Zilde

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Zilde () or Zero-tilde (which the common name is a portmanteau of), is the empty numeric vector. It is the shape of any scalar, although its own shape is ,0. This is because, as a vector, it has exactly one axis, and this axis has length 0. Zilde is equivalent to 0 and 0 and 00. Being numeric, Zilde's prototype is 0.

Zilde is notable for being an APL glyph which represents an array rather than a primitive function or primitive operator. In most APLs it is the only array literal which is produced using its own token rather than being part of a family of array literals like numeric literals, strings, or system constants (an exception is SHARP APL's nil (), which is the same as ).

It should be noted that the empty numeric vector () is distinct from the empty character vector ('') even though they have the same shape and the same elements:

      /=''
1
      ''
0

This is because ='' itself returns an empty numeric vector, and reducing an empty vector with the Logical And function () yields the identity element of Logical And, which is 1. However, match takes empty array prototypes into account as well as shapes and elements, so it indicates that the arrays are different.


APL built-ins [edit]
Primitive functions
Scalar
Monadic ConjugateNegateSignumReciprocalMagnitudeExponentialNatural LogarithmFloorCeilingFactorialNotPi TimesRollTypeImaginarySquare Root
Dyadic AddSubtractTimesDivideResiduePowerLogarithmMinimumMaximumBinomialComparison functionsBoolean functions (And, Or, Nand, Nor) ∙ GCDLCMCircularComplexRoot
Non-Scalar
Structural ShapeReshapeTallyDepthRavelEnlistTableCatenateReverseRotateTransposeRazeMixSplitEncloseNestCut (K)PairLinkPartitioned EnclosePartition
Selection FirstPickTakeDropUniqueIdentitySelectReplicateExpandSet functions (IntersectionUnionWithout) ∙ Bracket indexingIndex
Selector Index generatorGradeIndex OfInterval IndexIndicesDeal
Computational MatchNot MatchMembershipFindNub SieveEncodeDecodeMatrix InverseMatrix DivideFormatExecuteMaterialiseRange
Primitive operators Monadic EachCommuteConstantReplicateExpandReduceWindowed ReduceScanOuter ProductKeyI-beamSpawnFunction axis
Dyadic BindCompositions (Compose, Reverse Compose, Beside, Atop, Over) ∙ Inner ProductPowerAtUnderRankDepthVariantStencilCut (J)
Quad names
Arrays Index originMigration levelAtomic vector
Functions Case convertUnicode convert
Operators SearchReplace