Proving ground confluence of equational specifications modulo axioms

Francisco Durán, José Meseguer, Camilo Rocha

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


Terminating functional programs should be deterministic, i.e., should evaluate to a unique result, regardless of the evaluation order. For equational functional programs such determinism is exactly captured by the ground confluence property. For terminating equations this is equivalent to ground local confluence, which follows from local confluence. Checking local confluence by computing critical pairs is the standard way to check ground confluence. The problem is that some perfectly reasonable equational programs are not locally confluent and it can be very hard or even impossible to make them so by adding more equations. We propose a three-step strategy to prove that an equational program as is is ground confluent: First: apply the strategy proposed in [9] to use non-joinable critical pairs as completion hints to either achieve local confluence or reduce the number of critical pairs. Second: use the inductive inference system proposed in this paper to prove the remaining critical pairs ground joinable. Third: to show ground confluence of the original specification, prove also ground joinable the equations added. These methods apply to order-sorted and possibly conditional equational programs modulo axioms such as, e.g., Maude functional modules.

Original languageEnglish (US)
Title of host publicationRewriting Logic and Its Applications - 12th International Workshop, WRLA 2018, Held as a Satellite Event of ETAPS, 2018, Proceedings
EditorsVlad Rusu
PublisherSpringer-Verlag Berlin Heidelberg
Number of pages21
ISBN (Print)9783319998398
StatePublished - 2018
Event12th International Workshop on Rewriting Logic and its Applications, WRLA 2018 - Thessaloniki, Greece
Duration: Jun 14 2018Jun 15 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11152 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other12th International Workshop on Rewriting Logic and its Applications, WRLA 2018

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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