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Split composition: Difference between revisions
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'''Split-compose''' is a [[tacit]] construct, used to pre-process its argument(s) with the left and right-most operand before applying the middle operand between the result. Given functions < | '''Split-compose''' is a [[tacit]] construct, used to pre-process its argument(s) with the left and right-most operand 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>. | ||
The name was introduced by the [[I|I language]], where it is represented with < | The name was introduced by the [[I|I language]], where it is represented with <syntaxhighlight lang=apl inline>O</syntaxhighlight>, a higher-order function that applies first to the middle [[function]] and then the two outer functions (<syntaxhighlight lang=apl inline>O</syntaxhighlight> also represents the [[Over]] operator). It doesn't appear as a primitive in any APL, nor can it, because it is a [[composition]] of three functions, while a [[Function composition|compositional operator]] can take no more than two [[operands]]. This situation is identical to that of the [[fork]]. Both split-compose and fork can be constructed using two companion operators, tying together the three involved functions. | ||
In [[Extended Dyalog APL]] and [[dzaima/APL]], the construct 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 [[Extended Dyalog APL]] and [[dzaima/APL]], the construct 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: | ||
< | <syntaxhighlight lang=apl> | ||
5 ⍳⍛×∘| 5 ¯8 ¯2 ¯5 3 | 5 ⍳⍛×∘| 5 ¯8 ¯2 ¯5 3 | ||
5 16 6 20 15 | 5 16 6 20 15 | ||
</syntaxhighlight> | </syntaxhighlight> | ||
This is evaluated as < | This is evaluated as <syntaxhighlight lang=apl inline>(⍳5) × (|5 ¯8 ¯2 ¯5 3)</syntaxhighlight>. A further example concatenates the reciprocal of the left argument with the negation of the right: | ||
< | <syntaxhighlight lang=apl> | ||
2(,⍨∘÷⍨∘-⍨⍨)4 | 2(,⍨∘÷⍨∘-⍨⍨)4 | ||
0.5 ¯4 | 0.5 ¯4 | ||
</syntaxhighlight> | </syntaxhighlight> | ||
This is evaluated as < | This is evaluated as <syntaxhighlight lang=apl inline>(÷2) × (-4)</syntaxhighlight>. | ||
== Alternatives == | == Alternatives == | ||
In dialects that lack Reverse Compose (and even Compose), split-compose can be written 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]] (< | In dialects that lack Reverse Compose (and even Compose), split-compose can be written 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>: | ||
< | <syntaxhighlight lang=apl> | ||
5 ×⍨∘⍳⍨∘| 5 ¯8 ¯2 ¯5 3 | 5 ×⍨∘⍳⍨∘| 5 ¯8 ¯2 ¯5 3 | ||
5 16 6 20 15 | 5 16 6 20 15 | ||
| Line 23: | Line 23: | ||
0.5 ¯4 | 0.5 ¯4 | ||
</syntaxhighlight> | </syntaxhighlight> | ||
Note that < | Note that <syntaxhighlight lang=apl inline>g∘h⍨∘f⍨</syntaxhighlight> applies <syntaxhighlight lang=apl inline>f</syntaxhighlight> before <syntaxhighlight lang=apl inline>h</syntaxhighlight> which can matter for functions with side effects. For example, consider the following where <syntaxhighlight lang=apl inline>'x' f⍛g∘h 'y'</syntaxhighlight> would print <code>hfg</code>: | ||
< | <syntaxhighlight lang=apl> | ||
f←{⍞←⊃⎕SI} | f←{⍞←⊃⎕SI} | ||
g←{⍞←⊃⎕SI} | g←{⍞←⊃⎕SI} | ||
| Line 33: | Line 33: | ||
fhg | fhg | ||
</syntaxhighlight> | </syntaxhighlight> | ||
The equivalent fork is < | The equivalent fork is <syntaxhighlight lang=apl inline>f⍤⊣ g h⍤⊢</syntaxhighlight>, for example: | ||
< | <syntaxhighlight lang=apl> | ||
5 (⍳⍤⊣×|⍤⊢) 5 ¯8 ¯2 ¯5 3 | 5 (⍳⍤⊣×|⍤⊢) 5 ¯8 ¯2 ¯5 3 | ||
5 16 6 20 15 | 5 16 6 20 15 | ||