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 <jcsw...@gmail.com> 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 clojure@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+unsubscr...@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+unsubscr...@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. 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