Packages

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:

  • identity - xmap(ma)(identity, identity) == ma
  • composite - xmap(xmap(ma, f1, g1), f2, g2) == xmap(ma, f2 compose f1, g1, compose g2)

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/

http://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, IsomorphismDivide, IsomorphismDivisible, IsomorphismFunctor, IsomorphismInvariantFunctor, IsomorphismMonad, IsomorphismMonadError, IsomorphismMonadPlus, IsomorphismMonadReader, IsomorphismMonadState, IsomorphismMonadTell, IsomorphismNondeterminism, IsomorphismTraverse, IsomorphismTraverse1, Monad, MonadError, MonadListen, MonadPlus, MonadReader, MonadState, MonadTell, Nondeterminism, SndCovariant, SemigroupApply, Traverse, Traverse1, IsomorphismMonadCatchIO, IsomorphismMonadControlIO, IsomorphismMonadIO, MonadCatchIO, MonadControlIO, MonadIO, RegionTMonad
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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: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##(): Int
    Definition Classes
    AnyRef → Any
  3. final def ==(arg0: Any): Boolean
    Definition Classes
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  4. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  5. def clone(): AnyRef
    Attributes
    protected[java.lang]
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    Annotations
    @native() @throws( ... )
  6. final def eq(arg0: AnyRef): Boolean
    Definition Classes
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  7. def equals(arg0: Any): Boolean
    Definition Classes
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  8. def finalize(): Unit
    Attributes
    protected[java.lang]
    Definition Classes
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    Annotations
    @throws( classOf[java.lang.Throwable] )
  9. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  10. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  11. def invariantFunctorLaw: InvariantFunctorLaw
  12. val invariantFunctorSyntax: InvariantFunctorSyntax[F]
  13. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  14. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  15. final def notify(): Unit
    Definition Classes
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    @native()
  16. final def notifyAll(): Unit
    Definition Classes
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    @native()
  17. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
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  18. def toString(): String
    Definition Classes
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  19. final def wait(): Unit
    Definition Classes
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    @throws( ... )
  20. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
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    @throws( ... )
  21. final def wait(arg0: Long): Unit
    Definition Classes
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    Annotations
    @native() @throws( ... )
  22. 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.

  23. 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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