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 42
• The vector ,42
• The matrix ⍪42
• The three-dimensional array 1 1 1⍴42
• The nested scalar ⊂4 2

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.

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