Link

⊃

Link (⊃), or <source lang=j inline>;</syntaxhighlight> in J, is a dyadic primitive function which builds a nested vector out of the two arguments. Link is useful for building a nested array when stranding by juxtaposition is not available. Link first appeared as an extension to SHARP APL.

Examples

Link implements <source lang=apl inline>{(⊂⍺),⊆⍵}</syntaxhighlight> or <source lang=apl inline>,⍨∘⊂⍨∘⊆</syntaxhighlight>, that is, the concatenation of enclose of the left argument and nest (enclose if simple) of the right argument. This allows to chain the function over multiple arrays to form a nested array. Note that both SHARP APL and J use flat array model, so they allow boxing of a simple scalar.

<source lang=apl>

     1 2⊃3 4⊃5 6

┌───┬───┬───┐ │1 2│3 4│5 6│ └───┴───┴───┘

     1⊃2⊃3

┌─┬─┬─┐ │1│2│3│ └─┴─┴─┘

</syntaxhighlight>

Works in: SHARP APL

Because of the function's asymmetric nature, oddities may appear if the arrays are chained in a wrong order:

<source lang=apl>

     (1 2⊃3 4)⊃5 6

┌─────────┬───┐ │┌───┬───┐│5 6│ ││1 2│3 4││ │ │└───┴───┘│ │ └─────────┴───┘

</syntaxhighlight>

Works in: SHARP APL

Similarly, the chaining fails if the rightmost array is already nested:

<source lang=apl>

     1 2⊃3 4⊃<5 6

┌───┬───┬───┐ │1 2│3 4│5 6│ └───┴───┴───┘

</syntaxhighlight>

Works in: SHARP APL

What we really wanted was: <source lang=apl>

     1 2⊃3 4⊃<<5 6

┌───┬───┬─────┐ │1 2│3 4│┌───┐│ │ │ ││5 6││ │ │ │└───┘│ └───┴───┴─────┘

</syntaxhighlight>

Works in: SHARP APL

Link is different from Pair <source lang=apl inline>⍮</syntaxhighlight>, as Pair simply encloses both arguments and always produces a length-2 vector, so it cannot be used to construct a long nested array of uniform depth like Link does.

External links

Documentation

• J Dictionary, NuVoc