Reverse Compose: Difference between revisions

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{{Built-in|Reverse Compose|⍛}} is a [[primitive operator]] closely related to [[Beside]] (<syntaxhighlight lang=apl inline>∘</source>), which appears in [[Extended Dyalog APL]] and [[dzaima/APL]]. Called [[dyad|dyadically]] with function operands <syntaxhighlight lang=apl inline>f</source> and <syntaxhighlight lang=apl inline>g</source>, it uses <syntaxhighlight lang=apl inline>f</source> [[monad|monadically]] to pre-processes the left argument before applying <syntaxhighlight lang=apl inline>g</source> between the pre-processed left argument and the given right argument. <syntaxhighlight lang=apl inline>X f⍛g Y</source> is thus equivalent to <syntaxhighlight lang=apl inline>(f X) g Y</source>. The operator can be defined as the [[dop]] <syntaxhighlight lang=apl inline>{(⍺⍺ ⍺) ⍵⍵ ⍵}</source>. This dyadic definition matches the [[hook]] function Before, represented as <code>⊸</code> in [[BQN]].
{{Built-in|Reverse Compose|⍛}} is a [[primitive operator]] closely related to [[Beside]] (<syntaxhighlight lang=apl inline>∘</syntaxhighlight>), which appears in [[Extended Dyalog APL]] and [[dzaima/APL]]. Called [[dyad|dyadically]] with function operands <syntaxhighlight lang=apl inline>f</syntaxhighlight> and <syntaxhighlight lang=apl inline>g</syntaxhighlight>, it uses <syntaxhighlight lang=apl inline>f</syntaxhighlight> [[monad|monadically]] to pre-processes the left argument before applying <syntaxhighlight lang=apl inline>g</syntaxhighlight> between the pre-processed left argument and the given right argument. <syntaxhighlight lang=apl inline>X f⍛g Y</syntaxhighlight> is thus equivalent to <syntaxhighlight lang=apl inline>(f X) g Y</syntaxhighlight>. The operator can be defined as the [[dop]] <syntaxhighlight lang=apl inline>{(⍺⍺ ⍺) ⍵⍵ ⍵}</syntaxhighlight>. 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]], <syntaxhighlight lang=apl inline>f⍛g Y</source> evaluated to <syntaxhighlight 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 <syntaxhighlight lang=apl inline>Y f g Y</source>, matching Before. This later definition might also be written <syntaxhighlight lang=apl inline>f⍛g</source>{{←→}}<syntaxhighlight lang=apl inline>f⍛g⍨⍨</source>{{←→}}<syntaxhighlight lang=apl inline>g⍨∘f⍨</source>. In [[dzaima/APL]] the monadic case is simply an error.
Unlike Before, the [[monad]]ic case of Reverse Compose has differed across implementations. When introduced by [[Extended Dyalog APL]], <syntaxhighlight lang=apl inline>f⍛g Y</syntaxhighlight> evaluated to <syntaxhighlight lang=apl inline>g Y</syntaxhighlight>, 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 <syntaxhighlight lang=apl inline>Y f g Y</syntaxhighlight>, matching Before. This later definition might also be written <syntaxhighlight lang=apl inline>f⍛g</syntaxhighlight>{{←→}}<syntaxhighlight lang=apl inline>f⍛g⍨⍨</syntaxhighlight>{{←→}}<syntaxhighlight lang=apl inline>g⍨∘f⍨</syntaxhighlight>. In [[dzaima/APL]] the monadic case is simply an error.


== Common usage ==
== Common usage ==
Its plain usage is to pre-process left arguments without needing one or more applications of Commute (<syntaxhighlight lang=apl inline>⍨</source>). For example, the square of the left argument minus the right argument can be expressed as:
Its plain usage is to pre-process left arguments without needing one or more applications of Commute (<syntaxhighlight lang=apl inline>⍨</syntaxhighlight>). For example, the square of the left argument minus the right argument can be expressed as:


