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The Dual operator, written <code>¨</code>, appeared in 1983 both in [[Rationalized APL]] and [[SHARP APL]]<ref>[https://www.jsoftware.com/papers/satn45.htm "Language Extensions of May 1983"]. SATN-45, 1983-05-02.</ref> just after. In both cases it was defined to be a [[close composition]], so that the overall function has the rank of the right operand; this allows <code>¨></code> to serve the purpose of [[Each]] from a [[Nested array model|nested]] APL. Iverson changed the name to Under for his 1987 [[A Dictionary of APL]], and [[J]] uses this name as well. It includes both a close form <source lang=j inline>&.</source> like SHARP and a non-close form <source lang=j inline>&.:</source>. | The Dual operator, written <code>¨</code>, appeared in 1983 both in [[Rationalized APL]] and [[SHARP APL]]<ref>[https://www.jsoftware.com/papers/satn45.htm "Language Extensions of May 1983"]. SATN-45, 1983-05-02.</ref> just after. In both cases it was defined to be a [[close composition]], so that the overall function has the rank of the right operand; this allows <code>¨></code> to serve the purpose of [[Each]] from a [[Nested array model|nested]] APL. Iverson changed the name to Under for his 1987 [[A Dictionary of APL]], and [[J]] uses this name as well. It includes both a close form <source lang=j inline>&.</source> like SHARP and a non-close form <source lang=j inline>&.:</source>. | ||
However, [[Ken Iverson]] had defined the Dual operator with glyph <source lang=apl inline>⍢</source> 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. [[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 <source lang=apl inline>⍢×</source> and <source lang=apl inline>⍢|</source> 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. | However, [[Ken Iverson]] had defined the Dual operator with glyph <source lang=apl inline>⍢</source> 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. [[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 <source lang=apl inline>⍢×</source> and <source lang=apl inline>⍢|</source> 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. | |||
== External links == | == External links == | ||