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Abstract: We show that it is decidable whether a third-order matching problem in the polymorphic lambda calculus has a solution. The proof is constructive in the sense that an algorithm can be extracted from it that, given such a problem, returns a substitution if it has a solution and fail otherwise. 1 Introduction This paper is a contribution to the theory of (pattern) matching in higher order type theory. The starting point is the fact that third-order matching is decidable in the simply typed lambda ... (Update)
Context of citations to this paper: More
.... such as e.g. polymorphic calculi or Godel s system T, pattern matching is known to be undecidable in general [3] and decidable at third order [11, 12]. 2.1 Types Definition 1. The set T of types is the smallest set containing the constant symbol o (basic type) and such that oe...
.... and dependent types, and type constructors [9, 14] Third order matching is also decidable for simply [10] and polymorphically [15] typed terms, but generating all the matches is somewhat complicated by the fact that the set of matches is potentially in nite, even when...
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2: Third order matching is decidable - Dowek - 1992
BibTeX entry: (Update)
J. Springintveld. Third-order matching in the polymorphic lambda calculus. In G. Dowek, J. Heering, K. Meinke, and B. Moller, editors, Proc. Higher-Order Algebra, Logic and Term Rewriting, volume 1074 of LNCS, Paderborn, Germany, September 1995. Springer-Verlag. http://citeseer.ist.psu.edu/springintveld95thirdorder.html More
@inproceedings{ springintveld96thirdorder,
author = "J. G.~Springintveld",
title = "Third-order matching in the polymorphic lambda calculus",
booktitle = "Proceedings of the Second International Workshop on Higher-Order Algebra, Logic, and Term Rewriting ({HOA} '95)",
volume = "1074",
publisher = "Springer-Verlag",
editor = "G.~Dowek and J.~Heering and K.~Meinke and B.~M{\"o}ller",
pages = "221--238",
year = "1996",
url = "citeseer.ist.psu.edu/springintveld95thirdorder.html" }
Citations (may not include all citations):382 Lambda calculi with types - Barendregt - 1992
97 The undecidability of the second-order unification problem (context) - Goldfarb - 1981
86 Functional Programming (context) - Field, Harrison - 1989
37 Third order matching is decidable - Dowek - 1992
28 The Church-Rosser property for fij-reduction in typed -calcu.. (context) - Geuvers - 1992
27 Information and Control (context) - Coquand, Huet et al. - 1988
25 Modular proof of strong normalisation for the calculus of co.. (context) - Geuvers, Nederhof - 1989
19 A complete proof synthesis method for the cube of type syste.. (context) - Dowek - 1993
19 Representing Logics in Type Theory (context) - Gardner - 1992
13 A second-order pattern matching algorithm for the cube of ty.. (context) - Dowek - 1991
8 The undecidability of pattern matching in calculi where prim.. (context) - Dowek - 1993
8 On equivalence classes of interpolation equations (context) - Padovani - 1994
6 Third-order matching in the presence of type constructors - Springintveld - 1994
4 eme ordre dans les calculs avec types d (context) - Dowek, filtrage - 1991
2 Fourth order dual interpolation is decidable (context) - Padovani - 1994
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