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Higherorder Unification via Explicit Substitutions (Extended Abstract)
 Proceedings of LICS'95
, 1995
"... Higherorder unification is equational unification for βηconversion. But it is not firstorder equational unification, as substitution has to avoid capture. In this paper higherorder unification is reduced to firstorder equational unification in a suitable theory: the &lambda ..."
Abstract

Cited by 109 (13 self)
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Higherorder unification is equational unification for &beta;&eta;conversion. But it is not firstorder equational unification, as substitution has to avoid capture. In this paper higherorder unification is reduced to firstorder equational unification in a suitable theory: the &lambda;&sigma;calculus of explicit substitutions.
HigherOrder Equational Unification via Explicit Substitutions
 in Proceedings of the tenth UNIF Workshop
, 1996
"... . We show how to reduce the unification problem modulo fij conversion and a firstorder equational theory E, into a firstorder unification problem in a union of two nondisjoint equational theories including E and a calculus of explicit substitutions. A rulebased unification procedure in thi ..."
Abstract

Cited by 6 (3 self)
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. We show how to reduce the unification problem modulo fij conversion and a firstorder equational theory E, into a firstorder unification problem in a union of two nondisjoint equational theories including E and a calculus of explicit substitutions. A rulebased unification procedure in this combined theory is described and may be viewed as an extension of the one initially designed by G. Dowek, T. Hardin and C. Kirchner for performing unification of simply typed terms in a firstorder setting via the oecalculus of explicit substitutions. Additional rules are used to deal with the interaction between E and oe. 1 Introduction Unification modulo an equational theory plays an important role in automated deduction and in logic programming systems. For example, Prolog[NM88] is based on higherorder unification, ie. unification modulo the fijconversion. In order to design more expressive higherorder logic programming systems enhanced with a firstorder equational theory E,...