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I-Beam () is a primitive ambivalent function or monadic operator that takes a numeric code as an argument/operand and provides a range of ad-hoc operations. This range covers non-primitive functions, for example experimental features, interpreter-level control, access to the environment, and information about APL itself.


I-Beam was introduced in APL\360 as an ambivalent function for implementers to execute IBM System/360 (I-Beam being pronounced very similarly to IBM) instructions from program control. The convenience of this lead to I-Beam becoming directly available for use by anyone.[1] However, modern IBM-derived APLs replace all I-Beams with quad names. For example, 5 became ⎕DL (Delay) while changing time unit from jiffies of 1⁄300th of a second to a whole second.

Later, after it became common to use arrays as operands, Dyalog APL began using the glyph as an operator where the operand selects functionality. It is used for testing experimental features, some of which may eventually become primitives or quad name. For example, 819 became ⎕C (Case Convert), while introducing distinction between case folding (for case insensitive comparisons) and case mapping (for human presentation forms).


In general, I-Beam's numeric operand isn't intended to be easily recalled. But some are given meaningful names.

One method is to devise a name from the Roman numeral letters I, V, X, L, C, D, and M:[2]

I-Beam Numeral
Colour Coding CC (200)
Colour Coding Information CCI (201)
Called Monadically CM (900)
Line Count LC (50100)


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 DivideFormatExecuteMaterialiseRange
Primitive operators Monadic EachCommuteConstantReplicateExpandReduceWindowed ReduceScanOuter ProductKeyI-BeamSpawnFunction axis
Dyadic BindCompositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner ProductPowerAtUnderRankDepthVariantStencilCut (J)
Quad names
Arrays Index originMigration levelAtomic vector
Functions Name classCase convertUnicode convert
Operators SearchReplace