scalaz

Adjunction

abstract class Adjunction[F[_], G[_]] extends AnyRef

An adjunction formed by two functors F and G such that F is left-adjoint to G. The composite functor GF is a monad and the composite functor FG is a comonad.

The minimal defition is either (unit, counit) or (leftAdjunct, rightAdjunct)

Self Type
Adjunction[F, G]
Source
Adjunction.scala
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Instance Constructors

  1. new Adjunction()(implicit F: Functor[F], G: Functor[G])

Value Members

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

    Definition Classes
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  2. final def !=(arg0: Any): Boolean

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  3. final def ##(): Int

    Definition Classes
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  4. final def ==(arg0: AnyRef): Boolean

    Definition Classes
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  5. final def ==(arg0: Any): Boolean

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  6. implicit val F: Functor[F]

  7. implicit val G: Functor[G]

  8. final def asInstanceOf[T0]: T0

    Definition Classes
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  9. def clone(): AnyRef

    Attributes
    protected[java.lang]
    Definition Classes
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    Annotations
    @throws( ... )

  10. implicit val comonad: Comonad[[α]F[G[α]]]

    Every adjunction gives rise to a comonad.

  11. def compose[P[_], Q[_]](implicit A: -|[P, Q]): -|[[α]P[F[α]], [α]G[Q[α]]]

    Adjunctions compose in a natural fashion.

    Adjunctions compose in a natural fashion. If F -| G is an adjunction, and P -| Q is an adjunction, then PF -| GQ is an adjunction. In fact, adjunctions in Scala form a monoid.

  12. def counit[A](a: F[G[A]]): A

    Extracts a value out of the comonad.

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

    Definition Classes
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  14. def equals(arg0: Any): Boolean

    Definition Classes
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  15. def finalize(): Unit

    Attributes
    protected[java.lang]
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    @throws( classOf[java.lang.Throwable] )

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

    Definition Classes
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  17. def hashCode(): Int

    Definition Classes
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  18. final def isInstanceOf[T0]: Boolean

    Definition Classes
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  19. def leftAdjunct[A, B](a: ⇒ A)(f: (F[A]) ⇒ B): G[B]

    Every F-algebra maps to a G-coalgebra.

  20. implicit val monad: Monad[[α]G[F[α]]]

    Every adjunction gives rise to a monad.

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

    Definition Classes
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  22. final def notify(): Unit

    Definition Classes
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  23. final def notifyAll(): Unit

    Definition Classes
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  24. implicit val representable: Representable[G, F[Unit]]

    Every adjunction is representable.

  25. def rightAdjunct[A, B](a: F[A])(f: (A) ⇒ G[B]): B

    Every G-coalgebra maps to an F-algebra.

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

    Definition Classes
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  27. def toString(): String

    Definition Classes
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  28. def unit[A](a: ⇒ A): G[F[A]]

    Puts a value into the monad.

  29. final def wait(): Unit

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    @throws( ... )

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

    Definition Classes
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    @throws( ... )

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

    Definition Classes
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    @throws( ... )

  32. implicit val zapFG: Zap[F, G]

    Adjoint functors annihilate each other.

  33. implicit val zapGF: Zap[G, F]

    Adjoint functors annihilate each other.

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