# 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 [edit]
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Built-ins | Primitives (functions, operators) ∙ Quad name |

Array model | Shape ∙ Rank ∙ Depth ∙ Bound ∙ Index (Indexing) ∙ Axis ∙ Ravel ∙ Ravel order ∙ Element ∙ Scalar ∙ Vector ∙ Matrix ∙ Simple scalar ∙ Simple array ∙ Nested array ∙ Cell ∙ Major cell ∙ Subarray ∙ Empty array ∙ Prototype |

Data types | Number (Boolean, Complex number) ∙ Character (String) ∙ Box ∙ Namespace ∙ Function array |

Concepts and paradigms | Conformability (Scalar extension, Leading axis agreement) ∙ Scalar function (Pervasion) ∙ Identity element ∙ Complex floor ∙ Total array ordering ∙ Tacit programming (Function composition, Close composition) ∙ Glyph |

Errors | LIMIT ERROR ∙ RANK ERROR ∙ SYNTAX ERROR ∙ DOMAIN ERROR ∙ LENGTH ERROR ∙ INDEX ERROR ∙ VALUE ERROR |