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International Symposium on Formal Methods

FM 2019: Formal Methods – The Next 30 Years pp 502–518Cite as

Unification in Matching Logic

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11800))

Abstract

Matching Logic is a framework for specifying programming language semantics and reasoning about programs. Its formulas are called patterns and are built with variables, symbols, connectives and quantifiers. A pattern is a combination of structural components (term patterns), which must be matched, and constraints (predicate patterns), which must be satisfied. Dealing with more than one structural component in a pattern could be cumbersome because it involves multiple matching operations. A source for getting patterns with many structural components is the conjunction of patterns. Here, we propose a method that uses a syntactic unification algorithm to transform conjunctions of structural patterns into equivalent patterns having only one structural component and some additional constraints. We prove the soundness and the completeness of our approach, and we provide sound strategies to generate certificates for the equivalences.

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Notes

  1. 1.

    Note that \(\bot \) is different from the (bold) symbol \(\pmb \perp \) used in Sect. 3.

  2. 2.

    The other two axioms (A) and (B) in [3] correspond to Injectivity and No confusion, different constructors.

  3. 3.

    We thank to the anonymous referee for having noticed this similarity.

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Acknowledgements

We thank the anonymous reviewers for their insightful comments. We would like to especially thank the Kore developers and researchers: Phillip Harris, Traian Şerbănuţă and Virgil Şerbănuţă for their valuable assistance and feedback. They helped us with our proof generation strategy and they suggested improvements for our current work. We also want to specially thank Grigore Roşu for the fruitful discussions that we had about this topic at FROM 2018. This work was supported by a grant of the “Alexandru Ioan Cuza” University of Iaşi, within the Research Grants program, Grant UAIC, ctr. no. 6/01-01-2017.

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Authors and Affiliations

  1. Alexandru Ioan Cuza University, Iaşi, Romania

    Andrei Arusoaie & Dorel Lucanu

Authors
  1. Andrei Arusoaie
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  2. Dorel Lucanu
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Correspondence to Andrei Arusoaie .

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Editors and Affiliations

  1. Consiglio Nazionale delle Ricerche, Pisa, Italy

    Maurice H. ter Beek

  2. Macquarie University, Sydney, NSW, Australia

    Annabelle McIver

  3. University of Minho, Braga, Portugal

    José N. Oliveira

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Arusoaie, A., Lucanu, D. (2019). Unification in Matching Logic. In: ter Beek, M., McIver, A., Oliveira, J. (eds) Formal Methods – The Next 30 Years. FM 2019. Lecture Notes in Computer Science(), vol 11800. Springer, Cham. https://doi.org/10.1007/978-3-030-30942-8_30

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