Higher-Order Rewrite Systems and Their Confluence

Abstract

We introduce Higher-Order Rewrite Systems (HRS) which extend term rewriting to-terms. HRS can describe computations on arbitrary terms with bound variables. We show that rewriting is closely related to undirected equational reasoning , and extend three connuence results from term rewriting to HRS: the critical pair lemma by Knuth and Bendix, connuence of rewriting modulo equations a la Huet, and connuence of orthogonal HRS.

DOI: 10.1016/S0304-3975(97)00143-6

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@article{Mayr1998HigherOrderRS, title={Higher-Order Rewrite Systems and Their Confluence}, author={Richard Mayr and Tobias Nipkow}, journal={Theor. Comput. Sci.}, year={1998}, volume={192}, pages={3-29} }