Packages

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

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

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

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Type Members

  1. trait DensityLaw extends AnyRef
  2. abstract type X

Abstract Value Members

  1. abstract def f: (F[X]) => Y
  2. abstract val fb: F[X]

Concrete Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##: Int
    Definition Classes
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  3. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  4. final def asInstanceOf[T0]: T0
    Definition Classes
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  5. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.CloneNotSupportedException]) @native()
  6. def densityLaw: DensityLaw
  7. def densityToAdjunction[X[_]](implicit F: Functor[F], A: Adjunction[F, X]): F[X[Y]]
  8. def densityToCoyoneda: Coyoneda[F, X]
  9. def densityToLan: Lan[F, F, Y]

    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
    Definition Classes
    AnyRef
  11. def equals(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef → Any
  12. def finalize(): Unit
    Attributes
    protected[lang]
    Definition Classes
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    Annotations
    @throws(classOf[java.lang.Throwable])
  13. final def getClass(): Class[_ <: AnyRef]
    Definition Classes
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    Annotations
    @native()
  14. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  15. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  16. def lowerDensity(implicit C: Cobind[F]): F[Y]

    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]
  18. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  19. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  20. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  21. def runDensity: Y
  22. final def synchronized[T0](arg0: => T0): T0
    Definition Classes
    AnyRef
  23. def toString(): String
    Definition Classes
    AnyRef → Any
  24. final def wait(): Unit
    Definition Classes
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    Annotations
    @throws(classOf[java.lang.InterruptedException])
  25. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
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    Annotations
    @throws(classOf[java.lang.InterruptedException])
  26. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws(classOf[java.lang.InterruptedException]) @native()

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