Density comonad #2029
Density comonad #2029
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| sealed abstract class DensityInstances1 { | ||
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| /** Density is a Functor for free */ | ||
| implicit def functorInstance[F[_]]: Functor[Density[F, ?]] = new DensityFunctor[F]{} |
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functorInstance and cobindInstance unnecessary because same restriction as comonadInstance.
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@stephen-lazaro I have noticed you have done some great job at implementing Density (https://github.com/stephen-lazaro/persians/blob/master/src/main/scala/sl/persians/Density.scala). In particular you got further in implementing Apply and Applicative instances and some nice work around Cofree. Do you want to contribute to this PR? |
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@lemastero Sure! I would be happy to. Thanks for thinking of me! |
merge origin
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| /** Density is a free Comonad */ | ||
| private trait DensityComonad[F[_]] extends Comonad[Density[F, ?]] with DensityCobind[F] { |
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We can just define all methods in DensityComonad and remove DensityCobind and DensityFunctor.
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DensityCobind and DensityFunctor removed: 4e3d574
@stephen-lazaro It seems Density Comonad is interesting concept yet has not much application. |
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@lemastero I've proposed |
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The symmetry is useful for learning. I'm happy to add the instances regardless, as I think they are interesting. |
Density Comonad based on Haskell implementation: kan-extensions/Control.Comonad.Density
Density complete the duality matrix of kan extensions:
| Yoneda | Codensity | Kan |
| Coyoneda | Density | Lan |
It is simpler version of Left Kan Extension. It is also Comonad for free like Day, CoFree.
It is already implemented in Purescript and Haskell:
Some methods in Haskell Control.Monad.Co use it: diter dctrlM
It was studied on blogs:
People play around with it:
I have turned the relationship between Density and Lan as laws:
lanToDensity(d.densityToLan) == dlanToDensity(l).densityToLan == lProbably it would be nice to add, as a law, relationship between density and Cobind:
d.lowerDensity andThen liftDensity = dI think it is worth to add, so people might play around with it. WDYT?