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  and , it uses   monadically to pre-processes the left argument before applying   between the pre-processed left argument and the given right argument. is thus equivalent to. 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,  evaluated to , but the later Dyalog APL Vision, and Kap, define it to be  , matching Before. This later definition might also be written. 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!

Documentation

 * Kap
 * BQN (as )

Publications

 * APL model