Less than or Equal to

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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 ConjugateNegateSignumNotRollType
Dyadic AddSubtractEqual to (Xnor) ∙ Not Equal to (Xor) ∙ MinimumMaximumComparison functions
Non-Scalar
Structural ShapeReshapeTallyDepthRavelReverseRazeMixCut (K)PairReplicatePartitioned Enclose
Selection TakeDropUniqueIdentitySelect
Selector Index generatorInterval IndexIndices
Computational MatchNot MatchNub SieveFormatExecute
Primitive operators Monadic EachReplicate
Dyadic Reverse Compose
Quad names
Arrays Index originMigration level
Functions
Operators
Other ZildeHigh minusFunction axis