Proof Relevant Corecursive Resolution

Peng Fu, Ekaterina Komendantskaya, Tom Schrijvers, Andrew Pond

Research output: Chapter in Book/Report/Conference proceedingConference contribution

16 Citations (Scopus)

Abstract

Resolution lies at the foundation of both logic programming and type class context reduction in functional languages. Terminating derivations by resolution have well-defined inductive meaning, whereas some non-terminating derivations can be understood coinductively. Cycle detection is a popular method to capture a small subset of such derivations. We show that in fact cycle detection is a restricted form of coinductive proof, in which the atomic formula forming the cycle plays the rôle of coinductive hypothesis. This paper introduces a heuristic method for obtaining richer coinductive hypotheses in the form of Horn formulas. Our approach subsumes cycle detection and gives coinductive meaning to a larger class of derivations. For this purpose we extend resolution with Horn formula resolvents and corecursive evidence generation. We illustrate our method on non-terminating type class resolution problems.

Original languageEnglish
Title of host publicationFunctional and Logic Programming
Subtitle of host publication13th International Symposium, FLOPS 2016, Kochi, Japan, March 4-6, 2016, Proceedings
EditorsOleg Kiselyov, Andy King
PublisherSpringer International Publishing
Pages126-143
Number of pages18
ISBN (Electronic)9783319296043
ISBN (Print)9783319296036
DOIs
Publication statusPublished - 2016
Event13th International Symposium on Functional and Logic Programming 2016 - Kochi, Japan
Duration: 4 Mar 20166 Mar 2016

Publication series

NameLecture Notes in Computer Science
PublisherSpringer International Publishing
Volume9613
ISSN (Print)0302-9743

Conference

Conference13th International Symposium on Functional and Logic Programming 2016
Abbreviated titleFLOPS 2016
CountryJapan
CityKochi
Period4/03/166/03/16

Keywords

  • Coinductive proofs
  • Corecursion
  • Haskell type class inference
  • Horn clause logic
  • Resolution

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

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