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Total array ordering: Difference between revisions
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Total array ordering (view source)
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Some dialects do not implement a true ''total'' order because they support arrays without defining an order for them. | Some dialects do not implement a true ''total'' order because they support arrays without defining an order for them. | ||
Dyalog APL excludes [[simple scalar]]s other than nulls, [[number]]s or [[character]]s (namely [[namespace]]s, [[object]]s, and [[object representation]]s), because ordering those was considered "contentious but of little incremental benefit."<ref name=bfh>[[Adám Brudzewsky|Brudzewsky, A.]], [[Jay Foad|J. Foad]], and R. Hui. [https://www.jsoftware.com/papers/TAOaxioms.htm TAO Axioms]. 2018-02-02.</ref> [[Roger Hui]] has argued that these scalars are not truly arrays, and are not in the scope of a total array ordering. However, the [[dfns workspace]] includes an APL model which is truly total, though it differs from the native implementation in ordering characters before numbers instead of the opposite.<ref>[[Dfns workspace]]. [http://dfns.dyalog.com/n_le.htm <syntaxhighlight lang=apl inline>le</ | Dyalog APL excludes [[simple scalar]]s other than nulls, [[number]]s or [[character]]s (namely [[namespace]]s, [[object]]s, and [[object representation]]s), because ordering those was considered "contentious but of little incremental benefit."<ref name=bfh>[[Adám Brudzewsky|Brudzewsky, A.]], [[Jay Foad|J. Foad]], and R. Hui. [https://www.jsoftware.com/papers/TAOaxioms.htm TAO Axioms]. 2018-02-02.</ref> [[Roger Hui]] has argued that these scalars are not truly arrays, and are not in the scope of a total array ordering. However, the [[dfns workspace]] includes an APL model which is truly total, though it differs from the native implementation in ordering characters before numbers instead of the opposite.<ref>[[Dfns workspace]]. [http://dfns.dyalog.com/n_le.htm <syntaxhighlight lang=apl inline>le</syntaxhighlight>] ― Total array ordering (TAO) comparison.</ref> | ||
NARS2000's excludes [[complex number]]s (including quaternions and octonions) from the ordering. It should be noted that these numbers do not belong to any [[wikipedia:ordered field|ordered field]]: any ordering that remains the same after adding a constant could not be compatible with multiplication in the sense that the product of any two numbers greater than zero is greater than zero.<ref name=bfh/> | NARS2000's excludes [[complex number]]s (including quaternions and octonions) from the ordering. It should be noted that these numbers do not belong to any [[wikipedia:ordered field|ordered field]]: any ordering that remains the same after adding a constant could not be compatible with multiplication in the sense that the product of any two numbers greater than zero is greater than zero.<ref name=bfh/> | ||