Total array ordering: Difference between revisions
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In APL, a '''total array ordering''', or '''TAO''', is an [[ordering]] on all arrays which is used by [[Grade]] and [[Interval Index]]. Traditionally ordering is defined only for [[simple]] arrays of the same [[shape]], so TAO refers to the extension to [[Nested array|nested]] or [[ | In APL, a '''total array ordering''', or '''TAO''', is an [[ordering]] on all arrays which is used by [[Grade]] and [[Interval Index]]. Traditionally ordering is defined only for [[simple]] arrays of the same [[shape]], so TAO refers to the extension to [[Nested array|nested]] or [[box]]ed arrays of arbitrary [[shape]] and [[rank]]. While [[J]] has had such an ordering since an early version, total array ordering in APL was first seen in [[Dyalog APL 17.0]]. | ||
Dyalog's ordering is not a true total order because it does not handle arrays containing [[simple | Dyalog's ordering is not a true total order because it does not handle arrays containing [[simple scalar]]s other than [[number]]s or [[character]]s, such as [[namespace]]s or [[object]]s. [[Roger Hui]] has argued that these scalars are not truly arrays, and are not in the scope of a total array ordering. | ||
The name "total array ordering" is taken partly from the mathematical concept of a [ | The name "total array ordering" is taken partly from the mathematical concept of a [[wikipedia:total order|total order]], which must order any two elements, with elements ordering equally only if they are identical. This concept is transferred to APL by specifying that arrays should only order equally if they [[match]]. | ||
== External links == | == External links == | ||
Revision as of 11:17, 15 November 2019
In APL, a total array ordering, or TAO, is an ordering on all arrays which is used by Grade and Interval Index. Traditionally ordering is defined only for simple arrays of the same shape, so TAO refers to the extension to nested or boxed arrays of arbitrary shape and rank. While J has had such an ordering since an early version, total array ordering in APL was first seen in Dyalog APL 17.0.
Dyalog's ordering is not a true total order because it does not handle arrays containing simple scalars other than numbers or characters, such as namespaces or objects. Roger Hui has argued that these scalars are not truly arrays, and are not in the scope of a total array ordering.
The name "total array ordering" is taken partly from the mathematical concept of a total order, which must order any two elements, with elements ordering equally only if they are identical. This concept is transferred to APL by specifying that arrays should only order equally if they match.
External links
TAO Axioms for Dyalog APL