Less than or Equal to

From APL Wiki
Jump to navigation Jump to search
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

When the arguments to Less than or Equal to are Boolean, it is the material implication Boolean function, 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.

Less than or Equal to Scan is an occasionally used pattern related to Less than Scan. While <\ changes all 1s after the first to 0, \ changes all 0s after the first to 1. Thus \A ~<\~A.

      \ 1 0 1 0 0 0 1 0
1 0 1 1 1 1 1 1

\ appears in the FinnAPL idiom library as entry 350, "Not first zero".

External links

Documentation


APL built-ins [edit]
Primitive functions
Scalar
Monadic ConjugateNegateSignumReciprocalMagnitudeExponentialNatural LogarithmFloorCeilingFactorialNotPi TimesRollType
Dyadic AddSubtractTimesDivideResiduePower (function)LogarithmMinimumMaximumBinomialComparison functionsBoolean functions (AndOrNandNor) ∙ CircleComplex
Non-Scalar
Structural ShapeReshapeTallyDepthRavelEnlistTableCatenateReverseRotateTransposeRazeMixSplitEncloseNestCut (K)PairPartitioned EnclosePartition
Selection FirstPickTakeDropUniqueIdentitySelectReplicateExpand ∙ Set functions (IntersectionUnionWithout) ∙ Bracket indexSquad Indexing
Selector Index generatorGrade UpGrade DownIndex OfInterval IndexIndicesDeal
Computational MatchNot MatchMembershipFindNub SieveBaseRepresentMatrix InverseMatrix DivideFormatExecuteMaterialise
Primitive operators Monadic EachCommuteConstantReplicateReduceWindowed ReduceScanOuter ProductKeyI-beamSpawnFunction axis
Dyadic Inner ProductPower (operator)Rank (operator)BindBesideReverse ComposeAtopOverAtVariantStencil
Quad names
Arrays Index originMigration level
Functions
Operators