Less than or Equal to: Difference between revisions

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== Boolean function ==
== Boolean function ==
{{Main|Boolean function}}
{{Main|Boolean function}}
When used as a [[Boolean function]] (that is, with argument consisting entirely of 0s and 1s), it represents [[wikipedia:converse implication|converse implication]]:
When used as a [[Boolean function]] (that is, with argument consisting entirely of 0s and 1s), it represents [[wikipedia:Material conditional|material implication]], also known as the [[wikipedia:IMPLY gate|IMPLY gate]]:
{|class=wikitable
{|class=wikitable
!<source lang=apl inline>≤</source>!!<source lang=apl inline>0</source>!!<source lang=apl inline>1</source>
!<source lang=apl inline>≤</source>!!<source lang=apl inline>0</source>!!<source lang=apl inline>1</source>
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|<source lang=apl inline>0</source>||<source lang=apl inline>1</source>
|<source lang=apl inline>0</source>||<source lang=apl inline>1</source>
|}
|}
 
In the context of logic, it can be read as ''implies''.
== External links ==
== External links ==



Revision as of 08:32, 29 March 2020

Main article: Comparison function

Less than or Equal to () is a comparison function which tests whether the left argument is tolerantly less than or equal to the right argument, returning 1 if this is the case and 0 otherwise. It is the negation of Less than (<), and in fact was called Not greater in APL\360.

Boolean function

Main article: Boolean function

When used as a Boolean function (that is, with argument consisting entirely of 0s and 1s), it represents material implication, also known as the IMPLY gate:

0 1
0 1 1
1 0 1

In the context of logic, it can be read as implies.

External links

Documentation


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