scalaz

InvariantFunctor

trait InvariantFunctor[F[_]] extends AnyRef

Unary type constructor that supports an xmap operation that converts an F[A] to an F[B] given two functions, A => B and B => A.

An invariant functor must satisfy two laws:

Also known as an exponential functor.

Self Type
InvariantFunctor[F]
Source
InvariantFunctor.scala
See also

scalaz.InvariantFunctor.InvariantFunctorLaw

http://comonad.com/reader/2008/rotten-bananas/

https://hackage.haskell.org/packages/archive/invariant/latest/doc/html/Data-Functor-Invariant.html

Linear Supertypes
AnyRef, Any
Known Subclasses
Align, Applicative, ApplicativePlus, Apply, Bind, BindRec, Cobind, Comonad, ComonadStore, Contravariant, Distributive, Divide, Divisible, Functor, IsomorphismAlign, IsomorphismApplicative, IsomorphismApplicativePlus, IsomorphismApply, IsomorphismBind, IsomorphismBindRec, IsomorphismCobind, IsomorphismComonad, IsomorphismComonadStore, IsomorphismContravariant, IsomorphismDistributive, IsomorphismDivide, IsomorphismDivisible, IsomorphismFunctor, IsomorphismInvariantFunctor, IsomorphismMonad, IsomorphismMonadError, IsomorphismMonadPlus, IsomorphismMonadReader, IsomorphismMonadState, IsomorphismMonadTell, IsomorphismNondeterminism, IsomorphismTraverse, IsomorphismTraverse1, Monad, MonadError, MonadListen, MonadPlus, MonadReader, MonadState, MonadTell, Nondeterminism, SemigroupApply, SndCovariant, Traverse, Traverse1
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Type Members

  1. trait InvariantFunctorLaw extends AnyRef

Abstract Value Members

  1. abstract def xmap[A, B](ma: F[A], f: (A) ⇒ B, g: (B) ⇒ A): F[B]

    Converts ma to a value of type F[B] using the provided functions f and g.

Concrete Value Members

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

    Definition Classes
    AnyRef

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

    Definition Classes
    Any

  3. final def ##(): Int

    Definition Classes
    AnyRef → Any

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

    Definition Classes
    AnyRef

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

    Definition Classes
    Any

  6. final def asInstanceOf[T0]: T0

    Definition Classes
    Any

  7. def clone(): AnyRef

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

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

    Definition Classes
    AnyRef

  9. def equals(arg0: Any): Boolean

    Definition Classes
    AnyRef → Any

  10. def finalize(): Unit

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

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

    Definition Classes
    AnyRef → Any

  12. def hashCode(): Int

    Definition Classes
    AnyRef → Any

  13. def invariantFunctorLaw: InvariantFunctorLaw

  14. val invariantFunctorSyntax: InvariantFunctorSyntax[F]

  15. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any

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

    Definition Classes
    AnyRef

  17. final def notify(): Unit

    Definition Classes
    AnyRef

  18. final def notifyAll(): Unit

    Definition Classes
    AnyRef

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

    Definition Classes
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  20. def toString(): String

    Definition Classes
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  21. final def wait(): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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

    Definition Classes
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    Annotations
    @throws( ... )

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

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

  24. def xmapb[A, B](ma: F[A])(b: Bijection[A, B]): F[B]

    Converts ma to a value of type F[B] using the provided bijection.

  25. def xmapi[A, B](ma: F[A])(iso: Isomorphism.<=>[A, B]): F[B]

    Converts ma to a value of type F[B] using the provided isomorphism.

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