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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 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.
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 ...
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]
Rewriting s to t by a rule l::=r.If l and r are related by a rewrite relation, so are s and t.A simplification ordering always relates l and s, and similarly r and t.. In theoretical computer science, in particular in automated reasoning about formal equations, reduction orderings are used to prevent endless loops.
Given a set E of equations between terms, the following inference rules can be used to transform it into an equivalent convergent term rewrite system (if possible): [4] [5] They are based on a user-given reduction ordering (>) on the set of all terms; it is lifted to a well-founded ordering ( ) on the set of rewrite rules by defining (s → t) (l → r) if
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 ...
Jan Willem Klop (born 1945) is a professor of applied logic at Vrije Universiteit in Amsterdam.He holds a Ph.D. in mathematical logic from Utrecht University.Klop is known for his work on the algebra of communicating processes, co-author of TeReSe [2] and his fixed point combinator [3]