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{{Built-in|Each|¨}} is a [[primitive operator|primitive]] [[monadic operator]] which applies its [[operand]] to each [[element]] of the [[argument]]s, and returns an array whose elements are the results. If two arguments are given, their elements are matched using [[conformability]] rules.
{{Built-in|Each|¨}} is a [[primitive operator|primitive]] [[monadic operator]] which applies its [[operand]] to each [[element]] of the [[argument]]s, and returns an array whose elements are the results. If two arguments are given, their elements are matched using [[conformability]] rules.
== Definition ==
Each is defined only in [[Nested array model|nested]] APLs. Some [[Flat array model|flat]] APLs obtain analogous functionality by using an [[Under]] operator with [[close composition]] along with the [[Function rank|rank]]-0 function [[Disclose]] (or Unbox). In [[SHARP APL]] this is written <syntaxhighlight lang=apl inline>f¨></syntaxhighlight>. In [[J]] it is <syntaxhighlight lang=j inline>f&.></syntaxhighlight>.


Each is defined only in [[Nested array model|nested]] APLs. Some [[Flat array model|flat]] APLs obtain analogous functionality by using an [[Under]] operator with [[close composition]] along with the [[Function rank|rank]]-0 function [[Disclose]] (or Unbox). In [[SHARP APL]] this is written <source lang=apl inline>f¨></source>. In [[J]] it is <source lang=j inline>f&.></source>.
Each differs from the [[Rank operator]] with rank 0 in that the operand arguments and results are not [[enclose]]d. As the [[elements]] of a nested array they need not be [[scalar]]. <syntaxhighlight lang=apl inline>f¨</syntaxhighlight> can therefore be defined as <syntaxhighlight lang=apl inline>⊂⍤f⍥⊃⍤0</syntaxhighlight>.


Each differs from the [[Rank operator]] with rank 0 in that the operand arguments and results are not [[enclose]]d. As the [[elements]] of a nested array they need not be [[scalar]].
The Each operator has no effect on [[scalar function]]s, since these functions already map over each array element. For example, both expressions below have the same meaning, since <syntaxhighlight lang=apl inline>+</syntaxhighlight> is a scalar function.
<syntaxhighlight lang=apl>
      1 + 1 2 3 4
2 3 4 5
      1 +¨ 1 2 3 4
2 3 4 5
</syntaxhighlight>
 
== Examples ==
<syntaxhighlight lang=apl>
      1,1 2 3 ⍝ join 1 with 1 2 3
1 1 2 3
      1,¨1 2 3 ⍝ join 1 with each element of 1 2 3
┌───┬───┬───┐
│1 1│1 2│1 3│
└───┴───┴───┘
 
      x←'abc' 'def' 'ghi'
      ⌽x ⍝ reverse x
┌───┬───┬───┐
│ghi│def│abc│
└───┴───┴───┘
      ⌽¨x ⍝ reverse each element of x
┌───┬───┬───┐
│cba│fed│ihg│
└───┴───┴───┘
</syntaxhighlight>
 
=== Mapping ===
It is very common to pair up an entire array with each element of a different array. There are two common ways to do this using Each. The first is to [[enclose]] the argument that is to be used as a whole for each element of the other array:
<syntaxhighlight lang=apl>
      (⊂10 20 30),¨1 2 3  ⍝ Computes (10 20 30,1)(10 20 30,2)(10 20 30,3)
┌──────────┬──────────┬──────────┐
│10 20 30 1│10 20 30 2│10 20 30 3│
└──────────┴──────────┴──────────┘
      10 20 30,¨⊂1 2 3    ⍝ Computes (10,1 2 3)(20,1 2 3)(30,1 2 3)
┌────────┬────────┬────────┐
│10 1 2 3│20 1 2 3│30 1 2 3│
└────────┴────────┴────────┘
</syntaxhighlight>
The other method is by [[bind]]ing the argument that is to be used as a whole to the function, deriving a monadic function, which is then applied using Each:
<syntaxhighlight lang=apl>
      10 20 30∘,¨1 2 3  ⍝ Computes (10 20 30,1)(10 20 30,2)(10 20 30,3)
┌──────────┬──────────┬──────────┐
│10 20 30 1│10 20 30 2│10 20 30 3│
└──────────┴──────────┴──────────┘
      ,∘1 2 3¨10 20 30  ⍝ Computes (10,1 2 3)(20,1 2 3)(30,1 2 3)
┌────────┬────────┬────────┐
│10 1 2 3│20 1 2 3│30 1 2 3│
└────────┴────────┴────────┘
</syntaxhighlight>
Note how binding a right argument derives a monadic function which still takes its single argument on the right.
=== Selecting ===
An enclosed array is a [[scalar]], which is subject to [[scalar extension]]. This can be used to simulate [[Outer Product|outer product]] by a one-sided Each (pair the entire right argument with each element of the left argument, or vice versa). An application of this behavior is the "chipmunk idiom" <syntaxhighlight lang=apl inline>X⊃¨⊂Y</syntaxhighlight>, which simulates <syntaxhighlight lang=apl inline>Y[X]</syntaxhighlight> for (possibly nested) [[vector]] Y and [[simple]] X:
 
<syntaxhighlight lang=apl>
      (2 2⍴1 2 2 1)⊃¨⊂(1 2)(3 4)(5 6)  ⍝ Computes (1 2)(3 4)(5 6)[2 2⍴1 2 2 1]
┌───┬───┐
│1 2│3 4│
├───┼───┤
│3 4│1 2│
└───┴───┘
</syntaxhighlight>


== External links ==
== External links ==
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* [https://help.dyalog.com/latest/index.htm#Language/Primitive%20Operators/Each%20with%20Monadic%20Operand.htm Dyalog] (monadic operand), [https://help.dyalog.com/latest/index.htm#Language/Primitive%20Operators/Each%20with%20Dyadic%20Operand.htm Dyalog] (dyadic operand)
* [https://help.dyalog.com/latest/index.htm#Language/Primitive%20Operators/Each%20with%20Monadic%20Operand.htm Dyalog] (monadic operand), [https://help.dyalog.com/latest/index.htm#Language/Primitive%20Operators/Each%20with%20Dyadic%20Operand.htm Dyalog] (dyadic operand)
* [http://microapl.com/apl_help/ch_020_020_900.htm APLX]
* [http://microapl.com/apl_help/ch_020_020_900.htm APLX]
* [https://mlochbaum.github.io/BQN/doc/map.html#each BQN]


{{APL built-ins}}
{{APL built-ins}}[[Category:Primitive operators]]
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