Fritz Carlson: Difference between revisions

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'''Orthogonality''' as a property of [[term rewriting system]]s 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 (term rewriting)|overlap]] between them.  
 
Orthogonal term rewriting systems have the consequent property that all reducible expressions (redexes) within a term are completely disjoint -- that is, the redexes share no common function symbol.
 
For example, the term rewriting system with reduction rules
: <math> \rho_1\ :\ f(x, y) \rightarrow g(y)  </math>
: <math> \rho_2\ :\ h(y) \rightarrow f(g(y), y) </math>
is orthogonal -- it is easy to observe that each reduction rule is left-linear, and the left hand side of each reduction rule shares no function symbol in common, so there is no overlap.
 
Orthogonal term rewriting systems are [[confluence (term rewriting)|confluent]].
 
{{comp-sci-stub}}
 
[[Category:Rewriting systems]]

Latest revision as of 19:26, 28 December 2014

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