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Abstract: Higher-order unification is equational unification for βη-conversion. But it is not first-order equational unification, as substitution has to avoid capture. In this paper higher-order unification is reduced to first-order equational unification in a suitable theory: the λσ-calculus of explicit substitutions. (Update)
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BibTeX entry: (Update)
Gilles Dowek, Th`er'ese Hardin, and Claude Kirchner. Higher-order unification via explicit substitutions. In Tenth Annual IEEE Symposium on Logic in Computer Science, pages 366--374, San Diego, California, June 1995. IEEE Computer Society Press. http://citeseer.ist.psu.edu/article/dowek95higherorder.html More
@inproceedings{ dowek95higherorder,
author = "Gilles Dowek and Th{\'e}r{\`e}se Hardin and Claude Kirchner",
title = "Higher-Order Unification via Explicit Substitutions",
booktitle = "Proceedings of the Tenth Annual Symposium on Logic in Computer Science",
month = "June",
publisher = "IEEE Computer Society Press",
address = "San Diego, California",
editor = "D. Kozen",
pages = "366--374",
year = "1995",
url = "citeseer.ist.psu.edu/article/dowek95higherorder.html" }
Citations (may not include all citations):382 Lambda calculi with types - Barendregt - 1992
137 Journal of Functional Programming (context) - Abadi, Cardelli et al. - 1991
125 Solving equations in abstract algebras: a rule-based survey .. (context) - Jouannaud, Kirchner - 1991
114 Building-in equational theories (context) - Plotkin - 1972
42 Resolution in type theory (context) - Andrews - 1971
32 Higherorder unication via explicit substitutions (context) - Dowek, Hardin et al. - 1994
25 Elsevier Science Publishers B (context) - Barendregt, its et al. - 1984
19 A complete proof synthesis method for the cube of type syste.. (context) - Dowek - 1993
15 Higher order unication revisited: Complete sets of tranforma.. (context) - Snyder, Gallier - 1989
5 ConAEuence properties of weak and strong calculi of explicit.. (context) - Curien, Hardin et al. - 1992
5 Normalizing narrowing for weakly terminating and conAEuent s.. (context) - Werner - 1994
4 A unication algorithm for typed lambda calculus (context) - Huet - 1975
3 tude pour les substitutions explicites (context) - Curien, Rios et al. - 1991
2 Higher-order unication via combinators (context) - Dougherty - 1993
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