Singleton: Difference between revisions

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A '''singleton''' is an [[array]] with [[bound]] 1. Equivalently, its [[shape]] consists entirely of 1s. It may have any [[rank]]. For example, all the following are singletons:
A '''singleton''' is an [[Array model|array]] with [[bound]] 1. Equivalently, its [[shape]] consists entirely of 1s. It may have any [[rank]]. For example, all the following are singletons:


* The [[scalar]] <source lang=apl inline>42</source>
* The [[scalar]] <source lang=apl inline>42</source>

Revision as of 08:57, 13 May 2020

A singleton is an array with bound 1. Equivalently, its shape consists entirely of 1s. It may have any rank. For example, all the following are singletons:

Whether an array X is a singleton can be determined with 1/X or, less efficiently, with 1=≢,X.

Every scalar X is a singleton, because 1/X, or alternatively 1=≢,X.

Singletons may be subject to singleton extension.

APL features [edit]
Built-ins Primitives (functions, operators) ∙ Quad name
Array model ShapeRankDepthBoundIndex (Indexing) ∙ AxisRavelRavel orderElementScalarVectorMatrixSimple scalarSimple arrayNested arrayCellMajor cellSubarrayEmpty arrayPrototype
Data types Number (Boolean, Complex number) ∙ Character (String) ∙ BoxNamespaceFunction array
Concepts and paradigms Conformability (Scalar extension, Leading axis agreement) ∙ Scalar function (Pervasion) ∙ Identity elementComplex floorTotal array orderingTacit programming (Function composition, Close composition) ∙ Glyph
Errors LIMIT ERRORRANK ERRORSYNTAX ERRORDOMAIN ERRORLENGTH ERRORINDEX ERRORVALUE ERROR