Without

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~

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>

Works in: Dyalog APL

External Links

Documentation


APL built-ins [edit]
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