Simplifying the signature in second-order unification

  • Authors:

  • Jordi Levy;Mateu Villaret

  • Affiliations:

  • IIIA, CSIC, Campus de la UAB, Barcelona, Spain;IMA, UdG, Campus de Montilivi, Girona, Spain

  • Venue:
  • Applicable Algebra in Engineering, Communication and Computing
  • Year:
  • 2009

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Abstract

Second-Order Unification is undecidable even for very specialized fragments. The signature plays a crucial role in these fragments. If all symbols are monadic, then the problem is NP-complete, whereas it is enough to have just one binary constant to lose decidability. In this work we reduce Second-Order Unification to Second-Order Unification with a signature that contains just one binary function symbol and constants. The reduction is based on partially currying the equations by using the binary function symbol for explicit application @. Our work simplifies the study of Second-Order Unification and some of its variants, like Context Unification and Bounded Second-Order Unification.