Difference between revisions of "Zilde"
m (Glyphs category) 

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* <source lang=apl inline>,¨⍬</source> gives an empty vector of 1element numeric vectors, identical to <source lang=apl inline>0⍴⊂,0</source>.  * <source lang=apl inline>,¨⍬</source> gives an empty vector of 1element numeric vectors, identical to <source lang=apl inline>0⍴⊂,0</source>.  
* <source lang=apl inline>⍪¨⍬</source> gives an empty vector of 1by1 numeric matrices, identical to <source lang=apl inline>0⍴⊂,0</source>.  * <source lang=apl inline>⍪¨⍬</source> gives an empty vector of 1by1 numeric matrices, identical to <source lang=apl inline>0⍴⊂,0</source>.  
−  {{APL builtins}}{{APL glyphs}}[[Category:Primitive arrays]]  +  {{APL builtins}}{{APL glyphs}}[[Category:Primitive arrays]][[Category:Glyphs]] 
Revision as of 20:32, 24 November 2020
⍬

Zilde (⍬
), or Zerotilde (which the common name is a portmanteau of), is the empty numeric vector. It shares its name with the glyph used to represent it, a zero overstruck with a tilde. 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.
The glyph Zilde is notable in that it represents an array rather than a primitive function or primitive operator. This usage was introduced in NARS and included in Dyalog APL and many other dialects influenced by these. In most of these 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. A similar special literal is SHARP APL's nil (∘
), which corresponds to ⊂⍬
, and Dyalog APL's namespace reference to the root of the workspace (#
).
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 0row 0column numeric matrix, identical to0 0⍴0
.⍪⍬
gives a 0row 0column numeric matrix, identical to0 1⍴0
.,¨⍬
gives an empty vector of 1element numeric vectors, identical to0⍴⊂,0
.⍪¨⍬
gives an empty vector of 1by1 numeric matrices, identical to0⍴⊂,0
.
APL glyphs [edit]  

Information  Glyph ∙ Typing glyphs (on Linux) ∙ Unicode ∙ Fonts ∙ Mnemonics 
Individual glyphs  Jot (∘ ) ∙ Right Shoe (⊃ ) ∙ Up Arrow (↑ ) ∙ Zilde (⍬ ) ∙ High minus (¯ ) ∙ Dot (. ) ∙ Del (∇ )
