Expression reduction systems and extensions: An overview. (English) Zbl 1171.68510
Middeldorp, Aart (ed.) et al., Processes, terms and cycles: steps on the road to infinity. Essays dedicated to Jan Willem Klop on the occasion of his 60th birthday. Berlin: Springer (ISBN 3-540-30911-X/pbk). Lecture Notes in Computer Science 3838, 496-553 (2005).
Summary: 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.
For the entire collection see [Zbl 1097.68007].
For the entire collection see [Zbl 1097.68007].
