Split composition

Split-compose is a point-free construct, used to pre-process its argument(s) with the left and right-most operand before applying the middle operand between the result. The name was introduced by the I language, where it's represented with O, a higher-order function that applies first to the middle function and then the two outer functions (O also represents the Over operator). It doesn't appear as a primitive in any APL.

Given functions F, G, and H, the split composition on arguments x and y is defined as (F x) G (H y).

In BQN, the construct can be formed using Before (⊸) and After (⟜), two compositional operators. In this example, we multiply the range of the left argument, with the absolute value of the right.

    5 ↕⊸×⟜| 5‿¯8‿¯2‿¯5‿3
⟨ 0 8 4 15 12 ⟩

Monadically, the right argument can be duplicated and split-compose will be applied asymmetrically, similar to hook

    +´⊸÷⟜≠ ↕10 
⟨ 4.5 ⟩
# This is evaluated as (↕10) +´⊸÷⟜≢ ↕10

Monadically, split-compose is precisely equivalent to a fork.

    (+´÷≠) ↕10
4.5

In dialects that lack Before, split-compose can be defined differently.

In Dyalog APL you may form the expression with Beside (∘) and Commute (⍨)

g∘h⍨∘f⍨

g⍨∘f⍨∘h⍨⍨

For example:

     ÷⍨∘(+/)⍨∘≢⍨⍨ ⍳10
4.5

Whilst these expressions will return the same results (if the functions f, g, and h are pure) the evaluation order is not identical.

And (most commonly) as a fork:

f⍤⊣ g h⍤⊢

See also

• Tacit programming