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Boolean: Difference between revisions
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Text replacement - "</source>" to "</syntaxhighlight>"
m (Text replacement - "<source" to "<syntaxhighlight") Tags: Mobile edit Mobile web edit |
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+/ 3 1 4 1 5 9 2 < 5 | +/ 3 1 4 1 5 9 2 < 5 | ||
5 | 5 | ||
</ | </syntaxhighlight> | ||
With [[index origin]] 0, Booleans can also be used as [[Index|indices]] into an array. | With [[index origin]] 0, Booleans can also be used as [[Index|indices]] into an array. | ||
<syntaxhighlight lang=apl> | <syntaxhighlight lang=apl> | ||
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'-+'[3 1 4 1 5 9 2 < 5] | '-+'[3 1 4 1 5 9 2 < 5] | ||
++++--+ | ++++--+ | ||
</ | </syntaxhighlight> | ||
The use of numbers for Booleans also allows functions to be extended from a Boolean domain to a more general domain. The function [[Compress]] was originally defined to take a Boolean left argument and use it as a filter for the right argument (removing right argument values corresponding to 0), but has generally now been replaced by an extension called [[Replicate]] which can copy right argument values multiple times. | The use of numbers for Booleans also allows functions to be extended from a Boolean domain to a more general domain. The function [[Compress]] was originally defined to take a Boolean left argument and use it as a filter for the right argument (removing right argument values corresponding to 0), but has generally now been replaced by an extension called [[Replicate]] which can copy right argument values multiple times. | ||
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0 4 1 2 0 0 0 / '3141592' | 0 4 1 2 0 0 0 / '3141592' | ||
1111411 | 1111411 | ||
</ | </syntaxhighlight> | ||
== Boolean functions == | == Boolean functions == | ||
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{|class=wikitable | {|class=wikitable | ||
! <syntaxhighlight lang=apl inline>f 0</ | ! <syntaxhighlight lang=apl inline>f 0</syntaxhighlight> !! <syntaxhighlight lang=apl inline>f 1</syntaxhighlight> !! Function | ||
|- | |- | ||
| 0 || 0 || Constant 0 | | 0 || 0 || Constant 0 | ||
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| 0 || 1 || Identity | | 0 || 1 || Identity | ||
|- | |- | ||
| 1 || 0 || <syntaxhighlight lang=apl inline>~</ | | 1 || 0 || <syntaxhighlight lang=apl inline>~</syntaxhighlight> [[Not]] | ||
|- | |- | ||
| 1 || 1 || Constant 1 | | 1 || 1 || Constant 1 | ||
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{|class=wikitable | {|class=wikitable | ||
! <syntaxhighlight lang=apl inline>0 f 0</ | ! <syntaxhighlight lang=apl inline>0 f 0</syntaxhighlight> !! <syntaxhighlight lang=apl inline>0 f 1</syntaxhighlight> !! <syntaxhighlight lang=apl inline>1 f 0</syntaxhighlight> !! <syntaxhighlight lang=apl inline>1 f 1</syntaxhighlight> !! Function | ||
|- | |- | ||
| 0 || 0 || 0 || 0 || Constant 0 | | 0 || 0 || 0 || 0 || Constant 0 | ||
|- | |- | ||
| 0 || 0 || 0 || 1 || <syntaxhighlight lang=apl inline>∧</ | | 0 || 0 || 0 || 1 || <syntaxhighlight lang=apl inline>∧</syntaxhighlight> [[And]], <syntaxhighlight lang=apl inline>⌊</syntaxhighlight> [[Minimum]] , <syntaxhighlight lang=apl inline>×</syntaxhighlight> [[Times]] | ||
|- | |- | ||
| 0 || 0 || 1 || 0 || <syntaxhighlight lang=apl inline>></ | | 0 || 0 || 1 || 0 || <syntaxhighlight lang=apl inline>></syntaxhighlight> [[Greater Than]] | ||
|- | |- | ||
| 0 || 0 || 1 || 1 || Left argument | | 0 || 0 || 1 || 1 || Left argument | ||
|- | |- | ||
| 0 || 1 || 0 || 0 || <syntaxhighlight lang=apl inline><</ | | 0 || 1 || 0 || 0 || <syntaxhighlight lang=apl inline><</syntaxhighlight> [[Less Than]], <syntaxhighlight lang=apl inline>|</syntaxhighlight> [[Residue]] | ||
|- | |- | ||
| 0 || 1 || 0 || 1 || Right argument | | 0 || 1 || 0 || 1 || Right argument | ||
|- | |- | ||
| 0 || 1 || 1 || 0 || <syntaxhighlight lang=apl inline>≠</ | | 0 || 1 || 1 || 0 || <syntaxhighlight lang=apl inline>≠</syntaxhighlight> [[Not Equal]] | ||
|- | |- | ||
| 0 || 1 || 1 || 1 || <syntaxhighlight lang=apl inline>∨</ | | 0 || 1 || 1 || 1 || <syntaxhighlight lang=apl inline>∨</syntaxhighlight> [[Or]], <syntaxhighlight lang=apl inline>⌈</syntaxhighlight> [[Maximum]] | ||
|- | |- | ||
| 1 || 0 || 0 || 0 || <syntaxhighlight lang=apl inline>⍱</ | | 1 || 0 || 0 || 0 || <syntaxhighlight lang=apl inline>⍱</syntaxhighlight> [[Nor]] | ||
|- | |- | ||
| 1 || 0 || 0 || 1 || <syntaxhighlight lang=apl inline>=</ | | 1 || 0 || 0 || 1 || <syntaxhighlight lang=apl inline>=</syntaxhighlight> [[Equal]] | ||
|- | |- | ||
| 1 || 0 || 1 || 0 || Right argument negation | | 1 || 0 || 1 || 0 || Right argument negation | ||
|- | |- | ||
| 1 || 0 || 1 || 1 || <syntaxhighlight lang=apl inline>≥</ | | 1 || 0 || 1 || 1 || <syntaxhighlight lang=apl inline>≥</syntaxhighlight> [[Greater Than or Equal]], <syntaxhighlight lang=apl inline>*</syntaxhighlight> [[Power]] | ||
|- | |- | ||
| 1 || 1 || 0 || 0 || Left argument negation | | 1 || 1 || 0 || 0 || Left argument negation | ||
|- | |- | ||
| 1 || 1 || 0 || 1 || <syntaxhighlight lang=apl inline>≤</ | | 1 || 1 || 0 || 1 || <syntaxhighlight lang=apl inline>≤</syntaxhighlight> [[Less Than or Equal]], <syntaxhighlight lang=apl inline>!</syntaxhighlight> [[Binomial]] | ||
|- | |- | ||
| 1 || 1 || 1 || 0 || <syntaxhighlight lang=apl inline>⍲</ | | 1 || 1 || 1 || 0 || <syntaxhighlight lang=apl inline>⍲</syntaxhighlight> [[Nand]] | ||
|- | |- | ||
| 1 || 1 || 1 || 1 || Constant 1 | | 1 || 1 || 1 || 1 || Constant 1 | ||