Without
Revision as of 10:58, 11 September 2022 by Adám Brudzewsky (talk  contribs) (Text replacement  "<source" to "<syntaxhighlight")
~

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