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Published in:
2005 | OriginalPaper | Chapter
Expression Reduction Systems and Extensions: An Overview
Authors : John Glauert, Delia Kesner, Zurab Khasidashvili
Published in: Processes, Terms and Cycles: Steps on the Road to Infinity
Publisher: Springer Berlin Heidelberg
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Expression Reduction Systems is a formalism for higher-order rewriting, extending Term Rewriting Systems and the lambda-calculus. Here we give an overview of results in the literature concerning ERSs. We review confluence, normalization and perpetuality results for orthogonal ERSs. Some of these results are extended to orthogonal conditional ERSs. Further, ERSs with patterns are introduced and their confluence is discussed. Finally, higher-order rewriting is translated into equational first-order rewriting. The technique develops an isomorphic model of ERSs with variable names, based on de Bruijn indices.