Higher-order beta matching with solutions in long beta-eta normal form

Authors:
Kristian Støvring
Affiliations:
BRICS (Basic Research in Computer Science), Department of Computer Science, University of Aarhus, Aarhus N, Denmark
Venue:
Nordic Journal of Computing - Selected papers of the 17th nordic workshop on programming theory (NWPT'05), October 19-21, 2005
Year:
2006

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Abstract

Higher-order matching is a special case of unification of simply-typed lambda-terms: in a matching equation, one of the two sides contains no unification variables. Loader has recently shown that higher-order matching up to beta equivalence is undecidable, but decidability of higher-order matching up to beta-eta equivalence is a long-standing open problem.We show that higher-order matching up to beta-eta equivalence is decidable if and only if a restricted form of higher-order matching up to beta equivalence is decidable: the restriction is that solutions must be in long beta-eta normal form.