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When the resulting function is used [[monadic]]ally, it has the same behaviour as if the [[Beside]] or [[Atop (operator)|Atop]] operator had been used: | When the resulting function is used [[monadic]]ally, it has the same behaviour as if the [[Beside]] or [[Atop (operator)|Atop]] operator had been used: | ||
{| | {| | ||
|< | |<syntaxhighlight lang=apl> (g ⍥ h) ⍵</syntaxhighlight>|| {{←→}} ||<syntaxhighlight lang=apl>g (h ⍵)</syntaxhighlight> | ||
|} | |} | ||
When the resulting function is used [[dyadic]]ally, both arguments are pre-processed: | When the resulting function is used [[dyadic]]ally, both arguments are pre-processed: | ||
{| | {| | ||
|< | |<syntaxhighlight lang=apl>⍺ (g ⍥ h) ⍵</syntaxhighlight>|| {{←→}} ||<syntaxhighlight lang=apl>(h ⍺) g (h ⍵)</syntaxhighlight> | ||
|} | |} | ||
== Examples == | == Examples == | ||
< | <syntaxhighlight lang=apl> | ||
x←3 1 2 | x←3 1 2 | ||
y←4 6 5 | y←4 6 5 | ||
| Line 20: | Line 20: | ||
(⌈/x)+⌈/y | (⌈/x)+⌈/y | ||
9 | 9 | ||
</ | </syntaxhighlight> | ||
== Close composition == | == Close composition == | ||
In [[SHARP APL]] and [[J]], Over is implemented as a [[close composition]], meaning that (using SHARP syntax) < | In [[SHARP APL]] and [[J]], Over is implemented as a [[close composition]], meaning that (using SHARP syntax) <syntaxhighlight lang=apl inline>f⍤g</syntaxhighlight> has the overall [[function rank]] of <syntaxhighlight lang=apl inline>g</syntaxhighlight>. J uses <code>&</code> for the close form and <code>&:</code> for the rankless form that appears in modern APLs. | ||
== History == | == History == | ||
[[Ken Iverson]] defined Over in 1978 as part of | [[Ken Iverson]] defined Over in 1978 as part of [[Operators and Functions]],<ref>[[Ken Iverson]]. [https://www.jsoftware.com/papers/opfns.htm ''Operators and Functions''], §8 Composition and Duality. IBM Research Report #RC7091. 1978-04-26.</ref> with the glyph <syntaxhighlight lang=apl inline>¨</syntaxhighlight>. 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>⍤</syntaxhighlight> and name "on", 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 glyph < | The glyph <syntaxhighlight lang=apl inline>⍥</syntaxhighlight> appeared in [[NARS2000]], with name "Composition", by 2011.<ref>[http://wiki.nars2000.org/index.php?title=Composition Composition]. [[NARS2000]] Wiki.</ref> The name "Over" was used in [[Dyalog APL 18.0]], suggested by [[Adám Brudzewsky]].<ref>Adam Brudzewsky. Chat message {{m|42021088}}. [[APL Orchard]]. 31 Dec 2017.</ref> Over also appears in [[dzaima/APL]] (since 2018, before Dyalog 18.0), [[April]], and [[Kap]]. | ||
== External links == | == External links == | ||
| Line 38: | Line 38: | ||
* [https://help.dyalog.com/latest/#Language/Primitive%20Operators/Over.htm Dyalog] | * [https://help.dyalog.com/latest/#Language/Primitive%20Operators/Over.htm Dyalog] | ||
* J [https://www.jsoftware.com/help/dictionary/d632.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/ampco NuVoc] | * J [https://www.jsoftware.com/help/dictionary/d632.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/ampco NuVoc] | ||
* [https://mlochbaum.github.io/BQN/doc/compose.html BQN] | |||
== References == | == References == | ||
<references/> | <references/> | ||
{{APL built-ins}}[[Category:Primitive operators]][[Category:Composition operators]] | {{APL built-ins}}[[Category:Primitive operators]][[Category:Composition operators]] | ||
Latest revision as of 21:33, 28 January 2024
⍥
|
Over (⍥) is a primitive dyadic operator which takes two function operands and produces a derived function which pre-processes the argument(s) using the monadic right operand, before applying the left operand on/between the result(s).
Explanation
When the resulting function is used monadically, it has the same behaviour as if the Beside or Atop operator had been used:
(g ⍥ h) ⍵ |
g (h ⍵) |
When the resulting function is used dyadically, both arguments are pre-processed:
⍺ (g ⍥ h) ⍵ |
(h ⍺) g (h ⍵) |
Examples
x←3 1 2
y←4 6 5
x +⍥(⌈/) y ⍝ add the max of x and max of y
9
⍝ same as
(⌈/x)+⌈/y
9
Close composition
In SHARP APL and J, Over is implemented as a close composition, meaning that (using SHARP syntax) f⍤g has the overall function rank of g. J uses & for the close form and &: for the rankless form that appears in modern APLs.
History
Ken Iverson defined Over in 1978 as part of Operators and Functions,[1] with the glyph ¨. He called it Composition, as there was no Atop operator. It was added to SHARP APL as a close composition with glyph ⍤ and name "on", with a limited implementation in 1981[2] followed by a full implementation in 1983 with the introduction of function rank.[3]
The glyph ⍥ appeared in NARS2000, with name "Composition", by 2011.[4] The name "Over" was used in Dyalog APL 18.0, suggested by Adám Brudzewsky.[5] Over also appears in dzaima/APL (since 2018, before Dyalog 18.0), April, and Kap.
External links
Lessons
Documentation
- Dyalog
- J Dictionary, NuVoc
- BQN
References
- ↑ Ken Iverson. Operators and Functions, §8 Composition and Duality. IBM Research Report #RC7091. 1978-04-26.
- ↑ "Composition and Enclosure". SATN-41, 1981-06-20.
- ↑ "Language Extensions of May 1983". SATN-45, 1983-05-02.
- ↑ Composition. NARS2000 Wiki.
- ↑ Adam Brudzewsky. Chat message 42021088. APL Orchard. 31 Dec 2017.