Reduction Strategies and Acyclicity

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. Dedicated to Jean-Pierre Jouannaud on the occasion of his 60th birthday

• Type: Conference
• Year: 2007
• Where: BIRTHDAY
• Authors: Jan Willem Klop, Vincent van Oostrom, Femke van Raamsdonk
• Keywords: Applied Computing, BIRTHDAY 2007, Orthogonal Rewrite Systems, Reduction Cycles, Reduction Strategies