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{{Built-in|Less than or Equal to|<nowiki>≤</nowiki>}} is a [[comparison function]] which tests whether the left [[argument]] is [[Tolerant comparison|tolerantly]] less than or equal to the right argument, returning 1 if this is the case and 0 otherwise. It is the [[Not|negation]] of [[Less than]] (<source lang=apl inline><</source>), and in fact was called '''Not greater''' in [[APL\360]]. | {{Built-in|Less than or Equal to|<nowiki>≤</nowiki>}} is a [[comparison function]] which tests whether the left [[argument]] is [[Tolerant comparison|tolerantly]] less than or equal to the right argument, returning 1 if this is the case and 0 otherwise. It is the [[Not|negation]] of [[Less than]] (<source lang=apl inline><</source>), 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 [[wikipedia:Material conditional|material implication]] [[Boolean function]], also known as the [[wikipedia:IMPLY gate|IMPLY gate]]: | |||
::{|class=wikitable | |||
!<source lang=apl inline>≤</source>!!<source lang=apl inline>0</source>!!<source lang=apl inline>1</source> | |||
|- | |||
!<source lang=apl inline>0</source> | |||
|<source lang=apl inline>1</source>||<source lang=apl inline>1</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''. | |||
Less than or Equal to [[Scan]] is an occasionally used pattern related to [[Less than]] Scan. While <source lang=apl inline><\</source> changes all 1s after the first to 0, <source lang=apl inline>≤\</source> changes all 0s after the first to 1. Thus <source lang=apl inline>≤\A</source> {{←→}} <source lang=apl inline>~<\~A</source>. | |||
<source lang=apl> | |||
≤\ 1 0 1 0 0 0 1 0 | |||
1 0 1 1 1 1 1 1 | |||
</source> | |||
<source lang=apl inline>≤\</source> appears in the [[FinnAPL idiom library]] as entry 350, "Not first zero". | |||
== External links == | == External links == | ||
| Line 7: | Line 27: | ||
=== Documentation === | === Documentation === | ||
* [ | * [https://help.dyalog.com/latest/index.htm#Language/Primitive%20Functions/Less%20Or%20Equal.htm Dyalog] | ||
* [http://microapl.com/apl_help/ch_020_020_300.htm APLX] | * [http://microapl.com/apl_help/ch_020_020_300.htm APLX] | ||
* J [http://www.jsoftware.com/help/dictionary/d012.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/ltco#dyadic NuVoc] | * J [http://www.jsoftware.com/help/dictionary/d012.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/ltco#dyadic NuVoc] | ||
{{APL built-ins}} | {{APL built-ins}}[[Category:Primitive functions]][[Category:Comparison functions]] | ||