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{{Built-in|Under|⍢}} is a [[primitive operator|primitive]] [[dyadic operator]] which takes two [[function]] [[operand]]s. It pre-processes it's argument(s) with the monadic right operand, before applying the left operand on/between the result(s), then undoing the pre-processing.<ref>[https://mlochbaum.github.io/BQN/help/under.html BQN: Circle Jot (⌾)]</ref>
{{Built-in|Under|⍢}}, or '''Dual''' (<code>¨</code>), is a [[primitive operator|primitive]] [[dyadic operator]] which takes two [[function]] [[operand]]s. It pre-processes its argument(s) with the monadic right operand, before applying the left operand on/between the result(s), then undoing the pre-processing.<ref>[https://mlochbaum.github.io/BQN/help/under.html BQN: Circle Jot (⌾)]</ref>


== Model ==
== Model ==
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==External links==
== History ==


===References===
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>.
 
== External links ==
 
* [[J]]: <source lang=j inline>&.</source> [https://code.jsoftware.com/wiki/Vocabulary/ampdot NuVoc], [https://www.jsoftware.com/help/dictionary/d631.htm dictionary]; <source lang=j inline>&.:</source> [https://code.jsoftware.com/wiki/Vocabulary/ampdotco NuVoc], [https://www.jsoftware.com/help/dictionary/d631c.htm dictionary]
 
== References ==
<references/>
<references/>
{{APL built-ins}}[[Category:Primitive operators]][[Category:Composition operators]]
{{APL built-ins}}[[Category:Primitive operators]][[Category:Composition operators]]

Revision as of 15:52, 25 April 2022

⍢

Under (⍢), or Dual (¨), is a primitive dyadic operator which takes two function operands. It pre-processes its argument(s) with the monadic right operand, before applying the left operand on/between the result(s), then undoing the pre-processing.[1]

Model

In dialects that support user-defined operators and invertible functions, it can be defined as (or similar): 

       _U_ ← {⍺←{⍵ ⋄ ⍺⍺} ⋄ ⍵⍵⍣¯1⊢(⍵⍵ ⍺)⍺⍺(⍵⍵ ⍵)}

Examples

      ⍝ https://leetcode.com/problems/add-two-numbers/
      2 4 3 +_U_(10⊥⌽) 5 6 4
7 0 8

History

The Dual operator, written ¨, appeared in 1983 both in Rationalized APL and SHARP APL[2] 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 ¨> to serve the purpose of Each from a 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 &. like SHARP and a non-close form &.:.

External links

References

  1. ↑ BQN: Circle Jot (⌾)
  2. ↑ "Language Extensions of May 1983". SATN-45, 1983-05-02.
APL built-ins [edit]
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Dyadic Bind ∙ Compositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner Product ∙ Determinant ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut ∙ Direct definition (operator) ∙ Identity (Lev, Dex)
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