Reverse Compose

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> $\Leftrightarrow$ <syntaxhighlight lang=apl inline>f⍛g⍨⍨</source> $\Leftrightarrow$ <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>

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!<syntaxhighlight lang=apl>

     3 ¯1 4×⍛×∘|¯2 ¯7 1

2 ¯7 1

</source>

Works in: dzaima/APL, Extended Dyalog APL

References

↑ 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)
Operators	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

[1] JotUnderbar.aplo

[1]

Reverse Compose

Common usage

References

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