<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div class="">First consider how `and` and `or` work for booleans.</div><div class=""><br class=""></div><div class=""><br class=""></div><div class="">and (x ++ y) == and x && and y</div><div class=""><br class=""></div><div class="">For this to work we need `and [] == True`</div><div class=""><br class=""></div><div class="">or (x ++ y) == or x || or y</div><div class=""><br class=""></div><div class="">For this to work we need `or [] == False`</div><div class=""><br class=""></div><div class="">and and or are duals of each other.</div><div class=""><br class=""></div><div class=""><br class=""></div><div class="">There’s an analogue here to union and intersection which are also duals of each other.</div><div class=""><br class=""></div>We have: unions (x ++ y) == union (unions x) (unions y)<div class=""><br class=""></div><div class="">This requires `union [] == []` since any list xs could be split as `[] ++ xs`</div><div class=""><br class=""></div><div class="">We'd like to have: intersections (x ++ y) == intersect (intersections x) (intersections y)</div><div class=""><br class=""></div><div class="">For this kind of splitting property to make sense for intersections we’d need `intersections [] == listOfAllElementsOfThisType`, but it’s not easy to construct that list of all elements in general.</div><div class="">So instead we punt on the problem and refuse to define intersections on an empty list.</div><div class=""><br class=""></div><div class="">-glguy</div><div class=""><div class=""><div><br class=""><blockquote type="cite" class=""><div class="">On Dec 6, 2020, at 10:50 AM, Sven Panne <<a href="mailto:svenpanne@gmail.com" class="">svenpanne@gmail.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div dir="ltr" class=""><div dir="ltr" class="">Am So., 6. Dez. 2020 um 07:20 Uhr schrieb Reed Mullanix <<a href="mailto:reedmullanix@gmail.com" class="">reedmullanix@gmail.com</a>>:<br class=""></div><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr" class=""><div class="">[...]</div><div class=""> intersections :: Ord a => NonEmpty (Set a) -> Set a<br class=""> intersections (s :| ss) = Foldable.foldl' intersection s ss</div><div class="">[...]</div></div></blockquote><div class=""><br class=""></div><div class="">Why NonEmpty? I would expect "intersections [] = Set.empty", because the result contains all the elements which are in all sets, i.e. none. That's at least my intuition, is there some law which this would violate? </div></div></div>
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