Zilde: Difference between revisions
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{{Primitive|⍬|Zilde}} 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 it has [[rank]] 1 (i.e. it is a vector), so it has exactly one [[axis]] (i.e. its shape is a 1-element vector) with the length 0. (Zilde's shape cannot be Zilde, as that would indicate that it had rank 0, i.e. it were a scalar.) 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. | |||
Zilde is notable for being | 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]]. Exceptions are: | ||
* [[Dyalog APL]]'s <source lang=apl inline>#</source> which is the current [[workspace]]'s root [[namespace]] | |||
* [[SHARP APL]]'s <source lang=apl inline>∘</source> which is ''nil'', or <source lang=apl inline>⊂⍬</source> | |||
* [[NARS2000]] and [[ngn/apl]]'s <source lang=apl inline>∞</source> denoting infinity | |||
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>) while comparing "all" their elements would seem to indicate that they are identical: | |||
<source lang=apl> | |||
⍬≡'' | |||
0 | |||
∧/⍬='' | |||
1 | |||
</source> | |||
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. | |||
{{APL built-ins}} | {{APL built-ins}} | ||
Revision as of 19:52, 30 October 2019
Template:Primitive is the empty numeric vector. It is the shape of any scalar, although its own shape is ,0. This is because it has rank 1 (i.e. it is a vector), so it has exactly one axis (i.e. its shape is a 1-element vector) with the length 0. (Zilde's shape cannot be Zilde, as that would indicate that it had rank 0, i.e. it were a scalar.) 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. Exceptions are:
- Dyalog APL's
#which is the current workspace's root namespace - SHARP APL's
∘which is nil, or⊂⍬ - NARS2000 and ngn/apl's
∞denoting infinity
It should be noted that the empty numeric vector (⍬) is distinct from the empty character vector ('') while comparing "all" their elements would seem to indicate that they are identical:
⍬≡''
0
∧/⍬=''
1
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.