monoids Questions
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I'm trying to understand what Monoid is from a category theory perspective, but I'm a bit confused with the notation used to describe it. Here is Wikipedia:
In category theory, a monoid (or monoid...
Abnegate asked 18/5, 2019 at 15:41
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Is there any newtype in base that would basically achieve the following?
newtype SemigroupFlip a = SemigroupFlip a
instance Semigroup a => Semigroup (SemigroupFlip a) where
(SemigroupFlip a) &...
2
I've been experimenting with monoids and Distributives lately, and I think I've found something of interest (described in my answer) - are these already known structures? (I've been unable to find ...
Freon asked 9/6, 2022 at 0:1
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The free monoids are often being regarded as "list monoids". Yet, I am interested in other possible structures which might give us free monoids.
Firstly, let us go over the definition of ...
Sheya asked 16/9, 2020 at 20:57
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I am busy reading Bartosz Milewski's Category Theory book for programmers and I'm struggling with the depiction of non-identity morphisms when moving between describing a monoid as a set and a mono...
Rasp asked 22/6, 2022 at 7:25
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I have a type to describe post-calibration radiocarbon date probability distributions. The details and background don't matter for the question: It boils down to one probability value in _calPDFDen...
1
The Cartesian class from the constrained-category project is for categories, products of objects in which are objects in the same category yet again.
I wonder about the classes Cartesian extends:
c...
Chifforobe asked 2/7, 2021 at 19:55
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I'm trying to understand the motivation behind the MonadPlus. Why is it necessary if there are already the typeclasses Monad and Monoid?
Granted, instances of Monoid are concrete types, whereas in...
4
I watched this video on the composite pattern, where the main example is how to use the pattern as a mean to generate HTML code from a tree structure describing a todo list where each item can be i...
Frowsy asked 10/4, 2021 at 18:5
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I've read about monoid homomorphism from Monoid Morphisms, Products, and Coproducts and could not understand 100%.
The author says (emphasis original):
The length function maps from String to ...
Mavismavra asked 5/5, 2019 at 14:53
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The base library in Haskell has the following type synonyms in Data.Semigroup:
type ArgMin a b = Min (Arg a b)
type ArgMax a b = Max (Arg a b)
Here are links to the haddocks: ArgMin and ArgMax
W...
Nutritionist asked 20/11, 2020 at 12:54
3
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Suppose I have a type like
data Options = Options
{ _optionOne :: Maybe Integer
, _optionTwo :: Maybe Integer
, _optionThree :: Maybe String
} deriving Show
with many more fields. I would l...
1
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In this (very interesting) talk the speaker poses a question:
What is the e value for the float/std::min monoid.
In other words: what is the identity element for the monoid composed of standard C...
1
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On the one hand the monadic bind operator >>= is left associative (AFAIK). On the other hand the monad law demands associativity, i.e. evaluation order doesn't matter (like with monoids). Bes...
Pietje asked 7/9, 2020 at 11:56
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I am trying to define an instance:
newtype Join a = Join { getJoin :: a -> Bool }
deriving Generic
instance Monoid (Join a) where
f <> g = ???
mempty = ???
The goal is that the functi...
Ghat asked 19/7, 2020 at 16:22
3
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I have learnt about Monoidal being an alternative way to represent Applicative not so long ago. There is an interesting question on Typeclassopedia:
(Tricky) Prove that given your implementations...
Idell asked 17/7, 2020 at 7:31
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Perhaps neither of these statements are categorically precise, but a monad is often defined as "a monoid in the category of endofunctors"; a Haskell Alternative is defined as "a monoid on applicati...
Catboat asked 24/4, 2018 at 18:46
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While looking at the definition of Monoid I noticed that mconcat has the following definition (source):
mconcat :: Monoid a => [a] -> a
mconcat = foldr mappend mempty
Why would the signatu...
2
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I am reading the book 'Programming in Scala' (The red book).
In the chapter about Monoids, I understand what a Monoid homomorphism is, for example: The String Monoid M with concatenation and leng...
Hobbyhorse asked 11/9, 2019 at 11:19
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I have recently tried to find a good source on the difference between monads and monoids.
Could someone provide a link to a good resource on this or perhaps take one's time to elaborate on the si...
Offstage asked 16/3, 2012 at 23:58
5
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Who first said the following?
A monad is just a monoid in the
category of endofunctors, what's the
problem?
And on a less important note, is this true and if so could you give an explanation...
Clincher asked 6/10, 2010 at 6:55
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Instance MonadPlus IO is unique because mzero throws:
Prelude Control.Monad> mzero
*** Exception: user error (mzero)
So accordingly, MonadPlus IO implies that it is also intended for errors.
...
Groff asked 11/8, 2019 at 6:26
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There is a similar question I found here that asks almost the same thing, but not quite.
The question I have is how to compose a list of functions of type (a -> Bool) to be one function that is al...
Fradin asked 8/8, 2019 at 14:30
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I am getting very confused with these three concepts.
Is there any simple examples to illustrate the differences between
Category, Monoid and Monad ?
It would be very helpful if there is a illust...
Stakhanovism asked 31/3, 2013 at 5:44
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I am trying to understand Traversable with the help of https://namc.in/2018-02-05-foldables-traversals.
Somewhere the author mentioned the following sentence:
Traversable is to Applicative con...
Viperish asked 5/4, 2019 at 10:19
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