Reduction strategies and acyclicity

Authors:
Jan Willem Klop;Vincent van Oostrom;Femke van Raamsdonk
Affiliations:
Vrije Universiteit, Department of Theoretical Computer Science, Amsterdam and Radboud Universiteit Nijmegen, Department of Computer Science, Nijmegen and CWI, The Netherlands;Universiteit Utrecht, Department of Philosophy, Utrecht, The Netherlands;Vrije Universiteit, Department of Theoretical Computer Science, Amsterdam, The Netherlands
Venue:
Rewriting Computation and Proof
Year:
2007

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Abstract

In this paper we review some well-known theory about reduction strategies of various kinds: normalizing, outermost-fair, cofinal, Church-Rosser. A stumbling block in the definition of such strategies is the presence of reduction cycles that may 'trap' a strategy as it is memory-free. We exploit a recently (re)discovered fact that there are no reduction cycles in orthogonal rewrite systems when each term has a normal form, in order to enhance some of the theorems on strategies, both with respect to their scope and the proof of their correctness.