Nominal Unification from a Higher-Order Perspective

Authors:
Jordi Levy;Mateu Villaret
Affiliations:
Artificial Intelligence Research Institute (IIIA), Spanish Council for Scientific Research (CSIC), Barcelona, Spain;Departament d'Informàtica i Matemàtica Aplicada (IMA), Universitat de Girona (UdG), Girona, Spain
Venue:
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Year:
2008

Citing 13
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Abstract

Nominal Logic is an extension of first-order logic with equality, name-binding, name-swapping, and freshness of names. Contrarily to higher-order logic, bound variables are treated as atoms, and only free variables are proper unknowns in nominal unification. This allows "variable capture", breaking a fundamental principle of lambda-calculus. Despite this difference, nominal unification can be seen from a higher-order perspective. From this view, we show that nominal unification can be reduced to a particular fragment of higher-order unification problems: higher-order patterns unification. This reduction proves that nominal unification can be decided in quadratic deterministic time.