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Reference Kap and Uiua
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However, Iverson had defined the Dual operator with glyph <syntaxhighlight lang=apl inline>⍢</syntaxhighlight> in his 1978 paper [[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> using a non-close form because [[function rank]] had not yet been invented. [[NARS]] featured this operator in 1981, preceding SHARP's limited implementation. [[Roger Hui]] proposed Under with the same definition as a potential addition to [[Dyalog APL]] at [[Dyalog '15]], and it was added to both [[Extended Dyalog APL]] and [[dzaima/APL]] in 2018. | However, Iverson had defined the Dual operator with glyph <syntaxhighlight lang=apl inline>⍢</syntaxhighlight> in his 1978 paper [[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> using a non-close form because [[function rank]] had not yet been invented. [[NARS]] featured this operator in 1981, preceding SHARP's limited implementation. [[Roger Hui]] proposed Under with the same definition as a potential addition to [[Dyalog APL]] at [[Dyalog '15]], and it was added to both [[Extended Dyalog APL]] and [[dzaima/APL]] in 2018. | ||
Structural Under was developed by [[Marshall Lochbaum]] around 2017,<ref>[[Marshall Lochbaum]]. [https://mlochbaum.github.io/BQN/commentary/history.html#structural-under BQN's development history: Structural Under].</ref> and was included in Extended Dyalog initially and added to dzaima/APL in 2020. Later [[dzaima]] would implement <syntaxhighlight lang=apl inline>⍢×</syntaxhighlight> and <syntaxhighlight lang=apl inline>⍢|</syntaxhighlight> in the same spirit, now featured in dzaima/APL and [[dzaima/BQN]]. The language [[BQN]] has included structural and computational Under, using the glyph <code>⌾</code>, since its initial design in 2020. | Structural Under was developed by [[Marshall Lochbaum]] around 2017,<ref>[[Marshall Lochbaum]]. [https://mlochbaum.github.io/BQN/commentary/history.html#structural-under BQN's development history: Structural Under].</ref> and was included in Extended Dyalog initially and added to dzaima/APL in 2020. Later [[dzaima]] would implement <syntaxhighlight lang=apl inline>⍢×</syntaxhighlight> and <syntaxhighlight lang=apl inline>⍢|</syntaxhighlight> in the same spirit, now featured in dzaima/APL and [[dzaima/BQN]]. The language [[BQN]] has included structural and computational Under, using the glyph <code>⌾</code>, since its initial design in 2020. Structural Under also appears in [[Kap]] and [[Uiua]]. | ||
== External links == | == External links == | ||
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* [[J]]: <syntaxhighlight lang=j inline>&.</syntaxhighlight> [https://code.jsoftware.com/wiki/Vocabulary/ampdot NuVoc], [https://www.jsoftware.com/help/dictionary/d631.htm dictionary]; <syntaxhighlight lang=j inline>&.:</syntaxhighlight> [https://code.jsoftware.com/wiki/Vocabulary/ampdotco NuVoc], [https://www.jsoftware.com/help/dictionary/d631c.htm dictionary] | * [[J]]: <syntaxhighlight lang=j inline>&.</syntaxhighlight> [https://code.jsoftware.com/wiki/Vocabulary/ampdot NuVoc], [https://www.jsoftware.com/help/dictionary/d631.htm dictionary]; <syntaxhighlight lang=j inline>&.:</syntaxhighlight> [https://code.jsoftware.com/wiki/Vocabulary/ampdotco NuVoc], [https://www.jsoftware.com/help/dictionary/d631c.htm dictionary] | ||
* [https://mlochbaum.github.io/BQN/doc/under.html BQN] | * [https://mlochbaum.github.io/BQN/doc/under.html BQN] | ||
* [https://kapdemo.dhsdevelopments.com/reference.html#_structural_under Kap] | |||
* [https://www.uiua.org/docs/under Uiua] | |||
== References == | == References == | ||
<references/> | <references/> | ||
{{APL built-ins}}[[Category:Primitive operators]][[Category:Composition operators]] | {{APL built-ins}}[[Category:Primitive operators]][[Category:Composition operators]] | ||