Less than or Equal to: Difference between revisions

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(Scan idiom)
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== Boolean function ==
== Boolean function ==
{{Main|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]] function, 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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|}
|}
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><\</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 ==

Revision as of 09:22, 30 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

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


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