Difference between revisions of "Without"
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m (Text replacement  "http://help.dyalog.com" to "https://help.dyalog.com") 

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=== Documentation ===  === Documentation ===  
−  * [  +  * [https://help.dyalog.com/latest/#Language/Primitive%20Functions/Excluding.htm#Excluding Dyalog] 
* [http://microapl.com/apl_help/ch_020_020_410.htm APLX]  * [http://microapl.com/apl_help/ch_020_020_410.htm APLX]  
* J [https://www.jsoftware.com/help/dictionary/d121.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/minusdot#dyadic NuVoc]  * J [https://www.jsoftware.com/help/dictionary/d121.htm Dictionary], [https://code.jsoftware.com/wiki/Vocabulary/minusdot#dyadic NuVoc]  
{{APL builtins}}[[Category:Primitive functions]][[Category:Set functions]]  {{APL builtins}}[[Category:Primitive functions]][[Category:Set functions]] 
Latest revision as of 14:46, 14 July 2020
~

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 ~
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" (~X∊Y)/X
. This preserves the order and multiplicity in the left argument. Both arguments can be nested arrays.
'HELLO'~'GOODBYE'
HLL
A←'THIS' 'AND' 'THAT'
A~'TH' 'AND'
┌────┬────┐
│THIS│THAT│
└────┴────┘
Extension
Some dialects allow Without to work on major cells:
X←4 2⍴'AABBCCCC'
Y←3 2⍴'AABBAA'
X~Y
CC
CC
Works in: Extended Dyalog APL
Others can easily define such a function:
X←4 2⍴'AABBCCCC'
Y←3 2⍴'AABBAA'
Without←{⍺⌿⍨~(⍳≢⍺)∊⍺⍳⍵}
X Without Y
CC
CC
Works in: Dyalog APL
External Links
Documentation