Zilde

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Zilde () or Zero-tilde (which the common name is a portmanteau of), is the empty numeric vector. It is the shape of any scalar, although its own shape is ,0. This is because, as a vector, it has exactly one axis, and this axis has length 0. Zilde is equivalent to 0 and 0 and 00. Being numeric, Zilde's prototype is 0.

Zilde is notable for being an APL glyph which represents an array rather than a primitive function or primitive operator. In most APLs it is the only array literal which is produced using its own token rather than being part of a family of array literals like numeric literals, strings, or system constants (an exception is SHARP APL's nil (), which is the same as ).

It should be noted that the empty numeric vector () is distinct from the empty character vector ('') even though they have the same shape and the same elements:

      /=''
1
      ''
0

This is because ='' itself returns an empty numeric vector, and reducing an empty vector with the Logical And function () yields the identity element of Logical And, which is 1. However, match takes empty array prototypes into account as well as shapes and elements, so it indicates that the arrays are different.


APL built-ins [edit]
Primitive functions
Scalar
Monadic ConjugateNotRollType
Dyadic AddSubtractEqual to (Xnor) ∙ Not Equal to (Xor)
Non-Scalar
Structural ShapeReshapeTallyDepthRavelReverseRazeMixCut (K)
Selection TakeDropUniqueIdentity
Selector Interval Index
Computational MatchNot MatchNub Sieve
Primitive operators Each
Quad names
Arrays Index originMigration level
Functions
Operators
Other ZildeHigh minusFunction axis