Proving Ground Confluence of Equational Specifications Modulo Axioms

  • Francisco Durán
  • José Meseguer
  • Camilo RochaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11152)


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.



The authors would like to thank the anonymous referees for their helpful comments that helped us improve the paper. The first author was partially supported by Spanish MINECO/FEDER project TIN2014-52034-R and Univ. Málaga, Campus de Excelencia Internacional Andalucía Tech. The second author was partially supported by NRL under contract number N00173-17-1-G002. The third author was partially supported by CAPES, Colciencias, and INRIA via the STIC AmSud project “EPIC: EPistemic Interactive Concurrency” (Proc. No 88881.117603/2016-01).


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Francisco Durán
    • 1
  • José Meseguer
    • 2
  • Camilo Rocha
    • 3
    Email author
  1. 1.Universidad de MálagaMálagaSpain
  2. 2.University of Illinois, Urbana-ChampaignChampaignUSA
  3. 3.Pontificia Universidad JaverianaCaliColombia

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