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ABZ Languages and Tools in Industrial-Scale Application Read chapter Read first chapter

2018 | OriginalPaper | Chapter

An Automation-Friendly Set Theory for the B Method

Authors : Guillaume Bury, Simon Cruanes, David Delahaye, Pierre-Louis Euvrard

Published in: Abstract State Machines, Alloy, B, TLA, VDM, and Z

Publisher: Springer International Publishing

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Abstract

We propose an automation-friendly set theory for the B method. This theory is expressed using first order logic extended to polymorphic types and rewriting. Rewriting is introduced along the lines of deduction modulo theory, where axioms are turned into rewrite rules over both propositions and terms. We also provide experimental results of several tools able to deal with polymorphism and rewriting over a benchmark of problems in pure set theory (i.e. without arithmetic).

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Appendix
Available only for authorised users
Footnotes
1
The benchmark is available at: https://​github.​com/​delahayd/​bset.
 
2
Git version 7720d8c, available at: https://​gforge.​inria.​fr/​projects/​archsat.
 
Literature
1.
Abrial, J.-R.: The B-Book, Assigning Programs to Meanings. Cambridge University Press, Cambridge (1996). ISBN 0521496195CrossRef
2.
3.
Bury, G., Delahaye, D., Doligez, D., Halmagrand, P., Hermant, O.: Automated deduction in the B set theory using typed proof search and deduction modulo. In: Fehnker, A., McIver, A., Sutcliffe, G., Voronkov, A. (eds.) Logic for Programming, Artificial Intelligence and Reasoning (LPAR) - Short Presentations, vol. 35, pp. 42–58. EasyChair, Suva (Fiji), November 2015
4.
5.
Metadata
Title
An Automation-Friendly Set Theory for the B Method
Authors
Guillaume Bury
Simon Cruanes
David Delahaye
Pierre-Louis Euvrard
Copyright Year
2018
Book
Abstract State Machines, Alloy, B, TLA, VDM, and Z

Print ISBN: 978-3-319-91270-7

Electronic ISBN: 978-3-319-91271-4

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-91271-4_32

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