Refining Unification with Abstraction

12 pages•Published: June 3, 2023

Ahmed Bhayat, Konstantin Korovin, Laura Kovacs and Johannes Schoisswohl

Abstract

Automated reasoning with theories and quantifiers is a common demand in formal methods. A major challenge that arises in this respect comes with rewriting/simplifying terms that are equal with respect to a background first-order theory T , as equality reasoning in this context requires unification modulo T . We introduce a refined algorithm for unification with abstraction in T , allowing for a fine-grained control of equality constraints and substitutions introduced by standard unification with abstraction approaches. We experimentally show the benefit of our approach within first-order linear rational arithmetic.

Keyphrases: arithmetic, automated theorem proving, unification, unification with abstraction

In: Ruzica Piskac and Andrei Voronkov (editors). Proceedings of 24th International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 94, pages 36-47.

Links:	https://easychair.org/publications/paper/mHz7
	https://doi.org/10.29007/h65j

BibTeX entry

@inproceedings{LPAR2023:Refining_Unification_with_Abstraction,
  author    = {Ahmed Bhayat and Konstantin Korovin and Laura Kovacs and Johannes Schoisswohl},
  title     = {Refining Unification with Abstraction},
  booktitle = {Proceedings of 24th International Conference on Logic for Programming, Artificial Intelligence and Reasoning},
  editor    = {Ruzica Piskac and Andrei Voronkov},
  series    = {EPiC Series in Computing},
  volume    = {94},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/mHz7},
  doi       = {10.29007/h65j},
  pages     = {36-47},
  year      = {2023}}

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