Split composition: Difference between revisions

'''Split composition''' is a [[tacit]] pattern, used to pre-process argument(s) with the outer-most operands before applying the middle operand between the result. Given functions <syntaxhighlight lang=apl inline>f</syntaxhighlight>, <syntaxhighlight lang=apl inline>g</syntaxhighlight>, and <syntaxhighlight lang=apl inline>h</syntaxhighlight>, the split composition on arguments <syntaxhighlight lang=apl inline>x</syntaxhighlight> and <syntaxhighlight lang=apl inline>y</syntaxhighlight> is defined as <syntaxhighlight lang=apl inline>(f x) g (h y)</syntaxhighlight>.

This construct was introduced by the [[I|I language]] as "split-compose", where it is represented with <syntaxhighlight lang=apl inline>O</syntaxhighlight>. <syntaxhighlight lang=apl inline>O</syntaxhighlight> also represents the [[Over]] operator, as it is a split composition with identical outer operands.  

 

In [[Extended Dyalog APL]] and [[dzaima/APL]], a split composition can be formed using [[Reverse Compose]] (<code>⍛</code>) and [[Compose]] (<code>∘</code>). In this example, we multiply the [[interval]] (integers up until) of the left argument, with the [[Magnitude]] of the right:

In dialects that lack Reverse Compose (and even Compose), split compositions can be denoted either by defining the missing operator(s), or as a single derived function or [[fork]], if this is supported. For example, in [[Dyalog APL]] the expression can be formed with Compose and [[Commute]] (<syntaxhighlight lang=apl inline>⍨</syntaxhighlight>) as <syntaxhighlight lang=apl inline>g⍨∘f⍨∘h</syntaxhighlight>: