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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 [[box]]ed arrays of arbitrary [[shape]] and [[rank]]. While [[J]] has had such an ordering since | 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 1996 (release 3.01), 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 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. | 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. | ||