Pair: Difference between revisions

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(Reference for catenate over enclose in 1981)
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{{Built-in|Pair|⍮}} or '''Juxtapose''' is a [[primitive function]] equivalent to the [[dfn]] <source lang=apl inline>{⍺←,⊂ ⋄ ⍺ ⍵}</source> 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; <source lang=apl inline>,⍥⊂</source> using the [[Over]] [[operator]]<ref>[https://www.jsoftware.com/papers/satn41.htm "Composition and Enclosure"] §
{{Built-in|Pair|⍮}} or '''Juxtapose''' is a [[primitive function]] equivalent to the [[dfn]] <source 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; <source lang=apl inline>,⍥⊂</syntaxhighlight> using the [[Over]] [[operator]]<ref>[https://www.jsoftware.com/papers/satn41.htm "Composition and Enclosure"] §
Composition Operators. SATN-41, 1981-06-20.</ref> or <source lang=apl inline>,⍨∘⊂⍨∘⊂</source> using only the traditional operators [[Commute]] and [[Compose]]. It was introduced in [[Extended Dyalog APL]], and then adopted into [[dzaima/APL]].
Composition Operators. SATN-41, 1981-06-20.</ref> or <source lang=apl inline>,⍨∘⊂⍨∘⊂</syntaxhighlight> using only the traditional operators [[Commute]] and [[Compose]]. It was introduced in [[Extended Dyalog APL]], and then adopted into [[dzaima/APL]].


== Common usage ==
== Common usage ==
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│9 10 11│3 4 5│
│9 10 11│3 4 5│
└───────┴─────┘
└───────┴─────┘
</source>
</syntaxhighlight>
{{Works in|[[dzaima/APL]], [[Extended Dyalog APL]]}}
{{Works in|[[dzaima/APL]], [[Extended Dyalog APL]]}}


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9 10 11
9 10 11
3  4  5
3  4  5
</source>
</syntaxhighlight>
{{Works in|[[dzaima/APL]], [[Extended Dyalog APL]]}}
{{Works in|[[dzaima/APL]], [[Extended Dyalog APL]]}}


Revision as of 22:09, 10 September 2022

⍮

Pair (⍮) or Juxtapose is a primitive function equivalent to the dfn <source 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 catenation of the enclosed arguments; <source lang=apl inline>,⍥⊂</syntaxhighlight> using the Over operator[1] or <source lang=apl inline>,⍨∘⊂⍨∘⊂</syntaxhighlight> using only the traditional operators Commute and Compose. It was introduced in Extended Dyalog APL, and then adopted into dzaima/APL.

Common usage

Its plain usage is in pairing up two parallel values:

Try it online! <source lang=apl> 

     6 7 8(+⍮-)3

┌───────┬─────┐ │9 10 11│3 4 5│ └───────┴─────┘ </syntaxhighlight>

Works in: dzaima/APL, Extended Dyalog APL

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

Try it online! <source lang=apl> 

     6 7 8(+↑⍤⍮-)3

9 10 11 3 4 5 </syntaxhighlight>

Works in: dzaima/APL, Extended Dyalog APL

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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