Zilde

⍬

Zilde (⍬) or Zero-tilde (which the common name is a portmanteau of), is a glyph representing 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 0⍴0. 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.

Zilde can be used to concisely produce other empty arrays, for example:

• ⍬⊤⍬ gives a 0-row 0-column numeric matrix, identical to 0 0⍴0.
• ⍪⍬ gives a 0-row 0-column numeric matrix, identical to 0 1⍴0.
• ,¨⍬ gives an empty vector of 1-element numeric vectors, identical to 0⍴⊂,0.
• ⍪¨⍬ gives an empty vector of 1-by-1 numeric matrices, identical to 0⍴⊂,0.