Okay, I see now.
Thanks for the Socratic dialogue, at the onset of the day I knew nothing
about core.reducers. I feel fairly conversational now!
On Friday, January 24, 2014 7:44:03 PM UTC-5, Cedric Greevey wrote:
>
> 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 <jcs...@gmail.com<javascript:>
> > 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
>>>>>>>
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