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Atop (operator): Difference between revisions
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When the resulting function is used [[monadic]]ally, it has the same behaviour as if the [[Atop]] 2-train or any of the [[Beside]] or [[Over]] operators had been used: | When the resulting function is used [[monadic]]ally, it has the same behaviour as if the [[Atop]] 2-train or any of the [[Beside]] or [[Over]] operators had been used: | ||
{| | {| | ||
|< | |<syntaxhighlight lang=apl> (g ⍤ h) ⍵</source>|| {{←→}} ||<syntaxhighlight lang=apl>g (h ⍵)</source> | ||
|} | |} | ||
When the resulting function is used [[dyadic]]ally, the result is post-processed: | When the resulting function is used [[dyadic]]ally, the result is post-processed: | ||
{| | {| | ||
|< | |<syntaxhighlight lang=apl>⍺ (g ⍤ h) ⍵</source>|| {{←→}} ||<syntaxhighlight lang=apl>g (⍺ h ⍵)</source> | ||
|} | |} | ||
== Examples == | == Examples == | ||
< | <syntaxhighlight lang=apl> | ||
x←3 1 2 | x←3 1 2 | ||
y←4 6 5 | y←4 6 5 | ||
| Line 24: | Line 24: | ||
== Close composition == | == Close composition == | ||
In [[SHARP APL]] and [[J]], Atop is implemented as a [[close composition]], meaning that (using SHARP syntax) < | In [[SHARP APL]] and [[J]], Atop is implemented as a [[close composition]], meaning that (using SHARP syntax) <syntaxhighlight lang=apl inline>f⍥g</source> has the overall [[function rank]] of <syntaxhighlight lang=apl inline>g</source>. J uses <code>@</code> for the close form and <code>@:</code> for the rankless form that appears in modern APLs. | ||
== History == | == History == | ||
Atop was defined as subordinate to [[Over]] in [[Ken Iverson]]'s 1978 paper [[Operators and Functions]]: that is, the derived function < | Atop was defined as subordinate to [[Over]] in [[Ken Iverson]]'s 1978 paper [[Operators and Functions]]: that is, the derived function <syntaxhighlight lang=apl inline>f¨g</source> works as an Atop if <syntaxhighlight lang=apl inline>f</source> is strictly monadic or (in the dyadic case) <syntaxhighlight lang=apl inline>g</source> is strictly dyadic. He called it Composition, as there was no [[Atop operator]]. It was added to [[SHARP APL]] as a [[close composition]] with glyph <syntaxhighlight lang=apl inline>⍥</source> and name "upon" (initially "over"), with a limited implementation in 1981<ref>[https://www.jsoftware.com/papers/satn41.htm "Composition and Enclosure"]. SATN-41, 1981-06-20.</ref> followed by a full implementation in 1983 with the introduction of [[function rank]].<ref>[https://www.jsoftware.com/papers/satn45.htm "Language Extensions of May 1983"]. SATN-45, 1983-05-02.</ref> The name "Atop" was introduced by [[J]] (which uses "At" for its non-close form). The glyph <syntaxhighlight lang=apl inline>⍤</source> was chosen for [[Dyalog APL 18.0]], shared with the [[Rank operator]]. | ||
== External links == | == External links == | ||