No, the identity for intersection is a set that has everything, as
(intersection A Everything) = A no matter what A is.
On Fri, Jan 24, 2014 at 7:38 PM, Jarrod Swart <jcsw...@gmail.com> wrote:
> 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> 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
>>> 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.
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.
