Pair: Difference between revisions

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{{Built-in|Pair|⍮}} or '''Juxtapose''' is a [[primitive function]] equivalent to the [[dfn]] <syntaxhighlight lang=apl inline>{⍺←,⊂ ⋄ ⍺ ⍵}</syntaxhighlight> which aids in constructing nested arrays during [[tacit programming]] where [[stranding]] by juxtaposition is not available. It is also equivalent to 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"] §
{{Built-in|Pair|⍮}} or '''Juxtapose''' is a [[primitive]] [[ambivalent function]] that constructs a [[vector]] of its [[argument]]s. It 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. It was introduced in [[Extended Dyalog APL]] in 2018, and then adopted into [[dzaima/APL]]. It was added to [[BQN]] with the glyph <code>⋈</code> in 2021. The [[monadic]] case, which is similar to [[Enclose]] except that it gives a result of [[rank]] 1 rather than 0, is called '''Enlist''' in BQN, as well as [[K]], where it is the monadic case of <code>,</code> (K has no dyadic Pair primitive).
Composition Operators. SATN-41, 1981-06-20.</ref>. It was introduced in [[Extended Dyalog APL]], and then adopted into [[dzaima/APL]]. It was added to [[BQN]] with the glyph <code>⋈</code> in 2021.


== Common usage ==
== Common usage ==

Revision as of 15:44, 6 March 2024

⍮

Pair (⍮) or Juxtapose is a primitive ambivalent function that constructs a vector of its arguments. It 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. It was introduced in Extended Dyalog APL in 2018, and then adopted into dzaima/APL. It was added to BQN with the glyph ⋈ in 2021. The monadic case, which is similar to Enclose except that it gives a result of rank 1 rather than 0, is called Enlist in BQN, as well as K, where it is the monadic case of , (K has no dyadic Pair primitive).

Common usage

Its plain usage is in pairing up two parallel values:

Try it online! 

      6 7 8(+⍮-)3
┌───────┬─────┐
│9 10 11│3 4 5│
└───────┴─────┘
Works in: dzaima/APL, Extended Dyalog APL

It can also be combined with Mix to increase rank rather than depth:

Try it online! 

      6 7 8(+↑⍤⍮-)3
9 10 11
3  4  5
Works in: dzaima/APL, Extended Dyalog APL

External links

Documentation

See also

References

  1. ↑ "Composition and Enclosure" § Composition Operators. SATN-41, 1981-06-20.
APL built-ins [edit]
Primitives (Timeline) Functions
Scalar
Monadic Conjugate ∙ Negate ∙ Signum ∙ Reciprocal ∙ Magnitude ∙ Exponential ∙ Natural Logarithm ∙ Floor ∙ Ceiling ∙ Factorial ∙ Not ∙ Pi Times ∙ Roll ∙ Type ∙ Imaginary ∙ Square Root ∙ Round
Dyadic Add ∙ Subtract ∙ Times ∙ Divide ∙ Residue ∙ Power ∙ Logarithm ∙ Minimum ∙ Maximum ∙ Binomial ∙ Comparison functions ∙ Boolean functions (And, Or, Nand, Nor) ∙ GCD ∙ LCM ∙ Circular ∙ Complex ∙ Root
Non-Scalar
Structural Shape ∙ Reshape ∙ Tally ∙ Depth ∙ Ravel ∙ Enlist ∙ Table ∙ Catenate ∙ Reverse ∙ Rotate ∙ Transpose ∙ Raze ∙ Mix ∙ Split ∙ Enclose ∙ Nest ∙ Cut (K) ∙ Pair ∙ Link ∙ Partitioned Enclose ∙ Partition
Selection First ∙ Pick ∙ Take ∙ Drop ∙ Unique ∙ Identity ∙ Stop ∙ Select ∙ Replicate ∙ Expand ∙ Set functions (Intersection ∙ Union ∙ Without) ∙ Bracket indexing ∙ Index ∙ Cartesian Product ∙ Sort
Selector Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal ∙ Prefix and suffix vectors
Computational Match ∙ Not Match ∙ Membership ∙ Find ∙ Nub Sieve ∙ Encode ∙ Decode ∙ Matrix Inverse ∙ Matrix Divide ∙ Format ∙ Execute ∙ Materialise ∙ Range
Operators Monadic Each ∙ Commute ∙ Constant ∙ Replicate ∙ Expand ∙ Reduce ∙ Windowed Reduce ∙ Scan ∙ Outer Product ∙ Key ∙ I-Beam ∙ Spawn ∙ Function axis ∙ Identity (Null, Ident)
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)
Quad names Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector
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