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{{Built-in|Pair|⍮}} or '''Juxtapose''' 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]] | ||
Latest revision as of 17:16, 6 March 2024
⍮
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Pair (⍮) or Juxtapose is a primitive ambivalent function that constructs a vector of its arguments, present in Extended Dyalog APL, dzaima/APL, and BQN (as ⋈). 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 , (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 {⍺←,⊂ ⋄ ⍺ ⍵}, or the catenation of the enclosed arguments, written ,⍥⊂ using Over.[1] Pair aids in constructing nested arrays in tacit programming, where stranding by juxtaposition is not available.
Common usage
Its plain usage is in pairing up two parallel values:
6 7 8(+⍮-)3 ┌───────┬─────┐ │9 10 11│3 4 5│ └───────┴─────┘
It can also be combined with Mix to increase rank rather than depth:
6 7 8(+↑⍤⍮-)3 9 10 11 3 4 5
History
By 1982, Nial had defined four infix functions to join two arrays, enclosing any combination of them.[2] link encloses neither argument, giving Catenate, while pair encloses both, giving dyadic Pair. hitch encloses only the left to give Link, and append encloses the right.
In APL, Link precedes Pair significantly, as it was defined in SHARP APL in 1983,[3] 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 , as enlist, but dyadic , as catenate. Ambivalent Pair appears in I as ; 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 ⍮ in Extended Dyalog APL in 2018, and then adopted into dzaima/APL. It was added to BQN with the glyph ⋈ in 2021.
Documentation
- BQN (as
⋈)
References
- ↑ "Composition and Enclosure" § Composition Operators. SATN-41, 1981-06-20.
- ↑ Fl. Schmidt and M. A. Jenkins. Array diagrams and the Nial approach at APL82.
- ↑ "Language Extensions of May 1983". SATN-45, 1983-05-02.