Pair

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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:

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

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

References

  1. ↑ "Composition and Enclosure" § Composition Operators. SATN-41, 1981-06-20.
  2. ↑ Fl. Schmidt and M. A. Jenkins. Array diagrams and the Nial approach at APL82.
  3. ↑ "Language Extensions of May 1983". SATN-45, 1983-05-02.
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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