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In the [[nested array model]], an array's prototype is an array which gives information about the type and structure of its [[Element|elements]]. It is derived from the first element of the array in [[ravel order]], or, if the array is [[Empty array|empty]], from information stored alongside the array (usually this information is just the prototype itself). An array's prototype is used as a [[fill element]] for operations involving that array.
The '''prototype''' of an array is, in the [[nested array model]], an array which gives information about the type and structure of its [[element]]s. It is derived from the first element of the array in [[ravel order]], or, if the array is [[Empty array|empty]], from information stored alongside the array (usually this information is just the prototype itself). An array's prototype is used as a [[fill element]] for operations involving that array, and to determine some [[identity element]]s.
 
APLs with a [[flat array model]] do not typically store prototype information, instead using only the array's type ([[character]], [[numeric]], or [[Box|boxed]]) to determine its [[Fill element|fills]].


== Examples ==
== Examples ==


The prototype is used when an array is expanded or when empty elements are inserted in some other way. [[Take]] and [[Expand]] on a [[character]] array produce an array with spaces, because <code>' '</code> is the prototype of a character array:
The prototype is used when an array is expanded or when empty elements are inserted in some other way. [[Take]] and [[Expand]] on a [[character]] array produce an array with spaces, because <source lang=apl inline>' '</source> is the prototype of a character array:
<pre class=apl>
<source lang=apl>
       ¯12 ↑ 'whitespace'
       ¯12 ↑ 'whitespace'
   whitespace
   whitespace
       (5 1 5/1 ¯2 1) \ 'whitespace'
       (5 1 5/1 ¯2 1) \ 'whitespace'
white  space
white  space
</pre>
</source>


The [[Rank operator]] combines its left operand's result cells by extending them to a common shape like [[Mix]] does. Numeric vectors of different lengths will be expanded with <code>0</code>, the prototype for a simple numeric array.
The [[Rank operator]] combines its left operand's result cells by extending them to a common shape like [[Mix]] does. Numeric vectors of different lengths will be expanded with <source lang=apl inline>0</source>, the prototype for a simple numeric array.
<pre class=apl>
<source lang=apl>
       (⍳⍤0) 2 3 4
       (⍳⍤0) 2 3 4
1 2 0 0
1 2 0 0
1 2 3 0
1 2 3 0
1 2 3 4
1 2 3 4
</pre>
</source>
{{Works in|[[Dyalog APL]]}}
{{Works in|[[Dyalog APL]]}}


An array's prototype is based on its first element, so the array <code>a</code> below has a simple numeric prototype, as does any prefix of <code>a</code>. This property even applies to empty arrays: the expression <code>0 ↑ a</code> results in an empty array with the same prototype as <code>a</code>.  
An array's prototype is based on its first element, so the array <source lang=apl inline>a</source> below has a simple numeric prototype, as does any prefix of <source lang=apl inline>a</source>. This property even applies to empty arrays: the expression <source lang=apl inline>0 ↑ a</source> results in an empty array with the same prototype as <source lang=apl inline>a</source>.  
<pre class=apl>
<source lang=apl>
       ⊢a ← 5 'c' ¯2
       ⎕←a ← 5 'c' ¯2
5 c ¯2
5 c ¯2
       4 ↑ a
       4 ↑ a
Line 32: Line 30:
       4 ↑ 0 ↑ a
       4 ↑ 0 ↑ a
0 0 0 0
0 0 0 0
</pre>
</source>
{{Works in|[[Dyalog APL]]}}
{{Works in|[[Dyalog APL]]}}


The prototype of an array may be nested. Here, we inspect the prototype of an array containing both character and numeric data. In the prototype, all characters are converted to spaces and all numbers to zeros. Thus the prototype retains type and structure information but not specific values.
The prototype of an array may be [[nested]]. Here, we inspect the prototype of an array containing both character and numeric data. In the prototype, all characters are converted to spaces and all numbers to zeros. Thus the prototype retains type and structure information but not specific values.
<pre class=apl>
<source lang=apl>
       ⊢x ← ⊂'de'(3 4 5)  ⍝ A complicated scalar array
       ⎕←x ← ⊂'de'(3 4 5)  ⍝ A complicated scalar array
┌──────────┐
┌──────────┐
│┌──┬─────┐│
│┌──┬─────┐│
Line 54: Line 52:
│  │0 0 0│
│  │0 0 0│
└──┴─────┘
└──┴─────┘
</pre>
</source>
{{Works in|[[Dyalog APL]]}}
{{Works in|[[Dyalog APL]]}}
== Support ==
A few dialects have [[Type]] as a [[primitive function]], and in those, the prototype is simply the type of the first element:
<source lang=apl>
      ⊤↑ (1 2 'ab') 3 4
┌─┬─┬──┐
│0│0│  │
└─┴─┴──┘
</source>
{{Works in|[[NARS2000]]}}
<source lang=apl>
      ∊⊃ (1 2 'ab') 3 4
┌─┬─┬──┐
│0│0│  │
└─┴─┴──┘
</source>
{{Works in|[[Dyalog APL]] with [[migration level]]<nowiki>=</nowiki>0}}
However, an array's prototype can always be determined by reshaping the array to become empty, and then coercing out a fill element:
<source lang=apl>
      ⊃ 0 ⍴ (1 2 'ab') 3 4
┌─┬─┬──┐
│0│0│  │
└─┴─┴──┘
</source>
{{Works in|[[Dyalog APL]] with [[migration level]]<nowiki>≥</nowiki>2, [[APL2]], [[APLX]]}}
[https://tryapl.org/?a=%u2283%200%20%u2374%20%281%202%20%27ab%27%29%203%204&run Try it now!]
<source lang=apl>
      ⊃ 0 ⍴ (1 2 'ab') 3 4
┌─┬─┬──┐
│0│0│  │
└─┴─┴──┘
</source>
{{Works in|[[Dyalog APL]] with [[migration level]]<nowiki>=</nowiki>1}}
APLs with a [[flat array model]] do not typically store prototype information, instead using only the array's type ([[character]], [[numeric]], or [[Box|boxed]]) to determine its [[Fill element|fills]].
{{APL features}}[[Category:Array relationships]][[Category:Array characteristics]]
Retrieved from ‘https://aplwiki.com/wiki/Special:MobileDiff/738...4769’

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