Good points. But the "identity" thing is still what gets me. What is the identity of an intersection?
Like you said it can't be #{}. If you seed an intersection with #{} you get #{}, so you can't intersect from the empty set. The identity for an intersection is whatever the common element is, but how would you know that? On Friday, January 24, 2014 7:03:40 PM UTC-5, Cedric Greevey wrote: > > Intersection is associative and commutative: (intersection A B) = > (intersection B A) and (intersection A (intersection B C)) = (intersection > (intersection A B) C) = the elements common to all three sets. So it's > actually perfectly well-founded for use with reducers, at least in > principle, and intersecting A B C D can be parallelized sensibly by > parallel intersecting A B and C D and then intersecting the two resulting > sets. > > > On Fri, Jan 24, 2014 at 6:43 PM, Jarrod Swart <jcs...@gmail.com<javascript:> > > wrote: > >> If I understand you correctly I am in agreement. I don't think you could >> take this problem to clojure.core.reducers/reduce or fold because the >> problem is inherently sequential is it not? >> >> The reduction is basically (intersection (intersection (intersection A B) >> C) D). >> >> I was curious of this myself, how do I abstract out the order of the >> (reduce set/intersection ...). I couldn't think of one. >> >> Breaking this problem out into 'parallel' units of reduction isn't >> possible because the problem is dependent on order. Which reducers can't >> have, or so I think after what I have read today. >> >> >> On Friday, January 24, 2014 3:56:23 PM UTC-5, Cedric Greevey wrote: >> >>> An interesting question this raises is if there is any sensible way to >>> define (intersection). It would need to behave as an identity element for >>> intersection, so would need to behave as a set (so, (set? (intersection)) >>> => truthy) that contained everything (so, (contains? (intersection) foo) => >>> foo no matter what foo is; (partial contains? (intersection)) => identity). >>> The problem would be what to do with seq? Ideally an infinite seq that will >>> produce any particular value after finite time would be produced, but >>> there's no way to sensibly produce "any particular value" given the wide >>> variety of constructor semantics, builders, factory methods, things not >>> known to this particular runtime instance but that conceptually exist >>> somewhere, etc.; of course, the seq return is a dummy of sorts anyway since >>> you couldn't really use it sensibly to it might as well just return >>> (range). Printing should likely be overridden to just print >>> "(intersection)" rather than b0rk the REPL with a neverending stream of >>> integers (or whatever). >>> >>> But then it also subtly violates another property of Clojure set >>> objects: if (= a b), (not (identical? a b)), and (identical? (a-set a) a), >>> then (identical? (a-set b) a) and thus (not (identical? (a-set b) b)). The >>> latter is true under the hypothesis for every "real" set but would be false >>> for (intersection). >>> >>> Perhaps this is why (intersection) is not supported at this time, even >>> though (union) returns an empty set object, the identity element for the >>> union operation. >>> >>> >>> On Fri, Jan 24, 2014 at 3:34 PM, Jarrod Swart <jcs...@gmail.com> wrote: >>> >>>> Ah cool, thanks for posting your solution! >>>> >>>> On Friday, January 24, 2014 3:29:49 PM UTC-5, Tassilo Horn wrote: >>>> >>>>> Jarrod Swart <jcs...@gmail.com> writes: >>>>> >>>>> > The reason you can't get this to work is that r/map returns a >>>>> <reducible> >>>>> > not a <coll> for reduce to operate on. >>>>> >>>>> Ah, indeed. I couldn't see the forest for the trees. >>>>> >>>>> > I'm not sure of a solution because I'm not familiar with >>>>> > core.reducers. >>>>> >>>>> This works: >>>>> >>>>> (reduce set/intersection (r/foldcat (r/map set [[1 2] [3 1] [1 >>>>> 3]]))) >>>>> >>>>> Bye, >>>>> Tassilo >>>>> >>>> -- >>>> -- >>>> You received this message because you are subscribed to the Google >>>> Groups "Clojure" group. >>>> To post to this group, send email to clo...@googlegroups.com >>>> >>>> Note that posts from new members are moderated - please be patient with >>>> your first post. >>>> To unsubscribe from this group, send email to >>>> clojure+u...@googlegroups.com >>>> >>>> For more options, visit this group at >>>> http://groups.google.com/group/clojure?hl=en >>>> --- >>>> You received this message because you are subscribed to the Google >>>> Groups "Clojure" group. >>>> To unsubscribe from this group and stop receiving emails from it, send >>>> an email to clojure+u...@googlegroups.com. >>>> >>>> For more options, visit https://groups.google.com/groups/opt_out. >>>> >>> >>> -- >> -- >> You received this message because you are subscribed to the Google >> Groups "Clojure" group. >> To post to this group, send email to clo...@googlegroups.com<javascript:> >> Note that posts from new members are moderated - please be patient with >> your first post. >> To unsubscribe from this group, send email to >> clojure+u...@googlegroups.com <javascript:> >> For more options, visit this group at >> http://groups.google.com/group/clojure?hl=en >> --- >> You received this message because you are subscribed to the Google Groups >> "Clojure" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to clojure+u...@googlegroups.com <javascript:>. >> For more options, visit https://groups.google.com/groups/opt_out. >> > > -- -- You received this message because you are subscribed to the Google Groups "Clojure" group. 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