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Orthogonality as a property of term rewriting systems (TRSs) describes where the reduction rules of the system are all left-linear, that is each variable occurs only once on the left hand side of each reduction rule, and there is no overlap between them, i.e. the TRS has no critical pairs.
A term rewriting given by a set of rules can be viewed as an abstract rewriting system as defined above, with terms as its objects and as its rewrite relation. For example, x ∗ ( y ∗ z ) → ( x ∗ y ) ∗ z {\displaystyle x*(y*z)\rightarrow (x*y)*z} is a rewrite rule, commonly used to establish a normal form with respect to the ...
A term rewriting system is said to be orthogonal if it is left-linear and is non-ambiguous. Orthogonal term rewriting systems are confluent. In certain cases, the word normal is used to mean orthogonal, particularly in the geometric sense as in the normal to a surface.
Parallel outermost and Gross-Knuth reduction are hypernormalizing for all almost-orthogonal term rewriting systems, meaning that these strategies will eventually reach a normal form if it exists, even when performing (finitely many) arbitrary reductions between successive applications of the strategy. [8]
The converse of a rewrite order is again a rewrite order. While rewrite orders exist that are total on the set of ground terms ("ground-total" for short), no rewrite order can be total on the set of all terms. [note 3] [5] A term rewriting system {l 1::=r 1,...,l n::=r n, ...} is terminating if its rules are a subset of a reduction ordering ...
Download as PDF; Printable version; In other projects Wikidata item; ... Pages in category "Rewriting systems" The following 36 pages are in this category, out of 36 ...
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