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{{Main|Comparison function}} | {{Main|Comparison function}} | ||
{{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><</ | {{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><</syntaxhighlight>), and in fact was called '''Not greater''' in [[APL\360]]. | ||
== Boolean function == | == 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]]: | 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 | ::{|class=wikitable | ||
!<source lang=apl inline>≤</ | !<source lang=apl inline>≤</syntaxhighlight>!!<source lang=apl inline>0</syntaxhighlight>!!<source lang=apl inline>1</syntaxhighlight> | ||
|- | |- | ||
!<source lang=apl inline>0</ | !<source lang=apl inline>0</syntaxhighlight> | ||
|<source lang=apl inline>1</ | |<source lang=apl inline>1</syntaxhighlight>||<source lang=apl inline>1</syntaxhighlight> | ||
|- | |- | ||
!<source lang=apl inline>1</ | !<source lang=apl inline>1</syntaxhighlight> | ||
|<source lang=apl inline>0</ | |<source lang=apl inline>0</syntaxhighlight>||<source lang=apl inline>1</syntaxhighlight> | ||
|} | |} | ||
In the context of logic, it can be read as ''implies''. | 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><\</ | Less than or Equal to [[Scan]] is an occasionally used pattern related to [[Less than]] Scan. While <source lang=apl inline><\</syntaxhighlight> changes all 1s after the first to 0, <source lang=apl inline>≤\</syntaxhighlight> changes all 0s after the first to 1. Thus <source lang=apl inline>≤\A</syntaxhighlight> {{←→}} <source lang=apl inline>~<\~A</syntaxhighlight>. | ||
<source lang=apl> | <source lang=apl> | ||
≤\ 1 0 1 0 0 0 1 0 | ≤\ 1 0 1 0 0 0 1 0 | ||
1 0 1 1 1 1 1 1 | 1 0 1 1 1 1 1 1 | ||
</ | </syntaxhighlight> | ||
<source lang=apl inline>≤\</ | <source lang=apl inline>≤\</syntaxhighlight> appears in the [[FinnAPL idiom library]] as entry 350, "Not first zero". | ||
== External links == | == External links == |