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Conference paper

A verified prover based on ordered resolution

In Proceedings of the 8th Acm Sigplan International Conference on Certified Programs and Proofs — 2019, pp. 152-165

By Schlichtkrull, Anders1,2; Blanchette, Jasmin Christian3; Traytel, Dmitriy4

Edited by Mahboubi, Assia; Myreen, Magnus O.

From

Department of Applied Mathematics and Computer Science, Technical University of Denmark1

Formal Methods, Department of Applied Mathematics and Computer Science, Technical University of Denmark2

Vrije Universiteit Amsterdam3

Swiss Federal Institute of Technology Zurich4

The superposition calculus, which underlies first-order theorem provers such as E, SPASS, and Vampire, combines ordered resolution and equality reasoning. As a step towards verifying modern provers, we specify, using Isabelle/HOL, a purely functional first-order ordered resolution prover and establish its soundness and refutational completeness.

Methodologically, we apply stepwise refinement to obtain, from an abstract nondeterministic specification, a verified deterministic program, written in a subset of Isabelle/HOL from which we extract purely functional Standard ML code that constitutes a semidecision procedure for first-order logic.

Language: English
Publisher: Association for Computing Machinery
Year: 2019
Pages: 152-165
Proceedings: 8th ACM SIGPLAN International Conference on Certified Programs and Proofs
Journal subtitle: Proceedings of the 8th Acm Sigplan International Conference on Certified Programs and Proofs
ISBN: 1450362222 and 9781450362221
Types: Conference paper
DOI: 10.1145/3293880.3294100
ORCIDs: Schlichtkrull, Anders
Keywords

Automatic theorem provers First-order logic Proof assistants Stepwise refinement

Other keywords

Automated reasoning Logic Logic and verification Theory of computation automatic theorem provers first-order logic proof assistants stepwise refinement

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