Power (operator)

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Power () is a primitive dyadic operator that performs bounded looping, unbounded looping, and function inverses in NARS2000, Dyalog APL, and related implementations like ngn/apl, dzaima/APL, and Extended Dyalog APL.


A call to Power is of the form X(f⍣g)Y, where

  • X is an optional argument.
  • f is a function. If X is given, then it is bound to f so X f⍣g Y is equivalent to X∘f⍣g Y.
  • g can be an array or a function.

Power repeatedly applies f to Y based on the type of operand g:

  • Function: Must be dyadic and must return a boolean singleton. The previous iteration value is provided as the right argument to f, and the current iteration value is given as the left argument. f is repeatedly applied until this function returns 1.
  • Integer: Applies f g times to Y. If g is negative, then the inverse of f (if available) is applied.
  • Integer Array: In Extended Dyalog APL, g can be an integer array. Each integer i in g will be replaced by ⊂(f⍣i)Y.


Some basic examples:

      1 (+⍣3) 5 ⍝ Fixed number of iterations
      (2∘×⍣3) 5 ⍝ No X given
      1 +∘÷⍣= 1 ⍝ iterate till fixed point

A well-known use for Power is iterating until a fixed point is reached.

      (∨.∧⍨∨⊢)⍣≡3 3⍴0 0 1 1 0 1 1 0 1 ⍝ Transitive closure of an adjacency matrix
1 0 1
1 0 1
1 0 1

Power is also used to access function inverses.

1 0 1

External Links



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