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Compose () or Composition is the most common name for the primitive dyadic operator denoted with a Jot () introduced by NARS and included in the Dyalog APL family. On the APL Wiki, Compose is divided into its two cases, Beside when both operands are functions, and Bind when one is a function and the other an array.

Composition assembles functions and arguments to form derived functions. This provides the glue with which to put together functions and arguments so that operator's arguments can be more complex than single functions.[1]

In Ken Iverson's designs Rationalized APL, A Dictionary of APL, and the J language, the composition () or Compose (&) refers to a different kind of composition, the Over operator.

More recently, the term "composition" is used in Dyalog APL to refer to any of a family of operators including Beside and Bind (), Commute and Constant (), Atop (), and Over ().[2] Extended Dyalog APL and dzaima/APL add to this list the operators Under () and Reverse Compose ().


  1. Carl M. Cheney. APL*PLUS Nested Arrays System (NARS reference manual). STSC. 1981.
  2. Marshall Lochbaum. Tacit Techniques with Dyalog version 18.0 Operators (slides) at Dyalog '19.
APL built-ins [edit]
Primitive functions
Monadic ConjugateNegateSignumReciprocalMagnitudeExponentialNatural LogarithmFloorCeilingFactorialNotPi TimesRollTypeImaginarySquare Root
Dyadic AddSubtractTimesDivideResiduePowerLogarithmMinimumMaximumBinomialComparison functionsBoolean functions (And, Or, Nand, Nor) ∙ GCDLCMCircularComplexRoot
Structural ShapeReshapeTallyDepthRavelEnlistTableCatenateReverseRotateTransposeRazeMixSplitEncloseNestCut (K)PairLinkPartitioned EnclosePartition
Selection FirstPickTakeDropUniqueIdentitySelectReplicateExpandSet functions (IntersectionUnionWithout) ∙ Bracket indexingIndex
Selector Index generatorGradeIndex OfInterval IndexIndicesDeal
Computational MatchNot MatchMembershipFindNub SieveEncodeDecodeMatrix InverseMatrix DivideFormatExecuteMaterialise
Primitive operators Monadic EachCommuteConstantReplicateExpandReduceWindowed ReduceScanOuter ProductKeyI-beamSpawnFunction axis
Dyadic BindCompositions (Compose, Reverse Compose, Beside, Atop, Over) ∙ Inner ProductPowerAtUnderRankDepthVariantStencil
Quad names
Arrays Index originMigration level
Functions Case convert
Operators SearchReplace