Reverse Compose

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Reverse Compose () or Behind 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 the later Dyalog APL Vision defines[1] it to be (f Y) 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!


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

External links




  1. Brudzewsky, Adám. Dyalog APL Vision. JotUnderbar.
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