Automated Deduction in the B Set Theory using Typed Proof Search and Deduction Modulo

17 pages•Published: December 18, 2015

Guillaume Bury, David Delahaye, Damien Doligez, Pierre Halmagrand and Olivier Hermant

Abstract

We introduce an encoding of the set theory of the B method using polymorphic types and deduction modulo, which is used for the automated verification of proof obligations in the framework of the BWare project. Deduction modulo is an extension of predicate calculus with rewriting both on terms and propositions. It is well suited for proof search in theories because it turns many axioms into rewrite rules. We also present the associated automated theorem prover Zenon Modulo, an extension of Zenon to polymorphic types and deduction modulo, along with its backend to the Dedukti universal proof checker, which also relies on types and deduction modulo, and which allows us to verify the proofs produced by Zenon Modulo. Finally, we assess our approach over the proof obligation benchmark provided by the BWare project.

Keyphrases: automated deduction, b method, deduction modulo, dedukti, set theory, typed proof search, zenon modulo

In: Ansgar Fehnker, Annabelle McIver, Geoff Sutcliffe and Andrei Voronkov (editors). LPAR-20. 20th International Conferences on Logic for Programming, Artificial Intelligence and Reasoning - Short Presentations, vol 35, pages 42-58.

Links:	https://easychair.org/publications/paper/qzr
	https://doi.org/10.29007/14v7

BibTeX entry

@inproceedings{LPAR-20:Automated_Deduction_B_Set,
  author    = {Guillaume Bury and David Delahaye and Damien Doligez and Pierre Halmagrand and Olivier Hermant},
  title     = {Automated Deduction in the B Set Theory using Typed Proof Search and Deduction Modulo},
  booktitle = {LPAR-20. 20th International Conferences on Logic for Programming, Artificial Intelligence and Reasoning - Short Presentations},
  editor    = {Ansgar Fehnker and Annabelle McIver and Geoff Sutcliffe and Andrei Voronkov},
  series    = {EPiC Series in Computing},
  volume    = {35},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/qzr},
  doi       = {10.29007/14v7},
  pages     = {42-58},
  year      = {2015}}

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