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Theoretical Computer Science 165:75-95, 1996. A Sequential Reduction Strategy

Summary: Theoretical Computer Science 165:75-95, 1996.
A Sequential Reduction Strategy
Sergio Antoy
Portland State University, U.S.A.
Aart Middeldorp
University of Tsukuba, Japan
Kennaway proved the remarkable result that every (almost) orthogonal term rewriting system
admits a computable sequential normalizing reduction strategy. In this paper we present a
computable sequential reduction strategy similar in scope, but simpler and more general.
Our strategy can be thought of as an outermost-fair-like strategy that is allowed to be unfair
to some redex of a term when contracting the redex is useless for the normalization of the
term. Unlike the strategy of Kennaway, our strategy does not rely on syntactic restrictions
that imply confluence. On the contrary, it can easily be applied to any term rewriting system,
and we show that the class of term rewriting systems for which our strategy is normalizing
properly includes all (almost) orthogonal systems. Our strategy is more versatile; in case of
(almost) orthogonal term rewriting systems, it can be used to detect certain cases of non-
termination. Our normalization proof is more accessible than Kennaway's. We also show


Source: Antoy, Sergio - Department of Computer Science, Portland State University


Collections: Computer Technologies and Information Sciences