[https://tio.run/##SyzI0U2pTMzJT9dNrShJzUtJTfn//1Hf1EdtE4wPT3/Uu@JR72xdo///AQ Try it online!]<syntaxhighlight lang=apl>
[https://tio.run/##SyzI0U2pTMzJT9dNrShJzUtJTfn//1Hf1EdtE4wPT3/Uu@JR72xdo///AQ Try it online!]<syntaxhighlight lang=apl>
       3×⍨⍛-2
       3×⍨⍛-2
7
7
</source>{{Works in|[[dzaima/APL]], [[Extended Dyalog APL]]}}
</syntaxhighlight>{{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 (that is, multiply it with) 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:
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       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]]}}
</syntaxhighlight>{{Works in|[[dzaima/APL]], [[Extended Dyalog APL]]}}
== References ==
== References ==
<references/>
<references/>
{{APL built-ins}}[[Category:Primitive operators]][[Category:Composition operators]]
{{APL built-ins}}[[Category:Primitive operators]][[Category:Composition operators]]

Revision as of 21:10, 10 September 2022

⍛

Reverse Compose (⍛) is a primitive operator closely related to Beside (∘), which appears in Extended Dyalog APL and dzaima/APL. 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 {(⍺⍺ ⍺) ⍵⍵ ⍵}. This dyadic definition matches the hook function Before, represented as ⊸ in BQN.

Unlike Before, the monadic case of Reverse Compose has differed across implementations. When introduced by Extended Dyalog APL, f⍛g Y evaluated to g Y, but Brudzewsky's later Dyalog APL Vision defines[1] it to be Y f g Y, matching Before. This later definition might also be written f⍛g f⍛g⍨⍨ g⍨∘f⍨. In dzaima/APL the monadic case is simply an error.

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:

Try it online!

      3×⍨⍛-2
7
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 (that is, multiply it with) the absolute value of the right argument:

Try it online!

      3 ¯1 4×⍛×∘|¯2 ¯7 1
2 ¯7 1
Works in: dzaima/APL, Extended Dyalog APL

References

  1. ↑ JotUnderbar.aplo
APL built-ins [edit]
Primitives (Timeline) Functions
Scalar
Monadic Conjugate ∙ Negate ∙ Signum ∙ Reciprocal ∙ Magnitude ∙ Exponential ∙ Natural Logarithm ∙ Floor ∙ Ceiling ∙ Factorial ∙ Not ∙ Pi Times ∙ Roll ∙ Type ∙ Imaginary ∙ Square Root ∙ Round
Dyadic Add ∙ Subtract ∙ Times ∙ Divide ∙ Residue ∙ Power ∙ Logarithm ∙ Minimum ∙ Maximum ∙ Binomial ∙ Comparison functions ∙ Boolean functions (And, Or, Nand, Nor) ∙ GCD ∙ LCM ∙ Circular ∙ Complex ∙ Root
Non-Scalar
Structural Shape ∙ Reshape ∙ Tally ∙ Depth ∙ Ravel ∙ Enlist ∙ Table ∙ Catenate ∙ Reverse ∙ Rotate ∙ Transpose ∙ Raze ∙ Mix ∙ Split ∙ Enclose ∙ Nest ∙ Cut (K) ∙ Pair ∙ Link ∙ Partitioned Enclose ∙ Partition
Selection First ∙ Pick ∙ Take ∙ Drop ∙ Unique ∙ Identity ∙ Stop ∙ Select ∙ Replicate ∙ Expand ∙ Set functions (Intersection ∙ Union ∙ Without) ∙ Bracket indexing ∙ Index ∙ Cartesian Product ∙ Sort
Selector Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal ∙ Prefix and suffix vectors
Computational Match ∙ Not Match ∙ Membership ∙ Find ∙ Nub Sieve ∙ Encode ∙ Decode ∙ Matrix Inverse ∙ Matrix Divide ∙ Format ∙ Execute ∙ Materialise ∙ Range
Operators Monadic Each ∙ Commute ∙ Constant ∙ Replicate ∙ Expand ∙ Reduce ∙ Windowed Reduce ∙ Scan ∙ Outer Product ∙ Key ∙ I-Beam ∙ Spawn ∙ Function axis ∙ Identity (Null, Ident)
Dyadic Bind ∙ Compositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner Product ∙ Determinant ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut ∙ Direct definition (operator) ∙ Identity (Lev, Dex)
Quad names Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector
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