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{{Built-in|⍬}} is the [[empty]] [[numeric]] [[vector]]. It is the [[shape]] of any [[scalar]], although its own shape is <source lang=apl inline>,0</source>. This is because, as a vector, it has exactly one [[axis]], and this axis has length 0. Zilde is equivalent to <source lang=apl inline>⍳0</source> and <source lang=apl inline>⍴0</source> and <source lang=apl inline>0⍴0</source>. Being [[numeric]], Zilde's [[prototype]] is 0. | {{Built-in|Zilde|⍬}}, or '''Zero-tilde''' (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 [[wikipedia:overstrike|overstruck]] with a tilde. It is the [[shape]] of any [[scalar]], although its own shape is <source lang=apl inline>,0</source>. This is because, as a vector, it has exactly one [[axis]], and this axis has length 0. Zilde is equivalent to <source lang=apl inline>⍳0</source> and <source lang=apl inline>⍴0</source> and <source lang=apl inline>0⍴0</source>. 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 literal]]s, [[string]]s, or [[system constant]]s. A similar special literal is [[SHARP APL]]'s [[nil]] (<source lang=apl inline>∘</source>), which corresponds to <source lang=apl inline>⊂⍬</source>, and Dyalog APL's [[namespace]] reference to the root of the [[workspace]] (<source lang=apl inline>#</source>). | |||
It should be noted that the empty numeric vector (<source lang=apl inline>⍬</source>) is distinct from the empty character vector (<source lang=apl inline>''</source>) even though they have the same shape and the same elements: | It should be noted that the empty numeric vector (<source lang=apl inline>⍬</source>) is distinct from the empty character vector (<source lang=apl inline>''</source>) even though they have the same shape and the same elements: | ||
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This is because <source lang=apl inline>⍬=''</source> itself returns an empty numeric vector, and reducing an empty vector with the [[Logical And]] function (<source lang=apl inline>∧</source>) yields the [[identity element]] of Logical And, which is 1. However, [[match]] takes [[empty]] array [[ | This is because <source lang=apl inline>⍬=''</source> itself returns an empty numeric vector, and reducing an empty vector with the [[Logical And]] function (<source lang=apl inline>∧</source>) yields the [[identity element]] of Logical And, which is 1. However, [[match]] takes [[empty]] array [[prototype]]s into account as well as shapes and elements, so it indicates that the arrays are different. | ||
{{APL built-ins}} | Zilde can be used to concisely produce other empty arrays, for example: | ||
* <source lang=apl inline>⍬⊤⍬</source> gives a 0-row 0-column numeric matrix, identical to <source lang=apl inline>0 0⍴0</source>. | |||
* <source lang=apl inline>⍪⍬</source> gives a 0-row 0-column numeric matrix, identical to <source lang=apl inline>0 1⍴0</source>. | |||
* <source lang=apl inline>,¨⍬</source> gives an empty vector of 1-element numeric vectors, identical to <source lang=apl inline>0⍴⊂,0</source>. | |||
* <source lang=apl inline>⍪¨⍬</source> gives an empty vector of 1-by-1 numeric matrices, identical to <source lang=apl inline>0⍴⊂,0</source>. | |||
{{APL built-ins}}{{APL glyphs}}[[Category:Primitive arrays]][[Category:Glyphs]] | |||