Split composition: Difference between revisions
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'''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. | '''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|I language]], where it's represented with <code>O</code>, a higher-order function that applies first to the middle function and then the two outer functions (<code>O</code> also represents the [[Over]] operator). It doesn't appear as a primitive in any APL. | ||
Given functions <source lang=apl inline>F</source>, <source lang=apl inline>G</source>, and <source lang=apl inline>H</source>, the split composition on arguments <source lang=apl inline>x</source> and <source lang=apl inline>y</source> is defined as <source lang=apl inline>(F x) G (H y)</source>. | Given functions <source lang=apl inline>F</source>, <source lang=apl inline>G</source>, and <source lang=apl inline>H</source>, the split composition on arguments <source lang=apl inline>x</source> and <source lang=apl inline>y</source> is defined as <source lang=apl inline>(F x) G (H y)</source>. | ||
Revision as of 13:56, 12 April 2022
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