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Scan (\, ) is a primitive monadic operator which takes a dyadic function operand and produces a monadic function which is equivalent to the reductions of the prefixes of the arguments. This operation is known as also known as cumulative reduction.


Scan is similar to Reduce, however all the intermediate results will be retained. That being said, unlike Reduce, Scan does not reduce the rank of its argument, i.e. performing a scan over an N-dimensional array will produce an N-dimensional array.


      +\⍳5 ⍝ plus-scan over range of integers from 1 to 5
1 3 6 10 15


Removing disconnected trailing 1s from a boolean mask:

      mask←1 1 1 1 0 1 1 0 0 1
1 1 1 1 0 1 1 0 0 1
      ∧\mask ⍝ and-scan mask
1 1 1 1 0 0 0 0 0 0

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APL built-ins [edit]
Primitives (Timeline) Functions
Monadic ConjugateNegateSignumReciprocalMagnitudeExponentialNatural LogarithmFloorCeilingFactorialNotPi TimesRollTypeImaginarySquare Root
Dyadic AddSubtractTimesDivideResiduePowerLogarithmMinimumMaximumBinomialComparison functionsBoolean functions (And, Or, Nand, Nor) ∙ GCDLCMCircularComplexRoot
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