An Interactive SMT Tactic in Coq using Abductive Reasoning

12 pages•Published: June 3, 2023

Haniel Barbosa, Chantal Keller, Andrew Reynolds, Arjun Viswanathan, Cesare Tinelli and Clark Barrett

Abstract

A well-known challenge in leveraging automatic theorem provers, such as satisfiability modulo theories (SMT) solvers, to discharge proof obligations from interactive theorem provers (ITPs) is determining which axioms to send to the solver together with the con- jecture to be proven. Too many axioms may confuse or clog the solver, while too few may make a theorem unprovable. When a solver fails to prove a conjecture, it is unclear to the user which case transpired. In this paper we enhance SMTCoq — an integration between the Coq ITP and the cvc5 SMT solver — with a tactic called abduce aimed at mitigating the uncertainty above. When the solver fails to prove the goal, the user may invoke abduce which will use abductive reasoning to provide facts that will allow the solver to prove the goal, if any.

Keyphrases: abduction, coq, cvc5, smtcoq

In: Ruzica Piskac and Andrei Voronkov (editors). Proceedings of 24th International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 94, pages 11-22.

Links:	https://easychair.org/publications/paper/lNvq
	https://doi.org/10.29007/432m

BibTeX entry

@inproceedings{LPAR2023:Interactive_SMT_Tactic_Coq,
  author    = {Haniel Barbosa and Chantal Keller and Andrew Reynolds and Arjun Viswanathan and Cesare Tinelli and Clark Barrett},
  title     = {An Interactive SMT Tactic in Coq using Abductive Reasoning},
  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/lNvq},
  doi       = {10.29007/432m},
  pages     = {11-22},
  year      = {2023}}

Download PDF Open PDF in browser