Reverse Compose: Difference between revisions

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{{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]].
{{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]].


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.
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.


== Common usage ==
== Common usage ==
Its plain usage is to pre-process left arguments without needing one or more applications of Commute (<source 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>⍨</source>). 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!]<source lang=apl>
[https://tio.run/##SyzI0U2pTMzJT9dNrShJzUtJTfn//1Hf1EdtE4wPT3/Uu@JR72xdo///AQ Try it online!]<syntaxhighlight lang=apl>
       3×⍨⍛-2
       3×⍨⍛-2
7
7
Line 12: Line 12:


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:
[https://tio.run/##SyzI0U2pSszMTfz//1Hf1EdtE4wVDq03VDA5PP1R72wg0TGj5tB6I6CYuYLh//8A Try it online!]<source lang=apl>
[https://tio.run/##SyzI0U2pSszMTfz//1Hf1EdtE4wVDq03VDA5PP1R72wg0TGj5tB6I6CYuYLh//8A Try it online!]<syntaxhighlight lang=apl>
       3 ¯1 4×⍛×∘|¯2 ¯7 1
       3 ¯1 4×⍛×∘|¯2 ¯7 1
2 ¯7 1
2 ¯7 1

Revision as of 21:06, 10 September 2022

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 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> 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 in BQN.

Unlike Before, the monadic 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 Brudzewsky's later Dyalog APL Vision defines[1] 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.

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:

Try it online!<syntaxhighlight lang=apl>

     3×⍨⍛-2

7

</source>

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!<syntaxhighlight lang=apl>

     3 ¯1 4×⍛×∘|¯2 ¯7 1

2 ¯7 1

</source>

References

APL built-ins [edit]
Primitive functions
Scalar
Monadic ConjugateNegateSignumReciprocalMagnitudeExponentialNatural LogarithmFloorCeilingFactorialNotPi TimesRollTypeImaginarySquare Root
Dyadic AddSubtractTimesDivideResiduePowerLogarithmMinimumMaximumBinomialComparison functionsBoolean functions (And, Or, Nand, Nor) ∙ GCDLCMCircularComplexRoot
Non-Scalar
Structural ShapeReshapeTallyDepthRavelEnlistTableCatenateReverseRotateTransposeRazeMixSplitEncloseNestCut (K)PairLinkPartitioned EnclosePartition
Selection FirstPickTakeDropUniqueIdentitySelectReplicateExpandSet functions (IntersectionUnionWithout) ∙ Bracket indexingIndex
Selector Index generatorGradeIndex OfInterval IndexIndicesDeal
Computational MatchNot MatchMembershipFindNub SieveEncodeDecodeMatrix InverseMatrix DivideFormatExecuteMaterialiseRange
Primitive operators Monadic EachCommuteConstantReplicateExpandReduceWindowed ReduceScanOuter ProductKeyI-BeamSpawnFunction axis
Dyadic BindCompositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner ProductPowerAtUnderRankDepthVariantStencilCut (J)
Quad names
Arrays Index originMigration levelAtomic vector
Functions Name classCase convertUnicode convert
Operators SearchReplace