Reverse Compose
⍛

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 preprocesses the left argument before applying g
between the preprocessed 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 {(⍺⍺ ⍺) ⍵⍵ ⍵}
.
Reverse compose was introduced in Extended Dyalog APL, and then adopted into dzaima/APL. Its dyadic case matches 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 precedence order is left to right, it considers the "reversed" APL form to be primary. The monadic case was discussed for a while in the APL Orchard.^{[1]} To be completely consistent with the other function composition, the left "leg" would be removed, making f⍛g Y
be equivalent to g Y
. However, this would never apply f
and would questionably be called a composition of f
and g
. Instead, it was concluded that the best solution would be to have f⍛g Y
be a hook, f⍛g⍨Y
, that is, f⍛g
f⍛g⍨⍨
g⍨∘f⍨
.
Common usage
Its plain usage is to preprocess 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:
3×⍨⍛2
7
It can also be combined with Beside to create the splitcompose 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:
3 ¯1 4×⍛×∘¯2 ¯7 1
2 ¯7 1
References
 ↑ Adám Brudzewsky. Message 60006135ff. APL Orchard. 29 Dec 2021.