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A term rewriting system R is orthogonal if for each rule l [right arrow] r [element of] R the left-hand side l is linear (left-linearity) and for each nonvariable subterm l[|.
In orthogonal term rewriting systems, every term not in normal form has a redex that must be reduced to compute the term's normal form.
Consequently, the defined functions of an inductively sequential term rewriting system are completely defined over their application domains [Guttag and Horning 1978; Thiel 1984] (i.
Consider the following term rewriting system for subtraction:
This term rewriting system is inductively sequential and a definitional tree, T, of the operation "-" has an exempt node for the pattern 0 - s(X), i.
Let R be a term rewriting system without rules for [approximately equals] and [conjunction].
Since weakly orthogonal term rewriting systems lack a notion of needed redex, the strong optimality results of needed narrowing cannot be preserved by weakly needed narrowing.
1995] to provide a complete narrowing calculus for applicative term rewriting systems (which model the higher-order features of current functional languages).
Strongly sequential and inductively sequential term rewriting systems.
The adequacy of term graph rewriting for simulating term rewriting.
Sequentiality in orthogonal term rewriting systems.
Implementation of term rewritings with the evaluation strategy.