Trait/Object

scalaz

Density

Related Docs: object Density | package scalaz

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trait Density[F[_], Y] extends AnyRef

Density Comonad.

Density is Left Kan Extension where both Functors are the same.

Without any restrictions on F we can define Functor, Cobind, Comonad for Density[F]. Density is Comonad for free.

Self Type
Density[F, Y]
Source
Density.scala
See also

http://comonad.com/reader/2011/a-product-of-an-imperfect-union/

https://hackage.haskell.org/package/kan-extensions/docs/Control-Comonad-Density.html

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Type Members

  1. trait DensityLaw extends AnyRef

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  2. abstract type X

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Abstract Value Members

  1. abstract def f: (F[X]) ⇒ Y

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  2. abstract val fb: F[X]

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Concrete Value Members

  1. final def !=(arg0: Any): Boolean

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  2. final def ##(): Int

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  3. final def ==(arg0: Any): Boolean

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  4. final def asInstanceOf[T0]: T0

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  5. def clone(): AnyRef

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  6. def densityLaw: DensityLaw

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  7. def densityToAdjunction[X[_]](implicit F: Functor[F], A: Adjunction[F, X]): F[X[Y]]

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  8. def densityToCoyoneda: Coyoneda[F, X]

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  9. def densityToLan: Lan[F, F, Y]

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    Density is left Kan extension of a Functor F along itself (Lan f f).

    Density is left Kan extension of a Functor F along itself (Lan f f).

    lanToDensity(d.densityToLan) == d lanToDensity(l).densityToLan == l

  10. final def eq(arg0: AnyRef): Boolean

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  11. def equals(arg0: Any): Boolean

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  12. def finalize(): Unit

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  13. final def getClass(): Class[_]

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  14. def hashCode(): Int

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  15. final def isInstanceOf[T0]: Boolean

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  16. def lowerDensity(implicit C: Cobind[F]): F[Y]

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    The natural isomorphism between a Comonad F and the Density F.

    The natural isomorphism between a Comonad F and the Density F.

    d.lowerDensity andThen liftDensity = d

  17. def map[A](fab: (Y) ⇒ A): Density[F, A]

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  18. final def ne(arg0: AnyRef): Boolean

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  19. final def notify(): Unit

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  20. final def notifyAll(): Unit

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  21. def runDensity: Y

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  22. final def synchronized[T0](arg0: ⇒ T0): T0

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  23. def toString(): String

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  24. final def wait(): Unit

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  25. final def wait(arg0: Long, arg1: Int): Unit

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  26. final def wait(arg0: Long): Unit

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