Link

Link (⊃), or ; 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 {(⊂⍺),⊆⍵} or ,⍨∘⊂⍨∘⊆, 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.

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

Works in: SHARP APL

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

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

Works in: SHARP APL

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

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

Works in: SHARP APL

What we really wanted was:

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

Works in: SHARP APL

Link is different from Pair ⍮, 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