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On Solving Nominal Fixpoint Equations

  • Mauricio Ayala-Rincón
  • Washington de Carvalho-Segundo
  • Maribel Fernández
  • Daniele Nantes-Sobrinho
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10483)

Abstract

In nominal syntax, variable binding is specified using atom-abstraction constructors, and alpha-equivalence is formalised using freshness constraints and atom swappings, which implement variable renamings. Composition of swappings gives rise to atom permutations. Algorithms to check equivalence, match and unify nominal terms have been extended to deal with terms where some operators are associative and/or commutative. In the case of nominal C-unification, problems are transformed into finite and complete families of fixpoint equations of the form Open image in new window , where \(\pi \) is a permutation. To generate nominal C-unifiers, a technique to obtain a sound and complete set of solutions for these equations is needed. In this work we show how complete sets of solutions for nominal fixpoint problems are built and discuss efficient techniques to generate solutions based on algebraic properties of permutations.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Mauricio Ayala-Rincón
    • 1
  • Washington de Carvalho-Segundo
    • 1
  • Maribel Fernández
    • 2
  • Daniele Nantes-Sobrinho
    • 1
  1. 1.Depts. de Matemática e Ciência da ComputaçãoUniversidade de BrasíliaBrasíliaBrazil
  2. 2.Department of InformaticsKing’s College LondonLondonUK

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