Reverse Compose
⍛

Reverse Compose (⍛
) or Behind is a primitive operator closely related to Beside (∘
), which appears in Extended Dyalog APL, dzaima/APL, and Kap. 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 {(⍺⍺ ⍺) ⍵⍵ ⍵}
. 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, and Kap, define 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 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