System Description)

Brown

Kaliszyk

2022

Lecture Notes in Computer Science

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Lash is a higher-order automated theorem prover created as a fork of the theorem prover Satallax. The basic underlying calculus of Satallax is a ground tableau calculus whose rules only use shallow information about the terms and formulas taking part in the rule. Lash uses new, efficient C representations of vital structures and operations. Most importantly, Lash uses a C representation of (normal) terms with perfect sharing along with a C implementation of normalizing substitutions. We describe the ways in which Lash differs from Satallax and the performance improvement of Lash over Satallax when used with analogous flag settings. With a 10 s timeout Lash outperforms Satallax on a collection TH0 problems from the TPTP. We conclude with ideas for continuing the development of Lash.

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“…The basic calculus of Satallax is a complete ground tableau calculus [5,6,2]. In recent years the top systems of the THF division of CASC are primarily based on resolution and superposition [11,3,8]. At the moment it is an open question whether there is a research and development path via which a tableau based prover could again become competitive.…”

Section: Introductionmentioning

confidence: 99%

Lash 1.0 (System Description)

Brown¹,

Kaliszyk²

2022

Preprint

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Lash is a higher-order automated theorem prover created as a fork of the theorem prover Satallax. The basic underlying calculus of Satallax is a ground tableau calculus whose rules only use shallow information about the terms and formulas taking part in the rule. Lash uses new, efficient C representations of vital structures and operations. Most importantly, Lash uses a C representation of (normal) terms with perfect sharing along with a C implementation of normalizing substitutions. We describe the ways in which Lash differs from Satallax and the performance improvement of Lash over Satallax when used with analogous flag settings. With a 10s timeout Lash outperforms Satallax on a collection TH0 problems from the TPTP. We conclude with ideas for continuing the development of Lash.

show abstract

Making Higher-Order Superposition Work

Cited by 16 publications

References 52 publications

Extending a High-Performance Prover to Higher-Order Logic

Extending a High-Performance Prover to Higher-Order Logic

Lash 1.0 (System Description)

Lash 1.0 (System Description)

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