Date: 20 Jun 2005

Higher-order equational unification via explicit substitutions

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We show how to reduce the unification problem modulo βη-conversion and a first-order equational theory E, into a first-order unification problem in a union of two non-disjoint equational theories including E and a calculus of explicit substitutions. A rule-based 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 λ-terms in a first-order setting via the λσ-calculus of explicit substitutions. Additional rules are used to deal with the interaction between E and λσ.