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Not (~) is a monadic scalar function that returns the logical negation of a Boolean argument—that is, 0 if the argument is 1 and 1 if it is 0. In some languages, such as J, it is extended so that Not x is equivalent to 1-x while in others, such as K, it is extended so that Not x is equivalent to 0=x.


      ~ 0 1 1 0 1
1 0 0 1 0

Attempting to negate a non-Boolean argument usually results in a DOMAIN ERROR. In some languages it may instead subtract the argument from one.

      ~ 0 0.5 1
      ~0 0.5 1


Not is the only Boolean function of a single argument which depends on that argument (it is not constant) and is not trivial (the same as Identity). Not is its own Inverse.


A Programming Language negates arrays using an overbar symbol like , matching a convention sometimes used in mathematics. In APL\360 the current symbol ~ was chosen, also due to its use in mathematics. Mathematical usage has arguably diverged from APL in this respect, as the negation of a variable is now more often written when a prefix operator is desired.

The arithmetic extension ~x 1-x was introduced to the array langauge family by J. For arguments in the interval this extension may be seen as a probabilistic interpretation of negation.


Extension Languages
None APL\360, APL2, APLX, SHARP APL, Dyalog APL, GNU APL, ngn/apl, dzaima/APL
1-⍵ J, BQN, Extended Dyalog APL
0=⍵ K

See also

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