Without: Difference between revisions
m (Text replacement  "http://help.dyalog.com" to "https://help.dyalog.com") 
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{{BuiltinWithout~}}, '''Set Difference''', '''Excluding''', or '''Less''', is a [[dyadic]] [[set function]] which computes the [[wikipedia:set differenceset difference]] of the two [[vector]] [[argumentarguments]]. It shares the [[glyph]] <source lang=apl inline>~</  {{BuiltinWithout~}}, '''Set Difference''', '''Excluding''', or '''Less''', is a [[dyadic]] [[set function]] which computes the [[wikipedia:set differenceset difference]] of the two [[vector]] [[argumentarguments]]. It shares the [[glyph]] <source lang=apl inline>~</syntaxhighlight> with the monadic function [[Not]].  
== Examples ==  == Examples ==  
Both arguments of Without is usually restricted to [[vectorvectors]]. Unlike sets in the mathematical sense, duplicate elements are allowed in both sides, and Without is usually implemented as "left argument filtered by the absence in the right argument" <source lang=apl inline>(~X∊Y)/X</  Both arguments of Without is usually restricted to [[vectorvectors]]. Unlike sets in the mathematical sense, duplicate elements are allowed in both sides, and Without is usually implemented as "left argument filtered by the absence in the right argument" <source lang=apl inline>(~X∊Y)/X</syntaxhighlight>. This preserves the order and multiplicity in the left argument. Both arguments can be [[nested arraynested arrays]].  
<source lang=apl>  <source lang=apl>  
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│THIS│THAT│  │THIS│THAT│  
└────┴────┘  └────┴────┘  
</  </syntaxhighlight>  
== Extension ==  == Extension ==  
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CC  CC  
CC  CC  
</  </syntaxhighlight>{{Works in[[Extended Dyalog APL]]}}  
Others can easily define such a function:  Others can easily define such a function:  
[https://tio.run/##SyzI0U2pTMzJT///P@JR2wQTBaNHvVvUHR2dnJyBQJ0rEihojBB0dFTnCs8sycgvLQFKVD/q3fWoZ/@j3hV1Go96Nz/qXAQU0HzU0QUSB/J7t9ZyPeqbClQZoQDVpRD5/z8A Try it online!]<source lang=apl>  [https://tio.run/##SyzI0U2pTMzJT///P@JR2wQTBaNHvVvUHR2dnJyBQJ0rEihojBB0dFTnCs8sycgvLQFKVD/q3fWoZ/@j3hV1Go96Nz/qXAQU0HzU0QUSB/J7t9ZyPeqbClQZoQDVpRD5/z8A Try it online!]<source lang=apl>  
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CC  CC  
CC  CC  
</  </syntaxhighlight>{{Works in[[Dyalog APL]]}}  
== External Links ==  == External Links ==  
Revision as of 10:24, 11 September 2022
~

Without (~
), Set Difference, Excluding, or Less, is a dyadic set function which computes the set difference of the two vector arguments. It shares the glyph <source lang=apl inline>~</syntaxhighlight> with the monadic function Not.
Examples
Both arguments of Without is usually restricted to vectors. Unlike sets in the mathematical sense, duplicate elements are allowed in both sides, and Without is usually implemented as "left argument filtered by the absence in the right argument" <source lang=apl inline>(~X∊Y)/X</syntaxhighlight>. This preserves the order and multiplicity in the left argument. Both arguments can be nested arrays.
<source lang=apl>
'HELLO'~'GOODBYE'
HLL
A←'THIS' 'AND' 'THAT' A~'TH' 'AND'
┌────┬────┐ │THIS│THAT│ └────┴────┘ </syntaxhighlight>
Extension
Some dialects allow Without to work on major cells: Try it online!<source lang=apl>
X←4 2⍴'AABBCCCC' Y←3 2⍴'AABBAA' X~Y
CC CC
</syntaxhighlight>
Others can easily define such a function: Try it online!<source lang=apl>
X←4 2⍴'AABBCCCC' Y←3 2⍴'AABBAA' Without←{⍺⌿⍨~(⍳≢⍺)∊⍺⍳⍵} X Without Y
CC CC
</syntaxhighlight>
External Links
Documentation