# Singleton

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:

• The scalar <syntaxhighlight lang=apl inline>42</source>
• The vector <syntaxhighlight lang=apl inline>,42</source>
• The matrix <syntaxhighlight lang=apl inline>⍪42</source>
• The three-dimensional array <syntaxhighlight lang=apl inline>1 1 1⍴42</source>
• The nested scalar <syntaxhighlight lang=apl inline>⊂4 2</source>

Whether an array <syntaxhighlight lang=apl inline>X</source> is a singleton can be determined with <syntaxhighlight lang=apl inline>1=×/⍴X</source> or, less efficiently, with <syntaxhighlight lang=apl inline>1=≢,X</source>.

Every scalar <syntaxhighlight lang=apl inline>X</source> is a singleton, because <syntaxhighlight lang=apl inline>1=×/⍴X</source>, or alternatively <syntaxhighlight lang=apl inline>1=≢,X</source>.

Singletons may be subject to singleton extension.

Only simple Boolean singletons are valid representations of logical true and false for the purposes of control structures.

APL features 
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