Prototype: Difference between revisions

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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 ==
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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>.  
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>.  
<source lang=apl>
<source lang=apl>
       ⊢a ← 5 'c' ¯2
       ⎕←a ← 5 'c' ¯2
5 c ¯2
5 c ¯2
       4 ↑ a
       4 ↑ a
Line 35: Line 33:
{{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.
<source lang=apl>
<source lang=apl>
       ⊢x ← ⊂'de'(3 4 5)  ⍝ A complicated scalar array
       ⎕←x ← ⊂'de'(3 4 5)  ⍝ A complicated scalar array
┌──────────┐
┌──────────┐
│┌──┬─────┐│
│┌──┬─────┐│
Line 56: Line 54:
</source>
</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]]

Revision as of 05:49, 9 June 2020

The prototype of an array is, in the nested array model, an array which gives information about the type and structure of its elements. It is derived from the first element of the array in ravel order, or, if the array is 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 elements.

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 ' ' is the prototype of a character array:

      ¯12 ↑ 'whitespace'
  whitespace
      (5 1 5/1 ¯2 1) \ 'whitespace'
white  space

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 0, the prototype for a simple numeric array.

      (⍳⍤0) 2 3 4
1 2 0 0
1 2 3 0
1 2 3 4
Works in: Dyalog APL

An array's prototype is based on its first element, so the array a below has a simple numeric prototype, as does any prefix of a. This property even applies to empty arrays: the expression 0 ↑ a results in an empty array with the same prototype as a.

      ⎕←a ← 5 'c' ¯2
5 c ¯2
      4 ↑ a
5 c ¯2 0
      4 ↑ 2 ↑ a
5 c 0 0
      4 ↑ 0 ↑ a
0 0 0 0
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.

      ⎕←x ← ⊂'de'(3 4 5)   ⍝ A complicated scalar array
┌──────────┐
│┌──┬─────┐│
││de│3 4 5││
│└──┴─────┘│
└──────────┘
      0 1 \ x             ⍝ Its fill element is nested
┌──────────┬──────────┐
│┌──┬─────┐│┌──┬─────┐│
││  │0 0 0│││de│3 4 5││
│└──┴─────┘│└──┴─────┘│
└──────────┴──────────┘
      e ← 0 ↑ x           ⍝ An empty array based on x
      ⊃e                  ⍝ Disclosing gets the prototype
┌──┬─────┐
│  │0 0 0│
└──┴─────┘
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:

      ⊤↑ (1 2 'ab') 3 4
┌─┬─┬──┐
│0│0│  │
└─┴─┴──┘
Works in: NARS2000
      ∊⊃ (1 2 'ab') 3 4
┌─┬─┬──┐
│0│0│  │
└─┴─┴──┘
Works in: Dyalog APL with migration level=0

However, an array's prototype can always be determined by reshaping the array to become empty, and then coercing out a fill element:

      ⊃ 0 ⍴ (1 2 'ab') 3 4
┌─┬─┬──┐
│0│0│  │
└─┴─┴──┘
Works in: Dyalog APL with migration level≥2, APL2, APLX

Try it now!

      ⊃ 0 ⍴ (1 2 'ab') 3 4
┌─┬─┬──┐
│0│0│  │
└─┴─┴──┘
Works in: Dyalog APL with migration level=1

APLs with a flat array model do not typically store prototype information, instead using only the array's type (character, numeric, or boxed) to determine its fills.

APL features [edit]
Built-ins Primitives (functions, operators) ∙ Quad name
Array model ShapeRankDepthBoundIndex (Indexing) ∙ AxisRavelRavel orderElementScalarVectorMatrixSimple scalarSimple arrayNested arrayCellMajor cellSubarrayEmpty arrayPrototype
Data types Number (Boolean, Complex number) ∙ Character (String) ∙ BoxNamespaceFunction array
Concepts and paradigms Conformability (Scalar extension, Leading axis agreement) ∙ Scalar function (Pervasion) ∙ Identity elementComplex floorArray ordering (Total) ∙ Tacit programming (Function composition, Close composition) ∙ GlyphLeading axis theoryMajor cell search
Errors LIMIT ERRORRANK ERRORSYNTAX ERRORDOMAIN ERRORLENGTH ERRORINDEX ERRORVALUE ERROREVOLUTION ERROR