Atop (operator)

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Atop () is a primitive dyadic operator which takes two function operands and produces a derived function which uses the left operand monadically to post-processes the result of the ambivalent right operand.

Explanation

When the resulting function is used monadically, it has the same behaviour as if the Atop 2-train or any of the Beside or Over operators had been used:

  (g ⍤ h) ⍵
g (h ⍵)

When the resulting function is used dyadically, the result is post-processed:

⍺ (g ⍤ h) ⍵
g (⍺ h ⍵)

Examples

      x←3 1 2
      y←4 6 5
      x -⍤⌈ y ⍝ the negation of the max of x y
¯4 ¯6 ¯5
      ⍝ same as
      -x⌈y
¯4 ¯6 ¯5

Close composition

In SHARP APL and J, Atop is implemented as a close composition, meaning that (using SHARP syntax) f⍥g has the overall function rank of g. J uses @ for the close form and @: for the rankless form that appears in modern APLs.

History

Atop was defined as subordinate to Over in Ken Iverson's 1978 paper Operators and Functions: that is, the derived function f¨g works as an Atop if f is strictly monadic or (in the dyadic case) g is strictly dyadic. He called it Composition, as there was no Atop operator. It was added to SHARP APL as a close composition with glyph and name "upon" (initially "over"), with a limited implementation in 1981[1] followed by a full implementation in 1983 with the introduction of function rank.[2] The name "Atop" was introduced by J (which uses "At" for its non-close form). The glyph was chosen for Dyalog APL 18.0, shared with the Rank operator.

External links

Lessons

Documentation

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 IndexIndicesDealPrefix and suffix vectors
Computational MatchNot MatchMembershipFindNub SieveEncodeDecodeMatrix InverseMatrix DivideFormatExecuteMaterialiseRange
Primitive operators Monadic EachCommuteConstantReplicateExpandReduceWindowed ReduceScanOuter ProductKeyI-BeamSpawnFunction axis
Dyadic BindCompositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner ProductPowerAtUnderRankDepthVariantStencilCut
Quad names Index originComparison toleranceMigration levelAtomic vector
  1. "Composition and Enclosure". SATN-41, 1981-06-20.
  2. "Language Extensions of May 1983". SATN-45, 1983-05-02.