Reverse Compose

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Reverse Compose (), also known as Before, is a primitive operator closely related to Beside (), also known as After. 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 fg Y is thus equivalent to (f X) g Y. The operator can be defined as the dop {(⍺⍺ ) ⍵⍵ }.

Reverse compose was introduced in Extended Dyalog APL, and then adopted into dzaima/APL. Its dyadic case matches to I's Hook (h), which is a reflected form of a J Hook, while Backhook (H) matches the ordinary Hook or Compose: because I's evaluation order is left to right, it considers the "reversed" APL form to be primary.

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 the absolute value of the right argument:

Try it online!

      3 ¯1 4××|¯2 ¯7 1
2 ¯7 1
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