Higher-Order Beta Matching with Solutions in Long Beta-Eta Normal Form

Kristian StÝvring.

June 2006

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

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Last modified: 2006-11-24 by webmaster.