# Reverse Compose: Difference between revisions

 `⍛`

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` ${\displaystyle \Leftrightarrow }$ `f⍛g⍨⍨` ${\displaystyle \Leftrightarrow }$ `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
```

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
```

## References

APL built-ins 
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)