Singleton
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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:
- 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.
| APL features [edit] | |
|---|---|
| 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 ∙ Array ordering (Total) ∙ Tacit programming (Function composition, Close composition) ∙ Glyph ∙ Leading axis theory ∙ Major cell search ∙ First-class function |
| Errors | LIMIT ERROR ∙ RANK ERROR ∙ SYNTAX ERROR ∙ DOMAIN ERROR ∙ LENGTH ERROR ∙ INDEX ERROR ∙ VALUE ERROR ∙ EVOLUTION ERROR |