The inverse of a monad. A monad is a way to structure computations in terms of values and sequences of computations using those values. Monads allow the programmer to build up computations using sequential building blocks, which can themselves be sequences of computations.
Questions tagged [comonad]
63 questions
14
votes
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Comonad duplicate function
Why when you define the function duplicate
duplicate :: w a -> w (w a)
for the Comonad typeclass (link) you have to modify all the elements "in the context" (i.e. change elements other than the current value of the context). Why not just…
Jackie
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14
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3 answers
Is the concept of an "interleaved homomorphism" a real thing?
I am in need of the following class of functions:
class InterleavedHomomorphic x where
interleaveHomomorphism :: (forall a . f a -> g a) -> x f -> x g
Obviously the name I invented for it is not in any way an official term for anything, and the…
dflemstr
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13
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Tree Functor and Foldable but with Nodes. Is there any generalization over it?
data Tree t = Empty | Node t (Tree t) (Tree t)
We can create Functor instance and use
fmap :: (t -> a) -> Tree t -> Tree a
But what if instead of (t -> a) I want (Tree t -> a) so I could have access to a whole (Node t) not just t
treeMap :: (Tree…
ais
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12
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2 answers
Applicative is to monad what X is to comonad
Can we solve this equation for X ?
Applicative is to monad what X is to comonad
nicolas
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12
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Every free monad over a ??? functor yields a comonad?
In this answer to "Can a monad be a comonad?" we see that
Every Cofree Comonad over an Alternative functor yields a Monad.
What would be the dual to this? Is there a class of functors that automatically make a free monad over them a comonad?
Petr
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11
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What would be the methods of a bi-comonad?
While musing what more useful standard class to suggest to this one
class Coordinate c where
createCoordinate :: x -> y -> c x y
getFirst :: c x y -> x
getSecond :: c x y -> y
addCoordinates :: (Num x, Num y) => c x y -> c x y -> c x y
it…
leftaroundabout
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8
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Fixed-point of a monadic and comonadic computation
In Haskell, Given a monad m, there is mfix :: (a -> m a) -> m a that computes the fixed-point of a monadic computation.
Dually, given a comonad w, there is cofix :: w (w a -> a) -> a that computes the fixed-point of a comonadic computations.
Now…
Bob
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8
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Alpha Beta Pruning with Recursion Schemes
I'm trying to get more proficient with recursion schemes as they have so far been really helpful for turning gnarly explicit recursion code into something less spike-y. One of the other tools I tend to reach for when implementing algorithms that can…
Ace shinigami
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8
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2 answers
Why can't I find any law violations for the NotQuiteCofree not-quite-comonad?
On Twitter, Chris Penner suggested an interesting comonad instance for "maps augmented with a default value". The relevant type constructor and instance are transcribed here (with cosmetic differences):
data MapF f k a = f a :< Map k (f a)
…
Asad Saeeduddin
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8
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Which Algebraic Pattern fits this type of tree?
I've got a puzzle for you,
I managed to write some code that would do these things using recursion-schemes, but it's incredibly messy
and that usually means that I missed a useful abstraction somewhere.
I'm designing a layout system for my text…
Chris Penner
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7
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How to work with AST with Cofree annotation?
I have this simple Expr AST and I can easily convert it to String.
import Prelude hiding (Foldable)
import qualified Prelude
import Data.Foldable as F
import Data.Functor.Foldable
import Data.Monoid
import Control.Comonad.Cofree
data ExprF r =…
ais
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6
votes
1 answer
Deriving a monad from a cofree comonad
Edward Kmett writes on his blog that using the Co newtype (from the kan-extensions package), it's possible to derive a Monad from any Comonad. I'd like to learn how to mechanically do this for any Cofree f a, as for some Cofree types I don't know a…
Johannes Riecken
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6
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Understanding Comonad's <$$>
Given the following from fp-course:
class Functor f where
(<$>) ::
(a -> b)
-> f a
-> f b
class Functor f => Extend f where
(<<=) ::
(f a -> b)
-> f a
-> f b
I defined <$$> as so:
(<$$>) ::
Comonad f =>
(a -> b)
…
Kevin Meredith
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Is there a generic way to decompose the free comonad over a failure monad into a “values stream and final error”?
The Cofree comonad is useful for iterating partial functions in a way that's polymorphic on the error type. Its coiter resembles forM-looping in an error monad, but it gathers the produced values in a pure/lazy manner and you only see an error at…
leftaroundabout
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What benefits do I get from creating an instance of Comonad
In my application, I'm trying to implement an animation system. In this system, animations are represented as a cyclic list of frames:
data CyclicList a = CL a [a]
We can (inefficiently) advance the animation as follows:
advance :: CyclicList a ->…
Mokosha
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