I see. Then what is about Dual and Endo? Especially Endo, I completely
confused....
2009/11/14 Eugene Kirpichov <ekirpic...@gmail.com>:
> There is an astonishing number of things in programming that are monoids:
> - Numbers, addition, 0
> - Numbers, multiplication, 1
> - Lists, concatenation, [] (including strings)
> - Sorted lists, merge with respect to a linear order, []
> - Sets, union, {}
> - Maps, left-biased or right-biased union, {}
> - Maps K->V, union where Vs for same K get merged in some other monoid, {}
> - For any M: Subsets of M, intersection, M
> - Any lattice with an upper bound, minimum, upper bound;
> symmetrically for a lower-bounded set
> - If (S, *, u) is a monoid, then (A -> S, \f g x -> f x * g x, \x ->
> u) is a monoid
> - Product (a,b) and co-product (Either) of monoids
> - Parsers, alternation, a parser that always fails
> - etc.
>
> The benefits of calling something a monoid arise from using
> general-purpose structures operating on monoids:
> - Finger trees http://apfelmus.nfshost.com/monoid-fingertree.html
> - Aforementioned maps which merge values for a key in a given monoid
> - Aforementioned monoids lifted to functions
> - Monoidal folds (Data.Foldable)
> - ...
>
> 2009/11/13 Magicloud Magiclouds <magicloud.magiclo...@gmail.com>:
>> Hi,
>> I have looked the concept of monoid and something related, but
>> still, I do not know why we use it?
>>
>> --
>> 竹密岂妨流水过
>> 山高哪阻野云飞
>>
>> _______________________________________________
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>>
>>
>
>
>
> --
> Eugene Kirpichov
> Web IR developer, market.yandex.ru
>
--
竹密岂妨流水过
山高哪阻野云飞
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