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{{Built-in|Pair|⍮}} is a [[primitive function]] | {{Built-in|Pair|⍮}} or '''Juxtapose''' is a [[primitive]] [[ambivalent function]] that constructs a [[vector]] of its [[argument]]s, present in [[Extended Dyalog APL]], [[dzaima/APL]], and [[BQN]] (as <code>⋈</code>). The [[monadic]] case is referred to as '''Half Pair''' in Extended Dyalog APL, and is similar to [[Enclose]] except that it gives a result of [[rank]] 1 rather than 0. This case is called '''Enlist''' in BQN, as well as [[K]], where it is the monadic case of <code>,</code> (K has no dyadic Pair primitive). Dyadic Pair is similar to the [[Link]] primitive in [[SHARP APL]] and [[J]], but Link has an asymmetric definition that adds its left argument to a vector right argument rather than creating a new vector. | ||
Pair can be implemented as the [[dfn]] <syntaxhighlight lang=apl inline>{⍺←,⊂ ⋄ ⍺ ⍵}</syntaxhighlight>, or the [[catenate|catenation]] of the [[enclose]]d arguments, written <syntaxhighlight lang=apl inline>,⍥⊂</syntaxhighlight> using [[Over]].<ref>[https://www.jsoftware.com/papers/satn41.htm "Composition and Enclosure"] § Composition Operators. SATN-41, 1981-06-20.</ref> Pair aids in constructing nested arrays in [[tacit programming]], where [[stranding]] by juxtaposition is not available. | |||
== Common usage == | == Common usage == | ||
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[https://tio.run/##SyzI0U2pSszMTfz//1Hf1EdtE8wUzBUsNLQf9a7T1TT@/x8A Try it online!] | [https://tio.run/##SyzI0U2pSszMTfz//1Hf1EdtE8wUzBUsNLQf9a7T1TT@/x8A Try it online!] | ||
< | <syntaxhighlight lang=apl> | ||
6 7 8(+⍮-)3 | 6 7 8(+⍮-)3 | ||
┌───────┬─────┐ | ┌───────┬─────┐ | ||
│9 10 11│3 4 5│ | │9 10 11│3 4 5│ | ||
└───────┴─────┘ | └───────┴─────┘ | ||
</ | </syntaxhighlight> | ||
{{Works in|[[dzaima/APL]], [[Extended Dyalog APL]]}} | {{Works in|[[dzaima/APL]], [[Extended Dyalog APL]]}} | ||
| Line 16: | Line 18: | ||
[https://tio.run/##SyzI0U2pSszMTfz//1Hf1EdtE8wUzBUsNLQftU181LvkUe86XU3j//8B Try it online!] | [https://tio.run/##SyzI0U2pSszMTfz//1Hf1EdtE8wUzBUsNLQftU181LvkUe86XU3j//8B Try it online!] | ||
< | <syntaxhighlight lang=apl> | ||
6 7 8(+↑⍤⍮-)3 | 6 7 8(+↑⍤⍮-)3 | ||
9 10 11 | 9 10 11 | ||
3 4 5 | 3 4 5 | ||
</ | </syntaxhighlight> | ||
{{Works in|[[dzaima/APL]], [[Extended Dyalog APL]]}} | {{Works in|[[dzaima/APL]], [[Extended Dyalog APL]]}} | ||
== History == | |||
By 1982, [[Nial]] had defined four infix functions to join two arrays, enclosing any combination of them.<ref>Fl. Schmidt and M. A. Jenkins. [https://doi.org/10.1145/800071.802258 Array diagrams and the Nial approach] at [[APL82]].</ref> <code>link</code> encloses neither argument, giving [[Catenate]], while <code>pair</code> encloses both, giving dyadic Pair. <code>hitch</code> encloses only the left to give [[Link]], and <code>append</code> encloses the right. | |||
In APL, [[Link]] precedes Pair significantly, as it was defined in [[SHARP APL]] in 1983,<ref>[https://www.jsoftware.com/papers/satn45.htm "Language Extensions of May 1983"]. SATN-45, 1983-05-02.</ref> and included in the initial version of [[J]] in 1990. | |||
In array languages based on the [[list model]], Pair also covers the functionality of [[Promote]] and [[Laminate]]. [[K]], released in the 1990s, defines monadic <code>,</code> as enlist, but dyadic <code>,</code> as [[catenate]]. Ambivalent Pair appears in [[I]] as <code>;</code> since 2012; no name is given in the documentation, but the implementation uses "itemize" (the same name as [[J]]'s Promote) and "cross". | |||
Pair was defined as <syntaxhighlight lang=apl inline>⍮</syntaxhighlight> in [[Extended Dyalog APL]] in 2018, and then adopted into [[dzaima/APL]]. It was added to [[BQN]] with the glyph <code>⋈</code> in 2021. | |||
== Documentation == | |||
* [https://mlochbaum.github.io/BQN/doc/pair.html BQN] (as <code>⋈</code>) | |||
== References == | |||
<references /> | |||
{{APL built-ins}}[[Category:Primitive functions]] | {{APL built-ins}}[[Category:Primitive functions]] | ||