Beside: Difference between revisions

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{{Built-in|Beside|∘}}, '''Compose''' or '''After''' is a [[primitive operator]]. It shares the glyph <source lang=apl inline>∘</source> with [[Bind]]. Called [[Dyadic function|dyadically]] with function operands <source lang=apl inline>f</source> and <source lang=apl inline>g</source>, it uses <source lang=apl inline>g</source> [[Monadic function|monadically]] to pre-processes the right argument before applying <source lang=apl inline>f</source> to the given left argument and pre-processed right argument. Called [[Monadic function|monadically]] with operands <source lang=apl inline>f</source> and <source lang=apl inline>g</source>, it applies <source lang=apl inline>f</source> to the result of applying <source lang=apl inline>g</source> to the argument.
{{Built-in|Beside|∘}}, '''Compose''' or '''After''' is a [[primitive operator]]. It shares the glyph [[Jot]] (<syntaxhighlight lang=apl inline>∘</syntaxhighlight>) with [[Bind]]. Called [[Dyadic function|dyadically]] with function [[operand]]s <syntaxhighlight lang=apl inline>f</syntaxhighlight> and <syntaxhighlight lang=apl inline>g</syntaxhighlight>, it uses <syntaxhighlight lang=apl inline>g</syntaxhighlight> [[Monadic function|monadically]] to pre-processes the right argument before applying <syntaxhighlight lang=apl inline>f</syntaxhighlight> to the given left argument and pre-processed right argument. Called [[Monadic function|monadically]] with operands <syntaxhighlight lang=apl inline>f</syntaxhighlight> and <syntaxhighlight lang=apl inline>g</syntaxhighlight>, it applies <syntaxhighlight lang=apl inline>f</syntaxhighlight> to the result of applying <syntaxhighlight lang=apl inline>g</syntaxhighlight> to the argument.


In usage, <source lang=apl inline>X f∘g Y</source> is equivalent to <source lang=apl inline>X f g Y</source>, and <source lang=apl inline>f∘g Y</source> is equivalent to <source lang=apl inline>f g Y</source>. Thus, beside can be defined as the [[dop]] <source lang=apl inline>{⍺←⊢ ⋄ ⍺ ⍺⍺ ⍵⍵ ⍵}</source>.
In usage, <syntaxhighlight lang=apl inline>X f∘g Y</syntaxhighlight> is equivalent to <syntaxhighlight lang=apl inline>X f g Y</syntaxhighlight>, and <syntaxhighlight lang=apl inline>f∘g Y</syntaxhighlight> is equivalent to <syntaxhighlight lang=apl inline>f g Y</syntaxhighlight>. Thus, beside can be defined as the [[dop]] <syntaxhighlight lang=apl inline>{⍺←⊢ ⋄ ⍺ ⍺⍺ ⍵⍵ ⍵}</syntaxhighlight>.


== Examples ==
== Examples ==
When use [[monadic]]ally, <source lang=apl inline>f∘g</source> behaves the same as [https://en.wikipedia.org/wiki/Function_composition function compositian].
When used [[monadic]]ally, <syntaxhighlight lang=apl inline>f∘g</syntaxhighlight> behaves the same as an [[atop]]:


<source lang=apl>
<syntaxhighlight lang=apl>
       -∘÷ 2  
       -∘÷ 2  
¯0.5
¯0.5
Line 12: Line 12:
       -(÷2)
       -(÷2)
¯0.5
¯0.5
</source>
</syntaxhighlight>


When use [[dyadic]]ally,  
When used [[dyadic]]ally, <syntaxhighlight lang=apl inline>f∘g</syntaxhighlight> forms a dyadic [[hook]]:


<source lang=apl>
<syntaxhighlight lang=apl>
       'oy'≡∘⌽'yo'
       'oy'≡∘⌽'yo'
1
1
Line 22: Line 22:
       'oy'≡⌽'yo'
       'oy'≡⌽'yo'
1
1
</source>
</syntaxhighlight>


When used with [[Commute]], <source lang=apl inline>f∘g</source> forms a [[Hook]].
When used monadically with [[Commute]], <syntaxhighlight lang=apl inline>f∘g</syntaxhighlight> forms a monadic [[hook]]:
<source lang=apl>
<syntaxhighlight lang=apl>
       ≡∘⌽⍨'UwU'
       ≡∘⌽⍨'UwU'
1
1
       ⍝ same as this, because operator is left-associative, unlike functions which is right-associative
       ⍝ same as this, because operators are left-associative, unlike functions which are right-associative
       'UwU'(≡∘⌽)⍨'UwU'
       (≡∘⌽)⍨'UwU'
1
1
       ⍝ same as
       ⍝ same as
       'UwU'≡⌽'UwU'
       'UwU'≡⌽'UwU'
1
1
</source>
</syntaxhighlight>


== External links ==
== External links ==
Line 44: Line 44:
=== Documentation ===
=== Documentation ===


* [https://help.dyalog.com/18.0/#Language/Primitive%20Operators/Beside.htm Dyalog]
* [https://help.dyalog.com/latest/#Language/Primitive%20Operators/Beside.htm Dyalog]


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

Latest revision as of 21:52, 10 September 2022

Beside (), Compose or After is a primitive operator. It shares the glyph Jot () with Bind. Called dyadically with function operands f and g, it uses g monadically to pre-processes the right argument before applying f to the given left argument and pre-processed right argument. Called monadically with operands f and g, it applies f to the result of applying g to the argument.

In usage, X fg Y is equivalent to X f g Y, and fg Y is equivalent to f g Y. Thus, beside can be defined as the dop { ⍺⍺ ⍵⍵ }.

Examples

When used monadically, fg behaves the same as an atop:

      -÷ 2 
¯0.5
      ⍝ same as
      -(÷2)
¯0.5

When used dyadically, fg forms a dyadic hook:

      'oy''yo'
1
      ⍝ same as
      'oy'≡⌽'yo'
1

When used monadically with Commute, fg forms a monadic hook:

      'UwU'
1
      ⍝ same as this, because operators are left-associative, unlike functions which are right-associative
      ()'UwU'
1
      ⍝ same as
      'UwU'≡⌽'UwU'
1

External links

Lessons

Documentation


APL built-ins [edit]
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Scalar
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Dyadic AddSubtractTimesDivideResiduePowerLogarithmMinimumMaximumBinomialComparison functionsBoolean functions (And, Or, Nand, Nor) ∙ GCDLCMCircularComplexRoot
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