Reverse Compose: Difference between revisions

Jump to navigation Jump to search
784 bytes added ,  13:44, 27 May 2022
Rewrite and simplify discussion of monadic case
(Rewrite and simplify discussion of monadic case)
(9 intermediate revisions by 2 users not shown)
Line 1: Line 1:
{{Built-in|Reverse Compose|⍛}}, also known as '''Before''', is a [[primitive operator]] closely related to [[Beside]] (<source lang=apl inline>∘</source>), also known as ''After''. Called [[dyad|dyadically]] with function operands <source lang=apl inline>f</source> and <source lang=apl inline>g</source>, it uses <source lang=apl inline>f</source> [[monad|monadically]] to pre-processes the left argument before applying <source lang=apl inline>g</source> between the pre-processed left argument and the given right argument. <source lang=apl inline>X f⍛g Y</source> is thus equivalent to <source lang=apl inline>(f X) g Y</source>. The operator can be defined as the [[dop]] <source lang=apl inline>{(⍺⍺ ⍺) ⍵⍵ ⍵}</source>. Reverse compose was introduced in [[Extended Dyalog APL]], and then adopted into [[dzaima/APL]].
{{Built-in|Reverse Compose|⍛}} is a [[primitive operator]] closely related to [[Beside]] (<source lang=apl inline>∘</source>), which appears in [[Extended Dyalog APL]] and [[dzaima/APL]]. Called [[dyad|dyadically]] with function operands <source lang=apl inline>f</source> and <source lang=apl inline>g</source>, it uses <source lang=apl inline>f</source> [[monad|monadically]] to pre-processes the left argument before applying <source lang=apl inline>g</source> between the pre-processed left argument and the given right argument. <source lang=apl inline>X f⍛g Y</source> is thus equivalent to <source lang=apl inline>(f X) g Y</source>. The operator can be defined as the [[dop]] <source lang=apl inline>{(⍺⍺ ⍺) ⍵⍵ ⍵}</source>. This dyadic definition matches the [[hook]] function Before, represented as <code>⊸</code> in [[BQN]].
 
Unlike Before, the [[monad]]ic case of Reverse Compose has differed across implementations. When introduced by [[Extended Dyalog APL]], <source lang=apl inline>f⍛g Y</source> evaluated to <source lang=apl inline>g Y</source>, but [[Adám Brudzewsky|Brudzewsky]]'s later Dyalog APL Vision defines<ref>[https://github.com/abrudz/dyalog_vision/blob/main/JotUnderbar.aplo JotUnderbar.aplo]</ref> it to be <source lang=apl inline>Y f g Y</source>, matching Before. This later definition might also be written <source lang=apl inline>f⍛g</source>{{←→}}<source lang=apl inline>f⍛g⍨⍨</source>{{←→}}<source lang=apl inline>g⍨∘f⍨</source>. In [[dzaima/APL]] the monadic case is simply an error.


== Common usage ==
== Common usage ==
Line 9: Line 11:
</source>{{Works in|[[dzaima/APL]], [[Extended Dyalog APL]]}}
</source>{{Works in|[[dzaima/APL]], [[Extended Dyalog APL]]}}


It can also be combined with Beside to create the [[split-compose]] construct. Here, we take the [[sign]] of the left argument and apply it to the absolute value of the right argument:
It can also be combined with Beside to create the [[split-compose]] construct. Here, we take the [[sign]] of the left argument and apply it to (that is, multiply it with) the absolute value of the right argument:
[https://tio.run/##SyzI0U2pSszMTfz//1Hf1EdtE4wVDq03VDA5PP1R72wg0TGj5tB6I6CYuYLh//8A Try it online!]<source lang=apl>
[https://tio.run/##SyzI0U2pSszMTfz//1Hf1EdtE4wVDq03VDA5PP1R72wg0TGj5tB6I6CYuYLh//8A Try it online!]<source lang=apl>
       3 ¯1 4×⍛×∘|¯2 ¯7 1
       3 ¯1 4×⍛×∘|¯2 ¯7 1
2 ¯7 1
2 ¯7 1
</source>{{Works in|[[dzaima/APL]], [[Extended Dyalog APL]]}}
</source>{{Works in|[[dzaima/APL]], [[Extended Dyalog APL]]}}
== References ==
<references/>
{{APL built-ins}}[[Category:Primitive operators]][[Category:Composition operators]]
{{APL built-ins}}[[Category:Primitive operators]][[Category:Composition operators]]

Navigation menu