Reverse Compose: Difference between revisions
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{{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>. | {{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]]. Its [[dyadic]] case matches to [[I]]'s Hook (<code>h</code>), which is a reflected form of a [[J]] [[Hook]], while Backhook (<code>H</code>) matches the ordinary [[Hook]] or [[Compose]]: because I's [[evaluation order]] is right | Reverse compose was introduced in [[Extended Dyalog APL]], and then adopted into [[dzaima/APL]]. Its [[dyadic]] case matches to [[I]]'s Hook (<code>h</code>), which is a reflected form of a [[J]] [[Hook]], while Backhook (<code>H</code>) matches the ordinary [[Hook]] or [[Compose]]: because I's [[evaluation order]] is left to right, it considers the "reversed" APL form to be primary. | ||
== Common usage == | == Common usage == | ||
Revision as of 15:27, 5 May 2020
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Reverse Compose (⍛), also known as Before, is a primitive operator closely related to Beside (∘), also known as After. Called dyadically with function operands f and g, it uses f monadically to pre-processes the left argument before applying g between the pre-processed left argument and the given right argument. X f⍛g Y is thus equivalent to (f X) g Y. The operator can be defined as the dop {(⍺⍺ ⍺) ⍵⍵ ⍵}.
Reverse compose was introduced in Extended Dyalog APL, and then adopted into dzaima/APL. Its dyadic case matches to I's Hook (h), which is a reflected form of a J Hook, while Backhook (H) matches the ordinary Hook or Compose: because I's evaluation order is left to right, it considers the "reversed" APL form to be primary.
Common usage
Its plain usage is to pre-process left arguments without needing one or more applications of Commute (⍨). For example, the square of the left argument minus the right argument can be expressed as:
3×⍨⍛-2 7
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:
3 ¯1 4×⍛×∘|¯2 ¯7 1 2 ¯7 1