Discrete Mathematics & Theoretical Computer Science


Volume 4 n° 1 (2000), pp. 11-30

author:Alexandre Boudet
title:Unification of Higher-order Patterns modulo Simple Syntactic Equational Theories
keywords:Unification, Higher-order unification
abstract:We present an algorithm for unification of higher-order patterns modulo simple syntactic equational theories as defined by Kirchner [14]. The algorithm by Miller [17] for pattern unification, refined by Nipkow [18] is first modified in order to behave as a first-order unification algorithm. Then the mutation rule for syntactic theories of Kirchner [13,14] is adapted to pattern Eunification. If the syntactic algorithm for a theory E terminates in the first-order case, then our algorithm will also terminate for pattern Eunification. The result is a DAG-solved form plus some equations of the form lambda x.F(x) = lambda x. F(x^{pi}) where x^{\pi} is a permutation of x When all function symbols are decomposable these latter equations can be discarded, otherwise the compatibility of such equations with the solved form remains open.
reference: Alexandre Boudet (2000), Unification of Higher-order Patterns modulo Simple Syntactic Equational Theories , Discrete Mathematics and Theoretical Computer Science 4, pp. 11-30
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