Link

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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[1].

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

References

  1. "Language Extensions of May 1983". SATN-45, 1983-05-02.


APL built-ins [edit]
Primitives (Timeline) Functions
Scalar
Monadic ConjugateNegateSignumReciprocalMagnitudeExponentialNatural LogarithmFloorCeilingFactorialNotPi TimesRollTypeImaginarySquare Root
Dyadic AddSubtractTimesDivideResiduePowerLogarithmMinimumMaximumBinomialComparison functionsBoolean functions (And, Or, Nand, Nor) ∙ GCDLCMCircularComplexRoot
Non-Scalar
Structural ShapeReshapeTallyDepthRavelEnlistTableCatenateReverseRotateTransposeRazeMixSplitEncloseNestCut (K)PairLinkPartitioned EnclosePartition
Selection FirstPickTakeDropUniqueIdentityStopSelectReplicateExpandSet functions (IntersectionUnionWithout) ∙ Bracket indexingIndexCartesian ProductSort
Selector Index generatorGradeIndex OfInterval IndexIndicesDealPrefix and suffix vectors
Computational MatchNot MatchMembershipFindNub SieveEncodeDecodeMatrix InverseMatrix DivideFormatExecuteMaterialiseRange
Operators Monadic EachCommuteConstantReplicateExpandReduceWindowed ReduceScanOuter ProductKeyI-BeamSpawnFunction axis
Dyadic BindCompositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner ProductDeterminantPowerAtUnderRankDepthVariantStencilCutDirect definition (operator)
Quad names Index originComparison toleranceMigration levelAtomic vector