Extensional Crisis and Proving Identity

Gupta, Ashutosh; Kovács, Laura; Kragl, Bernhard; Воронков, Андрей

doi:10.1007/978-3-319-11936-6_14

Cited by 14 publications

(17 citation statements)

References 18 publications

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“…To curb the explosion associated with extensionality, this axiom and all clauses derived from it are penalized by the clause selection heuristic. We also added the NegExt rule described in Section 3.2, which resembles Vampire's extensionality resolution rule [37].…”

Section: Methodsmentioning

confidence: 99%

Superposition for Lambda-Free Higher-Order Logic

Bentkamp

Blanchette

Cruanes

et al. 2018

Automated Reasoning

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We introduce refutationally complete superposition calculi for intentional and extensional clausal λ-free higher-order logic, two formalisms that allow partial application and applied variables. The calculi are parameterized by a term order that need not be fully monotonic, making it possible to employ the λ-free higher-order lexicographic path and Knuth-Bendix orders. We implemented the calculi in the Zipperposition prover and evaluated them on Isabelle/HOL and TPTP benchmarks. They appear promising as a stepping stone towards complete, highly efficient automatic theorem provers for full higherorder logic.Key words and phrases: superposition calculus, clausal lambda-free higher-order logic, refutational completeness.Extended version of Bentkamp et al., "Superposition for lambda-free higher-order logic" [11].

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Section: Methodsmentioning

confidence: 99%

Superposition for Lambda-Free Higher-Order Logic

Bentkamp

Blanchette

Cruanes

et al. 2018

Automated Reasoning

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“…Vampire uses the extensionality resolution rule [8] to efficiently reason with the extensionality axiom.…”

Section: Implementation In Vampirementioning

confidence: 99%

The vampire and the FOOL

Kotelnikov

Kovács

Reger

et al. 2016

Proceedings of the 5th ACM SIGPLAN Conference on Certified Programs and Proofs

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This paper presents new features recently implemented in the theorem prover Vampire, namely support for first-order logic with a first class boolean sort (FOOL) and polymorphic arrays. In addition to having a first class boolean sort, FOOL also contains if-then-else and let-in expressions. We argue that presented extensions facilitate reasoning-based program analysis, both by increasing the expressivity of first-order reasoners and by gains in efficiency.

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“…Moreover, it can be hard to efficiently reason about certain classes of program properties, unless special inference rules and heuristics are added to the theorem prover, see e.g. [8] when it comes to prove properties of data collections with extensionality axioms.…”

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confidence: 99%

A First Class Boolean Sort in First-Order Theorem Proving and TPTP

Kotelnikov

Kovács

Воронков

2015

Lecture Notes in Computer Science

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To support reasoning about properties of programs operating with boolean values one needs theorem provers to be able to natively deal with the boolean sort. This way, program properties can be translated to first-order logic and theorem provers can be used to prove program properties efficiently. However, in the TPTP language, the input language of automated first-order theorem provers, the use of the boolean sort is limited compared to other sorts, thus hindering the use of first-order theorem provers in program analysis and verification. In this paper, we present an extension FOOL of many-sorted first-order logic, in which the boolean sort is treated as a first-class sort. Boolean terms are indistinguishable from formulas and can appear as arguments to functions. In addition, FOOL contains if-then-else and let-in constructs. We define the syntax and semantics of FOOL and its model-preserving translation to first-order logic. We also introduce a new technique of dealing with boolean sorts in superposition-based theorem provers. Finally, we discuss how the TPTP language can be changed to support FOOL

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Extensional Crisis and Proving Identity

Cited by 14 publications

References 18 publications

Superposition for Lambda-Free Higher-Order Logic

Superposition for Lambda-Free Higher-Order Logic

The vampire and the FOOL

A First Class Boolean Sort in First-Order Theorem Proving and TPTP

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