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Associative Unification and Symbolic Reasoning Modulo Associativity in Maude

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Rewriting Logic and Its Applications (WRLA 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11152))

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Abstract

We have added support for associative unification to Maude 2.7.1. Associative unification is infinitary, i.e., there are unification problems \(u =^? v\) such that there is an infinite minimal set of unifiers, whereas associative-commutative unification is finitary. A unique feature of the associative unification algorithm implemented in Maude is that it is guaranteed to terminate with a finite and complete set of associative unifiers for a fairly large class of unification problems occurring in practice. For any problems outside this class, the algorithm returns a finite set of unifiers together with a warning that such set may be incomplete. This paper describes this associative unification algorithm implemented in Maude and also how other symbolic reasoning Maude features such as (i) variant generation; (ii) variant unification; and (iii) narrowing based symbolic reachability analysis have been extended to deal with associativity.

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Notes

  1. 1.

    Maude is publicly available at http://maude.cs.illinois.edu.

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Acknowledgements

Francisco Durán has been partially supported by Spanish MINECO/FEDER project TIN2014-52034-R and Univ. Málaga, Campus de Excelencia Internacional Andalucía Tech. Steven Eker was partially supported by NRL grant N00173-16-C-2005. Santiago Escobar was partially supported by the EU (FEDER) and the Spanish MINECO under grant TIN2015-69175-C4-1-R, by the Spanish Generalitat Valenciana under grant PROMETEOII/2015/013, and by the US Air Force Office of Scientific Research under award number FA9550-17-1-0286. Narciso Martí-Oliet has been partially supported by MINECO Spanish project TRACES (TIN2015–67522–C3–3R) and by Comunidad de Madrid program N-GREENS Software (S2013/ICE-2731). Jose Meseguer was partially supported by NRL under contract number N00173-17-1-G002. Carolyn Talcott was partially supported by ONR grants N0001415-1-2202, N00173-17-1-G002 and NRL grant N00173-16-C-2005.

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Authors and Affiliations

  1. Universidad de Málaga, Málaga, Spain

    Francisco Durán

  2. SRI International, Menlo Park, CA, USA

    Steven Eker & Carolyn Talcott

  3. Universitat Politècnica de València, València, Spain

    Santiago Escobar

  4. Universidad Complutense de Madrid, Madrid, Spain

    Narciso Martí-Oliet

  5. University of Illinois at Urbana-Champaign, Champaign, IL, USA

    José Meseguer

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  1. Francisco Durán
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  6. Carolyn Talcott
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Correspondence to Santiago Escobar .

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  1. Inria, Lille, France

    Vlad Rusu

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Durán, F., Eker, S., Escobar, S., Martí-Oliet, N., Meseguer, J., Talcott, C. (2018). Associative Unification and Symbolic Reasoning Modulo Associativity in Maude. In: Rusu, V. (eds) Rewriting Logic and Its Applications. WRLA 2018. Lecture Notes in Computer Science(), vol 11152. Springer, Cham. https://doi.org/10.1007/978-3-319-99840-4_6

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  • DOI: https://doi.org/10.1007/978-3-319-99840-4_6

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