Strongly sequential and inductively sequential term rewriting systems

by Michael Hanus, Salvador Lucas, Aart Middeldorp

Information Processing Letters, Vol. 67, No. 1, pp. 1-8, 1998
© Elsevier

The concept of definitional tree by Antoy serves to introduce control information into the bare set of rules of a constructor-based term rewriting system (TRS). TRSs whose rules can be arranged into a definitional tree are calledinductively sequential. By relying on the existence of such a definitional tree, an optimal rewriting strategy, theoutermost-needed strategyis defined. Optimality was proved w.r.t. the Huet and Léevy's theory of neededness. In this paper, we prove that strongly sequential and inductively sequential constructor-based TRSs coincide. We also show that outermost-needed rewriting only reduces strongly needed redexes.

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